At first sight, the previously described galactic cell association of a human body does not provide a natural clue for a ‘center’ of some kind. Which cell should be more important than others? Each one is active, each one does its ‘job’. Many ‘talk’ to many. Chemical substances are exchanged or by means of chemical substance exchange ‘electrical potentials’ are generated which can travel ‘faster’ and which can generate ‘impulse-like events’ which in turn activate chemical substances again. If one would make this ‘talking with chemical substances and electric potentials’ artificially audible, we would have a symphony of 127 trillion (127 x 10^12) single voices …
And yet, when we experience our human bodies in everyday life, we don’t see a huge cloud of galactic proportions of individual cells, we see a ‘delineated object’ with a surface that is ‘visible’; an object that can make ‘sounds’, that ‘smells’, that is ‘touchable’, that can ‘change’ and ‘move’. Moreover, it can ‘stuff things into itself’, and ‘gases’, ‘liquids’, and ‘more solid components’ also come out of it. Further it is obvious with longer observation that there are areas at the body which react to ‘light’ (eyes), to ‘sounds’ (ears), to ‘smells’ (nose), to ‘touch’ (skin), to ‘body positions’ (among other things sense of balance), to ‘temperature’ (skin), to ‘chemical compositions of substances in the mouth’ (taste organs in the mouth) and some more.
This everyday ‘experience’ suggests the assumption that the cells of our human body have spatially arranged themselves into ‘special networks’ [1], which show a high ‘degree of organization’, so pronounced that these networks appear like ‘one unit’, like a ‘single system’ with ‘input’ and ‘output’, and where complex processes take place between input and output. This opens up the possibility of viewing the galactic space of autonomous cells in a human body as a ‘collective of organized systems’ that appear to be in active exchange with each other.”[2], [4],[5]
In modern technical systems such as a car, an airplane, a computer, there is a ‘meta-level’ from which the whole system can be ‘controlled’. In the car the steering wheel, the brake, the gear shift etc., similarly in the airplane the cockpit with a multiplicity of instruments, or with the computer the input and output devices. However, for years an increasing ‘autonomy’ of these technical devices has been emerging, insofar as many control decisions of humans are shifted to ‘subsystems’, which thereby ‘self-perform’ more and more classical control performance of humans.[6].
In a human body there exists ‘parallel’ to the different body systems among other things the ‘nervous system’ with the ‘brain’ as central area, in which many ‘signals from the body systems’ run together and from which again ‘signals to the body systems’ are sent out. The brain with the nervous system seems to be a system of its own, which processes the incoming signals in different ‘neuronal processes’ and also sends out signals, which can cause ‘effects in the body systems’.[7] From the point of view of ‘functioning’ the brain with the nervous system can be understood as a kind of ‘meta-system’, in which properties of all other ‘body systems’ are ‘mapped’, find a ‘process-like interpretation’, and can be influenced (= ‘controlled’) to a certain degree with the help of these mappings and interpretations.
As the modern empirical sciences make visible more and more by their investigations and subsequent ‘interpretations’ (e.g. [4],[5]), the distinguishable body systems themselves have a very high complexity with their own ‘autonomy’ (stomach, liver, kidney, heart, …), which can be influenced only conditionally by the brain, but which conversely can also influence the brain. In addition, there is a hardly manageable amount of mutual influences via the immense ‘material flows’ in the blood circulation and in the body fluids.
For the context of this book, of particular interest here are those structures that are important for the ‘coordination of the different brains’ by means of ‘language’ and closely related to this are the ‘cognitive’ and ’emotional’ processes in the brain that are responsible for what ‘cognitive images are created in the mind’ with which a brain ‘interprets’ ‘itself’ and ‘everything else’.
How to describe the Human Being?
The description of the human cell galaxy as ‘subsystems’ with their own ‘input’ and ‘output’ and and including ‘inner processes’ – here simply called the ‘system function’ – can appear ‘simple’ at first sight, ‘normal’, or something else. We enter with this question the fundamental question, how we can describe the human cell galaxy – i.e. ‘ourselves’! – at all and furthermore maybe how we ‘should’ describe it: are there any criteria on the basis of which we should prefer a ‘certain way of description’?
In the case of the description of ‘nature’, of the ‘real world’, we may still be able to distinguish between ‘us’ and ‘nature’ (which, however, will later come out as a fallacy)), it becomes somewhat more difficult with the ‘description of ourselves’. If one wants to describe something, one needs certain conditions to be able to make a description. But what are these conditions if we want to describe ourselves? Doesn’t here the famous ‘cat bite into its own tail’?
In ‘normal everyday life’ [8] typical forms with which we describe are e.g. ‘pictures’, ‘photographs’, ‘videos’, ‘music’, ‘body movements’ and others, but above all linguistic expressions (spoken, written; everyday language, technical language; …).
Let’s stay for a moment with ‘everyday language (German, English, Italian, …).
As children we are born into a certain, already existing world with a respective ‘everyday life’ distinctive for each human person. At least one language is spoken in such an environment. If the parents are bilingual even two languages in parallel. If the environment is different from the language of the parents, then perhaps even three languages. And today, where also the environment becomes more and more ‘multi-cultural’, maybe even more than three languages are practiced.
No matter how many languages occur simultaneously for a person, each language has its own ‘rules’, its own ‘pronunciation’, its own ‘contextual reference’, its own ‘meanings’. These contexts can change; the language itself can change. And if someone grows up with not just one language, but more than one, then ‘in the person’, in the ‘speaker-listener’, there can naturally be multiple interactions between the different languages. Since this happens today in many places at the same time with more and more people, there are still hardly sufficient research results available that adequately describe this diversity in its specifics.
So, if we want to describe ‘ourselves’ as ‘part of the real world’, we should first of all accept and ‘consciously assume’ that we do not start at ‘point zero’ at the moment of describing, not as a ‘blank sheet’, but as a biological system which has a more or less long ‘learning process’ behind it. Thereby, the word ‘learning process’ as part of the language the author uses, is not a ‘neutral set of letters’, but likewise a ‘word’ of his language, which he shares with many other speakers of ‘German’. One must assume that each ‘speaker of German’ associates his own ‘individual conceptions’ with the word ‘learning process’. And also this word ‘conception’ is such a word, which as part of the spoken (and written) language normally does not come along ‘meaning-free’. In short, as soon as we speak, as soon as we link words in larger units to statements, we activate a set of ‘knowledge and skills’ that are somehow ‘present in us’, that we use ‘automatically’, and whose use is normally largely ‘unconscious’.”[9],[10]
When I, as the author of this text, now write down statements in the German language, I let myself be carried by a ‘wave of language usage’, so to speak, whose exact nature and effectiveness I cannot fully grasp at the moment of use (and this is the case for every language user). I can, however, when I have expressed myself, look more consciously at what has been expressed, and then — perhaps — see clearer whether and how I can place it in contexts known to me. Since also the ‘known to me’ is largely ‘unconscious’ and passes from ‘unconscious knowledge’ into ‘conscious’ knowledge, the task of a ‘clarification of speaking’ and the ‘meaning’ connected with it is always only fragmentarily, partially possible. The ‘conscious eye of knowledge’ is therefore perhaps comparable to a ‘shining knowledge bubble’ in the black sea of ‘unconscious knowledge’, which seems to be close to ‘not-knowing’ but it isn’t ‘not-knowing’: ‘unconscious knowledge’ is ‘inside the brain ‘real knowledge’, which ‘works’.
… to be continued …
COMMENTS
wkp := Wikipedia
[1] In microbiology as a part of evolutionary biology, one has recognized rudimentarily how the individual cells during the ‘growth process’ ‘communicate’ possible cooperations with other cells via chemical substances, which are ‘controlled’ by their respective individual ‘genetic program’. These processes can very well be described as ‘exchange of signals’, where these ‘signals’ do not occur in isolation, but are ‘related’ by the genetic program to other chemical substances and process steps. Through this ‘relating’, the chemical signal carriers, isolated in themselves, are embedded in a ‘space of meanings’ from which they find an ‘assignment’. This overall process fulfills all requirements of a ‘communication’. In this respect, it seems justified to speak of an ‘agreement’ between the individual cells, an ‘understanding’ about whether and how they want to ‘cooperate’ with each other.
[2] When thinking of complex connections between cells, one may first think of the cells in the brain (‘neurons’), certain types of which may have as many as 1000 dendrites (:= these are projections on an ‘axon’ and an axon is the ‘output’ on a neuron), each dendrite housing multiple synapses.[3] Since each synapse can be the endpoint of a connection to another synapse, it suggests that a complex network of the order of trillions (10^12) connections may exist here in a brain. In addition, there is also the system of blood vessels that run through the entire body and supply the approximately 36 trillion (10^12) body cells with various chemical substances.
[3] wkp [EN], Neuron, URL: https://en.wikipedia.org/wiki/Neuron, section ‚Connectivity‘, citation: „The human brain has some 8.6 x 1010 (eighty six billion neurons. Each neuron has on average 7,000 synaptic connections to other neurons. It has been estimated that the brain of a three-year-old child has about 1015 synapses (quadrillion). This number declines with age, stabilizing by adulthood. Estimates vary for an adult, ranging from 1014 to 5 x 1014 synapses (100 to 500 trillion).”
[4] Robert F.Schmidt, Gerhard Thews (Eds.), 1995, Physiologie des Menschen, 25th edition, Springer
[6] Famously, the example of the ‘auto-pilot’ on an airplane, software that can ‘steer’ the entire plane without human intervention.
[7] Thus, the position of the joints is continuously sent to the brain and, in the case of a ‘directed movement’, the set of current joint positions is used to trigger an ‘appropriate movement’ by sending appropriate signals ‘from the brain to the muscles’.
[8] Of course, also a certain fiction, because everyone ultimately experiences ‘his everyday life’ to a certain degree, which only partially overlaps with the ‘everyday life of another’.
[9] When children in school are confronted for the first time with the concept of a ‘grammar’, with ‘grammatical rules’, they will not understand what that is. Using concrete examples of language, they will be able to ‘link’ one or another ‘grammatical expression’ with linguistic phenomena, but they will not really understand the concept of grammar. This is due to the fact that the entire processes that take place in the ‘inside of a human being’ have been researched only in a very rudimentary way until today. It is in no way sufficient for the formulation of a grammar close to everyday life.
[10] Karl Erich Heidoplh, Walter Flämig, Wolfgang Motsch (ed.), (1980), Grundzüge einer Deutschen Grammatik, Akademie-Verlag, Berlin. Note: Probably the most systematized grammar of German to date, compiled by a German authors’ collective (at that time still the eastern part of Germany called ‘German Democratic Republic’ (GDR)). Precisely because the approach was very systematic, the authors could clearly see that grammar as a description of ‘regular forms’ reaches its limits where the ‘meaning’ of expressions comes into play. Since ‘meaning’ describes a state of affairs that takes place in the ‘inside of the human being’ (of course in intensive interaction with interactions of the body with the environment), a comprehensive objective description of the factor ‘meaning’ in interaction with the forms is always only partially possible.
The whole text shows a dynamic, which induces many changes. Difficult to plan ‘in advance’.
Perhaps, some time, it will look like a ‘book’, at least ‘for a moment’.
I have started a ‘book project’ in parallel. This was motivated by the need to provide potential users of our new oksimo.R software with a coherent explanation of how the oksimo.R software, when used, generates an empirical theory in the format of a screenplay. The primary source of the book is in German and will be translated step by step here in the uffmm.blog.
INTRODUCTION
In a rather foundational paper about an idea, how one can generalize ‘systems engineering’ [*1] to the art of ‘theory engineering’ [1] a new conceptual framework has been outlined for a ‘sustainable applied empirical theory (SAET)’. Part of this new framework has been the idea that the classical recourse to groups of special experts (mostly ‘engineers’ in engineering) is too restrictive in the light of the new requirement of being sustainable: sustainability is primarily based on ‘diversity’ combined with the ‘ability to predict’ from this diversity probable future states which keep life alive. The aspect of diversity induces the challenge to see every citizen as a ‘natural expert’, because nobody can know in advance and from some non-existing absolut point of truth, which knowledge is really important. History shows that the ‘mainstream’ is usually to a large degree ‘biased’ [*1b].
With this assumption, that every citizen is a ‘natural expert’, science turns into a ‘general science’ where all citizens are ‘natural members’ of science. I will call this more general concept of science ‘sustainable citizen science (SCS)’ or ‘Citizen Science 2.0 (CS2)’. The important point here is that a sustainable citizen science is not necessarily an ‘arbitrary’ process. While the requirement of ‘diversity’ relates to possible contents, to possible ideas, to possible experiments, and the like, it follows from the other requirement of ‘predictability’/ of being able to make some useful ‘forecasts’, that the given knowledge has to be in a format, which allows in a transparent way the construction of some consequences, which ‘derive’ from the ‘given’ knowledge and enable some ‘new’ knowledge. This ability of forecasting has often been understood as the business of ‘logic’ providing an ‘inference concept’ given by ‘rules of deduction’ and a ‘practical pattern (on the meta level)’, which defines how these rules have to be applied to satisfy the inference concept. But, looking to real life, to everyday life or to modern engineering and economy, one can learn that ‘forecasting’ is a complex process including much more than only cognitive structures nicely fitting into some formulas. For this more realistic forecasting concept we will use here the wording ‘common logic’ and for the cognitive adventure where common logic is applied we will use the wording ‘common science’. ‘Common science’ is structurally not different from ‘usual science’, but it has a substantial wider scope and is using the whole of mankind as ‘experts’.
The following chapters/ sections try to illustrate this common science view by visiting different special views which all are only ‘parts of a whole’, a whole which we can ‘feel’ in every moment, but which we can not yet completely grasp with our theoretical concepts.
CONTENT
Language (Main message: “The ordinary language is the ‘meta language’ to every special language. This can be used as a ‘hint’ to something really great: the mystery of the ‘self-creating’ power of the ordinary language which for most people is unknown although it happens every moment.”)
Concrete Abstract Statements (Main message: “… you will probably detect, that nearly all words of a language are ‘abstract words’ activating ‘abstract meanings’. …If you cannot provide … ‘concrete situations’ the intended meaning of your abstract words will stay ‘unclear’: they can mean ‘nothing or all’, depending from the decoding of the hearer.”)
True False Undefined (Main message: “… it reveals that ’empirical (observational) evidence’ is not necessarily an automatism: it presupposes appropriate meaning spaces embedded in sets of preferences, which are ‘observation friendly’.“
Beyond Now (Main message: “With the aid of … sequences revealing possible changes the NOW is turned into a ‘moment’ embedded in a ‘process’, which is becoming the more important reality. The NOW is something, but the PROCESS is more.“)
Playing with the Future (Main message: “In this sense seems ‘language’ to be the master tool for every brain to mediate its dynamic meaning structures with symbolic fix points (= words, expressions) which as such do not change, but the meaning is ‘free to change’ in any direction. And this ‘built in ‘dynamics’ represents an ‘internal potential’ for uncountable many possible states, which could perhaps become ‘true’ in some ‘future state’. Thus ‘future’ can begin in these potentials, and thinking is the ‘playground’ for possible futures.(but see [18])”)
Forecasting – Prediction: What? (This chapter explains the cognitive machinery behind forecasting/ predictions, how groups of human actors can elaborate shared descriptions, and how it is possible to start with sequences of singularities to built up a growing picture of the empirical world which appears as a radical infinite and indeterministic space. )
!!! From here all the following chapters have to be re-written !!!
Boolean Logic (Explains what boolean logic is, how it enables the working of programmable machines, but that it is of nearly no help for the ‘heart’ of forecasting.)
/* Often people argue against the usage of the wikipedia encyclopedia as not ‘scientific’ because the ‘content’ of an entry in this encyclopedia can ‘change’. This presupposes the ‘classical view’ of scientific texts to be ‘stable’, which presupposes further, that such a ‘stable text’ describes some ‘stable subject matter’. But this view of ‘steadiness’ as the major property of ‘true descriptions’ is in no correspondence with real scientific texts! The reality of empirical science — even as in some special disciplines like ‘physics’ — is ‘change’. Looking to Aristotle’s view of nature, to Galileo Galilei, to Newton, to Einstein and many others, you will not find a ‘single steady picture’ of nature and science, and physics is only a very simple strand of science compared to the live-sciences and many others. Thus wikipedia is a real scientific encyclopedia give you the breath of world knowledge with all its strengths and limits at once. For another, more general argument, see In Favour for Wikipedia */
[*1] Meaning operator ‘…’ : In this text (and in nearly all other texts of this author) the ‘inverted comma’ is used quite heavily. In everyday language this is not common. In some special languages (theory of formal languages or in programming languages or in meta-logic) the inverted comma is used in some special way. In this text, which is primarily a philosophical text, the inverted comma sign is used as a ‘meta-language operator’ to raise the intention of the reader to be aware, that the ‘meaning’ of the word enclosed in the inverted commas is ‘text specific’: in everyday language usage the speaker uses a word and assumes tacitly that his ‘intended meaning’ will be understood by the hearer of his utterance as ‘it is’. And the speaker will adhere to his assumption until some hearer signals, that her understanding is different. That such a difference is signaled is quite normal, because the ‘meaning’ which is associated with a language expression can be diverse, and a decision, which one of these multiple possible meanings is the ‘intended one’ in a certain context is often a bit ‘arbitrary’. Thus, it can be — but must not — a meta-language strategy, to comment to the hearer (or here: the reader), that a certain expression in a communication is ‘intended’ with a special meaning which perhaps is not the commonly assumed one. Nevertheless, because the ‘common meaning’ is no ‘clear and sharp subject’, a ‘meaning operator’ with the inverted commas has also not a very sharp meaning. But in the ‘game of language’ it is more than nothing 🙂
[*1b] That the main stream ‘is biased’ is not an accident, not a ‘strange state’, not a ‘failure’, it is the ‘normal state’ based on the deeper structure how human actors are ‘built’ and ‘genetically’ and ‘cultural’ ‘programmed’. Thus the challenge to ‘survive’ as part of the ‘whole biosphere’ is not a ‘partial task’ to solve a single problem, but to solve in some sense the problem how to ‘shape the whole biosphere’ in a way, which enables a live in the universe for the time beyond that point where the sun is turning into a ‘red giant’ whereby life will be impossible on the planet earth (some billion years ahead)[22]. A remarkable text supporting this ‘complex view of sustainability’ can be found in Clark and Harvey, summarized at the end of the text. [23]
[*2] The meaning of the expression ‘normal’ is comparable to a wicked problem. In a certain sense we act in our everyday world ‘as if there exists some standard’ for what is assumed to be ‘normal’. Look for instance to houses, buildings: to a certain degree parts of a house have a ‘standard format’ assuming ‘normal people’. The whole traffic system, most parts of our ‘daily life’ are following certain ‘standards’ making ‘planning’ possible. But there exists a certain percentage of human persons which are ‘different’ compared to these introduced standards. We say that they have a ‘handicap’ compared to this assumed ‘standard’, but this so-called ‘standard’ is neither 100% true nor is the ‘given real world’ in its properties a ‘100% subject’. We have learned that ‘properties of the real world’ are distributed in a rather ‘statistical manner’ with different probabilities of occurrences. To ‘find our way’ in these varying occurrences we try to ‘mark’ the main occurrences as ‘normal’ to enable a basic structure for expectations and planning. Thus, if in this text the expression ‘normal’ is used it refers to the ‘most common occurrences’.
[*3] Thus we have here a ‘threefold structure’ embracing ‘perception events, memory events, and expression events’. Perception events represent ‘concrete events’; memory events represent all kinds of abstract events but they all have a ‘handle’ which maps to subsets of concrete events; expression events are parts of an abstract language system, which as such is dynamically mapped onto the abstract events. The main source for our knowledge about perceptions, memory and expressions is experimental psychology enhanced by many other disciplines.
[*4] Characterizing language expressions by meaning – the fate of any grammar: the sentence ” … ‘words’ (= expressions) of a language which can activate such abstract meanings are understood as ‘abstract words’, ‘general words’, ‘category words’ or the like.” is pointing to a deep property of every ordinary language, which represents the real power of language but at the same time the great weakness too: expressions as such have no meaning. Hundreds, thousands, millions of words arranged in ‘texts’, ‘documents’ can show some statistical patterns’ and as such these patterns can give some hint which expressions occur ‘how often’ and in ‘which combinations’, but they never can give a clue to the associated meaning(s). During more than three-thousand years humans have tried to describe ordinary language in a more systematic way called ‘grammar’. Due to this radically gap between ‘expressions’ as ‘observable empirical facts’ and ‘meaning constructs’ hidden inside the brain it was all the time a difficult job to ‘classify’ expressions as representing a certain ‘type’ of expression like ‘nouns’, ‘predicates’, ‘adjectives’, ‘defining article’ and the like. Without regressing to the assumed associated meaning such a classification is not possible. On account of the fuzziness of every meaning ‘sharp definitions’ of such ‘word classes’ was never and is not yet possible. One of the last big — perhaps the biggest ever — project of a complete systematic grammar of a language was the grammar project of the ‘Akademie der Wissenschaften der DDR’ (‘Academy of Sciences of the GDR’) from 1981 with the title “Grundzüge einer Deutschen Grammatik” (“Basic features of a German grammar”). A huge team of scientists worked together using many modern methods. But in the preface you can read, that many important properties of the language are still not sufficiently well describable and explainable. See: Karl Erich Heidolph, Walter Flämig, Wolfgang Motsch et al.: Grundzüge einer deutschen Grammatik. Akademie, Berlin 1981, 1028 Seiten.
[*5] Differing opinions about a given situation manifested in uttered expressions are a very common phenomenon in everyday communication. In some sense this is ‘natural’, can happen, and it should be no substantial problem to ‘solve the riddle of being different’. But as you can experience, the ability of people to solve the occurrence of different opinions is often quite weak. Culture is suffering by this as a whole.
[1] Gerd Doeben-Henisch, 2022, From SYSTEMS Engineering to THEORYEngineering, see: https://www.uffmm.org/2022/05/26/from-systems-engineering-to-theory-engineering/(Remark: At the time of citation this post was not yet finished, because there are other posts ‘corresponding’ with that post, which are too not finished. Knowledge is a dynamic network of interwoven views …).
[1d] ‘usual science’ is the game of science without having a sustainable format like in citizen science 2.0.
[2] Science, see e.g. wkp-en: https://en.wikipedia.org/wiki/Science
Citation = “In modern science, the term “theory” refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with the scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction (“falsify“) of it. Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge,[1] in contrast to more common uses of the word “theory” that imply that something is unproven or speculative (which in formal terms is better characterized by the word hypothesis).[2] Scientific theories are distinguished from hypotheses, which are individual empirically testableconjectures, and from scientific laws, which are descriptive accounts of the way nature behaves under certain conditions.”
[2b] History of science in wkp-en: https://en.wikipedia.org/wiki/History_of_science#Scientific_Revolution_and_birth_of_New_Science
[3] Theory, see wkp-en: https://en.wikipedia.org/wiki/Theory#:~:text=A%20theory%20is%20a%20rational,or%20no%20discipline%20at%20all.
Citation = “A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory’s assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.”
Citation = “In modern science, the term “theory” refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with the scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction (“falsify“) of it. Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge,[1] in contrast to more common uses of the word “theory” that imply that something is unproven or speculative (which in formal terms is better characterized by the word hypothesis).[2] Scientific theories are distinguished from hypotheses, which are individual empirically testableconjectures, and from scientific laws, which are descriptive accounts of the way nature behaves under certain conditions.”
[4b] Empiricism in wkp-en: https://en.wikipedia.org/wiki/Empiricism
[4c] Scientific method in wkp-en: https://en.wikipedia.org/wiki/Scientific_method
Citation =”The scientific method is an empirical method of acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries). It involves careful observation, applying rigorous skepticism about what is observed, given that cognitive assumptions can distort how one interprets the observation. It involves formulating hypotheses, via induction, based on such observations; experimental and measurement-based statistical testing of deductions drawn from the hypotheses; and refinement (or elimination) of the hypotheses based on the experimental findings. These are principles of the scientific method, as distinguished from a definitive series of steps applicable to all scientific enterprises.[1][2][3] [4c]
and
Citation = “The purpose of an experiment is to determine whether observations[A][a][b] agree with or conflict with the expectations deduced from a hypothesis.[6]: Book I, [6.54] pp.372, 408 [b] Experiments can take place anywhere from a garage to a remote mountaintop to CERN’s Large Hadron Collider. There are difficulties in a formulaic statement of method, however. Though the scientific method is often presented as a fixed sequence of steps, it represents rather a set of general principles.[7] Not all steps take place in every scientific inquiry (nor to the same degree), and they are not always in the same order.[8][9]”
[5] Gerd Doeben-Henisch, “Is Mathematics a Fake? No! Discussing N.Bourbaki, Theory of Sets (1968) – Introduction”, 2022, https://www.uffmm.org/2022/06/06/n-bourbaki-theory-of-sets-1968-introduction/
[6] Logic, see wkp-en: https://en.wikipedia.org/wiki/Logic
[7] W. C. Kneale, The Development of Logic, Oxford University Press (1962)
[8] Set theory, in wkp-en: https://en.wikipedia.org/wiki/Set_theory
[9] N.Bourbaki, Theory of Sets , 1968, with a chapter about structures, see: https://en.wikipedia.org/wiki/%C3%89l%C3%A9ments_de_math%C3%A9matique
[10] = [5]
[11] Ludwig Josef Johann Wittgenstein ( 1889 – 1951): https://en.wikipedia.org/wiki/Ludwig_Wittgenstein
[12] Ludwig Wittgenstein, 1953: Philosophische Untersuchungen [PU], 1953: Philosophical Investigations [PI], translated by G. E. M. Anscombe /* For more details see: https://en.wikipedia.org/wiki/Philosophical_Investigations */
[13] Wikipedia EN, Speech acts: https://en.wikipedia.org/wiki/Speech_act
[14] While the world view constructed in a brain is ‘virtual’ compared to the ‘real word’ outside the brain (where the body outside the brain is also functioning as ‘real world’ in relation to the brain), does the ‘virtual world’ in the brain function for the brain mostly ‘as if it is the real world’. Only under certain conditions can the brain realize a ‘difference’ between the triggering outside real world and the ‘virtual substitute for the real world’: You want to use your bicycle ‘as usual’ and then suddenly you have to notice that it is not at that place where is ‘should be’. …
[15] Propositional Calculus, see wkp-en: https://en.wikipedia.org/wiki/Propositional_calculus#:~:text=Propositional%20calculus%20is%20a%20branch,of%20arguments%20based%20on%20them.
[16] Boolean algebra, see wkp-en: https://en.wikipedia.org/wiki/Boolean_algebra
[17] Boolean (or propositional) Logic: As one can see in the mentioned articles of the English wikipedia, the term ‘boolean logic’ is not common. The more logic-oriented authors prefer the term ‘boolean calculus’ [15] and the more math-oriented authors prefer the term ‘boolean algebra’ [16]. In the view of this author the general view is that of ‘language use’ with ‘logic inference’ as leading idea. Therefore the main topic is ‘logic’, in the case of propositional logic reduced to a simple calculus whose similarity with ‘normal language’ is widely ‘reduced’ to a play with abstract names and operators. Recommended: the historical comments in [15].
[18] Clearly, thinking alone can not necessarily induce a possible state which along the time line will become a ‘real state’. There are numerous factors ‘outside’ the individual thinking which are ‘driving forces’ to push real states to change. But thinking can in principle synchronize with other individual thinking and — in some cases — can get a ‘grip’ on real factors causing real changes.
[19] This kind of knowledge is not delivered by brain science alone but primarily from experimental (cognitive) psychology which examines observable behavior and ‘interprets’ this behavior with functional models within an empirical theory.
[20] Predicate Logic or First-Order Logic or … see: wkp-en: https://en.wikipedia.org/wiki/First-order_logic#:~:text=First%2Dorder%20logic%E2%80%94also%20known,%2C%20linguistics%2C%20and%20computer%20science.
[21] Gerd Doeben-Henisch, In Favour of Wikipedia, https://www.uffmm.org/2022/07/31/in-favour-of-wikipedia/, 31 July 2022
[22] The sun, see wkp-ed https://en.wikipedia.org/wiki/Sun (accessed 8 Aug 2022)
[23] By Clark, William C., and Alicia G. Harley – https://doi.org/10.1146/annurev-environ-012420-043621, Clark, William C., and Alicia G. Harley. 2020. “Sustainability Science: Toward a Synthesis.” Annual Review of Environment and Resources 45 (1): 331–86, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=109026069
[24] Sustainability in wkp-en: https://en.wikipedia.org/wiki/Sustainability#Dimensions_of_sustainability
[27] SDG 4 in wkp-en: https://en.wikipedia.org/wiki/Sustainable_Development_Goal_4
[28] Thomas Rid, Rise of the Machines. A Cybernetic History, W.W.Norton & Company, 2016, New York – London
[29] Doeben-Henisch, G., 2006, Reducing Negative Complexity by a Semiotic System In: Gudwin, R., & Queiroz, J., (Eds). Semiotics and Intelligent Systems Development. Hershey et al: Idea Group Publishing, 2006, pp.330-342
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[29] The idea that individual disciplines are not good enough for the ‘whole of knowledge’ is expressed in a clear way in a video of the theoretical physicist and philosopher Carlo Rovell: Carlo Rovelli on physics and philosophy, June 1, 2022, Video from the Perimeter Institute for Theoretical Physics. Theoretical physicist, philosopher, and international bestselling author Carlo Rovelli joins Lauren and Colin for a conversation about the quest for quantum gravity, the importance of unlearning outdated ideas, and a very unique way to get out of a speeding ticket.
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/* Comment: Gro Harlem Brundtland (Norway) has been the main coordinator of this document */
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Abstract: Extrapolating Beyond Suboptimal Demonstrations via Inverse Reinforcement Learning from Observations Daniel S. Brown * 1 Wonjoon Goo * 1 Prabhat Nagarajan 2 Scott Niekum 1 You can read in the abstract: “A critical flaw of existing inverse reinforcement learning (IRL) methods is their inability to significantly outperform the demonstrator. This is because IRL typically seeks a reward function that makes the demonstrator appear near-optimal, rather than inferring the underlying intentions of the demonstrator that may have been poorly executed in practice. In this paper, we introduce a novel reward-learning-from-observation algorithm, Trajectory-ranked Reward EXtrapolation (T-REX), that extrapolates beyond a set of (ap- proximately) ranked demonstrations in order to infer high-quality reward functions from a set of potentially poor demonstrations. When combined with deep reinforcement learning, T-REX outperforms state-of-the-art imitation learning and IRL methods on multiple Atari and MuJoCo bench- mark tasks and achieves performance that is often more than twice the performance of the best demonstration. We also demonstrate that T-REX is robust to ranking noise and can accurately extrapolate intention by simply watching a learner noisily improve at a task over time.”
In the abstract you can read: “For sophisticated reinforcement learning (RL) systems to interact usefully with real-world environments, we need to communicate complex goals to these systems. In this work, we explore goals defined in terms of (non-expert) human preferences between pairs of trajectory segments. We show that this approach can effectively solve complex RL tasks without access to the reward function, including Atari games and simulated robot locomotion, while providing feedback on less than one percent of our agent’s interactions with the environment. This reduces the cost of human oversight far enough that it can be practically applied to state-of-the-art RL systems. To demonstrate the flexibility of our approach, we show that we can successfully train complex novel behaviors with about an hour of human time. These behaviors and environments are considerably more complex than any that have been previously learned from human feedback.
In the abstract you can read: “Conceptual abstraction and analogy-making are key abilities underlying humans’ abilities to learn, reason, and robustly adapt their knowledge to new domains. Despite of a long history of research on constructing AI systems with these abilities, no current AI system is anywhere close to a capability of forming humanlike abstractions or analogies. This paper reviews the advantages and limitations of several approaches toward this goal, including symbolic methods, deep learning, and probabilistic program induction. The paper concludes with several proposals for designing challenge tasks and evaluation measures in order to make quantifiable and generalizable progress
In the abstract you can read: “Since its beginning in the 1950s, the field of artificial intelligence has cycled several times between periods of optimistic predictions and massive investment (“AI spring”) and periods of disappointment, loss of confidence, and reduced funding (“AI winter”). Even with today’s seemingly fast pace of AI breakthroughs, the development of long-promised technologies such as self-driving cars, housekeeping robots, and conversational companions has turned out to be much harder than many people expected. One reason for these repeating cycles is our limited understanding of the nature and complexity of intelligence itself. In this paper I describe four fallacies in common assumptions made by AI researchers, which can lead to overconfident predictions about the field. I conclude by discussing the open questions spurred by these fallacies, including the age-old challenge of imbuing machines with humanlike common sense.”
[] Stuart Russell, (2019), Human Compatible: AI and the Problem of Control, Penguin books, Allen Lane; 1. Edition (8. Oktober 2019)
In the preface you can read: “This book is about the past , present , and future of our attempt to understand and create intelligence . This matters , not because AI is rapidly becoming a pervasive aspect of the present but because it is the dominant technology of the future . The world’s great powers are waking up to this fact , and the world’s largest corporations have known it for some time . We cannot predict exactly how the technology will develop or on what timeline . Nevertheless , we must plan for the possibility that machines will far exceed the human capacity for decision making in the real world . What then ? Everything civilization has to offer is the product of our intelligence ; gaining access to considerably greater intelligence would be the biggest event in human history . The purpose of the book is to explain why it might be the last event in human history and how to make sure that it is not .”
[] David Adkins, Bilal Alsallakh, Adeel Cheema, Narine Kokhlikyan, Emily McReynolds, Pushkar Mishra, Chavez Procope, Jeremy Sawruk, Erin Wang, Polina Zvyagina, (2022), Method Cards for Prescriptive Machine-Learning Transparency, 2022 IEEE/ACM 1st International Conference on AI Engineering – Software Engineering for AI (CAIN), CAIN’22, May 16–24, 2022, Pittsburgh, PA, USA, pp. 90 – 100, Association for Computing Machinery, ACM ISBN 978-1-4503-9275-4/22/05, New York, NY, USA, https://doi.org/10.1145/3522664.3528600
In the abstract you can read: “Specialized documentation techniques have been developed to communicate key facts about machine-learning (ML) systems and the datasets and models they rely on. Techniques such as Datasheets, AI FactSheets, and Model Cards have taken a mainly descriptive approach, providing various details about the system components. While the above information is essential for product developers and external experts to assess whether the ML system meets their requirements, other stakeholders might find it less actionable. In particular, ML engineers need guidance on how to mitigate po- tential shortcomings in order to fix bugs or improve the system’s performance. We propose a documentation artifact that aims to provide such guidance in a prescriptive way. Our proposal, called Method Cards, aims to increase the transparency and reproducibil- ity of ML systems by allowing stakeholders to reproduce the models, understand the rationale behind their designs, and introduce adap- tations in an informed way. We showcase our proposal with an example in small object detection, and demonstrate how Method Cards can communicate key considerations that help increase the transparency and reproducibility of the detection model. We fur- ther highlight avenues for improving the user experience of ML engineers based on Method Cards.”
[] John H. Miller, (2022), Ex Machina: Coevolving Machines and the Origins of the Social Universe, The SFI Press Scholars Series, 410 pages Paperback ISBN: 978-1947864429 , DOI: 10.37911/9781947864429
In the announcement of the book you can read: “If we could rewind the tape of the Earth’s deep history back to the beginning and start the world anew—would social behavior arise yet again? While the study of origins is foundational to many scientific fields, such as physics and biology, it has rarely been pursued in the social sciences. Yet knowledge of something’s origins often gives us new insights into the present. In Ex Machina, John H. Miller introduces a methodology for exploring systems of adaptive, interacting, choice-making agents, and uses this approach to identify conditions sufficient for the emergence of social behavior. Miller combines ideas from biology, computation, game theory, and the social sciences to evolve a set of interacting automata from asocial to social behavior. Readers will learn how systems of simple adaptive agents—seemingly locked into an asocial morass—can be rapidly transformed into a bountiful social world driven only by a series of small evolutionary changes. Such unexpected revolutions by evolution may provide an important clue to the emergence of social life.”
In the abstract you can read: “Analyzing the spatial and temporal properties of information flow with a multi-century perspective could illuminate the sustainability of human resource-use strategies. This paper uses historical and archaeological datasets to assess how spatial, temporal, cognitive, and cultural limitations impact the generation and flow of information about ecosystems within past societies, and thus lead to tradeoffs in sustainable practices. While it is well understood that conflicting priorities can inhibit successful outcomes, case studies from Eastern Polynesia, the North Atlantic, and the American Southwest suggest that imperfect information can also be a major impediment to sustainability. We formally develop a conceptual model of Environmental Information Flow and Perception (EnIFPe) to examine the scale of information flow to a society and the quality of the information needed to promote sustainable coupled natural-human systems. In our case studies, we assess key aspects of information flow by focusing on food web relationships and nutrient flows in socio-ecological systems, as well as the life cycles, population dynamics, and seasonal rhythms of organisms, the patterns and timing of species’ migration, and the trajectories of human-induced environmental change. We argue that the spatial and temporal dimensions of human environments shape society’s ability to wield information, while acknowledging that varied cultural factors also focus a society’s ability to act on such information. Our analyses demonstrate the analytical importance of completed experiments from the past, and their utility for contemporary debates concerning managing imperfect information and addressing conflicting priorities in modern environmental management and resource use.”
In the uffmm review section the different papers and books are discussed from the point of view of the oksimo paradigm, which is embedded in the general view of a generalized ‘citizen science’ as a ‘computer aided sustainable applied empirical theory’ (CSAET). In the following text the author discusses the introduction of the book “Theory of Sets” from the series “Elements of Mathematics” by N.Bourbaki (1968) [1b]
CONTEXT
In the foundational post with the title “From SYSTEMS Engineering to THEORY Engineering” [3] the assumptions of the whole formalization approach in logic, mathematics and science are questioned as to narrow to allow a modern sustainable theory of science dealing explicitly with the future. To sharpen some of the arguments in that post it seems to be helpful to discuss one of the cornerstones of modern (formalized) mathematics substantiated in the book ‘Theory of sets’ from the Bourbaki group.[1a] It has to be mentioned that the question of the insufficiency of formalization has been discussed in the uffmm blog in several posts before. (cf. e.g. [2])
Formalization
preface
In the introduction to the ‘Set Theory Book’ the bourbaki group reveals a little bit of their meta-mathematical point of view, which finally belongs to the perspective of philosophy. At the one hand they try to be ‘radically formal’, but doing this they notice themselves that this is — by several reasons — only a ‘regulative idea’, somehow important for our thinking, but not completely feasible. This ‘practical impossibility’ is not necessarily a problem as long as one is conscious about this. The Bourbaki group is conscious about this problem, but different to their ‘rigor’ with the specialized formalization of mathematical ideas, they leave it widely ‘undefined’ what follows from the practical impossibility of being ‘completely rigorous’. In the following text it will be tried to describe the Bourbaki position with both dimensions: the idea of ‘formalization’ and the reality of ‘non-formalized realities’ which give the ‘ground’ for everything, even for the formalization. Doing this it will — hopefully — become clear that the idea of formalization was a great achievement in the philosophical and scientific thinking but it did not really solve our problems of understanding the world. The most important aspects of knowledge are ‘outside’ of this formalization approach, and many ‘problems’ which seem to bother our actual thinking are perhaps only ‘artifacts’ of this simplified formalization approach (somehow similar to the problems which have been induced by the metaphysical thinking of the older philosophy). To say it flatly: to introduce new names for old problems does not necessarily solve problems. It enables new ways of speaking and perhaps some new kinds of knowledge, but it does not really solve the big problems of knowledge. And the biggest problem of knowledge is — perhaps — the primary ‘knowledge machine’ itself: the biological actors which have brains to transform ‘reality’ in ‘virtual models’ in their brains and communication tools to ‘communicate’ these virtual models to enable a ‘collective intelligence’ as well as a ‘collective cooperation’. As long as we do not understand this we do not really understand the ‘process of knowing’.
before formalization
With the advent of the homo sapiens population on the planet earth about 300.000 years ago [4] it became possible that biological systems could transform their perceptions of the reality around their brains into ‘internal’, ‘virtual’ models, which enabled ‘reference points’ for ‘acting’ and a ‘cooperation’ which was synchronized by a ‘symbolic communication’. Those properties of the internal virtual models which have no clear ‘correspondence’ to the ‘reality between the brains’ are difficult to communicate.
Everyday symbolic communication refers to parts of the reality by certain types of expressions, which are ‘combined’ in manners which encode different types of ‘relations’ or even ‘changes’. Expressions which ‘refer’ to ‘concrete’ properties can be ‘overloaded’ by expressions which refer to other expressions, which in turn refer either again to expressions or to ‘concrete meanings’. Those objects which are the targets of a referring relation — concrete objects or other expressions — are here called ‘the meaning’ of the expressions. Thus the ‘meaning space’ is populated by either expressions related to ‘concrete’ properties or by ‘expressions pointing forward’ to other expressions and these ‘pointing-forward’ expressions are here called ‘abstract meaning’. While concrete meanings are usually ‘decidable’ in the everyday world situations as being ‘given’ (being ‘true’) or as ‘not being given’ (‘being false’), abstract meanings are as expressions ‘undefined’: they can lead to some concrete property which in turn perhaps can be decided or not.
The availability of ‘abstract expressions’ in ordinary language can be seen as a ‘problem’ or as a ‘blessing’. Being able to generate and use abstract terms manifests a great flexibility in talking — and thinking! — about possible realities which allow to overcome the dictatorship of the ‘now’ and the ‘individual single’. Without abstraction thinking would indeed be impossible. Thus if one understands that ‘thinking’ is a real process with sequences of different states which reveal eventually more abstract classes, structures, and changes, then abstraction is the ‘opener’ for more reality, the ‘enabler’ for a more broader and flexible knowledge. Only by ‘transcending’ the eternal ‘Now’ we get an access to phenomena like time, changes, all kinds of dynamics, and only thereby are ‘pictures of some possible future’ feasible!
Clearly, the potential of abstraction can also be a source of ‘non-real’ ideas, of ‘fantastic’ pictures, of ‘fake news’ and the like.
But these possible ‘failures’ — if they will be ‘recognized’ as failures! — are inevitable if one wants to dig out some ‘truth’ in the nearly infinite space of the unknown. Before the ‘knowledge that something is true’ one has to master a ‘path of trial and error’ consuming ‘time’ and ‘resources’.
This process of creating new abstract ideas to guide a search in the space of the unknown is the only key to find besides ‘errors’ sometimes some ‘truth’.
Thus the ‘problem’ with abstract ideas is an unavoidable condition to find necessary ‘truths’. Stepping back in the face of possible problems is no option to survive in the unknown future.
the formal view of the world according to bourbaki
Figure 1: Graphical interpretation of N.Bourbaki, Set Theory (1968), Introduction, ‘liberal version’
Language, object language, meta language
Talking about mathematical objects with their properties within an ordinary language is not simple because the expressions of an ordinary language are as such usually part of a network of meanings, which can overlap, which can be fuzzy, which are giving space for many interpretations. Additionally, that which is called a ‘mathematical object’ is not a kind of an object wich is given in the everyday world experience. What can be done in such a situation?
Bourbaki proposes to introduce a ‘specialized language’ constructed out of a finite set of elements constituting the ‘alphabet’ of a new language, together with ‘syntactical rules’, which describe how to construct with the elements of the alphabet chains of elements called ‘(well formed) expressions’, which constitute the ‘language’ LO, which shall be used to talk about mathematical objects.
But because mathematics is not restricted to ‘static objects’ but deals also with ‘transformations’ (‘changes’) of objects, one needs ‘successions of objects’ (‘sequences’), which are related by ‘operations with mathematical objects’. In this case the operations are also represented by ‘expressions’ but these expressions are expressions of a ‘higher order’ which have as referenced subject those expressions which are representing objects . Thus, Bourbaki needs right from the beginning two languages: an ‘object language’ (expressions of a language LO representing mathematical objects) and a ‘meta language’ LL (expressions referring to expressions of the object language LO including certain ‘types of changes’ occurring with the object language expressions). Thus a mathematical language Lm consists in the combination of an object language LO with a meta language LL (Lm = (LO,LL)).
And, what becomes clear by this procedure, to introduce such a kind of mathematical language Lm one needs another language talking about the mathematical language Lm, and this is either the everyday (normal) language L, which is assumed to be a language which everybody can ‘understand’ and ‘apply correctly’, or it is a third specialized language LLL, which can talk with special expressions about the mathematical language Lm. Independent of the decision which solution one prefers, finally the ordinary language L will become the meta language for all other thinkable meta languages.
Translating(?) math objects into formal expressions
If the formalized expressions of the mathematical language (Lm = (LO,LL)) would be the mathematical objects themselves, then mathematics would consist only of those expressions. And, because there would be no other criteria available, whatever expressions one would introduce, every expression would claim to be a relevant mathematical expression. This situation would be a ‘maximum of non-sense’ construct: nothing could be ‘false’.
Thus, the introduction of formal expressions of some language alone seems to be not enough to establish a language which is called a ‘mathematical’ language Lm different from other languages which talk about other kinds of objects. But what could it be which relates to ‘specific math objects’ which are not yet the expressions used to ‘refer’ to these specific math objects?
Everybody knows that the main reason for to ‘speak’ (or ‘write’) about math specific objects are humans which are claiming to be ‘mathematicians’ and which are claiming to have some ‘knowledge’ about specific objects called ‘math objects’ which are the ‘content’ which they ‘translate’ into the expressions of a certain language call ‘mathematical language’.[5] Thus, if the ‘math objects’ are not the used expressions themselves then these ‘math objects’ have to be located ‘inside of these talking humans’. According to modern science one would specify this ‘inside’ as ‘brain’, which is connected in complex ways to a body which in turn is connected to the ‘outside world of the body’. Until today it is not possible to ‘observe’ directly math objects assumed to be in the brain of the body of someone which claims to be a mathematician. Thus one mathematician A can not decide what another mathematician B has ‘available in his brain’ at some point of time.
Bourbaki is using some formulations in his introduction which gives some ‘flavor’ of this ‘being not able to translate it into a formalized mathematical language’. Thus at one position in the text Bourbaki is recurring to the “common sense” of the mathematicians [6] or to the “reader’s intuition”. [7] Other phrases refer to the “modes of reasoning” which cannot be formalized [8], or simply to the “experience” on which “the opinion rests”. [9] Expressions like ‘common sense’, ‘intuition’, ‘modes of reasoning’, and ‘experience’ are difficult to interpret. All these expressions describe something ‘inside’ the brains which cannot be observed directly. Thus, how can mathematician A know what mathematician B ‘means’ if he is uttering some statement or writes it down? Does it make a difference whether a mathematician is a man or a woman or is belonging to some other kind of a ‘gender’? Does it make a difference which ‘age’ the mathematician has? How ‘big’ he is? Which ‘weight’ he has?
Thus, from a philosophical point of view the question to the specific criteria which classify a language as a ‘mathematical language’ and not some other language leads us into a completely unsatisfying situation: there are no ‘hard facts’ which can give us a hint what ‘mathematical objects’ could be. What did we ‘overlook’ here? What is the key to the specific mathematical objects which inspired the brains of many many thousand people through centuries and centuries? Is mathematics a ‘big fake’ or is there more than this?
A mathematician as an ‘actor’?
Figure 2: Graphical interpretation of N.Bourbaki, Set Theory (1968), Introduction, ‘Actor view’
This last question “Is mathematics a ‘big fake’ or is there more than this?” can lead o the assumption, that it is not enough to talk about ‘mathematics’ by not including the mathematician itself. Only the mathematician is that ‘mysterious source’ of knowledge, which seems to trigger the production of ‘mathematical expressions’ in speaking or writing (or drawing). Thus a meta-mathematical — and thereby philosophical’ — ‘description’ of mathematics should have at least the ‘components’ (MA, LO,LL,L) with ‘MA’ as abbreviation for the set of actors where each element of the set MA is a mathematician, and — this is decisive ! — it is this math actor MA which is in possession of those ‘criteria’ which decide whether an expression E belongs the ‘mathematical language Lm‘ or not.
The phrase of the ‘mathematician’ as a ‘mysterious source of knowledge’ is justified by an ’empirical observational point of view’: nobody can directly look into the brain of a mathematician. Thus the question of what an expression called ‘mathematical expression’ can ‘mean’ is in such an empirical view not decidable and appears to be a ‘mystery’.
But in the reality of everyday life we can observe, that every human actor — not only mathematicians — seems to be able to use expressions of the everyday language with referring to ‘internal states’ of the brain in a way which seems to ‘work’. If we are talking about ‘pain with my teeth’ or about ‘being hungry or thirsty’ or ‘having an idea’ etc. then usually other human actors seem to ‘understand’ what one is uttering. The ‘evidence’ of a ‘working understanding’ is growing up by the ‘confirmation of expectations’: if oneself is hungry, then one has a certain kind of ‘feeling’ and usually this feeling leads — depending from the cultural patterns one is living in — to a certain kind of ‘behavior’, which has — usually — the ‘felt effect’ of being again ‘not hungry’. This functional relation of ‘feeling to be hungry’, ‘behavior of consuming something’, ‘feeling of being not hungry again’ is an association between ‘bodily functions’ common to all human actors and additionally it is a certain kind of observable behavior, which is common to all human actors too. And it seems to work that human actors are able to associate ‘common internal states’ with ‘common observable behavior’ and associate this observable behavior with the ‘presupposed internal states’ with certain kinds of ‘expressions’. Thus although the internal states are directly not observable, they can become ‘communicated by expressions’ because these internal states are — usually — ‘common to the internal experience of every human actor’.
From this follows the ‘assumption’ that we should extend the necessary elements for ‘inter-actor communication’ with the factor of ‘common human actor HA experience’ abbreviated as ‘HAX‘ (HA, HAX, MA, LO,LL,L), which is usually accompanied by certain kinds of observable behavior ‘BX‘, which can be used as point of reference for certain expressions ‘LX‘, which ‘point to’ the associated intern al states HAX, which are not directly observable. This yields the structure (HA, HAX, MA, BX, LO,LL,LX,L).
Having reached this state of assumptions, there arises an other assumption regarding the relationship between ‘expressions of a language’ — like (LO,LL,LX,L) — and those properties which are constituting the ‘meaning’ of these expressions. In this context ‘meaning’ is not a kind of an ‘object’ but a ‘relation’ between two different things, the expressions at one side and the properties ‘referred to’ on the other side. Moreover this ‘meaning relation’ seems not to be a ‘static’ relation but a ‘dynamic’ one, associating two different kinds of properties one to another. This reminds to that what mathematicians call a ‘mapping, a function’, and the engineers a ‘process, an operation’. If we abbreviate this ‘dynamic meaning relation’ with the sign ‘μ’, then we could agree to the convention ‘μX : LX <—> (BX,HAX)’ saying that there exists a meaning function μX which maps the special expressions of LX to the special internal experience HAX, which in turn is associated with the special behavior BX. Thus, we extend our hypothetical structure to the format (HA, HAX, MA, BX, LO,LL,LX,L,μX).
With these assumptions we are getting a first idea how human actors in general can communicate about internal, directly not observable states, with other human actors by using external language expressions. We have to notice that the assumed dynamic meaning relation μX itself has to be located ‘inside’ the body, inside’ the brain. This triggers the further assumption to have ‘internal counterparts’ of the external observable behavior as well as external expressions. From this follows the further assumption that there must exists some ‘translation/ transformation’ ‘τ’ which ‘maps’ the internal ‘counterparts’ of the observable behavior and the observable expressions into the external behavior.(cf. figure 2) Thus, we are reaching the further extended format: (HA, HAX, MA, BX, LO,LL,LX,L,μX,τ).
Mathematical objects
Accepting the basic assumptions about an internal meaning function μX as well an internal translation function τ narrows the space of possible answers about the nature of ‘math objects’ a little bit, but as such this is possibly not yet a satisfying answer. Or, have we nevertheless yet to assume that ‘math objects’ and related ‘modes of reasoning’ are also rooted in internal properties and dynamics of the brain which are ‘common to all humans’?
If one sees that every aspect of the human world view is encoded in some internal states of the brain, and that what we call ‘world’ is only given as a constructed virtual structure in the brains of bodies including all the different kinds of ‘memories’, then there is no real alternative to the assumption that ‘math objects’ and related ‘modes of reasoning’ have to be located in these — yet not completely decoded — inner structures and dynamics of the brain.
From the everyday experience — additionally enlightened by different scientific disciplines, e.g. experimental (neuro) psychology — we know that the brain is — completely automatic — producing all kinds of ‘abstractions’ from concrete ‘perceptions’, can produce any kinds of ‘abstractions of abstractions’, can ‘associate’ abstractions with other abstractions, can arrange many different kinds of memories to ‘arrangements’ representing ‘states’/ ‘situations’, ‘transformations of states’, ‘sequences of states’ and the like. Thus everything which a ‘mathematical reasoning’ HAm needs seems to be available as concrete brain state or brain activity, and this is not only ‘special’ for an individual person alone, it is the common structure of all brains.
Therefore one has to assume that the set of mathematicians MA is a ‘subset’ of the set of human actors HA in general. From this one can further assume that the ‘mathematical reasoning’ HAm is a subset of the general human everyday experience HAX. And, saying this, the meaning function μX as well as the translation function τ should be applicable also to the mathematical reasoning and the mathematical objects as well: (HA, MA, HAX, HAm, BX, LO,LL,LX,L,μX,τ).
These assumptions would explain why it is not only possible but ‘inevitable’ to use the everyday language L to introduce and to use a mathematical language Lm with different kinds of sub-languages (LO,LL, LLL, …). Thus in analogy to the ‘feeling’ ‘to be hungry’ with a cultural encoded kind of accompanying behavior BX we have to assume that the different kinds of internal states and transformations in the case of mathematical reasoning can be associated with an observable kind of ‘behavior’ by using ‘expressions’ embedded (encoded) in certain kinds of ‘behavior’ accepted as ‘typical mathematical’. Introducing expressions like ‘0’, ‘1’, ‘2’, …, ’10’, … (belonging to a language Lo) for certain kinds of ‘objects’ and expressions like ‘+’, ‘-‘ … for certain kinds of operations with these before introduced objects (belonging to a language LL) one can construct combined expressions like ‘1+2=3’ (belonging to a mathematical language Lm). To introduce ‘more abstract objects’ like ‘sets’, ‘relations’, ‘functions’ etc. which have no direct counterpart in the everyday world does not break the assumptions. The everyday language L operates already only with abstract objects like ‘cup’, ‘dog’, ‘house’ etc. The expression ‘cup’ is an abstract concept, which can easily be associated with any kind of concrete phenomena provided by perceptions introducing ‘sets of different properties’, which allow the construction of ‘subsets of properties’ constituting a kind of ‘signature’ for a certain abstract ‘class’ which only exists in the dynamics of the brain. Thus having a set C named ‘cup’ introduces ‘possible elements’, whose ‘interpretation’ can be realized by associating different kinds of sets of properties provided by ‘sensory perception’. But the ‘memory’ as well as the ‘thinking’ can also provide other kinds of properties which can be used too to construct other ‘classes’.
In this outlined perspective of brain dynamics mathematics appears to be a science which is using these brain dynamics in a most direct way without to recur to the the huge amount of everyday experiences. Thus, mathematical languages (today summarized in that language, which enables the so called ‘set theory’) and mathematical thinking in general seems to reflect the basic machinery of the brain processing directly across all different cultures. Engineers worldwide speaking hundreds of different ‘everyday languages’ can work together by using mathematics as their ‘common language’ because this is their ‘common thinking’ underlying all those different everyday languages.
Being a human means being able to think mathematically … besides many other things which characterizes a human actor.
Epiloge
Basically every ordinary language offers all elements which are necessary for mathematics (mathematics is the kernel of every language). But history illustrates that it can be helpful to ‘extend’ an ordinary language with additional expressions (Lo, LL, LLL, …). But the development of modern mathematics and especially computer science shows increasing difficulties by ‘cutting away’ everyday experience in case of elaborating structures, models, theories in a purely formal manner, and to use these formal structures afterwards to interpret the everyday world. This separates the formal productions from the main part of users, of citizens, leading into a situation where only a few specialist have some ‘understanding’ (usually only partially because the formalization goes beyond the individual capacity of understanding), but all others have no more an understanding at all. This has he flavor of a ‘cultural self-destruction’.
In the mentioned oksimo software as part of a new paradigm of a more advanced citizen science this problem of ‘cultural self-destruction’ is avoided because in the format of a ‘computer aided sustainable applied empirical theory (CSAET) the basic language for investigating possible futures is the ordinary language which can be extend as needed with quantifying properties. The computer is not any more needed for ‘understanding’ but only for ‘supporting’ the ‘usage’ of everyday language expressions. This enables the best of both worlds: human thinking as well as machine operations.
[4] Humans, How many years ago?, see: wkp (en): https://en.wikipedia.org/wiki/Human#:~:text=Homo%20sapiens,-Linnaeus%2C%201758&text=Anatomically%20modern%20humans%20emerged%20around,local%20populations%20of%20archaic%20humans.
[5] The difference between ‘talking’ about math objects and ‘writing’ is usually not thematised in the philosophy of mathematics. Because the ordinary language is the most general ‘meta language’ for all kinds of specialized languages and the primary source of the ordinary language then ‘speaking’ is perhaps not really a ‘trivial’ aspect in understanding the ‘meaning’ of any kind of language.
[6] “But formalized mathematics cannot in practice be written down in full, and therefore we must have confidence in what might be called the common sense of the mathematician …”. (p.11)
[7] “Sometimes we shall use ordinary language more loosely … and by indications which cannot be translated into formalized language and which are designed to help the reader to reconstruct the whole text. Other passages, equally untranslatable into formalized language, are introduced in order to clarify the ideas involved, if necessary by appealing to the reader’s intuition …”(p.11)
[8] “It may happen at some future date that mathematicians will agree to use modes of reasoning which cannot be formalized in the language described here : it would then be necessary, if not to change the language completely, at least to enlarge its rules of syntax.”(p.9)
[9] “To sum up, we believe that mathematics is destined to survive … but we cannot pretend that this opinion rests on anything more than experience.”(p.13)
In a preceding post I have outline the concept of an empirical theory based on a text from Popper 1971. In his article Popper points to a minimal structure of what he is calling an empirical theory. A closer investigation of his texts reveals many questions which should be clarified for a more concrete application of his concept of an empirical theory.
In this post it will be attempted to elaborate the concept of an empirical theory more concretely from a theoretical point of view as well as from an application point of view.
A Minimal Concept of an Empirical Theory
The figure shows the process of (i) observing phenomena, (ii) representing these in expressions of some language L, (iii) elaborating conjectures as hypothetical relations between different observations, (iv) using an inference concept to deduce some forecasts, and (v) compare these forecasts with those observations, which are possible in an assumed situation.
Empirical Basis
As starting point as well as a reference for testing does Popper assume an ’empirical basis’. The question arises what this means.
In the texts examined so far from Popper this is not well described. Thus in this text some ‘assumptions/ hypotheses’ will be formulated to describe some framework which should be able to ‘explain’ what an empirical basis is and how it works.
Experts
Those, who usually are building theories, are scientists, are experts. For a general concept of an ’empirical theory’ it is assumed here that every citizen is a ‘natural expert’.
Environment
Natural experts are living in ‘natural environments’ as part of the planet earth, as part of the solar system, as part of the whole universe.
Language
Experts ‘cooperate’ by using some ‘common language’. Here the ‘English language’ is used; many hundreds of other languages are possible.
Shared Goal (Changes, Time, Measuring, Successive States)
For cooperation it is necessary to have a ‘shared goal’. A ‘goal’ is an ‘idea’ about a possible state in the ‘future’ which is ‘somehow different’ to the given actual situation. Such a future state can be approached by some ‘process’, a series of possible ‘states’, which usually are characterized by ‘changes’ manifested by ‘differences’ between successive states. The concept of a ‘process’, a ‘sequence of states’, implies some concept of ‘time’. And time needs a concept of ‘measuring time’. ‘Measuring’ means basically to ‘compare something to be measured’ (the target) with ‘some given standard’ (the measuring unit). Thus to measure the height of a body one can compare it with some object called a ‘meter’ and then one states that the target (the height of the body) is 1,8 times as large as the given standard (the meter object). In case of time it was during many thousand years customary to use the ‘cycles of the sun’ to define the concept (‘unit’) of a ‘day’ and a ‘night’. Based on this one could ‘count’ the days as one day, two days, etc. and one could introduce further units like a ‘week’ by defining ‘One week compares to seven days’, or ‘one month compares to 30 days’, etc. This reveals that one needs some more concepts like ‘counting’, and associated with this implicitly then the concept of a ‘number’ (like ‘1’, ‘2’, …, ’12’, …) . Later the measuring of time has been delegated to ‘time machines’ (called ‘clocks’) producing mechanically ‘time units’ and then one could be ‘more precise’. But having more than one clock generates the need for ‘synchronizing’ different clocks at different locations. This challenge continues until today. Having a time machine called ‘clock’ one can define a ‘state’ only by relating the state to an ‘agreed time window’ = (t1,t2), which allows the description of states in a successive timely order: the state in the time-window (t1,t2) is ‘before’ the time-window (t2,t3). Then one can try to describe the properties of a given natural environment correlated with a certain time-window, e.g. saying that the ‘observed’ height of a body in time-window w1 was 1.8 m, in a later time window w6 the height was still 1.8 m. In this case no changes could be observed. If one would have observed at w6 1.9 m, then a difference is occurring by comparing two successive states.
Example: A County
Here we will assume as an example for a natural environment a ‘county’ in Germany called ‘Main-Kinzig Kreis’ (‘Kreis’ = ‘county’), abbreviated ‘MKK’. We are interested in the ‘number of citizens’ which are living in this county during a certain time-window, here the year 2018 = (1.January 2018, 31.December 2018). According to the statistical office of the state of Hessen, to which the MKK county belongs, the number of citizens in the MKK during 2018 was ‘418.950’.(cf. [2])
Observing the Number of Citizens
One can ask in which sense the number ‘418.950’ can be understood as an ‘observation statement’? If we understand ‘observation’ as the everyday expression for ‘measuring’, then we are looking for a ‘procedure’ which allows us to ‘produce’ this number ‘418.950’ associated with the unit ‘number of citizens during a year’. As everybody can immediately realize no single person can simply observe all citizens of that county. To ‘count’ all citizens in the county one had to ‘travel’ to all places in the county where citizens are living and count every person. Such a travelling would need some time. This can easily need more than 40 years working 24 hours a day. Thus, this procedure would not work. A different approach could be to find citizens in every of the 24 cities in the MKK [1] to help in this counting-procedure. To manage this and enable some ‘quality’ for the counting, this could perhaps work. An interesting experiment. Here we ‘believe’ in the number of citizens delivered by the statistical office of the state of Hessen [2], but keeping some reservation for the question how ‘good’ this number really is. Thus our ‘observation statement’ would be: “In the year 2018 418.950 citizens have been counted in the MKK (according to the information of the statistical office of the state of Hessen)” This observation statement lacks a complete account of the procedure, how this counting really happened.
Concrete and Abstract Words
There are interesting details in this observation statement. In this observation statement we notice words like ‘citizen’ and ‘MKK’. To talk about ‘citizens’ is not a talk about some objects in the direct environment. What we can directly observe are concrete bodies which we have learned to ‘classify’ as ‘humans’, enriched for example with ‘properties’ like ‘man’, ‘woman’, ‘child’, ‘elderly person’, neighbor’ and the like. Bu to classify someone as a ‘citizen’ deserves knowledge about some official procedure of ‘registering as a citizen’ at a municipal administration recorded in some certified document. Thus the word ‘citizen’ has a ‘meaning’ which needs some ‘concrete procedure to get the needed information’. Thus ‘citizen’ is not a ‘simple word’ but a ‘more abstract word’ with regard to the associated meaning. The same holds for the word ‘MKK’ short for ‘Main-Kinzig Kreis’. At a first glance ‘MKK’ appears as a ‘name’ for some entity. But this entity cannot directly be observed too. One component of the ‘meaning’ of the name ‘MKK’ is a ‘real geographical region’, whose exact geographic extensions have been ‘measured’ by official institutions marked in an ‘official map’ of the state of Hessen. This region is associated with an official document of the state of Hessen telling, that this geographical region has to be understood s a ‘county’ with the name MKK. There exist more official documents defining what is meant with the word ‘county’. Thus the word ‘MKK’ has a rather complex meaning which to understand and to check, whether everything is ‘true’, isn’t easy. The author of this post is living in the MKK and he would not be able to tell all the details of the complete meaning of the name ‘MKK’.
First Lessons Learned
Thus one can learn from these first considerations, that we as citizens are living in a natural environment where we are using observation statements which are using words with potentially rather complex meanings, which to ‘check’ deserves some serious amount of clarification.
Conjectures – Hypotheses
Changes
The above text shows that ‘observations as such’ show nothing of interest. Different numbers of citizens in different years have no ‘message’. But as soon as one arranges the years in a ‘time line’ according to some ‘time model’ the scene is changing: if the numbers of two consecutive years are ‘different’ then this ‘difference in numbers’ can be interpreted as a ‘change’ in the environment, but only if one ‘assumes’ that the observed phenomena (the number of counted citizens) are associated with some real entities (the citizens) whose ‘quantity’ is ‘represented’ in these numbers.[5]
And again, the ‘difference between consecutive numbers’ in a time line cannot be observed or measured directly. It is a ‘second order property’ derived from given measurements in time. Such a 2nd order property presupposes a relationship between different observations: they ‘show up’ in the expressions (here numbers), but they are connected back in the light of the agreed ‘meaning’ to some ‘real entities’ with the property ‘overall quantity’ which can change in the ‘real setting’ of these real entities called ‘citizens’.
In the example of the MKK the statistical office of the state of Hessen computed a difference between two consecutive years which has been represented as a ‘growth factor’ of 0,4%. This means that the number of citizens in the year 2018 will increase until the year 2019 as follows: number-citizens(2019) = number-citizens(2018) + (number of citizens(2018) * growth-factor). This means number-citizens(2019) =418.950 + (418.950 * 0.004) = 418.950 + 1.675,8 = 420.625,8
Applying change repeatedly
If one could assume that the ‘growth rate’ would stay constant through the time then one could apply the growth rate again and again onto the actual number of citizens in the MKK every year. This would yield the following simple table:
Year
Number
Growth Rate
2018
418.950,00
,0040
2019
420.625,80
2020
422.308,30
2021
423.997,54
2022
425.693,53
2023
427.396,30
Table: Simplified description of the increase of the number of citizens in the Main-Kinzig county in Germany with an assumed growth rate of 0,4% per year.
As we know from reality an assumption of a fixed growth rate for complex dynamic systems is not very probable.
Theory
Continuing the previous considerations one has to ask the question, how the layout of a ‘complete empirical theory’ would look like?
As I commented in the preceding post about Popper’s 1971 article about ‘objective knowledge’ there exists today no one single accepted framework for a formalized empirical theory. Therefore I will stay here with a ‘bottom-up’ approach using elements taken from everyday reasoning.
What we have until now is the following:
Before the beginning of a theory building process one needs a group of experts being part of a natural environment using the samelanguage which share a common goal which they want to enable.
The assumed natural environment is assumed from the experts as being a ‘process’ of consecutive states in time. The ‘granularity’ of the process depends from the used ‘time model’.
As a starting point they collect a set of statements talking about those aspects of a ‘selected state’ at some time t which they are interested in.
This set of statements describes a set of ‘observable properties’ of the selected state which is understood as a ‘subset’ of the properties of the natural environment.
Every statement is understood by the experts as being ‘true’ in the sense, that the ‘known meaning’ of a statement has an ‘observable counterpart’ in the situation, which can be ‘confirmed’ by each expert.
For each pair of consecutive states it holds that the set of statements of each state can be ‘equal’ or ‘can show ‘differences’.
A ‘difference’ between sets of statements can be interpreted as pointing to a ‘change in the real environment’.[5]
Observed differences can be described by special statements called ‘change statements’ or simply ‘rules’.
A change statement has the format ‘IF a set of statements ST* is a subset of the statements ST of a given state S, THEN with probability p, a set of statements ST+ will be added to the actual state S and a set of statements ST- will be removed from the statements ST of a given state S. This will result in a new succeeding state S* with the representing statements ST – (ST-) + (ST+) depending from the assumed probability p.
The list of change statements is an ‘open set’ according to the assumption, that an actual state is only a ‘subset’ of the real environment.
Until now we have an assumed state S, an assumed goal V, and an open set of change statements X.
Applying change statements to a given state S will generate a new state S*. Thus the application of a subset X’ of the open set of change statements X onto a given state S will here be called ‘generating a new state by a procedure’. Such a state-generating-procedure can be understood as an ‘inference’ (like in logic) oder as a ‘simulation’ (like in engineering).[6]
To write this in a more condensed format we can introduce some signs —– S,V ⊩ ∑ X S‘ —– saying: If I have some state S and a goal V then the simulator ∑ will according to the change statements X generate a new state S’. In such a setting the newly generated state S’ can be understood as a ‘theorem’ which has been derived from the set of statements in the state S which are assumed to be ‘true’. And because the derived new state is assumed to happen in some ‘future’ ‘after’ the ‘actual state S’ this derived state can also be understood as a ‘forecast’.
Because the experts can change all the time all parts ‘at will’ such a ‘natural empirical theory’ is an ‘open entity’ living in an ongoing ‘communication process’.
Second Lessons Learned
It is interestingly to know that from the set of statements in state S, which are assumed to be empirically true, together with some change statements X, whose proposed changes are also assumed to be ‘true’, and which have some probability P in the domain [0,1], one can forecast a set of statements in the state S* which shall be true, with a certainty being dependent from the preceding probability P and the overall uncertainty of the whole natural environment.
Confirmation – Non-Confirmation
A Theory with Forecasts
Having reached the formulation of an ordinary empirical theory T with the ingredients <S,V,X,⊩ ∑> and the derivation conceptS,V ⊩ ∑ X S‘ it is possible to generate theorems as forecasts. A forecast here is not a single statement st* but a whole state S* consisting of a finite set of statements ST* which ‘designate’ according to the ‘agreed meaning’ a set of ‘intended properties’ which need a set of ‘occurring empirical properties’ which can be observed by the experts. These observations are usually associated with ‘agreed procedures of measurement’, which generate as results ‘observation statements’/ ‘measurement statements’.
Within Time
Experts which are cooperating by ‘building’ an ordinary empirical theory are themselves part of a process in time. Thus making observations in the time-window (t1,t2) they have a state S describing some aspects of the world at ‘that time’ (t1,t2). When they then derive a forecast S* with their theory this forecast describes — with some probability P — a ‘possible state of the natural environment’ which is assumed to happen in the ‘future’. The precision of the predicted time when the forecasted statements in S* should happen depends from the assumptions in S.
To ‘check’ the ‘validity’ of such a forecast it is necessary that the overall natural process reaches a ‘point in time’ — or a time window — indicated by the used ‘time model’, where the ‘actual point in time’ is measured by an agreed time machine (mechanical clock). Because there is no observable time without a time machine the classification of a certain situation S* being ‘now’ at the predicted point of time depends completely from the used time machine.[7]
Given this the following can happen: According to the used theory a certain set of statements ST* is predicted to be ‘true’ — with some probability — either ‘at some time in the future’ or in the time-window (t1,t2) or at a certain point in time t*.
Validating Forecasts
If one of these cases would ‘happen’ then the experts would have the statements ST* of their forecast and a real situation in their natural environment which enables observations ‘Obs’ which are ‘translated’ into appropriate ‘observation statements’ STObs. The experts with their predicted statements ST* know a learned agreed meaning M* of their predicted statements ST* as intended-properties M* of ST*. The experts have also learned how they relate the intended meaning M* to the meaning MObs from the observation statements STobs. If the observed meaning MObs ‘agrees sufficiently well’ with the intended meaning M* then the experts would agree in a statement, that the intended meaning M* is ‘fulfilled’/ ‘satisfied’/ ‘confirmed’ by the observed meaning MObs. If not then it would stated that it is ‘not fulfilled’/ ‘not satisfied’/ ‘not confirmed’.
The ‘sufficient fulfillment’ of the intended meaning M* of a set of statements ST* is usually translated in a statement like “The statements ST* are ‘true'”. In the case of ‘no fulfillment’ it is unclear: this can be interpreted as ‘being false’ or as ‘being unclear’: No clear case of ‘being true’ and no clear case of ‘being false’.
Forecasting the Number of Citizens
In the used simple example we have the MKK county with an observed number of citizens in 2018 with 418950. The simple theory used a change statement with a growth factor of 0.4% per year. This resulted in the forecast with the number 420.625 citizens for the year 2019.
If the newly counting of the number of citizens in the years 2019 would yield 420.625, then there would be a perfect match, which could be interpreted as a ‘confirmation’ saying that the forecasted statement and the observed statement are ‘equal’ and therefore the theory seems to match the natural environment through the time. One could even say that the theory is ‘true for the observed time’. Nothing would follow from this for the unknown future. Thus the ‘truth’ of the theory is not an ‘absolute’ truth but a truth ‘within defined limits’.
We know from experience that in the case of forecasting numbers of citizens for some region — here a county — it is usually not so clear as it has been shown in this example.
This begins with the process of counting. Because it is very expensive to count the citizens of all cities of a county this happens only about every 20 years. In between the statistical office is applying the method of ‘forecasting projection’.[9] The state statistical office collects every year ‘electronically’ the numbers of ‘birth’, ‘death’, ‘outflow’, and ‘inflow’ from the individual cities and modifies with these numbers the last real census. In the case of the state of Hessen this was the year 2011. The next census in Germany will happen May 2022.[10] For such a census the data will be collected directly from the registration offices from the cities supported by a control survey of 10% of the population.
Because there are data from the statistical office of the state of Hessen for June 2021 [8:p.9] with saying that the MKK county had 421 936 citizens at 30. June 2021 we can compare this number with the theory forecast for the year 2021 with 423 997. This shows a difference in the numbers. The theory forecast is ‘higher’ than the observed forecast. What does this mean?
Purely arithmetically the forecast is ‘wrong’. The responsible growth factor is too large. If one would ‘adjust’ it in a simplified linear way to ‘0.24%’ then the theory could get a forecast for 2021 with 421 973 (observed: 421 936), but then the forecast for 2019 would be 419 955 (instead of 420 625).
This shows at least the following aspects:
The empirical observations as such can vary ‘a little bit’. One had to clarify which degree of ‘variance’ is due to the method of measurement and therefore this variance should be taken into account for the evaluation of a theoretical forecast.
As mentioned by the statistical office [9] there are four ‘factors’ which influence the final number of citizens in a region: ‘birth’, ‘death’, ‘outflow’, and ‘inflow’. These factors can change in time. Under ‘normal conditions’ the birth-rate and the death-rate are rather ‘stable’, but in case of an epidemic situation or even war this can change a lot. Outflow and inflow are very dynamic depending from many factors. Thus this can influence the growth factor a lot and these factors are difficult to forecast.
Third lessons Learned
Evaluating the ‘relatedness’ of some forecast F of an empirical theory T to the observations O in a given real natural environment is not a ‘clear-cut’ case. The ‘precision’ of such a relatedness depends from many factors where each of these factors has some ‘fuzziness’. Nevertheless as experience shows it can work in a limited way. And, this ‘limited way’ is the maximum we can get. The most helpful contribution of an ‘ordinary empirical theory’ seems to be the forecast of ‘What will happen if we have a certain set of assumptions’. Using such a forecast in the process of the experts this can help to improve to get some ‘informed guesses’ for planning.
Forecast
The next post will show, how this concept of an ordinary empirical theory can be used by applying the oksimo paradigm to a concrete case. See HERE.
Comments
[1] Cities of the MKK-county: 24, see: https://www.wegweiser-kommune.de/kommunen/main-kinzig-kreis-lk
[3] Karl Popper, „A World of Propensities“,(1988) and „Towards an Evolutionary Theory of Knowledge“, (1989) in: Karl Popper, „A World of Propensities“, Thoemmes Press, Bristol, (1990, repr. 1995)
[4] Karl Popper, „All Life is Problem Solving“, original a lecture 1991 in German, the first tome published (in German) „Alles Leben ist Problemlösen“ (1994), then in the book „All Life is Problem Solving“, 1999, Routledge, Taylor & Francis Group, London – New York
[5] This points to the concept of ‘propensity’ which the late Popper has discussed in the papers [3] and [4].
[6] This concept of a ‘generator’ or an ‘inference’ reminds to the general concept of Popper and the main stream philosophy of a logical derivation concept where a ‘set of logical rules’ defines a ‘derivation concept’ which allows the ‘derivation/ inference’ of a statement s* as a ‘theorem’ from an assumed set of statements S assumed to be true.
[7] The clock-based time is in the real world correlated with certain constellations of the real universe, but this — as a whole — is ‘changing’!
[8] Hessisches Statistisches Landesamt, “Die Bevölkerung der hessischen Gemeinden am 30. Juni 2021. Fortschreibungsergebnisse Basis Zensus 09. Mai 2011″, Okt. 2021, Wiesbaden, URL: https://statistik.hessen.de/sites/statistik.hessen.de/files/AI2_AII_AIII_AV_21-1hj.pdf
[9] Method of the forward projection of the statistical office of the State of Hessen: “Bevölkerung: Die Bevölkerungszahlen sind Fortschreibungsergebnisse, die auf den bei der Zensuszählung 2011 ermittelten Bevölkerungszahlen basieren. Durch Auswertung von elektronisch übermittelten Daten für Geburten und Sterbefälle durch die Standesämter, sowie der Zu- und Fortzüge der Meldebehörden, werden diese nach einer bundeseinheitlichen Fortschreibungsmethode festgestellt. Die Zuordnung der Personen zur Bevölkerung einer Gemeinde erfolgt nach dem Hauptwohnungsprinzip (Bevölkerung am Ort der alleinigen oder der Hauptwohnung).”([8:p.2]
[10] Statistical Office state of Hessen, Next census 2022: https://statistik.hessen.de/zahlen-fakten/zensus/zensus-2022/zensus-2022-kurz-erklaert
This text is part of a philosophy of science analysis of the case of the oksimo software (oksimo.com). A specification of the oksimo software from an engineering point of view can be found in four consecutive posts dedicated to the HMI-Analysis for this software.
POPPERs POSITION IN THE CHAPTERS 1-17
In my reading of the chapters 1-17 of Popper’s The Logic of Scientific Discovery [1] I see the following three main concepts which are interrelated: (i) the concept of a scientific theory, (ii) the point of view of a meta-theory about scientific theories, and (iii) possible empirical interpretations of scientific theories.
Scientific Theory
A scientific theory is according to Popper a collection of universal statements AX, accompanied by a concept of logical inference ⊢, which allows the deduction of a certain theorem t if one makes some additional concrete assumptions H.
Example: Theory T1 = <AX1,⊢>
AX1= {Birds can fly}
H1= {Peter is a bird}
⊢: Peter can fly
Because there exists a concrete object which is classified as a bird and this concrete bird with the name ‘Peter’ can fly one can infer that the universal statement could be verified by this concrete bird. But the question remains open whether all observable concrete objects classifiable as birds can fly.
One could continue with observations of several hundreds of concrete birds but according to Popper this would not prove the theory T1 completelytrue. Such a procedure can only support a numerical universality understood as a conjunction of finitely many observations about concrete birds like ‘Peter can fly’ & ‘Mary can fly’ & …. &’AH2 can fly’.(cf. p.62)
The only procedure which is applicable to a universal theory according to Popper is to falsify a theory by only one observation like ‘Doxy is a bird’ and ‘Doxy cannot fly’. Then one could construct the following inference:
AX1= {Birds can fly}
H2= {Doxy is a bird, Doxy cannot fly}
⊢: ‘Doxy can fly’ & ~’Doxy can fly’
If a statement A can be inferred and simultaneously the negation ~A then this is called a logical contradiction:
{AX1, H2} ⊢‘Doxy can fly’ & ~’Doxy can fly’
In this case the set {AX1, H2} is called inconsistent.
If a set of statements is classified as inconsistent then you can derive from this set everything. In this case you cannot any more distinguish between true or false statements.
Thus while the increase of the number of confirmed observations can only increase the trust in the axioms of a scientific theory T without enabling an absolute proof a falsification of a theory T can destroy the ability of this theory to distinguish between true and false statements.
Another idea associated with this structure of a scientific theory is that the universal statements using universal concepts are strictly speaking speculative ideas which deserve some faith that these concepts will be provable every time one will try it.(cf. p.33, 63)
Meta Theory, Logic of Scientific Discovery, Philosophy of Science
Talking about scientific theories has at least two aspects: scientific theories as objects and those who talk about these objects.
Those who talk about are usually Philosophers of Science which are only a special kind of Philosophers, e.g. a person like Popper.
Reading the text of Popper one can identify the following elements which seem to be important to describe scientific theories in a more broader framework:
A scientific theory from a point of view of Philosophy of Science represents a structure like the following one (minimal version):
MT=<S, A[μ], E, L, AX, ⊢, ET, E+, E-, true, false, contradiction, inconsistent>
In a shared empirical situation S there are some human actors A as experts producing expressions E of some language L. Based on their built-in adaptive meaning function μ the human actors A can relate properties of the situation S with expressions E of L. Those expressions E which are considered to be observable and classified to be true are called true expressions E+, others are called false expressions E-. Both sets of expressions are true subsets of E: E+ ⊂ E and E- ⊂ E. Additionally the experts can define some special set of expressions called axioms AX which are universal statements which allow the logical derivation of expressions called theorems of the theory T ET which are called logically true. If one combines the set of axioms AX with some set of empirically true expressions E+ as {AX, E+} then one can logically derive either only expressions which are logically true and as well empirically true, or one can derive logically true expressions which are empirically true and empirically false at the same time, see the example from the paragraph before:
{AX1, H2} ⊢‘Doxy can fly’ & ~’Doxy can fly’
Such a case of a logically derived contradiction A and ~A tells about the set of axioms AX unified with the empirical true expressions that this unified set confronted with the known true empirical expressions is becoming inconsistent: the axioms AX unified with true empirical expressions can not distinguish between true and false expressions.
Popper gives some general requirements for the axioms of a theory (cf. p.71):
Axioms must be free from contradiction.
The axioms must be independent , i.e . they must not contain any axiom deducible from the remaining axioms.
The axioms should be sufficient for the deduction of all statements belonging to the theory which is to be axiomatized.
While the requirements (1) and (2) are purely logical and can be proved directly is the requirement (3) different: to know whether the theory covers all statements which are intended by the experts as the subject area is presupposing that all aspects of an empirical environment are already know. In the case of true empirical theories this seems not to be plausible. Rather we have to assume an open process which generates some hypothetical universal expressions which ideally will not be falsified but if so, then the theory has to be adapted to the new insights.
Empirical Interpretation(s)
Popper assumes that the universal statements of scientific theories are linguistic representations, and this means they are systems of signs or symbols. (cf. p.60) Expressions as such have no meaning. Meaning comes into play only if the human actors are using their built-in meaning function and set up a coordinated meaning function which allows all participating experts to map properties of the empirical situation S into the used expressions as E+ (expressions classified as being actually true), or E- (expressions classified as being actually false) or AX (expressions having an abstract meaning space which can become true or false depending from the activated meaning function).
Examples:
Two human actors in a situation S agree about the fact, that there is ‘something’ which they classify as a ‘bird’. Thus someone could say ‘There is something which is a bird’ or ‘There is some bird’ or ‘There is a bird’. If there are two somethings which are ‘understood’ as being a bird then they could say ‘There are two birds’ or ‘There is a blue bird’ (If the one has the color ‘blue’) and ‘There is a red bird’ or ‘There are two birds. The one is blue and the other is red’. This shows that human actors can relate their ‘concrete perceptions’ with more abstract concepts and can map these concepts into expressions. According to Popper in this way ‘bottom-up’ only numerical universal concepts can be constructed. But logically there are only two cases: concrete (one) or abstract (more than one). To say that there is a ‘something’ or to say there is a ‘bird’ establishes a general concept which is independent from the number of its possible instances.
These concrete somethings each classified as a ‘bird’ can ‘move’ from one position to another by ‘walking’ or by ‘flying’. While ‘walking’ they are changing the position connected to the ‘ground’ while during ‘flying’ they ‘go up in the air’. If a human actor throws a stone up in the air the stone will come back to the ground. A bird which is going up in the air can stay there and move around in the air for a long while. Thus ‘flying’ is different to ‘throwing something’ up in the air.
The expression ‘A bird can fly’ understood as an expression which can be connected to the daily experience of bird-objects moving around in the air can be empirically interpreted, but only if there exists such a mapping called meaning function. Without a meaning function the expression ‘A bird can fly’ has no meaning as such.
To use other expressions like ‘X can fly’ or ‘A bird can Y’ or ‘Y(X)’ they have the same fate: without a meaning function they have no meaning, but associated with a meaning function they can be interpreted. For instance saying the the form of the expression ‘Y(X)’ shall be interpreted as ‘Predicate(Object)’ and that a possible ‘instance’ for a predicate could be ‘Can Fly’ and for an object ‘a bird’ then we could get ‘Can Fly(a Bird)’ translated as ‘The object ‘a Bird’ has the property ‘can fly” or shortly ‘A Bird can fly’. This usually would be used as a possible candidate for the daily meaning function which relates this expression to those somethings which can move up in the air.
Axioms and Empirical Interpretations
The basic idea with a system of axioms AX is — according to Popper — that the axioms as universal expressions represent a system of equations where the general terms should be able to be substituted by certain values. The set of admissible values is different from the set of inadmissible values. The relation between those values which can be substituted for the terms is called satisfaction: the values satisfy the terms with regard to the relations! And Popper introduces the term ‘model‘ for that set of admissible terms which can satisfy the equations.(cf. p.72f)
But Popper has difficulties with an axiomatic system interpreted as a system of equations since it cannot be refuted by the falsification of its consequences ; for these too must be analytic.(cf. p.73) His main problem with axioms is, that “the concepts which are to be used in the axiomatic system should be universal names, which cannot be defined by empirical indications, pointing, etc . They can be defined if at all only explicitly, with the help of other universal names; otherwise they can only be left undefined. That some universal names should remain undefined is therefore quite unavoidable; and herein lies the difficulty…” (p.74)
On the other hand Popper knows that “…it is usually possible for the primitive concepts of an axiomatic system such as geometry to be correlated with, or interpreted by, the concepts of another system , e.g . physics …. In such cases it may be possible to define the fundamental concepts of the new system with the help of concepts which were originally used in some of the old systems .”(p.75)
But the translation of the expressions of one system (geometry) in the expressions of another system (physics) does not necessarily solve his problem of the non-empirical character of universal terms. Especially physics is using also universal or abstract terms which as such have no meaning. To verify or falsify physical theories one has to show how the abstract terms of physics can be related to observable matters which can be decided to be true or not.
Thus the argument goes back to the primary problem of Popper that universal names cannot not be directly be interpreted in an empirically decidable way.
As the preceding examples (1) – (4) do show for human actors it is no principal problem to relate any kind of abstract expressions to some concrete real matters. The solution to the problem is given by the fact that expressions E of some language L never will be used in isolation! The usage of expressions is always connected to human actors using expressions as part of a language L which consists together with the set of possible expressions E also with the built-in meaning function μ which can map expressions into internal structures IS which are related to perceptions of the surrounding empirical situation S. Although these internal structures are processed internally in highly complex manners and are — as we know today — no 1-to-1 mappings of the surrounding empirical situation S, they are related to S and therefore every kind of expressions — even those with so-called abstract or universal concepts — can be mapped into something real if the human actors agree about such mappings!
Example:
Lets us have a look to another example.
If we take the system of axioms AX as the following schema: AX= {a+b=c}. This schema as such has no clear meaning. But if the experts interpret it as an operation ‘+’ with some arguments as part of a math theory then one can construct a simple (partial) model m as follows: m={<1,2,3>, <2,3,5>}. The values are again given as a set of symbols which as such must not ave a meaning but in common usage they will be interpreted as sets of numbers which can satisfy the general concept of the equation. In this secondary interpretation m is becoming a logically true (partial) model for the axiom Ax, whose empirical meaning is still unclear.
It is conceivable that one is using this formalism to describe empirical facts like the description of a group of humans collecting some objects. Different people are bringing objects; the individual contributions will be reported on a sheet of paper and at the same time they put their objects in some box. Sometimes someone is looking to the box and he will count the objects of the box. If it has been noted that A brought 1 egg and B brought 2 eggs then there should according to the theory be 3 eggs in the box. But perhaps only 2 could be found. Then there would be a difference between the logically derivedforecast of the theory 1+2 = 3 and the empirically measured value 1+2 = 2. If one would define all examples of measurement a+b=c’ as contradiction in that case where we assume a+b=c as theoretically given and c’ ≠ c, then we would have with ‘1+2 = 3′ & ~’1+2 = 3’ a logically derived contradiction which leads to the inconsistency of the assumed system. But in reality the usual reaction of the counting person would not be to declare the system inconsistent but rather to suggest that some unknown actor has taken against the agreed rules one egg from the box. To prove his suggestion he had to find this unknown actor and to show that he has taken the egg … perhaps not a simple task … But what will the next authority do: will the authority belief the suggestion of the counting person or will the authority blame the counter that eventually he himself has taken the missing egg? But would this make sense? Why should the counter write the notes how many eggs have been delivered to make a difference visible? …
Thus to interpret some abstract expression with regard to some observable reality is not a principal problem, but it can eventually be unsolvable by purely practical reasons, leaving questions of empirical soundness open.
SOURCES
[1] Karl Popper, The Logic of Scientific Discovery, First published 1935 in German as Logik der Forschung, then 1959 in English by Basic Books, New York (more editions have been published later; I am using the eBook version of Routledge (2002))
This text is part of a philosophy of science analysis of the case of the oksimo software (oksimo.com). A specification of the oksimo software from an engineering point of view can be found in four consecutive posts dedicated to the HMI-Analysis for this software.
THE OKSIMO EVENT SPACE
The characterization of the oksimo software paradigm starts with an informal characterization of the oksimo software event space.
EVENT SPACE
An event space is a space which can be filled up by observable events fitting to the species-specific internal processed environment representations [1], [2] here called internal environments [ENVint]. Thus the same externalenvironment [ENV] can be represented in the presence of 10 different species in 10 different internal formats. Thus the expression ‘environment’ [ENV] is an abstract concept assuming an objective reality which is common to all living species but indeed it is processed by every species in a species-specific way.
In a human culture the usual point of view [ENVhum] is simultaneous with all the other points of views [ENVa] of all the other other species a.
In the ideal case it would be possible to translate all species-specific views ENVa into a symbolic representation which in turn could then be translated into the human point of view ENVhum. Then — in the ideal case — we could define the term environment [ENV] as the sum of all the different species-specific views translated in a human specific language: ∑ENVa = ENV.
But, because such a generalized view of the environment is until today not really possible by practical reasons we will use here for the beginning only expressions related to the human specific point of view [ENVhum] using as language an ordinary language [L], here the English language [LEN]. Every scientific language — e.g. the language of physics — is understood here as a sub language of the ordinary language.
EVENTS
An event [EV] within an event space [ENVa] is a change[X] which can be observed at least from the members of that species [SP] a which is part of that environment ENV which enables a species-specific event space [ENVa]. Possibly there can be other actors around in the environment ENV from different species with their specific event space [ENVa] where the content of the different event spaces can possible overlap with regard to certain events.
A behavior is some observable movement of the body of some actor.
Changes X can be associated with certain behavior of certain actors or with non-actor conditions.
Thus when there are some human or non-human actors in an environment which are moving than they show a behavior which can eventually be associated with some observable changes.
CHANGE
Besides being associated with observable events in the (species specific) environment the expression change is understood here as a kind of inner state in an actor which can comparepast (stored) states Spast with an actual state Snow. If the past and actual state differ in some observable aspect Diff(Spast, Snow) ≠ 0, then there exists some change X, or Diff(Spast, Snow) = X. Usually the actor perceiving a change X will assume that this internal structure represents something external to the brain, but this must not necessarily be the case. It is of help if there are other human actors which confirm such a change perception although even this does not guarantee that there really is a change occurring. In the real world it is possible that a whole group of human actors can have a wrong interpretation.
SYMBOLIC COMMUNICATION AND MEANING
It is a specialty of human actors — to some degree shared by other non-human biological actors — that they not only can built up internal representations ENVint of the reality external to the brain (the body itself or the world beyond the body) which are mostly unconscious, partially conscious, but also they can built up structures of expressions of an internal language Lint which can be mimicked to a high degree by expressions in the body-external environment ENV called expressions of an ordinary language L.
For this to work one has to assume that there exists an internal mapping from internal representations ENVint into the expressions of the internal language Lint as
meaning : ENVint <—> Lint.
and
speaking: Lint —> L
hearing: Lint <— L
Thus human actors can use their ordinary language L to activate internal encodings/ decodings with regard to the internal representations ENVint gained so far. This is called here symbolic communication.
NO SPEECH ACTS
To classify the occurrences of symbolic expressions during a symbolic communication is a nearly infinite undertaking. First impressions of the unsolvability of such a classification task can be gained if one reads the Philosophical Investigations of Ludwig Wittgenstein. [5] Later trials from different philosophers and scientists — e.g. under the heading of speech acts [4] — can not fully convince until today.
Instead of assuming here a complete scientific framework to classify occurrences of symbolic expressions of an ordinary language L we will only look to some examples and discuss these.
KINDS OF EXPRESSIONS
In what follows we will look to some selected examples of symbolic expressions and discuss these.
(Decidable) Concrete Expressions [(D)CE]
It is assumed here that two human actors A and B speaking the same ordinary language L are capable in a concrete situation S to describeobjects OBJ and properties PROP of this situation in a way, that the hearer of a concrete expression E can decide whether the encoded meaning of that expression produced by the speakeris part of the observable situation S or not.
Thus, if A and B are together in a room with a wooden white table and there is a enough light for an observation then B can understand what A is saying if he states ‘There is a white wooden table.‘
To understand means here that both human actors are able to perceive the wooden white table as an object with properties, their brains will transform these external signals into internal neural signals forming an inner — not 1-to-1 — representationENVint which can further be mapped by the learned meaning function into expressions of the inner language Lint and mapped further — by the speaker — into the external expressions of the learned ordinary language L and if the hearer can hear these spoken expressions he can translate the external expressions into the internal expressions which can be mapped onto the learned internal representations ENVint. In everyday situations there exists a high probability that the hearer then can respond with a spoken ‘Yes, that’s true’.
If this happens that some human actor is uttering a symbolic expression with regard to some observable property of the external environment and the other human actor does respond with a confirmation then such an utterance is called here a decidable symbolic expression of the ordinary language L. In this case one can classify such an expression as being true. Otherwise the expression is classified as being not true.
The case of being not true is not a simple case. Being not true can mean: (i) it is actually simply not given; (ii) it is conceivable that the meaning could become true if the external situation would be different; (iii) it is — in the light of the accessible knowledge — not conceivable that the meaning could become true in any situation; (iv) the meaning is to fuzzy to decided which case (i) – (iii) fits.
Cognitive Abstraction Processes
Before we talk about (Undecidable) Universal Expressions [(U)UE] it has to clarified that the internal mappings in a human actor are not only non-1-to-1 mappings but they are additionally automatic transformation processes of the kind that concrete perceptions of concrete environmental matters are automatically transformed by the brain into different kinds of states which are abstracted states using the concrete incoming signals as a trigger either to start a new abstracted state or to modify an existing abstracted state. Given such abstracted states there exist a multitude of other neural processes to process these abstracted states further embedded in numerous different relationships.
Thus the assumed internal language Lint does not map the neural processes which are processing the concrete events as such but the processed abstracted states! Language expressions as such can never be related directly to concrete material because this concrete material has no direct neural basis. What works — completely unconsciously — is that the brain can detect that an actual neural pattern nn has some similarity with a given abstracted structure NN and that then this concrete pattern nn is internally classified as an instance of NN. That means we can recognize that a perceived concrete matter nn is in ‘the light of’ our available (unconscious) knowledge an NN, but we cannot argue explicitly why. The decision has been processed automatically (unconsciously), but we can become aware of the result of this unconscious process.
Universal (Undecidable) Expressions [U(U)E]
Let us repeat the expression ‘There is a white wooden table‘ which has been used before as an example of a concrete decidable expression.
If one looks to the different parts of this expression then the partial expressions ‘white’, ‘wooden’, ‘table’ can be mapped by a learned meaning function φ into abstracted structures which are the result of internal processing. This means there can be countable infinite many concrete instances in the external environment ENV which can be understood as being white. The same holds for the expressions ‘wooden’ and ‘table’. Thus the expressions ‘white’, ‘wooden’, ‘table’ are all related to abstracted structures and therefor they have to be classified as universal expressions which as such are — strictly speaking — not decidable because they can be true in many concrete situations with different concrete matters. Or take it otherwise: an expression with a meaning function φ pointing to an abstracted structure is asymmetric: one expression can be related to many different perceivable concrete matters but certain members of a set of different perceived concrete matters can be related to one and the same abstracted structure on account of similarities based on properties embedded in the perceived concrete matter and being part of the abstracted structure.
In a cognitive point of view one can describe these matters such that the expression — like ‘table’ — which is pointing to a cognitive abstracted structure ‘T’ includes a set of properties Π and every concrete perceived structure ‘t’ (caused e.g. by some concrete matter in our environment which we would classify as a ‘table’) must have a ‘certain amount’ of properties Π* that one can say that the properties Π* are entailed in the set of properties Π of the abstracted structure T, thus Π* ⊆ Π. In what circumstances some speaker-hearer will say that something perceived concrete ‘is’ a table or ‘is not’ a table will depend from the learning history of this speaker-hearer. A child in the beginning of learning a language L can perhaps call something a ‘chair’ and the parents will correct the child and will perhaps say ‘no, this is table’.
Thus the expression ‘There is a white wooden table‘ as such is not true or false because it is not clear which set of concrete perceptions shall be derived from the possible internal meaning mappings, but if a concrete situation S is given with a concrete object with concrete properties then a speaker can ‘translate’ his/ her concrete perceptions with his learned meaning function φ into a composed expression using universal expressions. In such a situation where the speaker is part of the real situation S he/ she can recognize that the given situation is an instance of the abstracted structures encoded in the used expression. And recognizing this being an instanceinterprets the universal expression in a way that makes the universal expression fitting to a real given situation. And thereby the universal expression is transformed by interpretation with φ into a concrete decidable expression.
SUMMING UP
Thus the decisive moment of turning undecidable universal expressions U(U)E into decidable concrete expressions (D)CE is a human actor A behaving as a speaker-hearer of the used language L. Without a speaker-hearer every universal expressions is undefined and neither true nor false.
makedecidable : S x Ahum x E —> E x {true, false}
This reads as follows: If you want to know whether an expression E is concrete and as being concrete is ‘true’ or ‘false’ then ask a human actor Ahum which is part of a concrete situation S and the human actor shall answer whether the expression E can be interpreted such that E can be classified being either ‘true’ or ‘false’.
The function ‘makedecidable()’ is therefore the description (like a ‘recipe’) of a real process in the real world with real actors. The important factors in this description are the meaning functions inside the participating human actors. Although it is not possible to describe these meaning functions directly one can check their behavior and one can define an abstract model which describes the observable behavior of speaker-hearer of the language L. This is an empirical model and represents the typical case of behavioral models used in psychology, biology, sociology etc.
SOURCES
[1] Jakob Johann Freiherr von Uexküll (German: [ˈʏkskʏl])(1864 – 1944) https://en.wikipedia.org/wiki/Jakob_Johann_von_Uexk%C3%BCll
[2] Jakob von Uexküll, 1909, Umwelt und Innenwelt der Tiere. Berlin: J. Springer. (Download: https://ia802708.us.archive.org/13/items/umweltundinnenwe00uexk/umweltundinnenwe00uexk.pdf )
[3] Wikipedia EN, Speech acts: https://en.wikipedia.org/wiki/Speech_act
[4] Ludwig Josef Johann Wittgenstein ( 1889 – 1951): https://en.wikipedia.org/wiki/Ludwig_Wittgenstein
[5] Ludwig Wittgenstein, 1953: Philosophische Untersuchungen [PU], 1953: Philosophical Investigations [PI], translated by G. E. M. Anscombe /* For more details see: https://en.wikipedia.org/wiki/Philosophical_Investigations */
Integrating Engineering and the Human Factor (info@uffmm.org) eJournal uffmm.org ISSN 2567-6458, February 27-March 16, 2021,
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de
Before one starts the HMI analysis some stakeholder — in our case are the users stakeholder as well as users in one role — have to present some given situation — classifiable as a ‘problem’ — to depart from and a vision as the envisioned goal to be realized.
Here we give a short description of the problem for the CM:MI paradigm and the vision, what should be gained.
Problem: Mankind on the Planet Earth
In this project the mankind on the planet earth is understood as the primary problem. ‘Mankind’ is seen here as the life form called homo sapiens. Based on the findings of biological evolution one can state that the homo sapiens has — besides many other wonderful capabilities — at least two extraordinary capabilities:
Outside to Inside
The whole body with the brain is able to convert continuously body-external events into internal, neural events. And the brain inside the body receives many events inside the body as external events too. Thus in the brain we can observe a mixup of body-external (outside 1) and body-internal events (outside 2), realized as set of billions of neural processes, highly interrelated. Most of these neural processes are unconscious, a small part is conscious. Nevertheless these unconscious and conscious events are neurally interrelated. This overall conversion from outside 1 and outside 2 into neural processes can be seen as a mapping. As we know today from biology, psychology and brain sciences this mapping is not a 1-1 mapping. The brain does all the time a kind of filtering — mostly unconscious — sorting out only those events which are judged by the brain to be important. Furthermore the brain is time-slicing all its sensory inputs, storing these time-slices (called ‘memories’), whereby these time-slices again are no 1-1 copies. The storing of time-sclices is a complex (unconscious) process with many kinds of operations like structuring, associating, abstracting, evaluating, and more. From this one can deduce that the content of an individual brain and the surrounding reality of the own body as well as the world outside the own body can be highly different. All kinds of perceived and stored neural events which can be or can become conscious are here called conscious cognitive substrates or cognitive objects.
Inside to Outside (to Inside)
Generally it is known that the homo sapiens can produce with its body events which have some impact on the world outside the body. One kind of such events is the production of all kinds of movements, including gestures, running, grasping with hands, painting, writing as well as sounds by his voice. What is of special interest here are forms of communications between different humans, and even more specially those communications enabled by the spoken sounds of a language as well as the written signs of a language. Spoken sounds as well as written signs are here called expressions associated with a known language. Expressions as such have no meaning (A non-speaker of a language L can hear or see expressions of the language L but he/she/x never will understand anything). But as everyday experience shows nearly every child starts very soon to learn which kinds of expressions belong to a language and with what kinds of shared experiences they can be associated. This learning is related to many complex neural processes which map expressions internally onto — conscious and unconscious — cognitive objects (including expressions!). This mapping builds up an internal meaning function from expressions into cognitive objects and vice versa. Because expressions have a dual face (being internal neural structures as well as being body-outside events by conversions from the inside to body-outside) it is possible that a homo sapiens can transmit its internal encoding of cognitive objects into expressions from his inside to the outside and thereby another homo sapiens can perceive the produced outside expression and can map this outside expression into an intern expression. As far as the meaning function of of the receiving homo sapiens is sufficiently similar to the meaning function of the sending homo sapiens there exists some probability that the receiving homo sapiens can activate from its memory cognitive objects which have some similarity with those of the sending homo sapiens.
Although we know today of different kinds of animals having some form of language, there is no species known which is with regard to language comparable to the homo sapiens. This explains to a large extend why the homo sapiens population was able to cooperate in a way, which not only can include many persons but also can stretch through long periods of time and can include highly complex cognitive objects and associated behavior.
Negative Complexity
In 2006 I introduced the term negative complexity in my writings to describe the fact that in the world surrounding an individual person there is an amount of language-encoded meaning available which is beyond the capacity of an individual brain to be processed. Thus whatever kind of experience or knowledge is accumulated in libraries and data bases, if the negative complexity is higher and higher than this knowledge can no longer help individual persons, whole groups, whole populations in a constructive usage of all this. What happens is that the intended well structured ‘sound’ of knowledge is turned into a noisy environment which crashes all kinds of intended structures into nothing or badly deformed somethings.
Entangled Humans
From Quantum Mechanics we know the idea of entangled states. But we must not dig into quantum mechanics to find other phenomena which manifest entangled states. Look around in your everyday world. There exist many occasions where a human person is acting in a situation, but the bodily separateness is a fake. While sitting before a laptop in a room the person is communicating within an online session with other persons. And depending from the social role and the membership in some social institution and being part of some project this person will talk, perceive, feel, decide etc. with regard to the known rules of these social environments which are represented as cognitive objects in its brain. Thus by knowledge, by cognition, the individual person is in its situation completely entangled with other persons which know from these roles and rules and following thereby in their behavior these rules too. Sitting with the body in a certain physical location somewhere on the planet does not matter in this moment. The primary reality is this cognitive space in the brains of the participating persons.
If you continue looking around in your everyday world you will probably detect that the everyday world is full of different kinds of cognitively induced entangled states of persons. These internalized structures are functioning like protocols, like scripts, like rules in a game, telling everybody what is expected from him/her/x, and to that extend, that people adhere to such internalized protocols, the daily life has some structure, has some stability, enables planning of behavior where cooperation between different persons is necessary. In a cognitively enabled entangled state the individual person becomes a member of something greater, becoming a super person. Entangled persons can do things which usually are not possible as long you are working as a pure individual person.[1]
Entangled Humans and Negative Complexity
Although entangled human persons can principally enable more complex events, structures, processes, engineering, cultural work than single persons, human entanglement is still limited by the brain capacities as well as by the limits of normal communication. Increasing the amount of meaning relevant artifacts or increasing the velocity of communication events makes things even more worse. There are objective limits for human processing, which can run into negative complexity.
Future is not Waiting
The term ‘future‘ is cognitively empty: there exists nowhere an object which can be called ‘future’. What we have is some local actual presence (the Now), which the body is turning into internal representations of some kind (becoming the Past), but something like a future does not exist, nowhere. Our knowledge about the future is radically zero.
Nevertheless, because our bodies are part of a physical world (planet, solar system, …) and our entangled scientific work has identified some regularities of this physical world which can be bused for some predictions what could happen with some probability as assumed states where our clocks are showing a different time stamp. But because there are many processes running in parallel, composed of billions of parameters which can be tuned in many directions, a really good forecast is not simple and depends from so many presuppositions.
Since the appearance of homo sapiens some hundred thousands years ago in Africa the homo sapiens became a game changer which makes all computations nearly impossible. Not in the beginning of the appearance of the homo sapiens, but in the course of time homo sapiens enlarged its number, improved its skills in more and more areas, and meanwhile we know, that homo sapiens indeed has started to crash more and more the conditions of its own life. And principally thinking points out, that homo sapiens could even crash more than only planet earth. Every exemplar of a homo sapiens has a built-in freedom which allows every time to decide to behave in a different way (although in everyday life we are mostly following some protocols). And this built-in freedom is guided by actual knowledge, by emotions, and by available resources. The same child can become a great musician, a great mathematician, a philosopher, a great political leader, an engineer, … but giving the child no resources, depriving it from important social contexts, giving it the wrong knowledge, it can not manifest its freedom in full richness. As human population we need the best out of all children.
Because the processing of the planet, the solar system etc. is going on, we are in need of good forecasts of possible futures, beyond our classical concepts of sharing knowledge. This is where our vision enters.
VISION: DEVELOPING TOGETHER POSSIBLE FUTURES
To find possible and reliable shapes of possible futures we have to exploit all experiences, all knowledge, all ideas, all kinds of creativity by using maximal diversity. Because present knowledge can be false — as history tells us –, we should not rule out all those ideas, which seem to be too crazy at a first glance. Real innovations are always different to what we are used to at that time. Thus the following text is a first rough outline of the vision:
Find a format
which allows anykinds of people
for any kind of given problem
with at least one vision of a possible improvement
together
to search and to find a path leading from the given problem (Now) to the envisioned improved state (future).
For all needed communication any kind of everyday language should be enough.
As needed this everyday language should be extendable with special expressions.
These considerations about possible paths into the wanted envisioned future state should continuously be supported by appropriate automaticsimulations of such a path.
These simulations should include automatic evaluations based on the given envisioned state.
As far as possible adaptive algorithms should be available to support the search, finding and identification of the best cases (referenced by the visions) within human planning.
REFERENCES or COMMENTS
[1] One of the most common entangled state in daily life is the usage of normal language! A normal language L works only because the rules of usage of this language L are shared by all speaker-hearer of this language, and these rules are explicit cognitive structures (not necessarily conscious, mostly unconscious!).
Integrating Engineering and the Human Factor (info@uffmm.org)
eJournal uffmm.org ISSN 2567-6458, Nov 8, 2020
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de
In daily life we experience today a multitude of perspectives in all areas. While our bodies are embedded in real world scenarios our minds are filled up with perceptions, emotions, ideas, memories of all kinds. What links us to each other is language. Language gives us the power to overcome the isolation of our individual brains located in individual bodies. And by this, our language, we can distribute and share the inner states of our brains, pictures of life as we see it. And it is this open web of expressions which spreads to the air, to the newspapers and books, to the data bases in which the different views of the world are manifested.
SORTING IDEAS SCIENTIFICALLY
While our bodies touching reality outside the bodies, our brains are organizing different kinds of order, finally expressed — only some part of it — in expressions of some language. While our daily talk is following mostly automatically some naive patterns of ordering does empirical science try to order the expressions more consciously following some self-defined rules called methods, called scientific procedures to enable transparency, repeatability, decidability of the hypothesized truth of is symbolic structures.
But because empirical science wants to be rational by being transparent, repeatable, measurable, there must exist an open discourse which is dealing with science as an object: what are the ingredients of science? Under which conditions can science work? What does it mean to ‘measure’ something? And other questions like these.
PHILOSOPHY OF SCIENCE
That discipline which is responsible for such a discourse about science is not science itself but another instance of thinking and speaking which is called Philosophy ofScience. Philosophy of science deals with all aspects of science from the outside of science.
PHILOSOPHY
Philosophy of Science dealing with empirical sciences as an object has a special focus and it can be reflected too from another point of view dealing with Philosophy of Science as an object. This relationship reflects a general structure of human thinking: every time we have some object of our thinking we are practicing a different point of view talking about the actual object. While everyday thinking leads us directly to Philosophy as our active point of view an object like empirical science does allow an intermediate point of view called Philosophy of Science leading then to Philosophy again.
Philosophy is our last point of reflection. If we want to reflect the conditions of our philosophical thinking than our thinking along with the used language tries to turn back on itself but this is difficult. The whole history of Philosophy shows this unending endeavor as a consciousness trying to explain itself by being inside itself. Famous examples of this kind of thinking are e.g. Descartes, Kant, Fichte, Schelling, Hegel, and Husserl.
These examples show there exists no real way out.
PHILOSOPHY ENHANCED BY EMPIRICAL SCIENCES ? !
At a first glance it seems contradictory that Philosophy and Empirical Sciences could work ‘hand in hand’. But history has shown us, that this is to a certain extend possible; perhaps it is a major break through for the philosophical understanding of the world, especially also of men themselves.
Modern empirical sciences like Biology and Evolutionary Biology in cooperation with many other empirical disciplines have shown us, that the actual biological systems — including homo sapiens — are products of a so-called evolutionary process. And supported by modern empirical disciplines like Ethology, Psychology, Physiology, and Brain Sciences we could gain some first knowledge how our body works, how our brain, how our observable behavior is connected to this body and its brain.
While Philosopher like Kant or Hegel could investigate their own thinking only from the inside of their consciousness, the modern empirical sciences can investigate the human thinking from the outside. But until now there is a gap: We have no elaborated theory about the relationship between the inside of the consciousness and the outside knowledge about body and brain.
Thus what we need is a hybrid theory mapping the inside to the outside and revers. There are some first approaches headed under labels like Neuro-Psychology or Neuro-Phenomenology, but these are not yet completely clarified in their methodology in their relationship to Philosophy.
If one can describe to some extend the Phenomena of the consciousness from the inside as well as the working of the brain translated to its behavioral properties, then one can start first mappings like those, which have been used in this blog to establish the theory for the komega software.
SOCIOLOGY
Sociology is only one empirical discipline between many others. Although the theory of this blog is using many disciplines simultaneously Sociology is of special interest because it is that kind of empirical disciplines which is explicitly dealing with human societies with subsystems called cities.
The komega software which we are developing is understood here as enabling a system of interactions as part of a city understood as a system. If we understand Sociology as an empirical science according to some standard view of empirical science then it is possible to describe a city as an input-output system whose dynamics can become influenced by this komega software if citizens are using this software as part of their behavior.
STANDARD VIEW OF EMPIRICAL SCIENCE
Without some kind of a Standard View of Empirical Science it is not possible to design a discipline — e.g. Sociology — as an empirical discipline. Although it seems that everybody thinks that we have such a ‘Standard View of Empirical Science’, in the real world of today one must state that we do not have such a view. In the 80ties of the20th century it looked for some time as if we have it, but if you start searching the papers, books and schools today You will perceive a very fuzzy field called Philosophy of Science and within the so-called empirical sciences you will not found any coherent documented view of a ‘Standard View of Empirical Science’.
Because it is difficult to see how a process can look like which enables such a ‘Standard View of Empirical Science’ again, we will try to document the own assumptions for our theory as good as possible. Inevitably this will mostly have the character of only a ‘fragment’, an ‘incomplete outline’. Perhaps there will again be a time where sciences is back to have a commonly accepted view how science should look like to be called empirical science.
The two papers of Tarski, which I do discuss here, have been published in 1936. Occasionally I have already read these paper many years ago but at that time I could not really work with these papers. Formally they seemed to be ’correct’, but in the light of my ’intuition’ the message appeared to me somehow ’weird’, not really in conformance with my experience of how knowledge and language are working in the real world. But at that time I was not able to explain my intuition to myself sufficiently. Nevertheless, I kept these papers – and some more texts of Tarski – in my bookshelves for an unknown future when my understanding would eventually change…
This happened the last days.
To work within the Generative Cultural Anthropology [GCA] Theory one needs a practical tool which allows the construction of dynamic world models, the storage of these models, their usage within a simulation game environment together with an evaluation tool. Basic requirements for such
a tool will be described here with the example called a Hybrid Simulation Game Environment [HSGE]. To prepare a simulation game one needs an iterative development process which follows some general assumptions. In this paper the subject of discussion is the observer-world-framework.
To work within the Generative Cultural Anthropology [GCA] Theory one needs a practical tool which allows the construction of dynamic world models, the storage of these models, their usage within a simulation game environment together with an evaluation tool. To prepare a simulation game within a Hybrid Simulation Game Environment [HSGE] one needs an
iterative development process which is described below.
CASE STUDY – SIMULATION GAMES – PHASE 1: Iterative Development of a Dynamic World Model – Part of the Generative Cultural Anthropology [GCA] Theory
Contents
1 Overview of the Whole Development Process
2 Cognitive Aspects of Symbolic Expressions
3 Symbolic Representations and Transformations
4 Abstract-Concrete Concepts
5 Implicit Structures Embedded in Experience
5.1 Example 1
In this section several case studies will be presented. It will be shown, how the DAAI paradigm can be applied to many different contexts . Since the original version of the DAAI-Theory in Jan 18, 2020 the concept has been further developed centering around the concept of a Collective Man-Machine Intelligence [CM:MI] to address now any kinds of experts for any kind of simulation-based development, testing and gaming. Additionally the concept now can be associated with any kind of embedded algorithmic intelligence [EAI] (different to the mainstream concept ‘artificial intelligence’). The new concept can be used with every normal language; no need for any special programming language! Go back to the overall framework.
COLLECTION OF PAPERS
There exists only a loosely order between the different papers due to the character of this elaboration process: generally this is an experimental philosophical process. HMI Analysis applied for the CM:MI paradigm.
FROM DAAI to GCA. Turning Engineering into Generative Cultural Anthropology. This paper gives an outline how one can map the DAAI paradigm directly into the GCA paradigm (April-19,2020): case1-daai-gca-v1
A first GCA open research project [GCA-OR No.1]. This paper outlines a first open research project using the GCA. This will be the framework for the first implementations (May-5, 2020): GCAOR-v0-1
Engineering and Society. A Case Study for the DAAI Paradigm – Introduction. This paper illustrates important aspects of a cultural process looking to the acting actors where certain groups of people (experts of different kinds) can realize the generation, the exploration, and the testing of dynamical models as part of a surrounding society. Engineering is clearly not separated from society (April-9, 2020): case1-population-start-part0-v1
Bootstrapping some Citizens. This paper clarifies the set of general assumptions which can and which should be presupposed for every kind of a real world dynamical model (April-4, 2020): case1-population-start-v1-1
Hybrid Simulation Game Environment [HSGE]. This paper outlines the simulation environment by combing a usual web-conference tool with an interactive web-page by our own (23.May 2020): HSGE-v2 (May-5, 2020): HSGE-v0-1
The Observer-World Framework. This paper describes the foundations of any kind of observer-based modeling or theory construction.(July 16, 2020)
Comments on Thomas Rid (2016), Rise of the machines. A cybernetics History. W.W.Norton & Company, Independent Publishers Since 1923 (New York – London). /* The German edition: maschinen dämmerung. eine kurze geschichte der kybernetik published 2016 by the Publisher Propyläen, owned by Ullstein Buchverlag GmbH (Berlin) */ (Last change: Sept 29, 2021)
Review of the book Why the World Needs Anthropologists edited by Dan Podjed, Meta Gorup, Pavel Borecký & Carla Guerrón Montero, 2021 (already distributed November 2020), Publisher: Routledge (Landon – New York)(Last change: December 1, 2020)
Review of Tarski (1936) On the concept of logical consequence, (1936) The establishment of scientific semantics, in one paper. (published 8.August 2020)
Review of EU’s trustworthy AI Ethic with Denning & Denning (2020) and other authors from the point of view of GCA theory (May-11, 2020).
Review of Tsu and Nourbakhsh (2020), When Human-Computer Interaction Meets Community Citizen Science. Empowering communities through citizen science. In the Proceedings of the 2017 CHI Conference on Human Factors in Computing Systems, ACM 2017: review-Tsu-et-2020-acm-CommunitySciences (April-6, 2020)
Review of Nancy Leveson (2020), Are you sure your software will not kill anyone?, Communications of the ACM, February 2020, Vol.63, No.2, pp.25-28: review-leveson-2020-acm-yourSWwillNotKill
Review of Miller & Page (2007), Complex Adaptive Systems. An Introduction to Computational Models of Social Life, example No.1 from Chapter 7: review-santa-fe-2-miller-page-2007-example-c7-no1c (PDF, Febr 5, 2020)
Review of Miller & Page (2007), Complex Adaptive Systems. An Introduction to Computational Models of Social Life, Chapters 1-7,final: review-santa-fe-1-miller-page-2007-cc1-7-final (PDF, final, Febr 1,2020)
Review of Cathy Stein Greenblat (1988), DESIGNING GAMES and SIMULATIONS, Completereview-greenblat-1988-1-2
Review of Alan Newell and Herbert A.Simon (1972), Human Problem Solving (Last update: Oct 9, 2019): review-newell-simon-1972-V1-4 Comment: This document will be replaced several times by the next extended version with the discussion of the text. One document spans in the end one complete chapter.
Review of Peter Gärdenfors (2014), Geometry of Meaning. Semantics Based on Conceptual Spaces, Part 1, A Review from a Philosophical Point of View: review-gaerdenfors2014-c1-2
Review of Charles R.Gallistel, (1990), The Organization of Learning. Part 1, A Review from a Philosophical Point of View: review-gallistel-part1-C1
Remark: There have been many more reviews before this review section but these have been written in German and are located in the philosophy blog of G.Doeben Henisch.
Last change: 23.February 2019 (continued the text)
Last change: 24.February 2019 (extended the text)
CONTEXT
In the overview of the AAI paradigm version 2 you can find this section dealing with the philosophical perspective of the AAI paradigm. Enjoy reading (or not, then send a comment :-)).
THE DAILY LIFE PERSPECTIVE
The perspective of Philosophy is rooted in the everyday life perspective. With our body we occur in a space with other bodies and objects; different features, properties are associated with the objects, different kinds of relations an changes from one state to another.
From the empirical sciences we have learned to see more details of the everyday life with regard to detailed structures of matter and biological life, with regard to the long history of the actual world, with regard to many interesting dynamics within the objects, within biological systems, as part of earth, the solar system and much more.
A certain aspect of the empirical view of the world is the fact, that some biological systems called ‘homo sapiens’, which emerged only some 300.000 years ago in Africa, show a special property usually called ‘consciousness’ combined with the ability to ‘communicate by symbolic languages’.
Figure 1: General setting of the homo sapiens species (simplified)
As we know today the consciousness is associated with the brain, which in turn is embedded in the body, which is further embedded in an environment.
Thus those ‘things’ about which we are ‘conscious’ are not ‘directly’ the objects and events of the surrounding real world but the ‘constructions of the brain’ based on actual external and internal sensor inputs as well as already collected ‘knowledge’. To qualify the ‘conscious things’ as ‘different’ from the assumed ‘real things’ ‘outside there’ it is common to speak of these brain-generated virtual things either as ‘qualia’ or — more often — as ‘phenomena’ which are different to the assumed possible real things somewhere ‘out there’.
PHILOSOPHY AS FIRST PERSON VIEW
‘Philosophy’ has many facets. One enters the scene if we are taking the insight into the general virtual character of our primary knowledge to be the primary and irreducible perspective of knowledge. Every other more special kind of knowledge is necessarily a subspace of this primary phenomenological knowledge.
There is already from the beginning a fundamental distinction possible in the realm of conscious phenomena (PH): there are phenomena which can be ‘generated’ by the consciousness ‘itself’ — mostly called ‘by will’ — and those which are occurring and disappearing without a direct influence of the consciousness, which are in a certain basic sense ‘given’ and ‘independent’, which are appearing and disappearing according to ‘their own’. It is common to call these independent phenomena ’empirical phenomena’ which represent a true subset of all phenomena: PH_emp ⊂ PH. Attention: These empirical phenomena’ are still ‘phenomena’, virtual entities generated by the brain inside the brain, not directly controllable ‘by will’.
There is a further basic distinction which differentiates the empirical phenomena into those PH_emp_bdy which are controlled by some processes in the body (being tired, being hungry, having pain, …) and those PH_emp_ext which are controlled by objects and events in the environment beyond the body (light, sounds, temperature, surfaces of objects, …). Both subsets of empirical phenomena are different: PH_emp_bdy ∩ PH_emp_ext = 0. Because phenomena usually are occurring associated with typical other phenomena there are ‘clusters’/ ‘pattern’ of phenomena which ‘represent’ possible events or states.
Modern empirical science has ‘refined’ the concept of an empirical phenomenon by introducing ‘standard objects’ which can be used to ‘compare’ some empirical phenomenon with such an empirical standard object. Thus even when the perception of two different observers possibly differs somehow with regard to a certain empirical phenomenon, the additional comparison with an ’empirical standard object’ which is the ‘same’ for both observers, enhances the quality, improves the precision of the perception of the empirical phenomena.
From these considerations we can derive the following informal definitions:
Something is ‘empirical‘ if it is the ‘real counterpart’ of a phenomenon which can be observed by other persons in my environment too.
Something is ‘standardized empirical‘ if it is empirical and can additionally be associated with a before introduced empirical standard object.
Something is ‘weak empirical‘ if it is the ‘real counterpart’ of a phenomenon which can potentially be observed by other persons in my body as causally correlated with the phenomenon.
Something is ‘cognitive‘ if it is the counterpart of a phenomenon which is not empirical in one of the meanings (1) – (3).
It is a common task within philosophy to analyze the space of the phenomena with regard to its structure as well as to its dynamics. Until today there exists not yet a complete accepted theory for this subject. This indicates that this seems to be some ‘hard’ task to do.
BRIDGING THE GAP BETWEEN BRAINS
As one can see in figure 1 a brain in a body is completely disconnected from the brain in another body. There is a real, deep ‘gap’ which has to be overcome if the two brains want to ‘coordinate’ their ‘planned actions’.
Luckily the emergence of homo sapiens with the new extended property of ‘consciousness’ was accompanied by another exciting property, the ability to ‘talk’. This ability enabled the creation of symbolic languages which can help two disconnected brains to have some exchange.
But ‘language’ does not consist of sounds or a ‘sequence of sounds’ only; the special power of a language is the further property that sequences of sounds can be associated with ‘something else’ which serves as the ‘meaning’ of these sounds. Thus we can use sounds to ‘talk about’ other things like objects, events, properties etc.
The single brain ‘knows’ about the relationship between some sounds and ‘something else’ because the brain is able to ‘generate relations’ between brain-structures for sounds and brain-structures for something else. These relations are some real connections in the brain. Therefore sounds can be related to ‘something else’ or certain objects, and events, objects etc. can become related to certain sounds. But these ‘meaning relations’ can only ‘bridge the gap’ to another brain if both brains are using the same ‘mapping’, the same ‘encoding’. This is only possible if the two brains with their bodies share a real world situation RW_S where the perceptions of the both brains are associated with the same parts of the real world between both bodies. If this is the case the perceptions P(RW_S) can become somehow ‘synchronized’ by the shared part of the real world which in turn is transformed in the brain structures P(RW_S) —> B_S which represent in the brain the stimulating aspects of the real world. These brain structures B_S can then be associated with some sound structures B_A written as a relation MEANING(B_S, B_A). Such a relation realizes an encoding which can be used for communication. Communication is using sound sequences exchanged between brains via the body and the air of an environment as ‘expressions’ which can be recognized as part of a learned encoding which enables the receiving brain to identify a possible meaning candidate.
DIFFERENT MODES TO EXPRESS MEANING
Following the evolution of communication one can distinguish four important modes of expressing meaning, which will be used in this AAI paradigm.
VISUAL ENCODING
A direct way to express the internal meaning structures of a brain is to use a ‘visual code’ which represents by some kinds of drawing the visual shapes of objects in the space, some attributes of shapes, which are common for all people who can ‘see’. Thus a picture and then a sequence of pictures like a comic or a story board can communicate simple ideas of situations, participating objects, persons and animals, showing changes in the arrangement of the shapes in the space.
Figure 2: Pictorial expressions representing aspects of the visual and the auditory sens modes
Even with a simple visual code one can generate many sequences of situations which all together can ‘tell a story’. The basic elements are a presupposed ‘space’ with possible ‘objects’ in this space with different positions, sizes, relations and properties. One can even enhance these visual shapes with written expressions of a spoken language. The sequence of the pictures represents additionally some ‘timely order’. ‘Changes’ can be encoded by ‘differences’ between consecutive pictures.
FROM SPOKEN TO WRITTEN LANGUAGE EXPRESSIONS
Later in the evolution of language, much later, the homo sapiens has learned to translate the spoken language L_s in a written format L_w using signs for parts of words or even whole words. The possible meaning of these written expressions were no longer directly ‘visible’. The meaning was now only available for those people who had learned how these written expressions are associated with intended meanings encoded in the head of all language participants. Thus only hearing or reading a language expression would tell the reader either ‘nothing’ or some ‘possible meanings’ or a ‘definite meaning’.
Figure 3: A written textual version in parallel to a pictorial version
If one has only the written expressions then one has to ‘know’ with which ‘meaning in the brain’ the expressions have to be associated. And what is very special with the written expressions compared to the pictorial expressions is the fact that the elements of the pictorial expressions are always very ‘concrete’ visual objects while the written expressions are ‘general’ expressions allowing many different concrete interpretations. Thus the expression ‘person’ can be used to be associated with many thousands different concrete objects; the same holds for the expression ‘road’, ‘moving’, ‘before’ and so on. Thus the written expressions are like ‘manufacturing instructions’ to search for possible meanings and configure these meanings to a ‘reasonable’ complex matter. And because written expressions are in general rather ‘abstract’/ ‘general’ which allow numerous possible concrete realizations they are very ‘economic’ because they use minimal expressions to built many complex meanings. Nevertheless the daily experience with spoken and written expressions shows that they are continuously candidates for false interpretations.
FORMAL MATHEMATICAL WRITTEN EXPRESSIONS
Besides the written expressions of everyday languages one can observe later in the history of written languages the steady development of a specialized version called ‘formal languages’ L_f with many different domains of application. Here I am focusing on the formal written languages which are used in mathematics as well as some pictorial elements to ‘visualize’ the intended ‘meaning’ of these formal mathematical expressions.
Fig. 4: Properties of an acyclic directed graph with nodes (vertices) and edges (directed edges = arrows)
One prominent concept in mathematics is the concept of a ‘graph’. In the basic version there are only some ‘nodes’ (also called vertices) and some ‘edges’ connecting the nodes. Formally one can represent these edges as ‘pairs of nodes’. If N represents the set of nodes then N x N represents the set of all pairs of these nodes.
In a more specialized version the edges are ‘directed’ (like a ‘one way road’) and also can be ‘looped back’ to a node occurring ‘earlier’ in the graph. If such back-looping arrows occur a graph is called a ‘cyclic graph’.
Fig.5: Directed cyclic graph extended to represent ‘states of affairs’
If one wants to use such a graph to describe some ‘states of affairs’ with their possible ‘changes’ one can ‘interpret’ a ‘node’ as a state of affairs and an arrow as a change which turns one state of affairs S in a new one S’ which is minimally different to the old one.
As a state of affairs I understand here a ‘situation’ embedded in some ‘context’ presupposing some common ‘space’. The possible ‘changes’ represented by arrows presuppose some dimension of ‘time’. Thus if a node n’ is following a node n indicated by an arrow then the state of affairs represented by the node n’ is to interpret as following the state of affairs represented in the node n with regard to the presupposed time T ‘later’, or n < n’ with ‘<‘ as a symbol for a timely ordering relation.
Fig.6: Example of a state of affairs with a 2-dimensional space configured as a grid with a black and a white token
The space can be any kind of a space. If one assumes as an example a 2-dimensional space configured as a grid –as shown in figure 6 — with two tokens at certain positions one can introduce a language to describe the ‘facts’ which constitute the state of affairs. In this example one needs ‘names for objects’, ‘properties of objects’ as well as ‘relations between objects’. A possible finite set of facts for situation 1 could be the following:
TOKEN(T1), BLACK(T1), POSITION(T1,1,1)
TOKEN(T2), WHITE(T2), POSITION(T2,2,1)
NEIGHBOR(T1,T2)
CELL(C1), POSITION(1,2), FREE(C1)
‘T1’, ‘T2’, as well as ‘C1’ are names of objects, ‘TOKEN’, ‘BACK’ etc. are names of properties, and ‘NEIGHBOR’ is a relation between objects. This results in the equation:
These facts describe the situation S1. If it is important to describe possible objects ‘external to the situation’ as important factors which can cause some changes then one can describe these objects as a set of facts in a separated ‘context’. In this example this could be two players which can move the black and white tokens and thereby causing a change of the situation. What is the situation and what belongs to a context is somewhat arbitrary. If one describes the agriculture of some region one usually would not count the planets and the atmosphere as part of this region but one knows that e.g. the sun can severely influence the situation in combination with the atmosphere.
Fig.7: Change of a state of affairs given as a state which will be enhanced by a new object
Let us stay with a state of affairs with only a situation without a context. The state of affairs is a ‘state’. In the example shown in figure 6 I assume a ‘change’ caused by the insertion of a new black token at position (2,2). Written in the language of facts L_fact we get:
Thus the new state S2 is generated out of the old state S1 by unifying S1 with the set of new facts: S2 = S1 ∪ {TOKEN(T3), BLACK(T3), POSITION(2,2), NEIGHBOR(T3,T2)}. All the other facts of S1 are still ‘valid’. In a more general manner one can introduce a change-expression with the following format:
This can be read as follows: The follow-up state S2 is generated out of the state S1 by adding to the state S1 the set of facts { … }.
This layout of a change expression can also be used if some facts have to be modified or removed from a state. If for instance by some reason the white token should be removed from the situation one could write:
These simple examples demonstrate another fact: while facts about objects and their properties are independent from each other do relational facts depend from the state of their object facts. The relation of neighborhood e.g. depends from the participating neighbors. If — as in the example above — the object token T2 disappears then the relation ‘NEIGHBOR(T1,T2)’ no longer holds. This points to a hierarchy of dependencies with the ‘basic facts’ at the ‘root’ of a situation and all the other facts ‘above’ basic facts or ‘higher’ depending from the basic facts. Thus ‘higher order’ facts should be added only for the actual state and have to be ‘re-computed’ for every follow-up state anew.
If one would specify a context for state S1 saying that there are two players and one allows for each player actions like ‘move’, ‘insert’ or ‘delete’ then one could make the change from state S1 to state S2 more precise. Assuming the following facts for the context:
PLAYER(PB1), PLAYER(PW1), HAS-THE-TURN(PB1)
In that case one could enhance the change statement in the following way:
This would read as follows: given state S1 the player PB1 inserts a black token at position (2,2); this yields a new state S2.
With or without a specified context but with regard to a set of possible change statements it can be — which is the usual case — that there is more than one option what can be changed. Some of the main types of changes are the following ones:
RANDOM
NOT RANDOM, which can be specified as follows:
With PROBABILITIES (classical, quantum probability, …)
DETERMINISTIC
Furthermore, if the causing object is an actor which can adapt structurally or even learn locally then this actor can appear in some time period like a deterministic system, in different collected time periods as an ‘oscillating system’ with different behavior, or even as a random system with changing probabilities. This make the forecast of systems with adaptive and/ or learning systems rather difficult.
Another aspect results from the fact that there can be states either with one actor which can cause more than one action in parallel or a state with multiple actors which can act simultaneously. In both cases the resulting total change has eventually to be ‘filtered’ through some additional rules telling what is ‘possible’ in a state and what not. Thus if in the example of figure 6 both player want to insert a token at position (2,2) simultaneously then either the rules of the game would forbid such a simultaneous action or — like in a computer game — simultaneous actions are allowed but the ‘geometry of a 2-dimensional space’ would not allow that two different tokens are at the same position.
Another aspect of change is the dimension of time. If the time dimension is not explicitly specified then a change from some state S_i to a state S_j does only mark the follow up state S_j as later. There is no specific ‘metric’ of time. If instead a certain ‘clock’ is specified then all changes have to be aligned with this ‘overall clock’. Then one can specify at what ‘point of time t’ the change will begin and at what point of time t*’ the change will be ended. If there is more than one change specified then these different changes can have different timings.
THIRD PERSON VIEW
Up until now the point of view describing a state and the possible changes of states is done in the so-called 3rd-person view: what can a person perceive if it is part of a situation and is looking into the situation. It is explicitly assumed that such a person can perceive only the ‘surface’ of objects, including all kinds of actors. Thus if a driver of a car stears his car in a certain direction than the ‘observing person’ can see what happens, but can not ‘look into’ the driver ‘why’ he is steering in this way or ‘what he is planning next’.
A 3rd-person view is assumed to be the ‘normal mode of observation’ and it is the normal mode of empirical science.
Nevertheless there are situations where one wants to ‘understand’ a bit more ‘what is going on in a system’. Thus a biologist can be interested to understand what mechanisms ‘inside a plant’ are responsible for the growth of a plant or for some kinds of plant-disfunctions. There are similar cases for to understand the behavior of animals and men. For instance it is an interesting question what kinds of ‘processes’ are in an animal available to ‘navigate’ in the environment across distances. Even if the biologist can look ‘into the body’, even ‘into the brain’, the cells as such do not tell a sufficient story. One has to understand the ‘functions’ which are enabled by the billions of cells, these functions are complex relations associated with certain ‘structures’ and certain ‘signals’. For this it is necessary to construct an explicit formal (mathematical) model/ theory representing all the necessary signals and relations which can be used to ‘explain’ the obsrvable behavior and which ‘explains’ the behavior of the billions of cells enabling such a behavior.
In a simpler, ‘relaxed’ kind of modeling one would not take into account the properties and behavior of the ‘real cells’ but one would limit the scope to build a formal model which suffices to explain the oservable behavior.
This kind of approach to set up models of possible ‘internal’ (as such hidden) processes of an actor can extend the 3rd-person view substantially. These models are called in this text ‘actor models (AM)’.
HIDDEN WORLD PROCESSES
In this text all reported 3rd-person observations are called ‘actor story’, independent whether they are done in a pictorial or a textual mode.
As has been pointed out such actor stories are somewhat ‘limited’ in what they can describe.
It is possible to extend such an actor story (AS) by several actor models (AM).
An actor story defines the situations in which an actor can occur. This includes all kinds of stimuli which can trigger the possible senses of the actor as well as all kinds of actions an actor can apply to a situation.
The actor model of such an actor has to enable the actor to handle all these assumed stimuli as well as all these actions in the expected way.
While the actor story can be checked whether it is describing a process in an empirical ‘sound’ way, the actor models are either ‘purely theoretical’ but ‘behavioral sound’ or they are also empirically sound with regard to the body of a biological or a technological system.
A serious challenge is the occurrence of adaptiv or/ and locally learning systems. While the actor story is a finite description of possible states and changes, adaptiv or/ and locally learning systeme can change their behavior while ‘living’ in the actor story. These changes in the behavior can not completely be ‘foreseen’!
COGNITIVE EXPERT PROCESSES
According to the preceding considerations a homo sapiens as a biological system has besides many properties at least a consciousness and the ability to talk and by this to communicate with symbolic languages.
Looking to basic modes of an actor story (AS) one can infer some basic concepts inherently present in the communication.
Without having an explicit model of the internal processes in a homo sapiens system one can infer some basic properties from the communicative acts:
Speaker and hearer presuppose a space within which objects with properties can occur.
Changes can happen which presuppose some timely ordering.
There is a disctinction between concrete things and abstract concepts which correspond to many concrete things.
There is an implicit hierarchy of concepts starting with concrete objects at the ‘root level’ given as occurence in a concrete situation. Other concepts of ‘higher levels’ refer to concepts of lower levels.
There are different kinds of relations between objects on different conceptual levels.
The usage of language expressions presupposes structures which can be associated with the expressions as their ‘meanings’. The mapping between expressions and their meaning has to be learned by each actor separately, but in cooperation with all the other actors, with which the actor wants to share his meanings.
It is assume that all the processes which enable the generation of concepts, concept hierarchies, relations, meaning relations etc. are unconscious! In the consciousness one can use parts of the unconscious structures and processes under strictly limited conditions.
To ‘learn’ dedicated matters and to be ‘critical’ about the quality of what one is learnig requires some disciplin, some learning methods, and a ‘learning-friendly’ environment. There is no guaranteed method of success.
There are lots of unconscious processes which can influence understanding, learning, planning, decisions etc. and which until today are not yet sufficiently cleared up.
