Since the release of the chatbot ‘chatGPT’ to the larger public, a kind of ‘earthquake’ has been going through the media, worldwide, in many areas, from individuals to institutions, companies, government agencies …. everyone is looking for the ‘chatGPT experience’. These reactions are amazing, and frightening at the same time.
Remark: The text of this post represents a later ‘stage’ of my thinking about the usefulness of the chatGPT algorithm, which started with my first reflections in the text entitled “chatGBT about Rationality: Emotions, Mystik, Unconscious, Conscious, …” from 15./16.January 2023. The main text to this version is an English translation from an originally German text partially generated with the www.DeepL.com/Translator (free version).
FORM
The following lines form only a short note, since it is hardly worthwhile to discuss a ‘surface phenomenon’ so intensively, when the ‘deep structures’ should be explained. Somehow the ‘structures behind chatGPT’ seem to interest hardly anybody (I do not mean technical details of the used algorithms).
chatGPT as an object
The chatbot named ‘chatGPT’ is a piece of software, an algorithm that (i) was invented and programmed by humans. When (ii) people ask it questions, then (iii) it searches the database of documents known to it, which in turn have been created by humans, (iv) for text patterns that have a relation to the question according to certain formal criteria (partly given by the programmers). These ‘text finds’ are (v) also ‘arranged’ according to certain formal criteria (partly given by the programmers) into a new text, which (vi) should come close to those text patterns, which a human reader is ‘used’ to accept as ‘meaningful’.
Text surface – text meaning – truthfulness
A normal human being can distinguish – at least ‘intuitively’ – between the (i) ‘strings’ used as ‘expressions of a language’ and those (ii) ‘knowledge elements’ (in the mind of the hearer-speaker) which are as such ‘independent’ of the language elements, but which (iii) can be ‘freely associated’ by speakers-hearers of a language, so that the correlated ‘knowledge elements’ become what is usually called the ‘meaning’ of the language elements. [1] Of these knowledge elements (iv), every language participant already ‘knows’ ‘pre-linguistically’, as a learning child [2], that some of these knowledge elements are ‘correlatable’ with circumstances of the everyday world under certain circumstances. And the normal language user also ‘intuitively’ (automatically, unconsciously) has the ability to assess such correlation – in the light of the available knowledge – as (v) ‘possible’ or (vi) as rather ‘improbable’ or (vi) as ‘mere fancifulness’.”[3]
The basic ability of a human being to be able to establish a ‘correlation’ of meanings with (intersubjective) environmental facts is called – at least by some – philosophers ‘truth ability’ and in the execution of truth ability one then also can speak of ‘true’ linguistic utterances or of ‘true statements’.[5]
Distinctions like ‘true’, ‘possibly true’, ‘rather not true’ or ‘in no case true’ indicate that the reality reference of human knowledge elements is very diverse and ‘dynamic’. Something that was true a moment ago may not be true the next moment. Something that has long been dismissed as ‘mere fantasy’ may suddenly appear as ‘possible’ or ‘suddenly true’. To move in this ‘dynamically correlated space of meaning’ in such a way that a certain ‘inner and outer consistency’ is preserved, is a complex challenge, which has not yet been fully understood by philosophy and the sciences, let alone even approximately ‘explained’.
The fact is: we humans can do this to a certain extent. Of course, the more complex the knowledge space is, the more diverse the linguistic interactions with other people become, the more difficult it becomes to completely understand all aspects of a linguistic statement in a situation.
‘Air act’ chatGPT
Comparing the chatbot chatGPT with these ‘basic characteristics’ of humans, one can see that chatGPT can do none of these things. (i) It cannot ask questions meaningfully on its own, since there is no reason why it should ask (unless someone induces it to ask). (ii) Text documents (of people) are sets of expressions for him, for which he has no independent assignment of meaning. So he could never independently ask or answer the ‘truth question’ – with all its dynamic shades. He takes everything at ‘face value’ or one says right away that he is ‘only dreaming’.
If chatGPT, because of its large text database, has a subset of expressions that are somehow classified as ‘true’, then the algorithm can ‘in principle’ indirectly determine ‘probabilities’ that other sets of expressions that are not classified as ‘true’ then do ‘with some probability’ appear to be ‘true’. Whether the current chatGPT algorithm uses such ‘probable truths’ explicitly is unclear. In principle, it translates texts into ‘vector spaces’ that are ‘mapped into each other’ in various ways, and parts of these vector spaces are then output again in the form of a ‘text’. The concept of ‘truth’ does not appear in these mathematical operations – to my current knowledge. If, then it would be also only the formal logical concept of truth [4]; but this lies with respect to the vector spaces ‘above’ the vector spaces, forms with respect to these a ‘meta-concept’. If one wanted to actually apply this to the vector spaces and operations on these vector spaces, then one would have to completely rewrite the code of chatGPT. If one would do this – but nobody will be able to do this – then the code of chatGPT would have the status of a formal theory (as in mathematics) (see remark [5]). From an empirical truth capability chatGPT would then still be miles away.
Hybrid illusory truths
In the use case where the algorithm named ‘chatGPT’ uses expression sets similar to the texts that humans produce and read, chatGPT navigates purely formally and with probabilities through the space of formal expression elements. However, a human who ‘reads’ the expression sets produced by chatGPT automatically (= unconsciously!) activates his or her ‘linguistic knowledge of meaning’ and projects it into the abstract expression sets of chatGBT. As one can observe (and hears and reads from others), the abstract expression sets produced by chatGBT are so similar to the usual text input of humans – purely formally – that a human can seemingly effortlessly correlate his meaning knowledge with these texts. This has the consequence that the receiving (reading, listening) human has the ‘feeling’ that chatGPT produces ‘meaningful texts’. In the ‘projection’ of the reading/listening human YES, but in the production of chatGPT NO. chatGBT has only formal expression sets (coded as vector spaces), with which it calculates ‘blindly’. It does not have ‘meanings’ in the human sense even rudimentarily.
Back to the Human?
(Last change: 27.February 2023)
How easily people are impressed by a ‘fake machine’ to the point of apparently forgetting themselves in face of the machine by feeling ‘stupid’ and ‘inefficient’, although the machine only makes ‘correlations’ between human questions and human knowledge documents in a purely formal way, is actually frightening [6a,b], [7], at least in a double sense: (i)Instead of better recognizing (and using) one’s own potentials, one stares spellbound like the famous ‘rabbit at the snake’, although the machine is still a ‘product of the human mind’. (ii) This ‘cognitive deception’ misses to better understand the actually immense potential of ‘collective human intelligence’, which of course could then be advanced by at least one evolutionary level higher by incorporating modern technologies. The challenge of the hour is ‘Collective Human-Machine Intelligence’ in the context of sustainable development with priority given to human collective intelligence. The current so-called ‘artificial (= machine) intelligence’ is only present by rather primitive algorithms. Integrated into a developed ‘collective human intelligence’ quite different forms of ‘intelligence’ could be realized, ones we currently can only dream of at most.
Commenting on other articles from other authors about chatGPT
(Last change: 14.April 2023)
[7], [8],[9],[11],[12],[13],[14]
Comments
(Last change: 3.April 2023)
wkp-en: en.wikipedia.org
[1] In the many thousands of ‘natural languages’ of this world one can observe how ‘experiential environmental facts’ can become ‘knowledge elements’ via ‘perception’, which are then correlated with different expressions in each language. Linguists (and semioticians) therefore speak here of ‘conventions’, ‘freely agreed assignments’.
[2] Due to physical interaction with the environment, which enables ‘perceptual events’ that are distinguishable from the ‘remembered and known knowledge elements’.
[3] The classification of ‘knowledge elements’ as ‘imaginations/ fantasies’ can be wrong, as many examples show, like vice versa, the classification as ‘probably correlatable’ can be wrong too!
[4] Not the ‘classical (Aristotelian) logic’ since the Aristotelian logic did not yet realize a stricCommenting on other articles from other authors about chatGPTt separation of ‘form’ (elements of expression) and ‘content’ (meaning).
[5] There are also contexts in which one speaks of ‘true statements’ although there is no relation to a concrete world experience. For example in the field of mathematics, where one likes to say that a statement is ‘true’. But this is a completely ‘different truth’. Here it is about the fact that in the context of a ‘mathematical theory’ certain ‘basic assumptions’ were made (which must have nothing to do with a concrete reality), and one then ‘derives’ other statements starting from these basic assumptions with the help of a formal concept of inference (the formal logic). A ‘derived statement’ (usually called a ‘theorem’), also has no relation to a concrete reality. It is ‘logically true’ or ‘formally true’. If one would ‘relate’ the basic assumptions of a mathematical theory to concrete reality by – certainly not very simple – ‘interpretations’ (as e.g. in ‘applied physics’), then it may be, under special conditions, that the formally derived statements of such an ’empirically interpreted abstract theory’ gain an ’empirical meaning’, which may be ‘correlatable’ under certain conditions; then such statements would not only be called ‘logically true’, but also ’empirically true’. As the history of science and philosophy of science shows, however, the ‘transition’ from empirically interpreted abstract theories to empirically interpretable inferences with truth claims is not trivial. The reason lies in the used ‘logical inference concept’. In modern formal logic there are almost ‘arbitrarily many’ different formal inference terms possible. Whether such a formal inference term really ‘adequately represents’ the structure of empirical facts via abstract structures with formal inferences is not at all certain! This pro’simulation’blem is not really clarified in the philosophy of science so far!
[6a] Weizenbaum’s 1966 chatbot ‘Eliza’, despite its simplicity, was able to make human users believe that the program ‘understood’ them even when they were told that it was just a simple algorithm. See the keyword ‚Eliza‘ in wkp-en: https://en.wikipedia.org/wiki/ELIZA
[6b] Joseph Weizenbaum, 1966, „ELIZA. A Computer Program For the Study of Natural Language. Communication Between Man And Machine“, Communications of the ACM, Vol.9, No.1, January 1966, URL: https://cse.buffalo.edu/~rapaport/572/S02/weizenbaum.eliza.1966.pdf . Note: Although the program ‘Eliza’ by Weizenbaum was very simple, all users were fascinated by the program because they had the feeling “It understands me”, while the program only mirrored the questions and statements of the users. In other words, the users were ‘fascinated by themselves’ with the program as a kind of ‘mirror’.
[7] Ted Chiang, 2023, “ChatGPT Is a Blurry JPEG of the Web. OpenAI’s chatbot offers paraphrases, whereas Google offers quotes. Which do we prefer?”, The NEW YORKER, February 9, 2023. URL: https://www.newyorker.com/tech/annals-of-technology/chatgpt-is-a-blurry-jpeg-of-the-web . Note: Chang looks to the chatGPT program using the paradigm of a ‘compression algorithm’: the abundance of information is ‘condensed/abstracted’ so that a slightly blurred image of the text volumes is created, not a 1-to-1 copy. This gives the user the impression of understanding at the expense of access to detail and accuracy. The texts of chatGPT are not ‘true’, but they ‘mute’.
[8] Dietmar Hansch, 2023, “The more honest name would be ‘Simulated Intelligence’. Which deficits bots like chatGBT suffer from and what that must mean for our dealings with them.”, FAZ Frankfurter Allgemeine Zeitung, March 1, 2023, p.N1 . Note: While Chiang (see [7]) approaches the phenomenon chatGPT with the concept ‘compression algorithm’ Hansch prefers the terms ‘statistical-incremental learning’ as well as ‘insight learning’. For Hansch, insight learning is tied to ‘mind’ and ‘consciousness’, for which he postulates ‘equivalent structures’ in the brain. Regarding insight learning, Hansch further comments “insight learning is not only faster, but also indispensable for a deep, holistic understanding of the world, which grasps far-reaching connections as well as conveys criteria for truth and truthfulness.” It is not surprising then when Hansch writes “Insight learning is the highest form of learning…”. With reference to this frame of reference established by Hansch, he classifies chatGPT in the sense that it is only capable of ‘statistical-incremental learning’. Further, Hansch postulates for humans, “Human learning is never purely objective, we always structure the world in relation to our needs, feelings, and conscious purposes…”. He calls this the ‘human reference’ in human cognition, and it is precisely this what he also denies for chatGPT. For common designation ‘AI’ as ‘Artificial Intelligence’ he postulates that the term ‘intelligence’ in this word combination has nothing to do with the meaning we associate with ‘intelligence’ in the case of humans, so in no case has the term intelligence anything to do with ‘insight learning’, as he has stated before. To give more expression to this fact of mismatch he would rather use the term ‘simulated intelligence’ (see also [9]). This conceptual strategy seems strange, since the term simulation [10] normally presupposes that there is a clear state of affairs, for which one defines a simplified ‘model’, by means of which the behavior of the original system can then be — simplified — viewed and examined in important respects. In the present case, however, it is not quite clear what the original system should be, which is to be simulated in the case of AI. There is so far no unified definition of ‘intelligence’ in the context of ‘AI’! As far as Hansch’s terminology itself is concerned, the terms ‘statistical-incremental learning’ as well as ‘insight learning’ are not clearly defined either; the relation to observable human behavior let alone to the postulated ‘equivalent brain structures’ is arbitrarily unclear (which is not improved by the relation to terms like ‘consciousness’ and ‘mind’ which are not defined yet).
[9] Severin Tatarczyk, Feb 19, 2023, on ‘Simulated Intelligence’: https://www.severint.net/2023/02/19/kompakt-warum-ich-den-begriff-simulierte-intelligenz-bevorzuge-und-warum-chatbots-so-menschlich-auf-uns-wirken/
[10] See the term ‘simulation’ in wkp-en: https://en.wikipedia.org/wiki/Simulation
[11] Doris Brelowski pointed me to the following article: James Bridle, 16.March 2023, „The stupidity of AI. Artificial intelligence in its current form is based on the wholesale appropriation of existing culture, and the notion that it is actually intelligent could be actively dangerous“, URL: https://www.theguardian.com/technology/2023/mar/16/the-stupidity-of-ai-artificial-intelligence-dall-e-chatgpt?CMP=Share_AndroidApp_Other . Comment: An article that knowledgeably and very sophisticatedly describes the interplay between forms of AI that are being ‘unleashed’ on the entire Internet by large corporations, and what this is doing to human culture and then, of course, to humans themselves. Two quotes from this very readable article: Quote 1: „The entirety of this kind of publicly available AI, whether it works with images or words, as well as the many data-driven applications like it, is based on this wholesale appropriation of existing culture, the scope of which we can barely comprehend. Public or private, legal or otherwise, most of the text and images scraped up by these systems exist in the nebulous domain of “fair use” (permitted in the US, but questionable if not outright illegal in the EU). Like most of what goes on inside advanced neural networks, it’s really impossible to understand how they work from the outside, rare encounters such as Lapine’s aside. But we can be certain of this: far from being the magical, novel creations of brilliant machines, the outputs of this kind of AI is entirely dependent on the uncredited and unremunerated work of generations of human artists.“ Quote 2: „Now, this didn’t happen because ChatGPT is inherently rightwing. It’s because it’s inherently stupid. It has read most of the internet, and it knows what human language is supposed to sound like, but it has no relation to reality whatsoever. It is dreaming sentences that sound about right, and listening to it talk is frankly about as interesting as listening to someone’s dreams. It is very good at producing what sounds like sense, and best of all at producing cliche and banality, which has composed the majority of its diet, but it remains incapable of relating meaningfully to the world as it actually is. Distrust anyone who pretends that this is an echo, even an approximation, of consciousness. (As this piece was going to publication, OpenAI released a new version of the system that powers ChatGPT, and said it was “less likely to make up facts”.)“
[12] David Krakauer in an Interview with Brian Gallagher in Nautilus, March 27, 2023, Does GPT-4 Really Understand What We’re Saying?, URL: https://nautil.us/does-gpt-4-really-understand-what-were-saying-291034/?_sp=d9a7861a-9644-44a7-8ba7-f95ee526d468.1680528060130. David Krakauer, an evolutionary theorist and president of the Santa Fe Institute for complexity science, analyzes the role of chat-GPT-4 models compared to the human language model and a more differentiated understanding of what ‘understanding’ and ‘Intelligence’ could mean. His main points of criticism are in close agreement with the position int he text above. He points out that (i) one has clearly to distinguish between the ‘information concept’ of Shannon and the concept of ‘meaning’. Something can represent a high information load but can nevertheless be empty of any meaning. Then he points out (ii) that there are several possible variants of the meaning of ‘understanding’. Coordinating with human understanding can work, but to understand in a constructive sense: no. Then Krakauer (iii) relates GPT-4 to the standard model of science which he characterizes as ‘parsimony’; chat-GPT-4 is clearly the opposite. Another point (iv) is the fact, that human experience has an ’emotional’ and a ‘physical’ aspect based on somato-sensory perceptions within its body. This is missing with GPT-4. This is somehow related (v) to the fact, that the human brain with its ‘algorithms’ is the product of millions of years of evolution in a complex environment. The GPT-4 algorithms have nothing comparable; they have only to ‘convince’ humans. Finally (vi) humans can generate ‘physical models’ inspired by their experience and can quickly argue by using such models. Thus Krakauer concludes “So the narrative that says we’ve rediscovered human reasoning is so misguided in so many ways. Just demonstrably false. That can’t be the way to go.”
[13] By Marie-José Kolly (text) and Merlin Flügel (illustration), 11.04.2023, “Chatbots like GPT can form wonderful sentences. That’s exactly what makes them a problem.” Artificial intelligence fools us into believing something that is not. A plea against the general enthusiasm. Online newspaper ‘Republik’ from Schweiz, URL: https://www.republik.ch/2023/04/11/chatbots-wie-gpt-koennen-wunderbare-saetze-bilden-genau-das-macht-sie-zum-problem? Here are some comments:
The text by Marie-José Kolly stands out because the algorithm named chatGPT(4) is characterized here both in its input-output behavior and additionally a comparison to humans is made at least to some extent.
The basic problem of the algorithm chatGPT(4) is (as also pointed out in my text above) that it has as input data exclusively text sets (also those of the users), which are analyzed according to purely statistical procedures in their formal properties. On the basis of the analyzed regularities, arbitrary text collages can then be generated, which are very similar in form to human texts, so much so that many people take them for ‘human-generated texts’. In fact, however, the algorithm lacks what we humans call ‘world knowledge’, it lacks real ‘thinking’, it lacks ‘own’ value positions, and the algorithm ‘does not understand’ its own text.
Due to this lack of its own reference to the world, the algorithm can be manipulated very easily via the available text volumes. A ‘mass production’ of ‘junk texts’, of ‘disinformation’ is thus very easily possible.
If one considers that modern democracies can only function if the majority of citizens have a common basis of facts that can be assumed to be ‘true’, a common body of knowledge, and reliable media, then the chatGPT(4) algorithm can massively destroy precisely these requirements for a democracy.
The interesting question then is whether chatGPT(4) can actually support a human society, especially a democratic society, in a positive-constructive way?
In any case, it is known that humans learn the use of their language from childhood on in direct contact with a real world, largely playfully, in interaction with other children/people. For humans ‘words’ are never isolated quantities, but they are always dynamically integrated into equally dynamic contexts. Language is never only ‘form’ but always at the same time ‘content’, and this in many different ways. This is only possible because humans have complex cognitive abilities, which include corresponding memory abilities as well as abilities for generalization.
The cultural-historical development from spoken language, via writing, books, libraries up to enormous digital data memories has indeed achieved tremendous things concerning the ‘forms’ of language and therein – possibly – encoded knowledge, but there is the impression that the ‘automation’ of the forms drives them into ‘isolation’, so that the forms lose more and more their contact to reality, to meaning, to truth. Language as a central moment of enabling more complex knowledge and more complex action is thus increasingly becoming a ‘parasite’ that claims more and more space and in the process destroys more and more meaning and truth.
[14] Gary Marcus, April 2023, Hoping for the Best as AI Evolves, Gary Marcus on the systems that “pose a real and imminent threat to the fabric of society.” Communications of the ACM, Volume 66, Issue 4, April 2023 pp 6–7, https://doi.org/10.1145/3583078 , Comment: Gary Marcus writes on the occasion of the effects of systems like chatGPT(OpenAI), Dalle-E2 and Lensa about the seriously increasing negative effects these tools can have within a society, to an extent that poses a serious threat to every society! These tools are inherently flawed in the areas of thinking, facts and hallucinations. At near zero cost, they can be used to create and execute large-scale disinformation campaigns very quickly. Looking to the globally important website ‘Stack Overflow’ for programmers as an example, one could (and can) see how the inflationary use of chatGPT due to its inherent many flaws pushes the Stack Overflow’s management team having to urge its users to completely stop using chatGPT in order to prevent the site’s collapse after 14 years. In the case of big players who specifically target disinformation, such a measure is ineffective. These players aim to create a data world in which no one will be able to trust anyone. With this in mind, Gary Marcus sets out 4 postulates that every society should implement: (1) Automatically generated not certified content should be completely banned; (2) Legally effective measures must be adopted that can prevent ‘misinformation’; (3) User accounts must be made tamper-proof; (4) A new generation of AI tools is needed that can verify facts. (Translated with partial support from www.DeepL.com/Translator (free version))
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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[] Andrew Y. Ng, Stuart J. Russell, Algorithms for Inverse Reinforcement Learning, ICML 2000: Proceedings of the Seventeenth International Conference on Machine LearningJune 2000 Pages 663–670
[] Pat Langley (ed.), ICML ’00: Proceedings of the Seventeenth International Conference on Machine Learning, Morgan Kaufmann Publishers Inc., 340 Pine Street, Sixth Floor, San Francisco, CA, United States, Conference 29 June 2000- 2 July 2000, 29.June 2000
Abstract: Extrapolating Beyond Suboptimal Demonstrations via Inverse Reinforcement Learning from Observations Daniel S. Brown * 1 Wonjoon Goo * 1 Prabhat Nagarajan 2 Scott Niekum 1 You can read in the abstract: “A critical flaw of existing inverse reinforcement learning (IRL) methods is their inability to significantly outperform the demonstrator. This is because IRL typically seeks a reward function that makes the demonstrator appear near-optimal, rather than inferring the underlying intentions of the demonstrator that may have been poorly executed in practice. In this paper, we introduce a novel reward-learning-from-observation algorithm, Trajectory-ranked Reward EXtrapolation (T-REX), that extrapolates beyond a set of (ap- proximately) ranked demonstrations in order to infer high-quality reward functions from a set of potentially poor demonstrations. When combined with deep reinforcement learning, T-REX outperforms state-of-the-art imitation learning and IRL methods on multiple Atari and MuJoCo bench- mark tasks and achieves performance that is often more than twice the performance of the best demonstration. We also demonstrate that T-REX is robust to ranking noise and can accurately extrapolate intention by simply watching a learner noisily improve at a task over time.”
In the abstract you can read: “For sophisticated reinforcement learning (RL) systems to interact usefully with real-world environments, we need to communicate complex goals to these systems. In this work, we explore goals defined in terms of (non-expert) human preferences between pairs of trajectory segments. We show that this approach can effectively solve complex RL tasks without access to the reward function, including Atari games and simulated robot locomotion, while providing feedback on less than one percent of our agent’s interactions with the environment. This reduces the cost of human oversight far enough that it can be practically applied to state-of-the-art RL systems. To demonstrate the flexibility of our approach, we show that we can successfully train complex novel behaviors with about an hour of human time. These behaviors and environments are considerably more complex than any that have been previously learned from human feedback.
In the abstract you can read: “Conceptual abstraction and analogy-making are key abilities underlying humans’ abilities to learn, reason, and robustly adapt their knowledge to new domains. Despite of a long history of research on constructing AI systems with these abilities, no current AI system is anywhere close to a capability of forming humanlike abstractions or analogies. This paper reviews the advantages and limitations of several approaches toward this goal, including symbolic methods, deep learning, and probabilistic program induction. The paper concludes with several proposals for designing challenge tasks and evaluation measures in order to make quantifiable and generalizable progress
In the abstract you can read: “Since its beginning in the 1950s, the field of artificial intelligence has cycled several times between periods of optimistic predictions and massive investment (“AI spring”) and periods of disappointment, loss of confidence, and reduced funding (“AI winter”). Even with today’s seemingly fast pace of AI breakthroughs, the development of long-promised technologies such as self-driving cars, housekeeping robots, and conversational companions has turned out to be much harder than many people expected. One reason for these repeating cycles is our limited understanding of the nature and complexity of intelligence itself. In this paper I describe four fallacies in common assumptions made by AI researchers, which can lead to overconfident predictions about the field. I conclude by discussing the open questions spurred by these fallacies, including the age-old challenge of imbuing machines with humanlike common sense.”
[] Stuart Russell, (2019), Human Compatible: AI and the Problem of Control, Penguin books, Allen Lane; 1. Edition (8. Oktober 2019)
In the preface you can read: “This book is about the past , present , and future of our attempt to understand and create intelligence . This matters , not because AI is rapidly becoming a pervasive aspect of the present but because it is the dominant technology of the future . The world’s great powers are waking up to this fact , and the world’s largest corporations have known it for some time . We cannot predict exactly how the technology will develop or on what timeline . Nevertheless , we must plan for the possibility that machines will far exceed the human capacity for decision making in the real world . What then ? Everything civilization has to offer is the product of our intelligence ; gaining access to considerably greater intelligence would be the biggest event in human history . The purpose of the book is to explain why it might be the last event in human history and how to make sure that it is not .”
[] David Adkins, Bilal Alsallakh, Adeel Cheema, Narine Kokhlikyan, Emily McReynolds, Pushkar Mishra, Chavez Procope, Jeremy Sawruk, Erin Wang, Polina Zvyagina, (2022), Method Cards for Prescriptive Machine-Learning Transparency, 2022 IEEE/ACM 1st International Conference on AI Engineering – Software Engineering for AI (CAIN), CAIN’22, May 16–24, 2022, Pittsburgh, PA, USA, pp. 90 – 100, Association for Computing Machinery, ACM ISBN 978-1-4503-9275-4/22/05, New York, NY, USA, https://doi.org/10.1145/3522664.3528600
In the abstract you can read: “Specialized documentation techniques have been developed to communicate key facts about machine-learning (ML) systems and the datasets and models they rely on. Techniques such as Datasheets, AI FactSheets, and Model Cards have taken a mainly descriptive approach, providing various details about the system components. While the above information is essential for product developers and external experts to assess whether the ML system meets their requirements, other stakeholders might find it less actionable. In particular, ML engineers need guidance on how to mitigate po- tential shortcomings in order to fix bugs or improve the system’s performance. We propose a documentation artifact that aims to provide such guidance in a prescriptive way. Our proposal, called Method Cards, aims to increase the transparency and reproducibil- ity of ML systems by allowing stakeholders to reproduce the models, understand the rationale behind their designs, and introduce adap- tations in an informed way. We showcase our proposal with an example in small object detection, and demonstrate how Method Cards can communicate key considerations that help increase the transparency and reproducibility of the detection model. We fur- ther highlight avenues for improving the user experience of ML engineers based on Method Cards.”
[] John H. Miller, (2022), Ex Machina: Coevolving Machines and the Origins of the Social Universe, The SFI Press Scholars Series, 410 pages Paperback ISBN: 978-1947864429 , DOI: 10.37911/9781947864429
In the announcement of the book you can read: “If we could rewind the tape of the Earth’s deep history back to the beginning and start the world anew—would social behavior arise yet again? While the study of origins is foundational to many scientific fields, such as physics and biology, it has rarely been pursued in the social sciences. Yet knowledge of something’s origins often gives us new insights into the present. In Ex Machina, John H. Miller introduces a methodology for exploring systems of adaptive, interacting, choice-making agents, and uses this approach to identify conditions sufficient for the emergence of social behavior. Miller combines ideas from biology, computation, game theory, and the social sciences to evolve a set of interacting automata from asocial to social behavior. Readers will learn how systems of simple adaptive agents—seemingly locked into an asocial morass—can be rapidly transformed into a bountiful social world driven only by a series of small evolutionary changes. Such unexpected revolutions by evolution may provide an important clue to the emergence of social life.”
In the abstract you can read: “Analyzing the spatial and temporal properties of information flow with a multi-century perspective could illuminate the sustainability of human resource-use strategies. This paper uses historical and archaeological datasets to assess how spatial, temporal, cognitive, and cultural limitations impact the generation and flow of information about ecosystems within past societies, and thus lead to tradeoffs in sustainable practices. While it is well understood that conflicting priorities can inhibit successful outcomes, case studies from Eastern Polynesia, the North Atlantic, and the American Southwest suggest that imperfect information can also be a major impediment to sustainability. We formally develop a conceptual model of Environmental Information Flow and Perception (EnIFPe) to examine the scale of information flow to a society and the quality of the information needed to promote sustainable coupled natural-human systems. In our case studies, we assess key aspects of information flow by focusing on food web relationships and nutrient flows in socio-ecological systems, as well as the life cycles, population dynamics, and seasonal rhythms of organisms, the patterns and timing of species’ migration, and the trajectories of human-induced environmental change. We argue that the spatial and temporal dimensions of human environments shape society’s ability to wield information, while acknowledging that varied cultural factors also focus a society’s ability to act on such information. Our analyses demonstrate the analytical importance of completed experiments from the past, and their utility for contemporary debates concerning managing imperfect information and addressing conflicting priorities in modern environmental management and resource use.”
In the uffmm review section the different papers and books are discussed from the point of view of the oksimo paradigm, which is embedded in the general view of a generalized ‘citizen science’ as a ‘computer aided sustainable applied empirical theory’ (CSAET). In the following text the author discusses the introduction of the book “Theory of Sets” from the series “Elements of Mathematics” by N.Bourbaki (1968) [1b]
CONTEXT
In the foundational post with the title “From SYSTEMS Engineering to THEORY Engineering” [3] the assumptions of the whole formalization approach in logic, mathematics and science are questioned as to narrow to allow a modern sustainable theory of science dealing explicitly with the future. To sharpen some of the arguments in that post it seems to be helpful to discuss one of the cornerstones of modern (formalized) mathematics substantiated in the book ‘Theory of sets’ from the Bourbaki group.[1a] It has to be mentioned that the question of the insufficiency of formalization has been discussed in the uffmm blog in several posts before. (cf. e.g. [2])
Formalization
preface
In the introduction to the ‘Set Theory Book’ the bourbaki group reveals a little bit of their meta-mathematical point of view, which finally belongs to the perspective of philosophy. At the one hand they try to be ‘radically formal’, but doing this they notice themselves that this is — by several reasons — only a ‘regulative idea’, somehow important for our thinking, but not completely feasible. This ‘practical impossibility’ is not necessarily a problem as long as one is conscious about this. The Bourbaki group is conscious about this problem, but different to their ‘rigor’ with the specialized formalization of mathematical ideas, they leave it widely ‘undefined’ what follows from the practical impossibility of being ‘completely rigorous’. In the following text it will be tried to describe the Bourbaki position with both dimensions: the idea of ‘formalization’ and the reality of ‘non-formalized realities’ which give the ‘ground’ for everything, even for the formalization. Doing this it will — hopefully — become clear that the idea of formalization was a great achievement in the philosophical and scientific thinking but it did not really solve our problems of understanding the world. The most important aspects of knowledge are ‘outside’ of this formalization approach, and many ‘problems’ which seem to bother our actual thinking are perhaps only ‘artifacts’ of this simplified formalization approach (somehow similar to the problems which have been induced by the metaphysical thinking of the older philosophy). To say it flatly: to introduce new names for old problems does not necessarily solve problems. It enables new ways of speaking and perhaps some new kinds of knowledge, but it does not really solve the big problems of knowledge. And the biggest problem of knowledge is — perhaps — the primary ‘knowledge machine’ itself: the biological actors which have brains to transform ‘reality’ in ‘virtual models’ in their brains and communication tools to ‘communicate’ these virtual models to enable a ‘collective intelligence’ as well as a ‘collective cooperation’. As long as we do not understand this we do not really understand the ‘process of knowing’.
before formalization
With the advent of the homo sapiens population on the planet earth about 300.000 years ago [4] it became possible that biological systems could transform their perceptions of the reality around their brains into ‘internal’, ‘virtual’ models, which enabled ‘reference points’ for ‘acting’ and a ‘cooperation’ which was synchronized by a ‘symbolic communication’. Those properties of the internal virtual models which have no clear ‘correspondence’ to the ‘reality between the brains’ are difficult to communicate.
Everyday symbolic communication refers to parts of the reality by certain types of expressions, which are ‘combined’ in manners which encode different types of ‘relations’ or even ‘changes’. Expressions which ‘refer’ to ‘concrete’ properties can be ‘overloaded’ by expressions which refer to other expressions, which in turn refer either again to expressions or to ‘concrete meanings’. Those objects which are the targets of a referring relation — concrete objects or other expressions — are here called ‘the meaning’ of the expressions. Thus the ‘meaning space’ is populated by either expressions related to ‘concrete’ properties or by ‘expressions pointing forward’ to other expressions and these ‘pointing-forward’ expressions are here called ‘abstract meaning’. While concrete meanings are usually ‘decidable’ in the everyday world situations as being ‘given’ (being ‘true’) or as ‘not being given’ (‘being false’), abstract meanings are as expressions ‘undefined’: they can lead to some concrete property which in turn perhaps can be decided or not.
The availability of ‘abstract expressions’ in ordinary language can be seen as a ‘problem’ or as a ‘blessing’. Being able to generate and use abstract terms manifests a great flexibility in talking — and thinking! — about possible realities which allow to overcome the dictatorship of the ‘now’ and the ‘individual single’. Without abstraction thinking would indeed be impossible. Thus if one understands that ‘thinking’ is a real process with sequences of different states which reveal eventually more abstract classes, structures, and changes, then abstraction is the ‘opener’ for more reality, the ‘enabler’ for a more broader and flexible knowledge. Only by ‘transcending’ the eternal ‘Now’ we get an access to phenomena like time, changes, all kinds of dynamics, and only thereby are ‘pictures of some possible future’ feasible!
Clearly, the potential of abstraction can also be a source of ‘non-real’ ideas, of ‘fantastic’ pictures, of ‘fake news’ and the like.
But these possible ‘failures’ — if they will be ‘recognized’ as failures! — are inevitable if one wants to dig out some ‘truth’ in the nearly infinite space of the unknown. Before the ‘knowledge that something is true’ one has to master a ‘path of trial and error’ consuming ‘time’ and ‘resources’.
This process of creating new abstract ideas to guide a search in the space of the unknown is the only key to find besides ‘errors’ sometimes some ‘truth’.
Thus the ‘problem’ with abstract ideas is an unavoidable condition to find necessary ‘truths’. Stepping back in the face of possible problems is no option to survive in the unknown future.
the formal view of the world according to bourbaki
Figure 1: Graphical interpretation of N.Bourbaki, Set Theory (1968), Introduction, ‘liberal version’
Language, object language, meta language
Talking about mathematical objects with their properties within an ordinary language is not simple because the expressions of an ordinary language are as such usually part of a network of meanings, which can overlap, which can be fuzzy, which are giving space for many interpretations. Additionally, that which is called a ‘mathematical object’ is not a kind of an object wich is given in the everyday world experience. What can be done in such a situation?
Bourbaki proposes to introduce a ‘specialized language’ constructed out of a finite set of elements constituting the ‘alphabet’ of a new language, together with ‘syntactical rules’, which describe how to construct with the elements of the alphabet chains of elements called ‘(well formed) expressions’, which constitute the ‘language’ LO, which shall be used to talk about mathematical objects.
But because mathematics is not restricted to ‘static objects’ but deals also with ‘transformations’ (‘changes’) of objects, one needs ‘successions of objects’ (‘sequences’), which are related by ‘operations with mathematical objects’. In this case the operations are also represented by ‘expressions’ but these expressions are expressions of a ‘higher order’ which have as referenced subject those expressions which are representing objects . Thus, Bourbaki needs right from the beginning two languages: an ‘object language’ (expressions of a language LO representing mathematical objects) and a ‘meta language’ LL (expressions referring to expressions of the object language LO including certain ‘types of changes’ occurring with the object language expressions). Thus a mathematical language Lm consists in the combination of an object language LO with a meta language LL (Lm = (LO,LL)).
And, what becomes clear by this procedure, to introduce such a kind of mathematical language Lm one needs another language talking about the mathematical language Lm, and this is either the everyday (normal) language L, which is assumed to be a language which everybody can ‘understand’ and ‘apply correctly’, or it is a third specialized language LLL, which can talk with special expressions about the mathematical language Lm. Independent of the decision which solution one prefers, finally the ordinary language L will become the meta language for all other thinkable meta languages.
Translating(?) math objects into formal expressions
If the formalized expressions of the mathematical language (Lm = (LO,LL)) would be the mathematical objects themselves, then mathematics would consist only of those expressions. And, because there would be no other criteria available, whatever expressions one would introduce, every expression would claim to be a relevant mathematical expression. This situation would be a ‘maximum of non-sense’ construct: nothing could be ‘false’.
Thus, the introduction of formal expressions of some language alone seems to be not enough to establish a language which is called a ‘mathematical’ language Lm different from other languages which talk about other kinds of objects. But what could it be which relates to ‘specific math objects’ which are not yet the expressions used to ‘refer’ to these specific math objects?
Everybody knows that the main reason for to ‘speak’ (or ‘write’) about math specific objects are humans which are claiming to be ‘mathematicians’ and which are claiming to have some ‘knowledge’ about specific objects called ‘math objects’ which are the ‘content’ which they ‘translate’ into the expressions of a certain language call ‘mathematical language’.[5] Thus, if the ‘math objects’ are not the used expressions themselves then these ‘math objects’ have to be located ‘inside of these talking humans’. According to modern science one would specify this ‘inside’ as ‘brain’, which is connected in complex ways to a body which in turn is connected to the ‘outside world of the body’. Until today it is not possible to ‘observe’ directly math objects assumed to be in the brain of the body of someone which claims to be a mathematician. Thus one mathematician A can not decide what another mathematician B has ‘available in his brain’ at some point of time.
Bourbaki is using some formulations in his introduction which gives some ‘flavor’ of this ‘being not able to translate it into a formalized mathematical language’. Thus at one position in the text Bourbaki is recurring to the “common sense” of the mathematicians [6] or to the “reader’s intuition”. [7] Other phrases refer to the “modes of reasoning” which cannot be formalized [8], or simply to the “experience” on which “the opinion rests”. [9] Expressions like ‘common sense’, ‘intuition’, ‘modes of reasoning’, and ‘experience’ are difficult to interpret. All these expressions describe something ‘inside’ the brains which cannot be observed directly. Thus, how can mathematician A know what mathematician B ‘means’ if he is uttering some statement or writes it down? Does it make a difference whether a mathematician is a man or a woman or is belonging to some other kind of a ‘gender’? Does it make a difference which ‘age’ the mathematician has? How ‘big’ he is? Which ‘weight’ he has?
Thus, from a philosophical point of view the question to the specific criteria which classify a language as a ‘mathematical language’ and not some other language leads us into a completely unsatisfying situation: there are no ‘hard facts’ which can give us a hint what ‘mathematical objects’ could be. What did we ‘overlook’ here? What is the key to the specific mathematical objects which inspired the brains of many many thousand people through centuries and centuries? Is mathematics a ‘big fake’ or is there more than this?
A mathematician as an ‘actor’?
Figure 2: Graphical interpretation of N.Bourbaki, Set Theory (1968), Introduction, ‘Actor view’
This last question “Is mathematics a ‘big fake’ or is there more than this?” can lead o the assumption, that it is not enough to talk about ‘mathematics’ by not including the mathematician itself. Only the mathematician is that ‘mysterious source’ of knowledge, which seems to trigger the production of ‘mathematical expressions’ in speaking or writing (or drawing). Thus a meta-mathematical — and thereby philosophical’ — ‘description’ of mathematics should have at least the ‘components’ (MA, LO,LL,L) with ‘MA’ as abbreviation for the set of actors where each element of the set MA is a mathematician, and — this is decisive ! — it is this math actor MA which is in possession of those ‘criteria’ which decide whether an expression E belongs the ‘mathematical language Lm‘ or not.
The phrase of the ‘mathematician’ as a ‘mysterious source of knowledge’ is justified by an ’empirical observational point of view’: nobody can directly look into the brain of a mathematician. Thus the question of what an expression called ‘mathematical expression’ can ‘mean’ is in such an empirical view not decidable and appears to be a ‘mystery’.
But in the reality of everyday life we can observe, that every human actor — not only mathematicians — seems to be able to use expressions of the everyday language with referring to ‘internal states’ of the brain in a way which seems to ‘work’. If we are talking about ‘pain with my teeth’ or about ‘being hungry or thirsty’ or ‘having an idea’ etc. then usually other human actors seem to ‘understand’ what one is uttering. The ‘evidence’ of a ‘working understanding’ is growing up by the ‘confirmation of expectations’: if oneself is hungry, then one has a certain kind of ‘feeling’ and usually this feeling leads — depending from the cultural patterns one is living in — to a certain kind of ‘behavior’, which has — usually — the ‘felt effect’ of being again ‘not hungry’. This functional relation of ‘feeling to be hungry’, ‘behavior of consuming something’, ‘feeling of being not hungry again’ is an association between ‘bodily functions’ common to all human actors and additionally it is a certain kind of observable behavior, which is common to all human actors too. And it seems to work that human actors are able to associate ‘common internal states’ with ‘common observable behavior’ and associate this observable behavior with the ‘presupposed internal states’ with certain kinds of ‘expressions’. Thus although the internal states are directly not observable, they can become ‘communicated by expressions’ because these internal states are — usually — ‘common to the internal experience of every human actor’.
From this follows the ‘assumption’ that we should extend the necessary elements for ‘inter-actor communication’ with the factor of ‘common human actor HA experience’ abbreviated as ‘HAX‘ (HA, HAX, MA, LO,LL,L), which is usually accompanied by certain kinds of observable behavior ‘BX‘, which can be used as point of reference for certain expressions ‘LX‘, which ‘point to’ the associated intern al states HAX, which are not directly observable. This yields the structure (HA, HAX, MA, BX, LO,LL,LX,L).
Having reached this state of assumptions, there arises an other assumption regarding the relationship between ‘expressions of a language’ — like (LO,LL,LX,L) — and those properties which are constituting the ‘meaning’ of these expressions. In this context ‘meaning’ is not a kind of an ‘object’ but a ‘relation’ between two different things, the expressions at one side and the properties ‘referred to’ on the other side. Moreover this ‘meaning relation’ seems not to be a ‘static’ relation but a ‘dynamic’ one, associating two different kinds of properties one to another. This reminds to that what mathematicians call a ‘mapping, a function’, and the engineers a ‘process, an operation’. If we abbreviate this ‘dynamic meaning relation’ with the sign ‘μ’, then we could agree to the convention ‘μX : LX <—> (BX,HAX)’ saying that there exists a meaning function μX which maps the special expressions of LX to the special internal experience HAX, which in turn is associated with the special behavior BX. Thus, we extend our hypothetical structure to the format (HA, HAX, MA, BX, LO,LL,LX,L,μX).
With these assumptions we are getting a first idea how human actors in general can communicate about internal, directly not observable states, with other human actors by using external language expressions. We have to notice that the assumed dynamic meaning relation μX itself has to be located ‘inside’ the body, inside’ the brain. This triggers the further assumption to have ‘internal counterparts’ of the external observable behavior as well as external expressions. From this follows the further assumption that there must exists some ‘translation/ transformation’ ‘τ’ which ‘maps’ the internal ‘counterparts’ of the observable behavior and the observable expressions into the external behavior.(cf. figure 2) Thus, we are reaching the further extended format: (HA, HAX, MA, BX, LO,LL,LX,L,μX,τ).
Mathematical objects
Accepting the basic assumptions about an internal meaning function μX as well an internal translation function τ narrows the space of possible answers about the nature of ‘math objects’ a little bit, but as such this is possibly not yet a satisfying answer. Or, have we nevertheless yet to assume that ‘math objects’ and related ‘modes of reasoning’ are also rooted in internal properties and dynamics of the brain which are ‘common to all humans’?
If one sees that every aspect of the human world view is encoded in some internal states of the brain, and that what we call ‘world’ is only given as a constructed virtual structure in the brains of bodies including all the different kinds of ‘memories’, then there is no real alternative to the assumption that ‘math objects’ and related ‘modes of reasoning’ have to be located in these — yet not completely decoded — inner structures and dynamics of the brain.
From the everyday experience — additionally enlightened by different scientific disciplines, e.g. experimental (neuro) psychology — we know that the brain is — completely automatic — producing all kinds of ‘abstractions’ from concrete ‘perceptions’, can produce any kinds of ‘abstractions of abstractions’, can ‘associate’ abstractions with other abstractions, can arrange many different kinds of memories to ‘arrangements’ representing ‘states’/ ‘situations’, ‘transformations of states’, ‘sequences of states’ and the like. Thus everything which a ‘mathematical reasoning’ HAm needs seems to be available as concrete brain state or brain activity, and this is not only ‘special’ for an individual person alone, it is the common structure of all brains.
Therefore one has to assume that the set of mathematicians MA is a ‘subset’ of the set of human actors HA in general. From this one can further assume that the ‘mathematical reasoning’ HAm is a subset of the general human everyday experience HAX. And, saying this, the meaning function μX as well as the translation function τ should be applicable also to the mathematical reasoning and the mathematical objects as well: (HA, MA, HAX, HAm, BX, LO,LL,LX,L,μX,τ).
These assumptions would explain why it is not only possible but ‘inevitable’ to use the everyday language L to introduce and to use a mathematical language Lm with different kinds of sub-languages (LO,LL, LLL, …). Thus in analogy to the ‘feeling’ ‘to be hungry’ with a cultural encoded kind of accompanying behavior BX we have to assume that the different kinds of internal states and transformations in the case of mathematical reasoning can be associated with an observable kind of ‘behavior’ by using ‘expressions’ embedded (encoded) in certain kinds of ‘behavior’ accepted as ‘typical mathematical’. Introducing expressions like ‘0’, ‘1’, ‘2’, …, ’10’, … (belonging to a language Lo) for certain kinds of ‘objects’ and expressions like ‘+’, ‘-‘ … for certain kinds of operations with these before introduced objects (belonging to a language LL) one can construct combined expressions like ‘1+2=3’ (belonging to a mathematical language Lm). To introduce ‘more abstract objects’ like ‘sets’, ‘relations’, ‘functions’ etc. which have no direct counterpart in the everyday world does not break the assumptions. The everyday language L operates already only with abstract objects like ‘cup’, ‘dog’, ‘house’ etc. The expression ‘cup’ is an abstract concept, which can easily be associated with any kind of concrete phenomena provided by perceptions introducing ‘sets of different properties’, which allow the construction of ‘subsets of properties’ constituting a kind of ‘signature’ for a certain abstract ‘class’ which only exists in the dynamics of the brain. Thus having a set C named ‘cup’ introduces ‘possible elements’, whose ‘interpretation’ can be realized by associating different kinds of sets of properties provided by ‘sensory perception’. But the ‘memory’ as well as the ‘thinking’ can also provide other kinds of properties which can be used too to construct other ‘classes’.
In this outlined perspective of brain dynamics mathematics appears to be a science which is using these brain dynamics in a most direct way without to recur to the the huge amount of everyday experiences. Thus, mathematical languages (today summarized in that language, which enables the so called ‘set theory’) and mathematical thinking in general seems to reflect the basic machinery of the brain processing directly across all different cultures. Engineers worldwide speaking hundreds of different ‘everyday languages’ can work together by using mathematics as their ‘common language’ because this is their ‘common thinking’ underlying all those different everyday languages.
Being a human means being able to think mathematically … besides many other things which characterizes a human actor.
Epiloge
Basically every ordinary language offers all elements which are necessary for mathematics (mathematics is the kernel of every language). But history illustrates that it can be helpful to ‘extend’ an ordinary language with additional expressions (Lo, LL, LLL, …). But the development of modern mathematics and especially computer science shows increasing difficulties by ‘cutting away’ everyday experience in case of elaborating structures, models, theories in a purely formal manner, and to use these formal structures afterwards to interpret the everyday world. This separates the formal productions from the main part of users, of citizens, leading into a situation where only a few specialist have some ‘understanding’ (usually only partially because the formalization goes beyond the individual capacity of understanding), but all others have no more an understanding at all. This has he flavor of a ‘cultural self-destruction’.
In the mentioned oksimo software as part of a new paradigm of a more advanced citizen science this problem of ‘cultural self-destruction’ is avoided because in the format of a ‘computer aided sustainable applied empirical theory (CSAET) the basic language for investigating possible futures is the ordinary language which can be extend as needed with quantifying properties. The computer is not any more needed for ‘understanding’ but only for ‘supporting’ the ‘usage’ of everyday language expressions. This enables the best of both worlds: human thinking as well as machine operations.
[4] Humans, How many years ago?, see: wkp (en): https://en.wikipedia.org/wiki/Human#:~:text=Homo%20sapiens,-Linnaeus%2C%201758&text=Anatomically%20modern%20humans%20emerged%20around,local%20populations%20of%20archaic%20humans.
[5] The difference between ‘talking’ about math objects and ‘writing’ is usually not thematised in the philosophy of mathematics. Because the ordinary language is the most general ‘meta language’ for all kinds of specialized languages and the primary source of the ordinary language then ‘speaking’ is perhaps not really a ‘trivial’ aspect in understanding the ‘meaning’ of any kind of language.
[6] “But formalized mathematics cannot in practice be written down in full, and therefore we must have confidence in what might be called the common sense of the mathematician …”. (p.11)
[7] “Sometimes we shall use ordinary language more loosely … and by indications which cannot be translated into formalized language and which are designed to help the reader to reconstruct the whole text. Other passages, equally untranslatable into formalized language, are introduced in order to clarify the ideas involved, if necessary by appealing to the reader’s intuition …”(p.11)
[8] “It may happen at some future date that mathematicians will agree to use modes of reasoning which cannot be formalized in the language described here : it would then be necessary, if not to change the language completely, at least to enlarge its rules of syntax.”(p.9)
[9] “To sum up, we believe that mathematics is destined to survive … but we cannot pretend that this opinion rests on anything more than experience.”(p.13)
This text is part of a philosophy of science analysis of the case of the oksimo software (oksimo.com). A specification of the oksimo software from an engineering point of view can be found in four consecutive posts dedicated to the HMI-Analysis for this software.[*]
THE BOOK: THEORY OF SETS
Covered under the pseudonym of N.Bourbaki [1] appeared 1970 the French edition of a book which 1968 already had been translated into English (reprinted 1970) called Theory of Sets.[2] This book is the first book of a series about ELEMENTS OF MATHEMATICS.
To classify this book about set theory as a book of Metamathematics and as such as a book in the perspective of Philosophy of Science will become clear if one starts reading the book.[3]
MATHEMATICS WITH ONE LANGUAGE
It is the basic conviction of the Bourbaki book, that “… it is known to be possible … to derive practically the whole of known mathematics from a single source the Theory of Sets.” (p.9) And from this Bourbaki concludes, that it will be sufficient “… to describe the principles of a single formalized language, to indicate how the Thory of Sets could be written in this language, and then to show how the various branches of mathematics … fit into this framework.”(p.9)
Thus, the content of mathematics — whatever it is — can according to Bourbaki be described in one single language [Lm] and the content will be called Theory of Sets [T] .
METAMATHEMATICS
Because the one single language Lm used to describe the Theory of Sets shall be a language with certain properties one has to define these properties with some other language, which is talking about Lm. As language for this job Bourbaki is using the ordinary language [Lo].(p.9) But the reasoning within which one is using this ordinary language is called metamathematics (cf. P.10f). Within the metamathematical point of view the language Lm under investigation is seen as a set of previously given objetcs without any kind of meaning, where only the assigned order is of importance.(cf. p.10): “… metamathematical ‘arguments’ usually assert that when a succession of operations has been performed on a text of a given type, then the final text will be of another given type.”(p.10)
What looks here at first glance as the complete formalization of mathematics it is not. Bourbaki states clearly that “formalized mathematics cannot in practice be written down in full“(p.11) There has to be assumed as ‘last resort’ the assumption of a common sense of the mathematician and the intuition of the reader. (cf. p.11)
COGNITIVE-SEMIOTIC TURN
This conflict between at one hand of the idea of a formalization of Mathematics by a formalized language Lm and on the other hand by the well known proof of Gödel [4] of the incompleteness of the axioms for classical arithmetic (cf. p.12) is not a real conflict as long as one takes into account — as Bourbaki points out — that the ‘content of mathematics’ is only given in different layers of languages (Lm, Lo, …) which again are embedded in a presupposed ‘common sense’ which is nothing else as the cognitive machinery of human persons including an embedded meaning function relating different kinds of knowledge into different kinds of — internal as well as external — expressions of some language L. Thus any kind of a ‘reduction of meaning’ seems never to be a ‘complete reduction’ but only a ‘technical reduction’ to introduce some ‘artificial (abstract) objetcs’ which can only work because of their embedding in some richer context.
This new perspective can be called the cognitive-semiotic turn which became possible by new insights of modern brain sciences in connection with pysychology and semiotics.
From this new point of view one can derive the idea of embedding metamathemics in a more advanced actor theory providing all the ingredients to make metamathematics more ‘rational’.
OUTLINE OF ACTOR THEORY
Figure 1: Actor theory first outline
The details of the Actor Theory [AT] can become quite complex. Here a first outline of the basic ideas and what this can mean for a metamathematical point of view of mathematics.
World is not World
The main idea is founded in the new insights of Biology and Neuro-Psychology of the handling of body-world interactions as exercised by humans. One of the main insights is rooted back to von Uexküll [5] more than 100 years ago, when he described how every biological organism perceives and handles some world outside of the body with the inner neuronal structures given! Thus different life forms in the same outside world W will peceive and act neuronally in different worlds! Brain X acts in world X which is somehow related to the outside world W as well as Brain Y acts in world Y which also is somehow related to the outside world W.
These basic insights relate as well to more developed life forms as such as humans are. We as humans do not perceive and think the world W outside of our bodies ‘as it is’ but only as our brain inside our body can process all the body states related to the outside world in the mode of the inside brain. Thus if the different human individuals would have different brains they would live in different worlds and their would be no chance of a simple communication. But as we know from physiological and behavioral studies humans can to some extend communicate successfully. Thus there exists inside of every human individual a human-processed world h(W) which is different from other life-forms like a rat, a worm, an octopus, etc.
From this basic insight it follows that if we speak about the worldW we do indeed not speak about the world W directly but about the world W as it is processed in a human-specific manner, the world h(W). This has many implications.
Because we know already that the world h(W) is not a static but a dynamic world depending from our learning history it can happen — and it happens all the time — that different individuals have different learning histories. This can result in quite strong differences of experience and knowledge attached to different individuals, which can prevent a simple understanding between such individuals: the learned world h1(W) can to some degree be different from the learned world h2(W) such that a simple and direct understanding will not be possible.
This difference between the outside world W and the processed inside world h(W) relates to the communication too! The spoken or written expressions E of some language L are belonging to the outside world. They have a counterpart in the inner world as inner expressions E*, which can be associated with all kinds of processed inner states of the inner world h(W) = W*. These possible — and learned — associations between inner expressions and inner states belonging to h(W) is assumed here to be that what commonly is called meaning. Thus one has to assume an internal meaning function μ which maps the internal expressions E* of some internal language L* into parts of the internally processed world h(W)=W* and vice versa. Thus we have μ: E* <—> W*. Thus μ(e*) would point to some part w* of the internally processed world W* as the ‘meaning’ of the internal expression e*.
This semiotic architecture of human beings enables a nearly infinite space of expressions as well as associated meanings definable during learning processes. This is powerful, but it is also very demanding for the speaker-hearer: to enable a succesful communication between different speaker-hearer these have to train their language usage under sufficient similar conditions thereby constructing individual meaning functions which work — hopefully — sufficiently similar. If not then communication can slow down, can produce lots of misunderstandings or can even break down completely. [6]
In the case of mathematics it is a long debated question whether mathematics can be reduced to the expressions Em of some mathematical language Lm or if mathematics has some mathematical objects on its own which are different from the expressions. If one would assume that mathematics has no objects on its own but only some expressions Em, then it would become difficult to argue whether exactly these expressions Em should be used and not some other expressions Ex. Moreover to classify expressions as ‘axioms’ or ‘theorems’ would be completely arbitrary. The only ‘anchor’ of non-arbitrariness would consist in some formal criteria of a formal consistency which would disable the formal generation of pairs of expressions {a,a*} where one is excluding the other. But even such a formal consistency presupposes some criteria which are beyond the expressions as such! Thus mathematics would need some criteria outside mathematics. This can be understood as an argument for metamathematics. But according to Bourbaki metamathematics is defined as a set of operations on given expressions without a specific meaning. This is not enough to establish formal consistency! Thus even metamathematics is pointing to something outside of given mathematical expressions. What can this be?
PART 2
To be continued …
COMMENTS
[*] More recent versions of the specification of the oksimo oftware can be found in the bolg oksimo.org. Unfortunately are the texts in that blog — at the time if this writing — still only in German. Hopefully this will change in the future.
[1] Bourbaki group in Wikipedia [EN]: https://en.wikipedia.org/wiki/Nicolas_Bourbaki
[2] N.Bourbaki (1970), Theory of Sets, Series: ELEMENTS OF MATHEMATICS, Springer, Berlin — Heidelberg — New York (Engl. Translation from the French edition 1970)
[3] The first time when the author of this text has encountered the book was some time between 1984 – 1987 while being a PhD-student at the Ludwig-Maximilians Univesty [LMU] in Munich. It was in a seminar with Prof. Peter Hinst about structural approaches to Philosophy of Science. The point of view at that time was completely different to the point of view applied in this text.
[4] Kurt Goedel.Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, i.Monatshefte fuer Mathematik und Physik, 38:173–98, 1931.
[5] Jakob von Uexküll, 1909, Umwelt und Innenwelt der Tiere. Berlin: J.Springer.
[6] Probably everybody has made the experience in his life of being part of a situation where nobody speaks a language, which one is used to speak …
The starting point of view in this blog has been and still is the point of engineering, especially the perspective of man-machine interface [MMI], later as Man-Machine Interaction, then accompanied by human-computer interaction [HCI] or human-machine interaction [HMI]. While MMI often is discussed in isolation, not as part of engineering, this blog emphasizes a point of view where MMI is understood as an integrated part of systems engineering. The past years have shown, that this integration makes a great difference in the overall layout as well as in the details of the used methods. This integration widened the scope of MMI to the context of engineering in a way which teared down many artificial boundaries in dealing with the subject of MMI. The analysis part of MMI can take into account not only the intended users and a limited set of tasks required for the usage of a system but it can extend the scope to the different kinds of contexts of the intended users as well as the intended service/product as such: cultural patterns, sustainable perspectives, climate relevance, political implications, and more. This triggers the question, whether there are other established scientific disciplines which are sharing this scope with MMI. Traditionally experimental and cognitive psychology has always played an important role as part of the MMI analysis. Different special disciplines like physiology or neuro-psychology, linguistics, phonetics etc. have played some role too. More recently culture and society have been brought more into the focus of MMI. What about sociology? What about anthropology? The following text discusses a possible role of anthropology in the light of the recent book Why The World Needs Anthropologists?
INTRODUCTION AND CONCLUSION
This review has the addendum ‘Part 1’ pointing to the fact, that this text does not deal with the whole book first, but only with some parts, the introduction and the conclusion.
An Introduction
The introduction of the book is asking, why does the world needs anthropologists?, and the main pattern of the introduction looks back to the old picture of anthropology, and then seeks to identify, what could/is the new paradigm which should be followed.
The roots of anthropology are located in the colonial activities of the British Empire as well as in the federal activities of the USA, which both had a strong bias to serve the political power more than to evolve a really free science. And an enduring gap between the more theoretical anthropology and an applied one is thematised although there existed always a strong inter-dependency between both.
To leave the close connection with primarily governmental interests and to see the relation between the theory and the different Applications more positive than negative anthropology is understood as challenged to rebrand its appearance in the public and in their own practice.
The most vital forces for such a rebranding seem to be rooted in more engagements in societal problems of public interests and thereby challenging the theory to widen their concept and methods.
Besides the classical methods of anthropology (cultural relativism, ethnography, comparison, and contextual understanding) anthropology has to show that it can make sense beyond pure data, deciphering ambiguity, complexity, and ambivalence, helping with diversity, investigating the interface between culture, technology, and environment.
What Is Left Out
After the introduction the main chapters of the book are left out in this text until later. The chapters in the book are giving examples to the questions, why the world needs anthropology, what have been the motivations for active anthropologists to become one, how they have applied anthropology, and which five tips they would give for practicing and theorizing.
Conclusion
In the conclusion of the book not the five questions are the guiding principle but ‘five axis that matter greatly’, and these five axis are circumscribed as (i) navigate the ethics of change; (ii) own-it in the sense, that an anthropologist should have a self-esteem for his/ her/ x profession and can co-create it with others; (iii) expand the skill-set; (iv) collaborate, co-create and study-up; (v) recommend as being advisors and consultants.
The stronger commitment with actual societal problems leads anthropology at the crossroads of many processes which require new views, new methods. To gain new knowledge and to do a new practice is not always accompanied by known ethical schemata. Doing this induces ethical questions which have not been known before in this way. While a new practice is challenging the old knowledge and induces a pressure for change, new versions of knowing can trigger new forms of practice as well. Theory and application are a dynamic pair where each part learns from the other.
The long-lasting preference of academic anthropology, thinking predominantly in the mind-setting of white-western-man, is more and more resolved by extending anthropology from academia to application, from man into the diversity of genders, from western culture into all the other cultures, from single persons to assemblies of diverse gatherings living an ongoing discourse with a growing publicity.
This widening of anthropological subjects and methods calls naturally for more interdisciplinarity, transdisciplinarity, and of a constructive attitude which looks ahead to possible futures of processes.
Close to this are expressions like collaboration and co-creation with others. In the theory dimension this is reflected by multiperspectivity and a holistic view. In societal development processes — like urban planning — there are different driving forces acting working top-down or acting working bottom-up.
Recommending solutions based on anthropological thinking ending in a yes or no, can be of help and can be necessary because real world processes can not only wait of final answers (which are often not realistic), they need again and again decisions to proceed now.
REFLECTIONS FOLLOWING THE INTRODUCTION AND THE CONCLUSION
The just referred texts making a fresh impression of a discipline in a dynamic movement.
General Knowledge Architecture
For the point of view of MMI (Man-Machine Interface, later HMI Human-Machine Interaction, in my theory extended to DAAI Distributed Actor-Actor Interaction) embedded in systems engineering with an openness for the whole context of society and culture arises the question whether such a dynamic anthropology can be of help.
To clarify this question let us have a short look to the general architecture of knowledge.
Within the everyday world philosophy can be understood as the most general point of view of knowing and thinking. Traditionally logic and mathematics can be understood as part of philosophy although today this has been changed. But there are no real reasons for this departure: logic and mathematics are not empirical sciences and they are not engineering.
Empirical science can be understood as specialized extension of philosophical thinking with identifiable characteristics which allow to differentiate to some extend different disciplines. Traditionally all the different disciplines of empirical science have a more theoretical part and a more applied part. But systematically they depend from each other. A theory is only an empirical one, if there exists a clear relationship to the everyday world, and certain aspects of the everyday world are only theoretical entities (data) if there exists a relationship to an explicit theory which gives a formal explanation.
Asking for a systematic place for engineering it is often said, that it belongs to the applied dimension of empirical science. But engineering has realized processes, buildings, machines long before there was a scientific framework for to do this, and engineering uses in its engineering processes lots of knowledge which is not part of science. On the other side, yes, engineering is using scientific knowledge as far as it is usable and it is also giving back many questions to science which are not yet solved sufficiently. Therefore it is sound to locate engineering besides science, but being part of philosophy dealing with the practical dimensions of life.
What About Anthropology?
While philosophy (with logic and mathematics) is ‘on top’ of empirical science and engineering, it is an interesting question where to place anthropology?
While empirical science as well as engineering are inheriting all what philosophy provides remains the question whether anthropology is more an empirical science or more engineering or some kind of a hybrid system with roots in empirical science as well as in engineering?
Looking back into history it could arise the impression that anthropology is more a kind of an empirical science with strong roots in academia, but doing fieldwork to feed the theories.
Looking to the new book it could support the image that anthropology should be more like engineering: identifying open problems in society and trying to transform these problems — like engineers — into satisfying solutions, at least on the level of counseling.
Because in our societies the universities have traditionally a higher esteem then the engineers — although the engineers are all trained by highly demanding university courses — it could be a bias in the thinking of anthropologist not to think of their discipline as engineering.
If one looks to the real world than everything which makes human societies livable is realized by engineers. Yes, without science many of the today solutions wouldn’t be possible, but no single scientific theory has ever enabled directly some practical stuff. And without the engineers there would not exist any of the modern machines used for measurements and experiments for science. Thus both are intimately interrelated: science inspires engineering and engineering inspires and enables science, but both are genuinely different and science and engineering play their own fundamental role.
Thus if I am reading the new book as engineer (attention: I am also a philosopher and I am trained in the Humanities too!) then I think there are more arguments to understand anthropology as engineering than as a pure empirical science. In the light of my distributed actor-actor interaction paradigm, which is a ‘spinoff’ of engineering and societal thinking it seems very ‘naturally’ to think of anthropology as a kind of social engineering.
Let us discuss both perspectives a bit more, thereby not excluding the hybrid version.
1) Anthropology as Engineering
The basic idea of engineering is to enable a change process which is completely transparent in all respects: Why, Who, Where, When, How etc. The process starts with explicit preferences turning some known reality into a problem on account of some visions which have been imagined and which have become ranked higher than the given known reality. And then the engineers try to organized an appropriate change process which will lead from the given situation to a new situation until some date in the future where the then given situation — the envisioned goal state — has become real and the situation from the beginning, which has been ranked down, has disappeared, or is at least weakened in a way that one can say, yes, it has changed.
Usually engineers are known to enable change processes which enable the production of everyday things (tools, products, machines, houses, plants, ships, airplanes, …), but to the extend that the engineering is touching the everyday life deeper and deeper (e.g. the global digital revolution absorbing more and more from the real life processes by transforming them into digital realities forcing human persons to act digitally and not any more with their bodies in the everyday world) the sharp boundary between engineering products and the societal life of human persons is vanishing. In such a context engineering is becoming social engineering even if the majority of traditional engineers this doesn’t see yet in this way. As the traditional discipline MMI Man-Machine Interface and then expanded to HMI Human-Machine Interaction and further morphed into DAAI Distributed Actor-Actor Interaction this already manifests, that the realm of human persons, yes the whole of society is already included in engineering. The border between machines and human actors is already at least fuzzy and the mixing of technical devices and human actors (as well as all other biological actors) has already gained a degree which does not allow any longer a separation.
These ideas would argue for the option to see anthropology as social engineering: thematizing all the important visions which seem to be helpful or important for a good future of modern mankind, and to help to organize change processes, which will support approaching this better future. That these visions can fail, can be wrong is part of the ever lasting battle of the homo sapiens to gain the right knowledge.
2) Anthropology as an Empirical Science
… to be continued …
3) Anthropology as a Hybrid Couple of Science and Engineering
… to be continued …
Integrating Engineering and the Human Factor (info@uffmm.org) eJournal uffmm.org ISSN 2567-6458
