The following text is a confluence of ideas that have been driving me for many months. Parts of it can be found as texts in all three blogs (Citizen Science 2.0 for Sustainable Development, Integrated Engineering and the Human Factor (this blog), Philosophy Now. In Search for a new Human Paradigm). The choice of the word ‘grammar’ [1] for the following text is rather unusual, but seems to me to reflect the character of the reflections well.
Sustainability for populations
The concept of sustainable development is considered here in the context of ‘biological populations’. Such populations are dynamic entities with many ‘complex properties’. For the analysis of the ‘sustainability’ of such populations, there is one aspect that seems ‘fundamental’ for a proper understanding. It is the aspect whether and how the members of a population – the actors – are interconnected or not.
An ‘unconnected’ set
If I have ‘actors’ of a ‘population’, which are in no direct ‘interaction’ with each other, then also the ‘acting’ of these actors is isolated from each other. In a wide area they probably do not ‘get in each other’s way’; in a narrow area they could easily hinder each other or even fight each other, up to mutual destruction.
It should be noted that even such disconnected actors must have minimal ‘knowledge’ about themselves and the environment, also minimal ’emotions’, in order to live at all.
Without direct interaction, an unconnected population will nevertheless die out relatively quickly as a population.
A ‘connected’ set
A ‘connected set’ exists if the actors of a population have a sufficient number of direct interactions through which they could ‘coordinate’ their knowledge about themselves and the world, as well as their emotions, to such an extent that they are capable of ‘coordinated action’. Thereby the single, individual actions become related to their possible effect to a ‘common (= social) action’ which can effect more than each of them would have been able to do individually.
The ’emotions’ involved must rather be such that they do not so much ‘delimit/exclude’, but rather ‘include/recognize’.
The ‘knowledge’ involved must be rather that it is not ‘static’ and not ‘unrealistic’, but rather ‘open’, ‘learning’ and ‘realistic’.
The ‘survival’ of a connected population is basically possible if the most important ‘factors’ of a survival are sufficiently fulfilled.
Transitions from – to
The ‘transition’ from an ‘unconnected’ to a ‘connected’ state of a population is not inevitable. The primary motive may simply be the ‘will to survive’ (an emotion), and the growing ‘insight’ (= knowledge) that this is only possible with ‘minimal cooperation’. An individual, however, can live in a state of ‘loner’ for the duration of his life, because he does not have to experience his individual death as a sufficient reason to ally with others. A population as such, however, can only survive if a sufficient number of individuals survive, interacting minimally with each other. The history of life on planet Earth suggests the working hypothesis that for 3.5 billion years there have always been sufficient members of a population in biological populations (including the human population) to counter the ‘self-destructive tendencies’ of individuals with a ‘constructive tendency’.
The emergence and the maintenance of a ‘connected population’ needs a minimum of ‘suitable knowledge’ and ‘suitable emotions’ to succeed.
It is a permanent challenge for all biological populations to shape their own emotions in such a way that they tend not to exclude, to despise, but rather to include and to recognize. Similarly, knowledge must be suitable for acquiring a realistic picture of oneself, others, and the environment so that the behavior in question is ‘factually appropriate’ and tends to be more likely to lead to ‘success’.
As the history of the human population shows, both the ‘shaping of emotions’ and the ‘shaping of powerful knowledge’ are usually largely underestimated and poorly or not at all organized. The necessary ‘effort’ is shied away from, one underestimates the necessary ‘duration’ of such processes. Within knowledge there is additionally the general problem that the ‘short time spans’ within an individual life are an obstacle to recognize and form such processes where larger time spans require it (this concerns almost all ‘important’ processes).
We must also note that ‘connected states’ of populations can also collapse again at any time, if those behaviors that make them possible are weakened or disappear altogether. Connections in the realm of biological populations are largely ‘undetermined’! They are based on complex processes within and between the individual actors. Whole societies can ‘topple overnight’ if an event destroys ‘trust in context’. Without trust no context is possible. The emergence and the passing away of trust should be part of the basic concern of every society in a state of interconnectedness.
Political rules of the game
‘Politics’ encompasses the totality of arrangements that members of a human population agree to organize jointly binding decision-making processes.[2] On a rough scale, one could place two extremes: (i) On the one hand, a population with a ‘democratic system’ [3] and a population with a maximally un-democratic system.[4]
As already noted in general for ‘connected systems’: the success of democratic systems is in no way determinate. Enabling and sustaining it requires the total commitment of all participants ‘by their own conviction’.
Basic reality ‘corporeality’
Biological populations are fundamentally characterized by a ‘corporeality’ which is determined through and through by ‘regularities’ of the known material structures. In their ‘complex formations’ biological systems manifest also ‘complex properties’, which cannot be derived simply from their ‘individual parts’, but the respective identifiable ‘material components’ of their ‘body’ together with many ‘functional connections’ are fundamentally subject to a multiplicity of ‘laws’ which are ‘given’. To ‘change’ these is – if at all – only possible under certain limited conditions.
All biological actors consist of ‘biological cells’ which are the same for all. In this, human actors are part of the total development of (biological) life on planet Earth. The totality of (biological) life is also called ‘biome’ and the total habitat of a biome is also called ‘biosphere’. [5] The population of homo sapiens is only a vanishingly small part of the biome, but with the homo sapiens typical way of life it claims ever larger parts of the biosphere for itself at the expense of all other life forms.
(Biological) life has been taking place on planet Earth for about 3.5 billion years.[6] Earth, as part of the solar system [7], has had a very eventful history and shows strong dynamics until today, which can and does have a direct impact on the living conditions of biological life (continental plate displacement, earthquakes, volcanic eruptions, magnetic field displacement, ocean currents, climate, …).
Biological systems generally require a continuous intake of material substances (with energy potentials) to enable their own metabolic processes. They also excrete substances. Human populations need certain amounts of ‘food’, ‘water’, ‘dwellings’, ‘storage facilities’, ‘means of transport’, ‘energy’, … ‘raw materials’, … ‘production processes’, ‘exchange processes’ … As the sheer size of a population grows, the material quantities required (and also wastes) multiply to orders of magnitude that can destroy the functioning of the biosphere.
Predictive knowledge
If a coherent population does not want to leave possible future states to pure chance, then it needs a ‘knowledge’ which is suitable to construct ‘predictions’ (‘prognoses’) for a possible future (or even many ‘variants of future’) from the knowledge about the present and about the past.
In the history of homo sapiens so far, there is only one form of knowledge that has been demonstrably demonstrated to be suitable for resilient sustainable forecasts: the knowledge form of empirical sciences. [8] This form of knowledge is so far not perfect, but a better alternative is actually not known. At its core, ’empirical knowledge’ comprises the following elements: (i) A description of a baseline situation that is assumed to be ’empirically true’; (ii) A set of ‘descriptions of change processes’ that one has been able to formulate over time, and from which one knows that it is ‘highly probable’ that the described changes will occur again and again under known conditions; (iii) An ‘inference concept’ that describes how to apply to the description of a ‘given current situation’ the known descriptions of change processes in such a way that one can modify the description of the current situation to produce a ‘modified description’ that describes a new situation that can be considered a ‘highly probable continuation’ of the current situation in the future. [9]
The just sketched ‘basic idea’ of an empirical theory with predictive ability can be realized concretely in many ways. To investigate and describe this is the task of ‘philosophy of science’. However, the vagueness found in dealing with the notion of an ’empirical theory’ is also found in the understanding of what is meant by ‘philosophy of science.'[9]
In the present text, the view is taken that the ‘basic concept’ of an empirical theory can be fully realized in normal everyday action using everyday language. This concept of a ‘General Empirical Theory’ can be extended by any special languages, methods and sub-theories as needed. In this way, the hitherto unsolved problem of the many different individual empirical disciplines could be solved almost by itself.[10]
Sustainable knowledge
In the normal case, an empirical theory can, at best, generate forecasts that can be said to have a certain empirically based probability. In ‘complex situations’ such a prognosis can comprise many ‘variants’: A, B, …, Z. Now which of these variants is ‘better’ or ‘worse’ in the light of an ‘assumable criterion’ cannot be determined by an empirical theory itself. Here the ‘producers’ and the ‘users’ of the theory are asked: Do they have any ‘preferences’ why e.g. variant ‘B’ should be preferred to variant ‘C”: “Bicycle, subway, car or plane?” , “Genetic engineering or not?”, “Pesticides or not?”, “Nuclear energy or not?”, “Uncontrolled fishing or not?” …
The ‘evaluation criteria’ to be applied actually themselves require ‘explicit knowledge’ for the estimation of a possible ‘benefit’ on the one hand, on the other hand the concept of ‘benefit’ is anchored in the feeling and wanting of human actors: Why exactly do I want something? Why does something ‘feel good’? …
Current discussions worldwide show that the arsenal of ‘evaluation criteria’ and their implementation offer anything but a clear picture.
COMMENTS
[1] For the typical use of the term ‘grammar’ see the English Wikipedia: https://en.wikipedia.org/wiki/Grammar. In the text here in the blog I transfer this concept of ‘language’ to that ‘complex process’ in which the population of the life form ‘homo sapiens’ tries to achieve an ‘overall state’ on planet earth that allows a ‘maximally good future’ for as much ‘life’ as possible (with humans as a sub-population). A ‘grammar of sustainability’ presupposes a certain set of basic conditions, factors, which ‘interact’ with each other in a dynamic process, in order to realize as many states as possible in a ‘sequence of states’, which enable as good a life as possible for as many as possible.
[2] For the typical usage of the term politics, see the English Wikipedia: https://en.wikipedia.org/wiki/Politics . This meaning is also assumed in the present text here.
[4] Of course, one could also choose completely different basic concepts for a scale. However, the concept of a ‘democratic system’ (with all its weaknesses) seems to me to be the ‘most suitable’ system in the light of the requirements for sustainable development; at the same time, however, it makes the highest demands of all systems on all those involved. That it came to the formation of ‘democracy-like’ systems at all in the course of history, actually borders almost on a miracle. The further development of such democracy-like systems fluctuates constantly between preservation and decay. Positively, one could say that the constant struggle for preservation is a kind of ‘training’ to enable sustainable development.
[5] For typical uses of the terms ‘biome’ and ‘biosphere’, see the corresponding entries in the English Wikipedia: ‘biome’: https://en.wikipedia.org/wiki/Biome, ‘biosphere’: https://en.wikipedia.org/wiki/Biosphere
[6] Some basic data for planet Earth: https://en.wikipedia.org/wiki/Earth
[7] Some basic data for the solar system: https://en.wikipedia.org/wiki/Solar_System
[8] If you will search for he term ‘Empirical Science’ you ill be disappointed, because the English Wikipedia (as well as the German Version) does not provide such a term. You have either to accept the term ‘Science’ ( https://en.wikipedia.org/wiki/Science ) or the term ‘Empiricism’ (https://en.wikipedia.org/wiki/Empiricism), but both do not cover the general properties of an Empirical theory.
[9] If you have a clock with hour and minute hands, which currently shows 11:04h, and you know from everyday experience that the minute hand advances by one stroke every minute, then you can conclude with a fairly high probability that the minute hand will advance by one stroke ‘very soon’. The initial description ‘The clock shows 11:04h’ would then be changed to that of the new description ‘The clock shows 11:05h’. Before the ’11:05h event’ the statement ‘The clock shows 11:05h’ would have the status of a ‘forecast’.
[10] A single discipline (physics, chemistry, biology, psychology, …) cannot conceptually grasp ‘the whole’ ‘out of itself’; it does not have to. The various attempts to ‘reduce’ any single discipline to another (physics is especially popular here) have all failed so far. Without a suitable ‘meta-theory’ no single discipline can free itself from its specialization. The concept of a ‘General Empirical Theory’ is such a meta-theory. Such a meta-theory fits into the concept of a modern philosophical thinking.
When it comes ‘to the oath’, when it is the task of creating descriptions of the world which are ‘verifiable’ by others, and which allow ‘verifiable predictions/conclusions’, then there is so far in the cultural history of mankind only one format known that makes this possible, the format of an ‘Empirical Theory’. If you try to look up the term ‘Empirical Theory’ in the German or English Wikipedia, you will be disappointed: this term does not exist there (as of November 10, 2022). This should cause astonishment, because it is so far the only and hardest criterion for a ‘truthful theory’ found in the last thousands of years. There are endless articles and books on this subject.
However, it is also part of the truth that the formats of texts that have become known so far with the claim to realize a verifiable empirical theory ultimately work with a so-called ‘formalization’, i.e. the language of logic and mathematics is used. One consequence of this is that the amount of possible readers and users of such theories is severely limited by this language alone. This is a major disadvantage, since it effectively ‘locks out’ the majority of citizens in a society.
But scientists themselves have a problem too: for formalized empirical theories, there is no supporting software that allows the text of a theory to be checked ‘with the push of a button’ at any time in the form of a simulation. Although there are — partly highly complex — simulation programs for support, these are not theories as such, but only algorithms and have to be laboriously created alongside the theory itself. If the text of the theory changes, such a change must be transferred laboriously into the algorithm. In general: an algorithm is a ‘function’ which is neither true nor false; a theory is a ‘statement’ which as such can be true or false (or it can stay ‘undefined’ with regard to ‘truth’ or ‘falsehood’).
After many years of research — since about the mid 1980s and then experimentally for about four years — an approach has emerged which puts the concept of a testable empirical theory at the center, and takes as the starting language for an empirical description of the world the ‘normal language of everyday life’ (any is possible). This language can be ‘extended’ at will (which is common in science), but instead of virtually ‘throwing away’ the everyday language after the extension, in the new approach the everyday language is not thrown away but remains the main language.
This new approach — labeled with the acronym ‘oksimo.R’ [1] — enables the users — every kind of citizens — to write down a text which automatically represents everything known from — even formalized — theories. Above all: every citizen can read and understand texts written in the oksimo.R format normally. Every text in the oksimo.R format is automatically equivalent to a full empirical theory, even if the authors — arbitrary citizens — do not know exactly what an empirical theory is. Furthermore: at the push of a button, any theory in the oksimo.R format can be run as a ‘simulation’, where the term ‘simulation’ is very concrete here: the core of the simulation is formed by an ‘inference concept’, which computes the respective possible ‘continuations’ (= ‘inferences’) from given ‘world descriptions’ extended by possible ‘changes’, and this not only once, but ‘again and again’, until this inference process is stopped on the basis of a given criterion. Since every inference is linked to an empirical truth claim, every inference can also be checked for its empirical validity.
While up to now formalized empirical theories are very difficult to compare or even to ‘unify’, this is no problem for empirical theories in the oksimo.R format: one can unify arbitrary empirical theories in the oksimo.R format ‘at the push of a button’ to one text only and one can then directly view its effects by simulation. Of course, actual ‘interactions’ between the different ‘theory parts’ only arise if there are ‘linguistic points of contact’. But exactly this can be seen immediately with a unified simulation: Either there are no interactions at all or you detect some interactions. These ‘some interactions’ can be analyzed further with regard to the question, what interacts and how.
By the way, all forms of artificial intelligence (ai) in the format of ‘machine learning (ML)’ known today — which usually represent very simple algorithms and which are in addition extremely dependent on a formulated task — can be used fruitfully in the context of an oksimo.R theory text by using these AI algorithms to search the ‘state space’ of possible conclusions for possible optimizations.
Furthermore, one can arbitrarily extend the empirical references to the real world through appropriate sensor technology and data connections (e.g., IoT), all in ‘web real-time’.
Additionally, one can link any server with an oksimo.R theory to any other web application.
Instead of ‘only’ developing and testing theories, oksimo.R theories can also be used to control processes or as training and text environments. Even (online) games are possible.
This opens up interesting possibilities for a new level in people’s ‘collective knowledge’ that goes beyond mere ‘text sets’.
COMMENTS
[1] The acronym ‘oksimo.R’ points back to a language project called ‘oksimo’ (‘open knowledge simulation modeling’), which has been documented a little bit in the German wikipedia ( https://de.wikipedia.org/wiki/Oksimo ). This project initiated by Gerd Doeben-Henisch had been 2009 stopped by him despite a great public awareness because of lack of resources. The ‘new oksimo’ as ‘oksimo.R’ means ‘oksimo reloaded’; it has somehow a similar intention but is designed with a completely different internal structure. It does not produce ‘algorithms’, it does produce ‘theories’.
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
[30] Döben-Henisch, G., Reinforcing the global heartbeat: Introducing the planet earth simulator project, In M. Faßler & C. Terkowsky (Eds.), URBAN FICTIONS. Die Zukunft des Städtischen. München, Germany: Wilhelm Fink Verlag, 2006, pp.251-263
[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.
[] By Azote for Stockholm Resilience Centre, Stockholm University – https://www.stockholmresilience.org/research/research-news/2016-06-14-how-food-connects-all-the-sdgs.html, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=112497386
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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 a preceding post I have illustrated how one can apply the concept of an empirical theory — highly inspired by Karl Popper — to an everyday problem given as a county and its demographic problem(s). In this post I like to develop this idea a little more.
AN EMPIRICAL THEORY AS A DEVELOPMENT PROCESS
The figure shows a simplified outline of the idea of an empirical theory being realized during a development process based on the interactions and the communication of citizens as ‘natural experts’.
CITIZENs – natural experts
As starting point we assume citizens understood as our ‘natural experts’ being members of a democratic society with political parties, an freely elected parliament, which can create some helpful laws for the societal life and some authorities serving the need of the citizens.
SYMBOLIC DESCRIPTIONS
To coordinate their actions by a sufficient communication the citizens produce symbolic descriptions to make public how they see the ‘given situation’, which kinds of ‘future states’ (‘goals’) they want to achieve, and a list of ‘actions’ which can ‘change/ transform’ the given situation step wise into the envisioned future state.
LEVELS OF ABSTRACTIONS
Using an everyday language — possibly enriched with some math expressions – one can talk about our world of experience on different levels of abstraction. To get a rather wide scope one starts with most abstract concepts, and then one can break down these abstract concepts more and more with concrete properties/ features until these concrete expressions are ‘touching the real experience’. It can be helpful — in most cases — not to describe everything in one description but one does a partition of ‘the whole’ into several more concrete descriptions to get the main points. Afterwards it should be possible to ‘unify’ these more concrete descriptions into one large picture showing how all these concrete descriptions ‘work together’.
LOGICAL INFERENCE BY SIMULATION
A very useful property of empirical theories is the possibility to derive from given assumptions and assumed rules of inference possible consequences which are ‘true’ if the assumptions an the rules of inference are ‘true’.
The above outlined descriptions are seen in this post as texts which satisfy the requirements of an empirical theory such that the ‘simulator’ is able to derive from these assumptions all possible ‘true’ consequences if these assumptions are assumed to be ‘true’. Especially will the simulator deliver not only one single consequence only but a whole ‘sequence of consequences’ following each other in time.
PURE WWW KNOWLEDGE SPACE
This simple outline describes the application format of the oksimo software which is understood here as a kind of a ‘theory machine’ for everybody.
It is assumed that a symbolic description is given as a pure text file or as a given HTML page somewhere in the world wide web [WWW].
The simulator realized as an oksimo program can load such a file and can run a simulation. The output will be send back as an HTML page.
No special special data base is needed inside of the oksimo application. All oksimo related HTML pages located by a citizen somewhere in the WWW are constituting a ‘global public knowledge space’ accessible by everybody.
DISTRIBUTED OKSIMO INSTANCES
An oksimo server positioned behind the oksimo address ‘oksimo.com’ can produce for a simulation demand a ‘simulator instance’ running one simulation. There can be many simulations running in parallel. A simulation can also be connected in real time to Internet-of-Things [IoT] instances to receive empirical data being used in the simulation. In ‘interactive mode’ an oksimo simulation does furthermore allow the participation of ‘actors’ which function as a ‘dynamic rule instance’: they receive input from the simulated given situation and can respond ‘on their own’. This turns a simulation into an ‘open process’ like we do encounter during ‘everyday real processes’. An ‘actor’ must not necessarily be a ‘human’ actor; it can also be a ‘non-human’ actor. Furthermore it is possible to establish a ‘simulation-meta-level’: because a simulation as a whole represents a ‘full theory’ on can feed this whole theory to an ‘artificial intelligence algorithm’ which dos not run only one simulation but checks the space of ‘all possible simulations’ and thereby identifies those sub-spaces which are — according to the defined goals — ‘zones of special interest’.
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
In this post a short summary of Poppers view of an empirical theory is outlined as he describes it in his article “Conjectural Knowledge: My Solution of the Problem of Induction” from 1971.[1] The view of Popper will be commented and the relationsship to the oksimo paradigm of the author will be outlined.
Empirical Theory according to Popper in a Nutshell
Figure: Popper’s concept from 1971 of an empirical theory, compressed in a nutshell. Graphic by Gerd Doeben-Henisch based on the article using Popper’s summarizing ideas on the pages 29-31
POPPER’S POSITION 1971
In this article from 1971 Popper discusses several positions. Finally he offers the following ‘demarcation’ between only two cases: ‘Pseudo Science’ and ‘Empirical Science’.(See p.29) In doing so this triggers the question how it is possible to declare something as an ‘objective empirical theory’ without claiming to have some ‘absolute truth’?
Although Popper denies to have some kind of absolute truth he will “not give up the search for truth”, which finally leads to a “true explanatory theory”.(cf. p.29) “Truth” plays the “role of a regulative idea”.(cf. p.30) Thus according to Popper one can “guess for truth” and some of the hypotheses “may well be true”.(cf.p.30)
In Popper’s view finally ‘observation’ shows up as that behaviour which enables the production of ‘statements’ as the ’empirical basis’ for all arguments.(cf.p.30) Empirical statements are a ‘function of the used language’.(cf. p.31)
This dimension of language leads Popper to the concept of ‘deductive logic’ which describes formal mechanisms to derive from a set of statements — which are assumed to be true — those statements, which are ‘true’ by logical deduction only. If statements are ‘logically false’ then this can be used to classify the set of assumed statements as ‘logically not consistent’. (cf. p.31)
comments on popper’s 1971-position 50 years later
The preceding outline of Popper’s position reveals a minimalist account of the ingredients of an ‘objective empirical theory’. But we as the readers of these ideas are living 50 years later. Our minds are shaped differently. The author of this text thinks that Popper is basically ‘true’, although there are some points in Popper’s argument, which deserve some comments.
Subjective – Absolute
Popper is moving between two boundaries: One boundary is the so called ‘subjective believe’ which can support any idea, and which thereby can include pure nonsense; the other boundary is ‘absolute truth’, which is requiring to hold all the time at all places although the ‘known world’ is evidently showing a steady change.
Empirical Basis
In searching for a possible position between these boundaries, which would allow a minimum of ‘rationality’, he is looking for an ’empirical Basis’ as a point of reference for a ‘rational theory’. He is locating such an empirical basis in ‘observation statements’ which can be used for ‘testing a theory’.
In his view a ‘rational empirical theory’ has to have a ‘set of statements’ (often called ‘assumptions’ of the theory or ‘axioms’) which are assumed to ‘describe the observable world’ in a way that these statements should be able to be ‘confirmed’ or be ‘falsified’.
Confirmation – Falsification
A ‘confirmation’ does not imply that the confirmed statement is ‘absolutely true’ (his basic conviction); but one can experience that a confirmed statement can function as a ‘hypothesis/ conjecture’ which ‘workes in the actual observation’. This does not exclude that it perhaps will not work in a future test. The pragmatical difference between ‘interesting conjectures’ and those which are of less interest is that a ‘repeated confirmation’ increases the ‘probability’, that such a confirmation can happen again. An ‘increasing probability’ can induce an ‘increased expectation’. Nevertheless, increased probabilities and associated increased expectations are no substitutes for ‘truth’.
A test which shows ‘no confirmation’ for a logically derived statement from the theory is difficult to interpret:
Case (i): A theory is claiming that a statement S refers to a proposition A to be ‘true in a certain experiment’, but in the real experiment the observation reveals a proposition B which translates to non-A which can interpreted as ‘the opposite to A is being the case’ (= being ‘true’). This outcome will be interpreted in the way that the proposition B interpreted as ‘non-A’ contradicts ‘A’ and this will be interpreted further in the way, that the statement S of the theory represents a partial contradiction to the observable world.
Case (ii): A theory is claiming that a statement S refers to a proposition A to be ‘true in a certain experiment’, but in the real experiment the observation reveals a proposition B ‘being the case’ (= being ‘true’) which shows a different proposition. And this outcome cannot be related to the proposition ‘A’ which is forecasted by the theory. If the statement ‘can not be interpreted sufficiently well’ then the situation is neither ‘true’ nor ‘false’; it is ‘undefined’.
Discussion: Case (ii) reveals that there exist an observable (empirical) fact which is not related to a certain ‘logically derived’ statement with proposition A. There can be many circumstances why the observation did not generate the ‘expected proposition A’. If one would assume that the observation is related to an ‘agreed process of generating an outcome M’, which can be ‘repeated at will’ from ‘everybody’, then the observed fact of a ‘proposition B distinguished from proposition A’ could be interpreted in the way, that the expectation of the theory cannot be reproduced with the agreed procedure M. This lets the question open, whether there could eventually exist another procedure M’ producing an outcome ‘A’. This case is for the actors which are running the procedure M with regard to the logically derived statement S talking about proposition A ‘unclear’, ‘not defined’, a ‘non-confirmation’. Otherwise it is at the same time no confirmation either.
Discussion: Case (i) seems — at a first glance — to be more ‘clear’ in its interpretation. Assuming here too that the observation is associated with an agreed procedure M producing the proposition B which can be interpreted as non-A (B = non-A). If everybody accepts this ‘classification’ of B as ‘non-A’, then by ‘purely logical reasons’ (depending from the assumed concept of logic !) ‘non-A’ contradicts ‘A’. But in the ‘real world’ with ‘real observations’ things are usually not as ‘clear-cut’ as a theory may assume. The observable outcome B of an agreed procedure M can show a broad spectrum of ‘similarities’ with proposition A varying between 100% and less. Even if one repeats the agreed procedure M several times it can show a ‘sequence of propositions <B1, B2, …, Bn>’ which all are not exactly 100% similar to proposition A. To speak in such a case (the normal case!), of a logical contradiction it is difficult if not impossible. The idea of Popper-1971 with a possible ‘falsification’ of a theory would then become difficult to interpret. A possible remedy for this situation could be to modify a theory in the way that a theory does forecast only statements with a proposition A which is represented as a ‘field of possible instances A = <a1, a2, …, am>’, where every ‘ai‘ represents some kind of a variation. In that modified case it would be ‘more probable’ to judge a non-confirmation between A as <a1, a2, …, am> and B as <B1, B2, …, Bn>, if one would take into account the ‘variability’ of a proposition.[3]
Having discussed the case of ‘non-confirmation’ in the described modified way this leads back again to the case of ‘confirmation’: The ‘fuzziness’ of observable facts even in the context of agreed procedures M of observation, which are repeatable by everyone (usually called measurement) requires for a broader concept of ‘similarity’ between ‘derived propositions’ and ‘observed propositions’. This is since long a hot debated point in the philosophy of science (see e.g. [4]). Until now does no general accepted solution exist for this problem.
Thus the clear idea of Popper to associate a theory candidate with a minimum of rationality by relating the theory in an agreed way to empirical observations becomes in the ‘dust of reality’ a difficult case. It is interesting that the ‘late Popper’ (1988-1991) has modified his view onto this subject a little bit more into the direction of the interpretation of observable events (cf. [5])
Logic as an Organon
In the discussion of the possible confirmation or falsification of a theory Popper uses two different perspectives: (i) in a more broader sense he is talking about the ‘process of justification’ of the theoretical statements with regard to an empirical basis relying on the ‘regulative idea of truth’, and (ii) in a more specialized sense he is talking about ‘deductive logic as an organon of criticism’. These two perspectives demand for more clarification.
While the meaning of the concept ‘theory’ is rather vague (statements, which have to be confirmed or falsified with respect to observational statements), the concept ‘deductive logic as an organon’ isn’t really clearer.
Until today we have two big paradigms of logic: (i) the ‘classical logic’ inspired by Aristotle (with many variants) and (ii) ‘modern formal logic’ (cf. [6]) in combination with modern mathematics (cf. [7],[8]). Both paradigms represent a whole universe of different variants, whose combinations into concrete formal empirical theories shows more than one paradigm.(cf. [4], [8], [10])
As outlined in the figure above the principal idea of logic in general follows the following schema: one has a set of expressions of some language L for which one assumes at least, that these expressions are classified as ‘true expressions’. According to an agreed procedure of ‘derivation’ one can derive (deduce, infer, …) other expressions of the language which are assumed to be classified as ‘true’ if the assumptions hold.[11]
The important point here is, that the modern concept of logic does not explain, what ‘true’ means nor exists there an explanation, how exactly a procedure looks like which enables the classification of an expression as ‘being true’. Logic works with the minimalist assumption that the ‘user of logic’ is using statements which he assumes to be ‘true’ independent of how this classification came into being. This frees the user of logic to deal with the cumbersome process of clarifying the meaning and the existence of something which makes a statement ‘true’, but on the other side the user of modern logic has no real control whether his ‘concept of derivation’ makes any sense in a real world, from which observation statements are generated claiming to be ’empirically true’, and that the relationships between these observational statements are appropriately ‘represented’ by the formal derivation concept. Until today there exists no ‘meta-theory’ which explains the relationship between the derivation concept of formal logic (there are many such concepts!) and the ‘dynamics of real events’.
Thus, if Popper mentions formal logic as a tool for the handling of assumed true statements of a theory, it is not really clear whether such a formal logical derivation really is appropriate to explain the ‘relationships between assumed true statements’ without knowing, which kind of reality is ‘designated’/ ‘referred to’ by such statements and their relationships between each other.
(Formalized) Theory and Logic
In his paper Popper does not explain too much what he is concretely mean with a (formalized) theory. Today there exist many different proposals of formalized theories for the usage as ’empirical theories’, but there is no commonly agreed final ‘template’ of a ‘formal empirical theory’.
Nevertheless we need some minimal conception to be able to discuss some of the properties of a theory more concretely. I will address this problem in another post accompanied with concrete applications.
COMMENTS
[1] Karl R.Popper, Conjectural Knowledge: My Solution of the Problem of Induction, in: [2], pp.1-31
[2] Karl R.Popper, Objective Knowledge. An Evolutionary Approach, Oxford University Press, London, 1972 (reprint with corrections 1973)
[3] In our everyday use of our ‘normal’ language it is the ‘normal’ case that a statement S like ‘There s a cup on the table’ can be interpreted in many different ways depending which concrete thing (= proposition B of the above examples) called a ‘cup’ or called ‘table’ can be observed.
[4] F. Suppe, Ed., The Structure of Scientific Theories, University of Illinois Press, Urbana, 2nd edition, 1979.
[6] William Kneale and Martha Kneale, The development of logic, Oxford University Press, Oxford, 1962 with several corrections and reprints 1986.
[7] Jean Dieudonnè, Geschichte der Mathematik 1700-1900, Friedrich Viehweg & Sohn, Braunschweig – Wiesbaden, 1985 (From the French edition “Abrégé d’histoire des mathématique 1700-1900, Hermann, Paris, 1978)
[8] Philip J.Davis & Reuben Hersh, The Mathematical Experience, Houghton Mifflin Company, Boston, 1981
[9] Nicolas Bourbaki, Elements of Mathematics. Theory of Sets, Springer-Verlag, Berlin, 1968
[10] Wolfgang Balzer, C.Ulises Moulines, Joseph D.Sneed, An Architectonic for Science. The Structuralist Program,D.Reidel Publ. Company, Dordrecht -Boston – Lancaster – Tokyo, 1987
[11] The usage of the terms ‘expression’, ‘proposition’, and ‘statement’ is in this text as follows: An ‘expression‘ is a string of signs from some alphabet A and which is accepted as ‘well formed expression’ of some language L. A ‘statement‘ is an utterance of some actor using expressions of the language L to talk ‘about’ some ‘experience’ — from the world of bodies or from his consciousness –, which is understood as the ‘meaning‘ of the statement. The relationship between the expressions of the statement and the meaning is located ‘in the actor’ and has been ‘learned’ by interactions with the world and himself. This hypothetical relationship is here called ‘meaning function φ’. A ‘proposition‘ is (i) the inner construct of the meaning of a statement (here called ‘intended proposition’) and (ii) that part of the experience, which is correlated with the inner construct of the stated meaning (here called ‘occurring proposition’). The special relationship between the intended proposition and the occurring proposition is often expressed as ‘referring to’ or ‘designate’. A statement is called to ‘hold’/ to be ‘true’ or ‘being the case’ if there exists an occurring proposition which is ‘similar enough’ to the intended proposition of the statement. If such an occurring proposition is lacking then the designation of the statement is ‘undefined’ or ‘non confirming’ the expectation.
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))
To support the development of exciting applications with the oksimo.R software as part of the general concept of ‘Citizen Science 2.0’ the oksimo team is running a blog [1] dedicated to all questions around the usage of the oksimo.R software. [2] Due to the dynamic development process there are different phases of different kinds of examples. Examples related to Level 1 of the oksimo.R software appeared before spring 2022. Examples with Level 2 appeared since spring 2022. Examples of Level 3 will start to appear during spring 2023. When examples of Level 3 will be available we will start working for Level 4.
More Recent oksimo.R Examples
With the writing of the first book related to the oksimo.R software all further examples will be published through this book accompanied with a webpage collecting all these examples. It is planned to finish a first experimental version of the text of the book (oksimo.org, uffmm.org) about summer 2023. After that it is planned to publish an official book with an international publisher.
Oksimo.R Examples with Level 2
Here a list of oksimo examples starting with simple examples with the oksimo software level 2 (while level 3 is already in preparation).
[1] The blog of the oksimo.R Team is primarily in German. But parts of the blog will also be reported or even directly translated into English texts as part of the uffmm.blog.
[2] The oksimo.R book can also be read as a ‘philosophical’ book, because the oksimo.R software is using everyday languages to deal with everyday problems (including typical ‘ordinary science’ cases as ‘sub-cases’ of everyday problems). There exists a great bulk of books and articles related to philosophical topics which until now have only a poor connection with the concepts of ‘software’, ’empirical theory’, ‘cognitive sciences’ as well as the different concepts of ‘intelligence’ outside philosophy. Thus the development of the oksimo.R paradigm and software is a great opportunity to bring all these different aspects of reality together to enable a more integrated (inter-disciplinary as well as trans-disciplinary) view.
Integrating Engineering and the Human Factor (info@uffmm.org)
eJournal uffmm.org ISSN 2567-6458, March 2, 2021,
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de
Last change: March 2, 2021 13:59h (Minor corrections)
Having a vision is that moment where something really new in the whole universe is getting an initial status in some real brain which can enable other neural events which can possibly be translated in bodily events which finally canchange the body-external outside world. If this possibility is turned into reality than the outside world has been changed.
When human persons (groups of homo sapiens specimens) as experts — here acting as stakeholder and intended users as one but in different roles! — have stated a problem and a vision document, then they have to translate these inevitably more fuzzy than clear ideas into the concrete terms of an everyday world, into something which can really work.
To enable a real cooperation the experts have to generate a symbolic description of their vision (called specification) — using an everyday language, possibly enhanced by special expressions — in a way that it can became clear to the whole group, which kind of real events, actions and processes are intended.
In the general case an engineering specification describes concrete forms of entanglements of human persons which enable these human persons to cooperate in a real situation. Thereby the translation of the vision inside the brain into the everyday body-external reality happens. This is the language of life in the universe.
WRITING A STORY
To elaborate a usable specification can metaphorically be understood as the writing of a new story: which kinds of actors will do something in certain situations, what kinds of other objects, instruments etc. will be used, what kinds of intrinsicmotivations and experiences are pushing individual actors, what are possible outcomes of situations with certain actors, which kind of cooperation is helpful, and the like. Such a story is called here Actor Story [AS].
COULD BE REAL
An Actor Story must be written in a way, that all participating experts can understand the language of the specification in a way that the content, the meaning of the specification is either decidable real or that it eventually can become real. At least the starting point of the story should be classifiable as being decidable actual real. What it means to be decidable actual real has to be defined and agreed between the participating experts before they start writing the Actor Story.
ACTOR STORY [AS]
An Actor Story assumes that the described reality is classifiable as a set of situations (states) and a situation as part of the Actor Story — abbreviated: situationAS — is understood as a set of expressions of some everyday language. Every expression being part of an situationAS can be decided as being real (= being true) in the understood real situation.
If the understood real situation is changing (by some event), then the describing situationAS has to be changed too; either some expressions have to be removed or have to be added.
Every kind of change in the real situation S* has to be represented in the actor story with the situationAS S symbolically in the format of a change rule:
X: If condition C is satisfied in S then with probability π add to S Eplus and remove from S Eminus.
or as a formula:
S’π = S + Eplus – Eminus
This reads as follows: If there is an situationAS S and there is a change rule X, then you can apply this change rule X with probability π onto S if the condition of X is satisfied in S. In that case you have to add Eplus to S and you have to remove Eminus from S. The result of these operations is the new (successor) state S’.
The expression C is satisfied in S means, that all elements of C are elements of S too, written as C ⊆ S. The expression add Eplus to S means, that the set Eplus is unified with the set S, written as Eplus ∪ S (or here: Eplus + S). The expression remove Eminus from S means, that the set Eminus is subtracted from the set S, written as S – Eminus.
The concept of apply change rule X to a given state S resulting in S’ is logically a kind of a derivation. Given S,X you will derive by applicating X the new S’. One can write this as S,X ⊢X S’. The ‘meaning’ of the sign ⊢ is explained above.
Because every successor state S’ can become again a given state S onto which change rules X can be applied — written shortly as X(S)=S’, X(S’)=S”, … — the repeated application of change rules X can generate a whole sequence of states, written as SQ(S,X) = <S’, S”, … Sgoal>.
To realize such a derivation in the real world outside of the thinking of the experts one needs a machine, a computer — formally an automaton — which can read S and X documents and can then can compute the derivation leading to S’. An automaton which is doing such a job is often called a simulator [SIM], abbreviated here as ∑. We could then write with more information:
S,X ⊢∑ S’
This will read: Given a setS of many states S and a set X of change rules we can derive by an actor story simulator ∑ a successor state S’.
A Model M=<S,X>
In this context of a set S and a set of change rules X we can speak of a model M which is defined by these two sets.
A Theory T=<M,∑>
Combining a model M with an actor story simulator ∑ enables a theory T which allows a set of derivations based on the model, written as SQ(S,X,⊢∑) = <S’, S”, … Sgoal>. Every derived final state Sgoal in such a derivation is called a theorem of T.
An Empirical Theory Temp
An empirical theory Temp is possible if there exists a theory T with a group of experts which are using this theory and where these experts can interpret the expressions used in theory T by their built-in meaning functions in a way that they always can decide whether the expressions are related to a real situation or not.
Evaluation [ε]
If one generates an Actor Story Theory [TAS] then it can be of practical importance to get some measure how good this theory is. Because measurement is always an operation of comparison between the subject x to be measured and some agreed standard s one has to clarify which kind of a standard for to be good is available. In the general case the only possible source of standards are the experts themselves. In the context of an Actor Story the experts have agreed to some vision [V] which they think to be a better state than a given state S classified as a problem [P]. These assumptions allow a possible evaluation of a given state S in the ‘light’ of an agreed vision V as follows:
ε: V x S —> |V ⊆ S|[%]
ε(V,S) = |V ⊆ S|[%]
This reads as follows: the evaluation ε is a mapping from the sets V and S into the number of elements from the set V included in the set S converted in the percentage of the number of elements included. Thus if no element of V is included in the set S then 0% of the vision is realized, if all elements are included then 100%, etc. As more ‘fine grained’ the set V is as more ‘fine grained’ the evaluation can be.
An Evaluated Theory Tε=<M,∑,ε>
If one combines the concept of a theory T with the concept of evaluation ε then one can use the evaluation in combination with the derivation in the way that every state in a derivation SQ(S,X,⊢∑) = <S’, S”, … Sgoal> will additionally be evaluated, thus one gets sequences of pairs as follows:
In the ideal case Sgoal is evaluated to 100% ‘good’. In real cases 100% is only an ideal value which usually will only be approximated until some threshold.
An Evaluated Theory Tε with Algorithmic Intelligence Tε,α=<M,∑,ε,α>
Because every theory defines a so-called problem space which is here enhanced by some evaluation function one can add an additional operation α (realized by an algorithm) which can repeat the simulator based derivations enhanced with the evaluations to identify those sets of theorems which are qualified as the best theorems according to some criteria given. This operation α is here called algorithmic intelligence of an actor story [αAS]. The existence of such an algorithmic intelligence of an actor story [αAS] allows the introduction of another derivation concept:
S,X ⊢∑,ε,α S* ⊆ S’
This reads as follows: Given a set S and a set X an evaluated theory with algorithmic intelligence Tε,α can derive a subset S* of all possible theorems S’ where S* matches certain given criteria within V.
WHERE WE ARE NOW
As it should have become clear now the work of HMI analysis is the elaboration of a story which can be done in the format of different kinds of theories all of which can be simulated and evaluated. Even better, the only language you have to know is your everyday language, your mother tongue (mathematics is understood here as a sub-language of the everyday language, which in some special cases can be of some help). For this theory every human person — in all ages! — can be a valuable colleague to help you in understanding better possible futures. Because all parts of an actor story theory are plain texts, everybody ran read and understand everything. And if different groups of experts have investigated different aspects of a common field you can merge all texts by only ‘pressing a button’ and you will immediately see how all these texts either work together or show discrepancies. The last effect is a great opportunity to improve learning and understanding! Together we represent some of the power of life in the universe.
The collection of papers in the Case Studies Section deals with the
possible applications of the general concept of a GCA Generative Cul- tural Anthropology to all kinds of cultural processes. The GCA paradigm
has been derived from the formalized DAAI Distributed Actor-Actor In- teraction theory, which in turn is a development based on the common HMI Human Machine Interaction paradigm reformulated within the Sys- tems Engineering paradigm. The GCA is a very general and strong theory
paradigm, but, saying this, it is for most people difficult to understand,
because it is highly interdisciplinary, and it needs some formal technical
skills, which are not too common. During the work in the last three
months it became clear, that the original HMI and DAAI approach can
also be understood as the case of something which one could call ACA Applied Cultural Anthropology as part of an GCA. The concept of ACA
is more or less directly understandable for most people.
In this review I discuss the ideas of the book The Psychology of Science (1966) from A.Maslow. His book is in a certain sense outstanding because the point of view is in one respect inspired by an artificial borderline between the mainstream-view of empirical science and the mainstream-view of psychotherapy. In another respect the book discusses a possible integrated view of empirical science with psychotherapy as an integral part. The point of view of the reviewer is the new paradigm of a Generative Cultural Anthropology[GCA]. Part II of this review reports some considerations reflecting the relationship of the point of view of Maslow and the point of view of GCA.
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.
An overview to the enhanced AAI theory version 2 you can find here. In this post we talk about the special topic how the actor story (AS) can be used for a modeling of the real world (RW).
AS AND REAL WORLD MODELING
In the preceding post you find a rough description how an actor story can be generated challenged by a problem P. Here I shall address the question, how this procedure can be used to model certain aspects of the real world and not some abstract ideas only.
There are two main elements of the actor story which can be related to the real world: (i) The start state of the actor story and the list of possible change expressions.
FACTS
A start state is a finite set of facts which in turn are — in the case of the mathematical language — constituted by names of objects associated with properties or relations. Primarily the possible meaning of these expressions is located in the cognitive structures of the actors. These cognitive structures are as such not empirical entities and are partially available in a state called consciousness. If some element of meaning is conscious andsimultaneously part of the inter-subjective space between different actors in a way that all participating actors can perceive these elements, then these elements are called empirical by everyday experience, if these facts can be decided between the participants of the situation. If there exist further explicit measurement procedures associating an inter-subjective property with inter-subjective measurement data then these elements are called genuineempirical data.
Thus the collection of facts constituting a state of an actor story can be realized as a set of empirical facts, at least in the format of empirical by everyday experience.
CHANGES
While a state represents only static facts, one needs an additional element to be able to model the dynamic aspect of the real world. This is realized by change expressions X.
The general idea of a change is that at least one fact f of an actual state (= NOW), is changed either by complete disappearance or by changing some of its properties or by the creation of a new fact f1. An object called ‘B1’ with the property being ‘red’ — written as ‘RED(B1)’ — perhaps changes its property from being ‘red’ to become ‘blue’ — written as ‘BLUE(B1)’ –. Then the set of facts of the actual state S0= {RED(B1)} will change to a successor state S1={BLUE(B1)}. In this case the old fact ‘RED(B1)’ has been deleted and the new fact ‘BLUE(B1)’ has been created. Another example: the object ‘B1’ has also a ‘weight’ measured in kg which changes too. Then the actual state was S0={RED(B1), WEIGHT(B1,kg,2.4)} and this state changed to the successor state S1= {BLUE(B1), WEIGHT(B1,kg,3.4)}.
The possible cause of a change can be either an object or the ‘whole state‘ representing the world.
The mapping from a given state s into a successor state s’ by subtracting facts f- and joining facts f+ is here called an action: S –> S-(f-) u (f+) or action(s) = s’ = s-(f-) u (f+) with s , s’ in S
Because an action has an actor as a carrier one can write action: S x A –> S-(f-) u (f+) or action_a(s) = s’.
The defining properties of such an action are given in the sets of facts to be deleted — written as ‘d:{f-}’ — and the sets of facts to be created — written ‘c:{f+}’ –.
A full change expression amounts then to the following format: <s,s’, obj-name, action-name, d:{…}, c:{…}>.
But this is not yet the whole story. A change can be deterministic or indeterministic.
The deterministic change is cause by a deterministic actor or by a deterministic world.
The indeterministic change can have several formats:e.g. classical probability or quantum-like probability or the an actor as cause, whose behavior is not completely deterministic.
Additionally there can be interactions between different objects which can cause a change and these changes happen in parallel, simultaneously. Depending from the assumed environment (= world) and some laws describing the behavior of this world it can happen, that different local actions can hinder each other or change the effect of the changes.
Independent of the different kinds of changes it can be required that all used change-expressions should be of that kind that one can state that they are empirical by everyday experience.
TIME
And there is even more to tell. A change has in everyday life a duration measured with certain time units generated by a technical device called a clock.
To improve the empirical precision of change expressions one has to add the duration of the change between the actual state s and the final state s’ showing all the deletes (f-) and creates (f+) which are caused by this change-expression. This can only be done if a standard clock is included in the facts represented by the actual time stamp of this clock. Thus with regard to such a standard time one can realize a change with duration (t,t’) exactly in coherence with the standard time. A special case is given when a change-expression describes the effects of its actions in a distributed manner by giving more than one time point (t,t1, …, tn) and associating different deletes and creates with different points of time. Those distributed effects can make an actor story rather complex and difficult to understand by human brains.
An overview to the enhanced AAI theory version 2 you can find here. In this post we talk about the fourth chapter dealing with the epistemology of actors within an AAI analysis process.
EPISTEMOLOGY AND THE EMPIRICAL SCIENCES
Epistemology is a sub-discipline of general philosophy. While a special discipline in empirical science is defined by a certain sub-set of the real world RW by empirical measurement methods generating empirical data which can be interpreted by a formalized theory, philosophy is not restricted to a sub-field of the real world. This is important because an empirical discipline has no methods to define itself. Chemistry e.g. can define by which kinds of measurement it is gaining empirical data and it can offer different kinds of formal theories to interpret these data including inferences to forecast certain reactions given certain configurations of matters, but chemistry is not able to explain the way how a chemist is thinking, how the language works which a chemist is using etc. Thus empirical science presupposes a general framework of bodies, sensors, brains, languages etc. to be able to do a very specialized — but as such highly important — job. One can define ‘philosophy’ then as that kind of activity which tries to clarify all these conditions which are necessary to do science as well as how cognition works in the general case.
Given this one can imagine that philosophy is in principle a nearly ‘infinite’ task. To get not lost in this conceptual infinity it is recommended to start with concrete processes of communications which are oriented to generate those kinds of texts which can be shown as ‘related to parts of the empirical world’ in a decidable way. This kind of texts is here called ’empirically sound’ or ’empirically true’. It is to suppose that there will be texts for which it seems to be clear that they are empirically sound, others will appear ‘fuzzy’ for such a criterion, others even will appear without any direct relation to empirical soundness.
In empirical sciences one is using so-called empirical measurement procedures as benchmarks to decided whether one has empirical data or not, and it is commonly assumed that every ‘normal observer’ can use these data as every other ‘normal observer’. But because individual, single data have nearly no meaning on their own one needs relations, sets of relations (models) and even more complete theories, to integrate the data in a context, which allows some interpretation and some inferences for forecasting. But these relations, models, or theories can not directly be inferred from the real world. They have to be created by the observers as ‘working hypotheses’ which can fit with the data or not. And these constructions are grounded in highly complex cognitive processes which follow their own built-in rules and which are mostly not conscious. ‘Cognitive processes’ in biological systems, especially in human person, are completely generated by a brain and constitute therefore a ‘virtual world’ on their own. This cognitive virtual world is not the result of a 1-to-1 mapping from the real world into the brain states. This becomes important in that moment where the brain is mapping this virtual cognitive world into some symbolic language L. While the symbols of a language (sounds or written signs or …) as such have no meaning the brain enables a ‘coding’, a ‘mapping’ from symbolic expressions into different states of the brain. In the light’ of such encodings the symbolic expressions have some meaning. Besides the fact that different observers can have different encodings it is always an open question whether the encoded meaning of the virtual cognitive space has something to do with some part of the empirical reality. Empirical data generated by empirical measurement procedures can help to coordinate the virtual cognitive states of different observers with each other, but this coordination is not an automatic process. Empirically sound language expressions are difficult to get and therefore of a high value for the survival of mankind. To generate empirically sound formal theories is even more demanding and until today there exists no commonly accepted concept of the right format of an empirically sound theory. In an era which calls itself ‘scientific’ this is a very strange fact.
EPISTEMOLOGY OF THE AAI-EXPERTS
Applying these general considerations to the AAI experts trying to construct an actor story to describe at least one possible path from a start state to a goal state, one can pick up the different languages the AAI experts are using and asking back under which conditions these languages have some ‘meaning’ and under which conditions these meanings can be called ’empirically sound’?
In this book three different ‘modes’ of an actor story will be distinguished:
A textual mode using some ordinary everyday language, thus using spoken language (stored in an audio file) or written language as a text.
A pictorial mode using a ‘language of pictures’, possibly enhanced by fragments of texts.
A mathematical mode using graphical presentations of ‘graphs’ enhanced by symbolic expressions (text) and symbolic expressions only.
For every mode it has to be shown how an AAI expert can generate an actor story out of the virtual cognitive world of his brain and how it is possible to decided the empirical soundness of the actor story.
This is a continuation from the post about QL Basics Concepts Part 1. The general topic here is the analysis of properties of human behavior, actually narrowed down to the statistical properties. From the different possible theories applicable to statistical properties of behavior here the one called CPT (classical probability theory) is selected for a short examination.
SUMMARY
An analysis of the classical probability theory shows that the empirical application of this theory is limited to static sets of events and probabilities. In the case of biological systems which are adaptive with regard to structure and cognition this does not work. This yields the question whether a quantum probability theory approach does work or not.
THE CPT IDEA
Before we are looking to the case of quantum probability theory (QLPT) let us examine the case of a classical probability theory (CPT) a little bit more.
Generally one has to distinguish the symbolic formal representation of a theory T and some domain of application D distinct from the symbolic representation.
In principle the domain of application D can be nearly anything, very often again another symbolic representation. But in the case of empirical applications we assume usually some subset of ’empirical events’ E of the ’empirical (real) world’ W.
For the following let us assume (for a while) that this is the case, that D is a subset of the empirical world W.
Talking about ‘events in an empirical real world’ presupposes that there there exists a ‘procedure of measurement‘ using a ‘previously defined standard object‘ and a ‘symbolic representation of the measurement results‘.
Furthermore one has to assume a community of ‘observers‘ which have minimal capabilities to ‘observe’, which implies ‘distinctions between different results’, some ‘ordering of successions (before – after)’, to ‘attach symbols according to some rules’ to measurement results, to ‘translate measurement results’ into more abstract concepts and relations.
Thus to speak about empirical results assumes a set of symbolic representations of those events as a finite set of symbolic representations which represent a ‘state in the real world’ which can have a ‘predecessor state before’ and – possibly — a ‘successor state after’ the ‘actual’ state. The ‘quality’ of these measurement representations depends from the quality of the measurement procedure as well as from the quality of the cognitive capabilities of the participating observers.
In the classical probability theory T_cpt as described by Kolmogorov (1932) it is assumed that there is a set E of ‘elementary events’. The set E is assumed to be ‘complete’ with regard to all possible events. The probability P is coming into play with a mapping from E into the set of positive real numbers R+ written as P: E —> R+ or P(E) = 1 with the assumption that all the individual elements e_i of E have an individual probability P(e_i) which obey the rule P(e_1) + P(e_2) + … + P(e_n) = 1.
In the formal theory T_cpt it is not explained ‘how’ the probabilities are realized in the concrete case. In the ‘real world’ we have to identify some ‘generators of events’ G, otherwise we do not know whether an event e belongs to a ‘set of probability events’.
Kolmogorov (1932) speaks about a necessary generator as a ‘set of conditions’ which ‘allows of any number of repetitions’, and ‘a set of events can take place as a result of the establishment of the condition’. (cf. p.3) And he mentions explicitly the case that different variants of the a priori assumed possible events can take place as a set A. And then he speaks of this set A also of an event which has taken place! (cf. p.4)
If one looks to the case of the ‘set A’ then one has to clarify that this ‘set A’ is not an ordinary set of set theory, because in a set every member occurs only once. Instead ‘A’ represents a ‘sequence of events out of the basic set E’. A sequence is in set theory an ‘ordered set’, where some set (e.g. E) is mapped into an initial segment of the natural numbers Nat and in this case the set A contains ‘pairs from E x Nat|\n’ with a restriction of the set Nat to some n. The ‘range’ of the set A has then ‘distinguished elements’ whereby the ‘domain’ can have ‘same elements’. Kolmogorov addresses this problem with the remark, that the set A can be ‘defined in any way’. (cf. p.4) Thus to assume the set A as a set of pairs from the Cartesian product E x Nat|\n with the natural numbers taken from the initial segment of the natural numbers is compatible with the remark of Kolmogorov and the empirical situation.
For a possible observer it follows that he must be able to distinguish different states <s1, s2, …, sm> following each other in the real world, and in every state there is an event e_i from the set of a priori possible events E. The observer can ‘count’ the occurrences of a certain event e_i and thus will get after n repetitions for every event e_i a number of occurrences m_i with m_i/n giving the measured empirical probability of the event e_i.
Example 1: Tossing a coin with ‘head (H)’ or ‘tail (T)’ we have theoretically the probabilities ‘1/2’ for each event. A possible outcome could be (with ‘H’ := 0, ‘T’ := 1): <((0,1), (0,2), (0,3), (1,4), (0,5)> . Thus we have m_H = 4, m_T = 1, giving us m_H/n = 4/5 and m_T/n = 1/5. The sum yields m_H/n + m_T/n = 1, but as one can see the individual empirical probabilities are not in accordance with the theory requiring 1/2 for each. Kolmogorov remarks in his text that if the number of repetitions n is large enough then will the values of the empirically measured probability approach the theoretically defined values. In a simple experiment with a random number generator simulating the tossing of the coin I got the numbers m_Head = 4978, m_Tail = 5022, which gives the empirical probabilities m_Head/1000 = 0.4977 and m_Teil/ 1000 = 0.5021.
This example demonstrates while the theoretical term ‘probability’ is a simple number, the empirical counterpart of the theoretical term is either a simple occurrence of a certain event without any meaning as such or an empirically observed sequence of events which can reveal by counting and division a property which can be used as empirical probability of this event generated by a ‘set of conditions’ which allow the observed number of repetitions. Thus we have (i) a ‘generator‘ enabling the events out of E, we have (ii) a ‘measurement‘ giving us a measurement result as part of an observation, (iii) the symbolic encoding of the measurement result, (iv) the ‘counting‘ of the symbolic encoding as ‘occurrence‘ and (v) the counting of the overall repetitions, and (vi) a ‘mathematical division operation‘ to get the empirical probability.
Example 1 demonstrates the case of having one generator (‘tossing a coin’). We know from other examples where people using two or more coins ‘at the same time’! In this case the set of a priori possible events E is occurring ‘n-times in parallel’: E x … x E = E^n. While for every coin only one of the many possible basic events can occur in one state, there can be n-many such events in parallel, giving an assembly of n-many events each out of E. If we keeping the values of E = {‘H’, ‘T’} then we have four different basic configurations each with probability 1/4. If we define more ‘abstract’ events like ‘both the same’ (like ‘0,0’, ‘1,1’) or ‘both different’ (like ‘0,1’. ‘1,0’), then we have new types of complex events with different probabilities, each 1/2. Thus the case of n-many generators in parallel allows new types of complex events.
Following this line of thinking one could consider cases like (E^n)^n or even with repeated applications of the Cartesian product operation. Thus, in the case of (E^n)^n, one can think of different gamblers each having n-many dices in a cup and tossing these n-many dices simultaneously.
Thus we have something like the following structure for an empirical theory of classical probability: CPT(T) iff T=<G,E,X,n,S,P*>, with ‘G’ as the set of generators producing out of E events according to the layout of the set X in a static (deterministic) manner. Here the set E is the set of basic events. The set X is a ‘typified set’ constructed out of the set E with t-many applications of the Cartesian operation starting with E, then E^n1, then (E^n1)^n2, …. . ‘n’ denotes the number of repetitions, which determines the length of a sequence ‘S’. ‘P*’ represents the ’empirical probability’ which approaches the theoretical probability P while n is becoming ‘big’. P* is realized as a tuple of tuples according to the layout of the set X where each element in the range of a tuple represents the ‘number of occurrences’ of a certain event out of X.
Example: If there is a set E = {0,1} with the layout X=(E^2)^2 then we have two groups with two generators each: <<G1, G2>,<G3,G4>>. Every generator G_i produces events out of E. In one state i this could look like <<0, 0>,<1,0>>. As part of a sequence S this would look like S = <….,(<<0, 0>,<1,0>>,i), … > telling that in the i-th state of S there is an occurrence of events like shown. The empirical probability function P* has a corresponding layout P* = <<m1, m2>,<m3,m4>> with the m_j as ‘counter’ which are counting the occurrences of the different types of events as m_j =<c_e1, …, c_er>. In the example there are two different types of events occurring {0,1} which requires two counters c_0 and c_1, thus we would have m_j =<c_0, c_1>, which would induce for this example the global counter structure: P* = <<<c_0, c_1>, <c_0, c_1>>,<<c_0, c_1>,<c_0, c_1>>>. If the generators are all the same then the set of basic events E is the same and in theory the theoretical probability function P: E —> R+ would induce the same global values for all generators. But in the empirical case, if the theoretical probability function P is not known, then one has to count and below the ‘magic big n’ the values of the counter of the empirical probability function can be different.
This format of the empirical classical probability theory CPT can handle the case of ‘different generators‘ which produce events out of the same basic set E but with different probabilities, which can be counted by the empirical probability function P*. A prominent case of different probabilities with the same set of events is the case of manipulations of generators (a coin, a dice, a roulette wheel, …) to deceive other people.
In the examples mentioned so far the probabilities of the basic events as well as the complex events can be different in different generators, but are nevertheless ‘static’, not changing. Looking to generators like ‘tossing a coin’, ‘tossing a dice’ this seams to be sound. But what if we look to other types of generators like ‘biological systems’ which have to ‘decide’ which possible options of acting they ‘choose’? If the set of possible actions A is static, then the probability of selecting one action a out of A will usually depend from some ‘inner states’ IS of the biological system. These inner states IS need at least the following two components:(i) an internal ‘representation of the possible actions’ IS_A as well (ii) a finite set of ‘preferences’ IS_Pref. Depending from the preferences the biological system will select an action IS_a out of IS_A and then it can generate an action a out of A.
If biological systems as generators have a ‘static’ (‘deterministic’) set of preferences IS_Pref, then they will act like fixed generators for ‘tossing a coin’, ‘tossing a dice’. In this case nothing will change. But, as we know from the empirical world, biological systems are in general ‘adaptive’ systems which enables two kinds of adaptation: (i) ‘structural‘ adaptation like in biological evolution and (ii) ‘cognitive‘ adaptation as with higher organisms having a neural system with a brain. In these systems (example: homo sapiens) the set of preferences IS_Pref can change in time as well as the internal ‘representation of the possible actions’ IS_A. These changes cause a shift in the probabilities of the events manifested in the realized actions!
If we allow possible changes in the terms ‘G’ and ‘E’ to ‘G+’ and ‘E+’ then we have no longer a ‘classical’ probability theory CPT. This new type of probability theory we can call ‘non-classic’ probability theory NCPT. A short notation could be: NCPT(T) iff T=<G+,E+,X,n,S,P*> where ‘G+’ represents an adaptive biological system with changing representations for possible Actions A* as well as changing preferences IS_Pref+. The interesting question is, whether a quantum logic approach QLPT is a possible realization of such a non-classical probability theory. While it is known that the QLPT works for physical matters, it is an open question whether it works for biological systems too.
REMARK: switching from static generators to adaptive generators induces the need for the inclusion of the environment of the adaptive generators. ‘Adaptation’ is generally a capacity to deal better with non-static environments.
