A General Theory of Knowledge

Listening to Theodorakis & Ritsos: Lianotragouda

There is a General Theory of Knowledge (GTOK) implicit in former weblog entries. It can better be made explicit. Let me first draw the diagram and then discuss it. Relevant weblogs are:

A General Theory of Knowledge (GTOK)

A General Theory of Knowledge (GTOK)

The diagram with above weblog entries is rather self-explanatory.

  • What I may need to explain as an author is how this relates to my own work.
  • A nice introduction to epistemology, at the level of the international baccalaureate (IB) programme is the book by Richard van de Lagemaat (CUP, now a new 2015 edition).
  • A general principle is that philosophy should use mathematics education as its empirical field of reference. When philosophy hangs in the air then it is at risk of getting lost. The education of mathematics has adequate challenge for dealing with abstract notions.

Some main steps in the diagram are:

  1. Jean Piaget introduced stages of development. Epistemology tends to focus on the last stage, with a fully developed rational being who wonders what can be known and how this can be achieved. It makes sense to distinguish stages in such questions however. Pierre van Hiele removed Piaget’s dependence of stages upon age, and turned the issue into a logical framework for epistemology. With the Definition & Reality methodology this framework is also empirically relevant. This is also very useful for the link of philosophy to education. See Pierre van Hiele and epistemology.
  2. Karl Popper turned Otto Selz’s methodology for psychology into a philosophy of science in general. This uses falsifiability as a demarcation between science and non-science. Since the Anglo-saxon world tends to distinguish science and the humanities (humaniora), the general term “theory of knowledge” (epistemology) will do.
  3. Selz inspired Adriaan de Groot to create his experiments with chess masters. Later De Groot continued in methodology, and it seems that he is the one who introduced the empirical cycle. His book Methodologie ends in depressing awareness that science cannot establish truth as in mathematics. Thus De Groot advances the uplifting Forum Theory, that focuses on the rules of conduct within the scientific community. While we may not discover the real truth we still can ask why we should trust these guys and gals.
  4. De Groot and Van Hiele were also inspired by their UvA math teacher Gerrit Mannoury (1867–1956). See this project about Mannoury and significa.
  5. The dashed arrow from Van Hiele to De Groot is the unfortunate failed transfer of the theory of levels of insight. De Groot refers to the thesis but missed this notion, see this discussion.
  6. My book A Logic of Exceptions (ALOE) (1981, 2007, 2011) is already deep into methodology. ALOE looks into the logical paradoxes and suggests that empirical sense may help to get rid of mathematical nonsense. There is a distinction between Gödel’s theorems and the interpretation that he gave to them. For the issue of volition, determinism and chance there is no experiment that allows to distinguish what is empirically the case. (I haven’t yet looked at the interpretation of the recent experiment with Bell’s equation at TU Delft, see the websites by Ronald Hanson and Richard Gill.)
  7. The abbreviation DRGTPE stands for the book Definition & Reality in the General Theory of Political Economy. This 2000, 2005, 2011 book had a precursor already called Background Papers to DRGTPE that collected papers from 1989-1992. This essentially gave the framework for political economy, in both mathematical model and empirical methodology. The 1994 book Trias Politica & Centraal Planbureau (TP & CPB) (in Dutch) referred to De Groot’s Forum Theory to clinch the argument for an Economic Supreme Court (ESC). Subsequently, DRGTPE 2000 contains a constitutional amendment how the ESC should satisfy such Forum rules.
  8. The news in November 2015 is that I have grown more aware of the importance of Forum Theory for the selection of definitions for applications. This element is implicit in the earlier development but it is useful to state it explicitly, given the importance of the role of definitions. Research groups might be characterised by the definitions that they select. It can depend upon the quality of the rules how flexible research groups are with experiments and adverse information.

Thus, to restate in text what is depicted in the last box in the diagram: This 2015 GTOK has the standard logic (with ALOE), methodology (with Forum Theory), and epistemology, and has more awareness of:

  • levels of insight or understanding
  • Definition & Reality methodology
  • Forum Theory is especially required for the application of definitions.

Some applications of this GTOK are:

(1) My forecast in 1990 (CPB memo 90-III-38) was that unemployment would continue to be high unless Parliament would redesign both the structure of policy making and some policies and markets. I repeated this forecast in 1992, 1994, 2000 extending with other risks like on environment and financial markets, and the condition of the Economic Supreme Court. In the period 1990-2007 Holland seemed to have a lower level of unemployment, which might be a cause for people not paying attention to the analysis. This lower level wasn’t achieved by better policies but by welfare payments (financed by natural gas) and by exporting unemployment by means of maintaining low wages (beggar thy neighbour). The 2007+ crisis and return to higher unemployment confirms my analysis. Though a major element relies on definitions, the forecast as a whole still was falsifiable. Of course the forecast was vague, and not specified with the year 2007, but we are dealing with structure. This also explains why I emphasize that Dirk Bezemer misinforms Sweden and Dutch Parliament: because he keeps silent about the theoretical confirmation given by the empirical experiment of 1990-2007.

(2) The scheme allows us to deal with the confusions by Stellan Ohlsson (abstract to concrete) and Ben Wilbrink (Van Hiele’s theory of levels wouldn’t be empirical).

(3) The scheme allows us to deal with the problem of universals. Van Hiele “demonstrated” the general applicability of the theory of levels by using the example of geometry. (And geometry uses demonstration as a method of proof too.) He mentioned that the theory had general applicability and mentioned chemistry and didactics as other examples, without working out those examples. Freudenthal neglected Van Hiele’s general claim, put him into the box of “geometry only”, and claimed that he, Freudenthal himself, had shown the applicability to mathematics in general. (See here.) Of course, Freudenthal also had the problem that a universal proof is impossible, since you would need to check each field of knowledge. However, now with the definition  reality methodology, we can take the levels of insight as a matter of definition. Like the law of conservation of energy defines what we regard as “energy”. The problem shifts to application. For this, there is Forum theory.


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