COMMON SCIENCE as Sustainable Applied Empirical Theory, besides ENGINEERING, in a SOCIETY

eJournal: uffmm.org
ISSN 2567-6458, 19.Juni 2022 – 15.September 2022
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

This is work in progress:

  1. The whole text shows a dynamic, which induces many changes. Difficult to plan ‘in advance’.
  2. Perhaps, some time, it will look like a ‘book’, at least ‘for a moment’.

CONTEXT and 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

  1. 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.”)
  2. 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.”)
  3. 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’.
  4. 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.“)
  5. 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])”)
  6. 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. )
  7. !!! From here all the following chapters have to be re-written !!!
  8. THE LOGIC OF EVERYDAY THINKING. Lets try an Example (Will probably be re-written too)
  9. 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.)
  10. … more re-writing will probably happen …
  11. Everyday Language: German Example
  12. Everyday Language: English
  13. Natural Logic
  14. Predicate Logic
  15. True Statements
  16. Formal Logic Inference: Preserving Truth
  17. Ordinary Language Inference: Preserving and Creating Truth
  18. Hidden Ontologies: Cognitively Real and Empirically Real
  19. AN INFERENCE IS NOT AUTOMATICALLY A FORECAST
  20. EMPIRICAL THEORY
  21. Side Trip to Wikipedia
  22. SUSTAINABLE EMPIRICAL THEORY
  23. CITIZEN SCIENCE 2.0
  24. … ???

COMMENTS

wkp-en := Englisch Wikipedia

/* 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 = “Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.[1][2]

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 testable conjectures, and from scientific laws, which are descriptive accounts of the way nature behaves under certain conditions.”

Citation = “New knowledge in science is advanced by research from scientists who are motivated by curiosity about the world and a desire to solve problems.[27][28] Contemporary scientific research is highly collaborative and is usually done by teams in academic and research institutions,[29] government agencies, and companies.[30][31] The practical impact of their work has led to the emergence of science policies that seek to influence the scientific enterprise by prioritizing the ethical and moral development of commercial productsarmamentshealth carepublic infrastructure, and environmental protection.”

[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.”

[4] Scientific theory, see: wkp-en: https://en.wikipedia.org/wiki/Scientific_theory

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 testable conjectures, 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

[25] Sustainable Development in wkp-en: https://en.wikipedia.org/wiki/Sustainable_development

[26] Marope, P.T.M; Chakroun, B.; Holmes, K.P. (2015). Unleashing the Potential: Transforming Technical and Vocational Education and Training (PDF). UNESCO. pp. 9, 23, 25–26. ISBN978-92-3-100091-1.

[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.

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Is Mathematics a Fake? No! Discussing N.Bourbaki, Theory of Sets (1968) – Introduction

eJournal: uffmm.org, ISSN 2567-6458,
6.June 2022 – 13.June 2022, 10:30h
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

SCOPE

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.

COMMENTS

Def: wkp := Wikipedia; en := English

[1a] Bourbaki Group, see: https://en.wikipedia.org/wiki/Nicolas_Bourbaki

[1b] Theory of Sets with a chapter about structures, see: https://en.wikipedia.org/wiki/%C3%89l%C3%A9ments_de_math%C3%A9matique

[2] Gerd Doeben-Henisch, “Extended Concept for Meaning Based Inferences, Version 1”, August 2020, see: https://www.uffmm.org/wp-content/uploads/2020/08/TruthTheoryExtended-v1.pdf

[3] Gerd Doeben-Henisch, “From SYSTEMS Engineering to THEORY Engineering”, June 2022, see: https://www.uffmm.org/2022/05/26/from-systems-engineering-to-theory-engineering/

[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)

THE OKSIMO CASE as SUBJECT FOR PHILOSOPHY OF SCIENCE. Part 1

eJournal: uffmm.org
ISSN 2567-6458, 22.March – 23.March 2021
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

CONTEXT

This text is part of a philosophy of science  analysis of the case of the oksimo software (oksimo.com). A specification of the oksimo software from an engineering point of view can be found in four consecutive  posts dedicated to the HMI-Analysis for  this software.

THE OKSIMO EVENT SPACE

The characterization of the oksimo software paradigm starts with an informal characterization  of the oksimo software event space.

EVENT SPACE

An event space is a space which can be filled up by observable events fitting to the species-specific internal processed environment representations [1], [2] here called internal environments [ENVint]. Thus the same external environment [ENV] can be represented in the presence of  10 different species  in 10 different internal formats. Thus the expression ‘environment’ [ENV] is an abstract concept assuming an objective reality which is common to all living species but indeed it is processed by every species in a species-specific way.

In a human culture the usual point of view [ENVhum] is simultaneous with all the other points of views [ENVa] of all the other other species a.

In the ideal case it would be possible to translate all species-specific views ENVa into a symbolic representation which in turn could then be translated into the human point of view ENVhum. Then — in the ideal case — we could define the term environment [ENV] as the sum of all the different species-specific views translated in a human specific language: ∑ENVa = ENV.

But, because such a generalized view of the environment is until today not really possible by  practical reasons we will use here for the beginning only expressions related to the human specific point of view [ENVhum] using as language an ordinary language [L], here  the English language [LEN]. Every scientific language — e.g. the language of physics — is understood here as a sub language of the ordinary language.

EVENTS

An event [EV] within an event space [ENVa] is a change [X] which can be observed at least from the  members of that species [SP] a which is part of that environment ENV which enables  a species-specific event space [ENVa]. Possibly there can be other actors around in the environment ENV from different species with their specific event space [ENVa] where the content of the different event spaces  can possible   overlap with regard to  certain events.

A behavior is some observable movement of the body of some actor.

Changes X can be associated with certain behavior of certain actors or with non-actor conditions.

Thus when there are some human or non-human  actors in an environment which are moving than they show a behavior which can eventually be associated with some observable changes.

CHANGE

Besides being   associated with observable events in the (species specific) environment the expression  change is understood here as a kind of inner state in an actor which can compare past (stored) states Spast with an actual state SnowIf the past and actual state differ in some observable aspect Diff(Spast, Snow) ≠ 0, then there exists some change X, or Diff(Spast, Snow) = X. Usually the actor perceiving a change X will assume that this internal structure represents something external to the brain, but this must not necessarily be the case. It is of help if there are other human actors which confirm such a change perception although even this does not guarantee that there really is a  change occurring. In the real world it is possible that a whole group of human actors can have a wrong interpretation.

SYMBOLIC COMMUNICATION AND MEANING

It is a specialty of human actors — to some degree shared by other non-human biological actors — that they not only can built up internal representations ENVint of the reality external to the  brain (the body itself or the world beyond the body) which are mostly unconscious, partially conscious, but also they can built up structures of expressions of an internal language Lint which can be mimicked to a high degree by expressions in the body-external environment ENV called expressions of an ordinary language L.

For this to work one  has  to assume that there exists an internal mapping from internal representations ENVint into the expressions of the internal language   Lint as

meaning : ENVint <—> Lint.

and

speaking: Lint —> L

hearing: Lint <— L

Thus human actors can use their ordinary language L to activate internal encodings/ decodings with regard to the internal representations ENVint  gained so far. This is called here symbolic communication.

NO SPEECH ACTS

To classify the occurrences of symbolic expressions during a symbolic communication  is a nearly infinite undertaking. First impressions of the unsolvability of such a classification task can be gained if one reads the Philosophical Investigations of Ludwig Wittgenstein. [5] Later trials from different philosophers and scientists  — e.g. under the heading of speech acts [4] — can  not fully convince until today.

Instead of assuming here a complete scientific framework to classify  occurrences of symbolic expressions of an ordinary language L we will only look to some examples and discuss these.

KINDS OF EXPRESSIONS

In what follows we will look to some selected examples of symbolic expressions and discuss these.

(Decidable) Concrete Expressions [(D)CE]

It is assumed here that two human actors A and B  speaking the same ordinary language L  are capable in a concrete situation S to describe objects  OBJ and properties PROP of this situation in a way, that the hearer of a concrete expression E can decide whether the encoded meaning of that expression produced by the speaker is part of the observable situation S or not.

Thus, if A and B are together in a room with a wooden  white table and there is a enough light for an observation then   B can understand what A is saying if he states ‘There is a white wooden table.

To understand means here that both human actors are able to perceive the wooden white table as an object with properties, their brains will transform these external signals into internal neural signals forming an inner — not 1-to-1 — representation ENVint which can further be mapped by the learned meaning function into expressions of the inner language Lint and mapped further — by the speaker — into the external expressions of the learned ordinary language L and if the hearer can hear these spoken expressions he can translate the external expressions into the internal expressions which can be mapped onto the learned internal representations ENVint. In everyday situations there exists a high probability that the hearer then can respond with a spoken ‘Yes, that’s true’.

If this happens that some human actor is uttering a symbolic expression with regard to some observable property of the external environment  and the other human actor does respond with a confirmation then such an utterance is called here a decidable symbolic expression of the ordinary language L. In this case one can classify such an expression  as being true. Otherwise the expression  is classified as being not true.

The case of being not true is not a simple case. Being not true can mean: (i) it is actually simply not given; (ii) it is conceivable that the meaning could become true if the external situation would be  different; (iii) it is — in the light of the accessible knowledge — not conceivable that the meaning could become true in any situation; (iv) the meaning is to fuzzy to decided which case (i) – (iii) fits.

Cognitive Abstraction Processes

Before we talk about (Undecidable) Universal Expressions [(U)UE] it has to clarified that the internal mappings in a human actor are not only non-1-to-1 mappings but they are additionally automatic transformation processes of the kind that concrete perceptions of concrete environmental matters are automatically transformed by the brain into different kinds of states which are abstracted states using the concrete incoming signals as a  trigger either to start a new abstracted state or to modify an existing abstracted state. Given such abstracted states there exist a multitude of other neural processes to process these abstracted states further embedded  in numerous  different relationships.

Thus the assumed internal language Lint does not map the neural processes  which are processing the concrete events as such but the processed abstracted states! Language expressions as such can never be related directly to concrete material because this concrete material  has no direct  neural basis.  What works — completely unconsciously — is that the brain can detect that an actual neural pattern nn has some similarity with a  given abstracted structure NN  and that then this concrete pattern nn  is internally classified as an instance of NN. That means we can recognize that a perceived concrete matter nn is in ‘the light of’ our available (unconscious) knowledge an NN, but we cannot argue explicitly why. The decision has been processed automatically (unconsciously), but we can become aware of the result of this unconscious process.

Universal (Undecidable) Expressions [U(U)E]

Let us repeat the expression ‘There is a white wooden table‘ which has been used before as an example of a concrete decidable expression.

If one looks to the different parts of this expression then the partial expressions ‘white’, ‘wooden’, ‘table’ can be mapped by a learned meaning function φ into abstracted structures which are the result of internal processing. This means there can be countable infinite many concrete instances in the external environment ENV which can be understood as being white. The same holds for the expressions ‘wooden’ and ‘table’. Thus the expressions ‘white’, ‘wooden’, ‘table’ are all related to abstracted structures and therefor they have to be classified as universal expressions which as such are — strictly speaking —  not decidable because they can be true in many concrete situations with different concrete matters. Or take it otherwise: an expression with a meaning function φ pointing to an abstracted structure is asymmetric: one expression can be related to many different perceivable concrete matters but certain members of  a set of different perceived concrete matters can be related to one and the same abstracted structure on account of similarities based on properties embedded in the perceived concrete matter and being part of the abstracted structure.

In a cognitive point of view one can describe these matters such that the expression — like ‘table’ — which is pointing to a cognitive  abstracted structure ‘T’ includes a set of properties Π and every concrete perceived structure ‘t’ (caused e.g. by some concrete matter in our environment which we would classify as a ‘table’) must have a ‘certain amount’ of properties Π* that one can say that the properties  Π* are entailed in the set of properties Π of the abstracted structure T, thus Π* ⊆ Π. In what circumstances some speaker-hearer will say that something perceived concrete ‘is’ a table or ‘is not’ a table will depend from the learning history of this speaker-hearer. A child in the beginning of learning a language L can perhaps call something   a ‘chair’ and the parents will correct the child and will perhaps  say ‘no, this is table’.

Thus the expression ‘There is a white wooden table‘ as such is not true or false because it is not clear which set of concrete perceptions shall be derived from the possible internal meaning mappings, but if a concrete situation S is given with a concrete object with concrete properties then a speaker can ‘translate’ his/ her concrete perceptions with his learned meaning function φ into a composed expression using universal expressions.  In such a situation where the speaker is  part of  the real situation S he/ she  can recognize that the given situation is an  instance of the abstracted structures encoded in the used expression. And recognizing this being an instance interprets the universal expression in a way  that makes the universal expression fitting to a real given situation. And thereby the universal expression is transformed by interpretation with φ into a concrete decidable expression.

SUMMING UP

Thus the decisive moment of turning undecidable universal expressions U(U)E into decidable concrete expressions (D)CE is a human actor A behaving as a speaker-hearer of the used  language L. Without a speaker-hearer every universal expressions is undefined and neither true nor false.

makedecidable :  S x Ahum x E —> E x {true, false}

This reads as follows: If you want to know whether an expression E is concrete and as being concrete is  ‘true’ or ‘false’ then ask  a human actor Ahum which is part of a concrete situation S and the human actor shall  answer whether the expression E can be interpreted such that E can be classified being either ‘true’ or ‘false’.

The function ‘makedecidable()’ is therefore  the description (like a ‘recipe’) of a real process in the real world with real actors. The important factors in this description are the meaning functions inside the participating human actors. Although it is not possible to describe these meaning functions directly one can check their behavior and one can define an abstract model which describes the observable behavior of speaker-hearer of the language L. This is an empirical model and represents the typical case of behavioral models used in psychology, biology, sociology etc.

SOURCES

[1] Jakob Johann Freiherr von Uexküll (German: [ˈʏkskʏl])(1864 – 1944) https://en.wikipedia.org/wiki/Jakob_Johann_von_Uexk%C3%BCll

[2] Jakob von Uexküll, 1909, Umwelt und Innenwelt der Tiere. Berlin: J. Springer. (Download: https://ia802708.us.archive.org/13/items/umweltundinnenwe00uexk/umweltundinnenwe00uexk.pdf )

[3] Wikipedia EN, Speech acts: https://en.wikipedia.org/wiki/Speech_act

[4] Ludwig Josef Johann Wittgenstein ( 1889 – 1951): https://en.wikipedia.org/wiki/Ludwig_Wittgenstein

[5] Ludwig Wittgenstein, 1953: Philosophische Untersuchungen [PU], 1953: Philosophical Investigations [PI], translated by G. E. M. Anscombe /* For more details see: https://en.wikipedia.org/wiki/Philosophical_Investigations */