November 2, 2010


ME + me: Wittgenstein in fashion...?

I continue being not well, and otherwise also as before, so I cannot do much. However, now and then I can do a little more. Being a philosopher, I felt inspired to take up my edition and notes on Wittgenstein's Tractatus (Logico-Philosophicus). The links just given are to the Wikipedia; and this is
The beginning of my translation and comments, with here the complete text of the Tractatus, and here my Wittgenstein-index.

Today there is more of the same and I inserted several of the summaries I promised yesterday. Also my title may remind a few Dutchman of a booklet by the Dutch author Willem Frederik Hermans, "Wittgenstein de mode en Kazemier niet", first published in 1967, which means in English "Wittgenstein in fashion and Kazemier not".

Dutch readers may consult the last link, which gives some more information about the book, the author and his ideas about Wittgenstein, all in Dutch. Incidentally, I have the second edition, which has the words "en Kazemier niet", which were absent in the first. The reason is that a Dutch professor of philosophy Kazemier, unknown before and after the event, had published some criticisms of Hermans, who at the time was one of Holland's best known authors, and Hermans did not like the criticism.

Also, it is true that at the time there was a bit of a Wittgenstein fashion at the time in Holland, although it also would be easy to exaggerate it, for example because it mostly was indeed a fashion: Most who wrote about Wittgenstein at the time hardly understood his work and knew little about his person, and only jumped on a bandwagon to be with it, and besides very soon after that fashion Marcuse and Marx came in fashion in Holland, who immediately - as the phrase then was and remained for decades - were deemed to be far more "socially relevant" ("maatschappelijk relevant", in Dutch) than anything else, implying in the average Dutch mind a moral excellence equal to their "social relevance", and Wittgenstein was soon after 1967 mostly forgotten again, and indeed is not an easy author whatever one thinks of him.

The main reason for my title of today is that I found this morning that I had 610 different visitors yesterday, which is almost 200 more than the daily avarage, and found that most of my readers yesterday read (about) Multatuli or Wittgenstein on my site, which was a pleasing discovery.

What this really means I don't know, but I do know that my extensive comments on either author are good, and that I know nothing like them, which was the main reason to write them, apart from the facts that Multatuli is one of my favourite authors and the only Dutch author I can read for hours without belly aches, and that Wittgenstein interested me a lot when I was between 17 and 20, because he was the first philosopher I knew of who had a serious interest in logic.

So today I uploaded more of and about Wittgenstein, namely my summaries of some of my own comments.

Here is the first such summary, just in case you are curious. It concerns the theses that have 2.01 as the beginning of their number - and if you have plowed through this, or skip to the end, you may find what you may learn from it. Incidentally, the links in it link to my Philosophical Dictionary and should be helpful.

What Wittgenstein tries to do in the theses (2.01..) at least in part amounts to articulating the foundations of what is now known as model-theory. This was effectively started by Gödel, Tarski and Mal'cev in the 1930ies, and became a specialism in mathematical logic in the 1950ies.

In this summary of the theses (2.01..) I'll say something about

1. What Wittgenstein was trying to do
2. The approach of model-theory
3. Some general theses about language and reality

1. What Wittgenstein was trying to do

What Wittgenstein was trying to do in (2.01..) and indeed in a considerable part of the Tractatus was to give a better explanation for what logic is and does than was given by Whitehead and Russell in the Principia Mathematica and probably also than by Frege in Grundgesetze der Arithmetik.

The first was especially needed, for close readers of the PM (Principia Mathematica) know that its introduction is not clear about quite a number of things it should have addresssed and explained in natural language - propositional functions, variables, truth, the theory of types, classes, paradoxes - than happens there.

It is not clear to me how much Wittgenstein knew of Frege's writings, that were all published before Russell's "Principles of Mathematics" and Whitehead and Russell's in the Principia Mathematica, and that were in the 20th Century discovered to be more clear and more useful than what Russell and Whitehead published about the foundations of logic and the relation of language and thought to reality and to mathematics.

It seems probable to me that in fact W. had not read most of Frege's writings about semantics, and also that he did not get far in the Grundgesetze der Arithmetik, that indeed is written in a quite forbidding symbolism.

In any case, what W. was trying to do can be outlined briefly as follows:

The PM, indeed following Frege for the most part, had analysed statements a consisting of (i) logical terms, like "not", "and", "all" and "is equal to" (ii) subject-terms, like "Aristotle", "Greeks", and "Zeus" (iii) predicate terms, like "human", "loves", "is greater than", and had schematized this by introducing abbreviating terms and logical rules and assumptions for these and some related terms.

Most of the rest of natural language and grammatical categories were abstracted from, which is to say that, if they occured were forced into the above schematism - which in Whitehead and Russell's use of it, as also in Frege's, had the great merit of articulating fairly to very precisely what the rules of inference, statements and terms of the surrected formal systems are and what is a proof for a statement in the language of the formal theory, and besides consisted of axioms that were or seemed adequate to state all or nearly all mathematics in, in the sense that it allowed the derivation of mathematics in the formal and logical systems that Frege and Whitehead and Russell had created for that purpose, namely to show that mathematics can be derived from logic, in the sense Frege and Whitehead and Russell believed they had codified it formally in their systems.

As it happens, Frege's system was shown to be inconsistent by Russell (but much later shown to be repairable and then to do what Frege had claimed for his system - see Boolos); Whitehead and Russell's system was shown to be much more complicated than necessary (see Ramsey); and in any case few mathematicians or philosophers agreed with Frege, Russell and Whitehead that mathematics was in fact nothing but logic.

The reason for the last disagreement was mostly that both Frege and Russel and Whitehead had found it necessary to assume at least one axiom that was not properly logical in any clear sense at all, such as an axiom of infinity: While it seems as if mathematics needs the concept of infinity to make sense of differential and integral calculus and of infinite series (such as 1/2+1/4+1/8+ ..+1/2n i+ ...) it also seems intuitively quite evident that the statement that there is an infinity of things, however much it may be needed for mathematics, is not really a logical assumption or axiom. And if it is not, then no proof that most or all of mathematics can be restated in the terms of the systems of Frege or Whitehead and Russell, which is true, and derived with the help of its axioms and principles of inference, which is also true, can be a proof that mathematics is nothing but logic.

To return to what Wittgenstein was trying to do:

To articulate clearly how statements involving logical operators, subjects and predicates may be able to represent anything, whether thoughts, facts or things, and indeed what are the assumptions involved in the logically and mathematically presumed apparatus of logical operators, subjects, predicates and formal proofs.

2. The approach of model-theory

In fact, Wittgenstein did not get far, and his explanations, that are mostly in terms of (i) the picture theory of meaning (statements are like pictures in representing whatever they represent) and (ii) tautologies and identities (the statements of logic and mathematics are true because they cannot be false and hold in any possible case, which is also what distinguishes them from other kinds of statements) were mostly not correct.

That is, more precisely: The picture theory of meaning as an explanation of how language succeeds in representing ideas and things was soon rejected by nearly everyone including Wittgenstein, and while W. had hit upon an important insight about mathematics and logic with his notion that these were - at least: the logiical statements - characterized by being true in all possible circumstances, unlike statements of fact, that are true only if the facts exist, and false otherwise, he did not clearly work out this insight.

In fact, something like it was worked out by the founders of model theory, that did succeed in providing a fairly clear semantics for formal languages, mostly in the 1950ies and 1960ies, after Wittgenstein's death, and with little or no inspiration from the Tractatus, and also in a somewhat peculiar fashion, that probably would not have found approval in Wittgenstein's eyes.

The fashion in which this happened was in fact that a formal language was supposed to be about sets or classes of things, and that one could elucidate what a formal language and its axioms amounted to by showing how the terms, axioms and statements of the language could be articulated in set theory, that then also could be used to prove statements about the statements and properties of the formal language (thus practising what was often called "metamathematics" or "metalogic", since it consisted of mathematical or logical statements and proofs about systems of mathematics and logic).

Formally and mathematically, model theory goes quite far and is able to shed considerable light on what a formal system in fact states and cannot state.

The two conceptual difficulties that remain are that (1) this in fact explains mathematics and logic in terms of set theory - which seems to need explanations themselves, and that (2) in many texts of model theory it is not clear what is really happening in terms of logic.

Both points involve a certain amount of circularity and circular reasoning, that indeed probable is unavoidable in principle (it is rather similar to one's needing the idea of meaning to explain the idea of meaning, and the idea of truth to explain truth).

The first point, that model theory does little more than reduce or explain logic and mathematics in terms of set theory is normally met by the claim that set theory is mathematics or embodies it, and cannot be avoided in clarifying what mathematics is - which is OK as far as it goes, but doesn't go very far since in the end it must assume set theory as fundamentally clear and given, which it isn't, and besides there are other foundations of mathematics than set theory, such as combinatory logic or systems of lambda calculus, that are as powerful as settheory mathematically speaking, while suggesting quite other approaches to semantics.

The second point is a major shortcoming that is rarely avoided, and notably it often is not clear what "the models" of model theory really are: Sets of real things; sets of ideas; sets of functions relating strings to some set of things called a domain again represented as a term in the set theory that is said to be a model for the formal system it is interpreting by mapping it to set-theoretical constructs...

In brief, things can get quite confusing, also because often the verbal introductions to the mathematics or logic of model theory are far from clear or unambiguous. ("Beginning Model Theory" by Jane Bridges is clear in most respects, but still is confusing if one is not aware of what has been said here.)

3. Some general theses about language and reality

As I said, W. tried in (2.01..) and indeed all of (2...) to explain how the logically and mathematically presumed apparatus of logical operators, subjects, predicates and formal proofs such as one can find in Whitehead and Russell's Principia Mathematica are capable of saying anything about reality, and about how language, ideas and the facts and processes of the real world are related.

Unfortunately, most of W.'s explanations involve his picture theory of meaning, and the idea that somehow reality has the same sort of structure as predicate and propositional logic: It consists of facts, which are whatever makes statements true, and it consists of objects as referred to by subject terms, and of forms as referred to by predicate terms, and that is about it, as far as W. was concerned, besides rather a lot more about this somehow "showing itself" in and through language without being articulable in language, which in turn propped up Wittgenstein's peculariar Wittgensteinian "mysticism". (Both will crop up later in the Tractatus.)

Here I will repeat and extend a number of points I made in my notes to (2.01..)

2. The correspondence theory of truth is presumed:

Statements represent because the subject-terms in the statements represent individual things or classes of things; the predicate-terms in the statement represent stuctures or classes of things; while - and here is a statement of the correspondence theory of truth - a statement is true precisely if the things represented by its subject-terms are related as or have the properties stated by the predicate term(s) in the statement: "Snow is white" is true precisely if indeed whatever is referred to by "Snow" indeed is one of the (sets of) things that is referred to by "white", and is false otherwise (namely in particular if something correctly called by the term "snow" is not something that is correctly called by the term "white").

In fact, this is not articulated clearly by Wittgenstein at all, but he probably did have a fair inkling of it, and indeed it was articulated first in the 1920ies, quite probably in part because some mathematicians tried to formally restate what is involved in the correspondence theory of truth. (See Tarski.)

2.011. To try to explain how human beings can learn anything at all with the help of language, the the Finite Characteristic Properties thesis is useful:

  • every (kind of) thing has some characteristic properties, and
  • the number of characteristic properties of a thing is finite, and
  • a (kind of) thing's characteristic properties are those properties which determine when
    anything is that (kind of) thing, and
  • a (kind of) thing's characteristic properties determine which structures it may be part of.

Indeed, this seems to be embodied in natural language, for this is used normally as if the FCP is true:

  1. All reasoning must start from assumptions, and all learning must involve the principle that one must try out what seems sensible and give up what doesn't work, and many things do seem to come in kinds,
  2. in language we proceed as if FCP is true, and that FCP, if true, explains at least to some extent why we can know what the world is like, and
  3. it seems that our perceptive system involves a similar principle, i.e. we recognize and
    reidentify perceptions as being identical or similar to other perceptions on the basis of a finite set of properties (perceptual features), and
  4. it can be proved - see e.g. Keynes and Broad - that if the FCP is true for real things, then some inductive generalizations may be supported, i.e. if the FCP is true, then we can learn from experience.
  5. The FCP goes some way in the direction of explaining and supporting kinds of things.

2.0121: An important principle involved in theorizing and talking of almost all kinds is the principle of adequacy:

  • The world may be and indeed seems to be such as to enable us to acquire sufficient true information about at least some of its constituents and their ways of behaviour so as to be adequate to some of our purposes, namely in the sense that we more often than not can realize our ends on the basis of very partial knowledge of all the (possibly) relevant fact - and indeed, after all, everybody who survived in the world such as it is must have guessed rightly often

2.0122: One further reason or assumption that enters into learning what the world is like is this:

  • Relevancy-postulate: As a matter of fact, all contingent facts are relevant to some facts and not relevant to other facts, in the probabilistic sense of "relevant": That learning that P is true, alters the probability that Q is true (making it larger or smaller than it was, which is why P is said to be relevant to Q), while learning that R is true does not alter the the probability that Q is true (which is why R then is said to be irrelevant to Q).

In fact, both relevance and irrelevance are necessary to make any test at all of a statement, since one can only test any particular prediction by assuming it is relevant to some statements, and specifically some statements the truth or falsity can be established empirically, and also one can only test it by assuming that most that happens while one is testing it is not relevant to its truth or falsity (for if anything whatsoever is relevant to anything else whatsoever, there is little chance of making decisive empirical tests).

2.0123: Three further assumptions that enter into the relation of language, though and reality are

  1. Natural kinds of structures: A - mathematically and linguistically - useful assumption is that reality consists of structures that may be sorted in natural kinds, where structures are composite things with interrelated parts, and natural kinds are classes of things with definite antecedents (that bring them about or make them more probable if true) and definite consequents (that they bring about or make more probable if true)
  2. The characteristic properties, and also many other properties of things, are such as to be invariant in time: They last as long as the things last, and therefore allow its being tested and allow the making of predictions and explanations (which are pointless if things can unaccountably change in time), and also is at the basis of making and testing inductive generalizations (to the effect that what has often been seen to be correlated will continue to be correlated, unless there arises a reason it is not).
  3. There is no reason to assume that reality is much like simple predicate or propositional logic - that indeed seem to be mostly as they are because natural language and human minds are as they are: There may be and very probably are far more complicated entities and structures then can be stated by only the logical apparatus involved in First Order Logic, namely things that can only be adequately represented by set theory, mereology, or higher mathematics (fields, differentials, matrices, differential manifolds etc.).

Note that none of the above was clearly seen or stated by W., which is the reason to insert this summary of some of my notes to (2.01..).

Sofar for that summary of my comments on Wittgenstein's theses starting with "2.01..".

If you can't make much of it, I'm sorry - I can only make it clearer by making it longer, and it may be that you need some knowledge of analytic philosophy and of mathematical logic to follow all or be interested at all.

Finally, to make good my promise that I would tell you what you may learn from it:

Either nothing much at all, namely if you are not interested in understanding how language, ideas and reality are or may be related, or else quite a lot, as I believe my comments make Wittgenstein's Tractatus a lot easier to understand, and unlike most commentators on the subject I am not playing academic games, but am only concerned with trying to understand and explain.

Have fun with it, or do something else that you like better!                           

P.S. The beginning of my translation and comments is under the link, and perhaps I should add a little more in clarification:

What there is on the moment is a reworking of my earlier hypertext edition of a series of manuscripts and typescripts on the Tractatus that I wrote mostly between 1967 and 1972 and never did anything with, except show it to a few friends, until I transformed parts of the last typescript to html and put it on line, I think originally in 1997.

That html-version was updated a little bit and reformatted quite a few times to ever new versions of my site, but was hardly changed or corrected, except for a few bits. The translation of the Tractatus in it originally was mine, since when I wrote my comments the Tractatus still was had copyright, and besides I did not like any of the English translations I had seen.

The translation I am using at present is the one to be found at Project Gutenberg but the one in my Notes still is partially mine. Eventually I will review this - health and energy permitting - but for the moment I just use what is there and is ready to be used.

Since I mentioned my health, I should mention that I do not know how long it will take me to finish this, or indeed whether I will finish it at all: With sufficient health I should be able to do it in a week or two; without it I am not able to do it at all.

Finally, a repetition of a remark I made before: Wittgenstein is widely supposed to have been a major philosophical genius. This may be one of the reasons he was and perhaps still is popular, and an explanation for my finding 610 different visitors on the one day I put something about Wittgenstein on line.

My own estimate of Wittgenstein is different from most, though not all: Not entering on the issue of who was and was not a genius, personally I am quite certain that Charles Sanders Peirce and Frank Plumpton Ramsey were considerably greater philosophers, logicians and mathematicians, and are also more interesting philosophers to read (and that especially because Wittgenstein is often far from clear while being quite pretensious, whereas his main thesis is that everybody else made major mistakes in philosophy because they lacked his refined insights into language and logic and because he seemed to have been fond of saying that what can be said at all, can be said clearly - which usually at best and at most is true eventually, after considerable amounts of thinking, rethinking and trying).

So I am not editing my writings about Wittgenstein because I am much interested in Wittgenstein, but because I am much interested in the type of problems and subjects he was interested and wrote about - let's say: the philosophies of science, mathematics, logic and language - and because I think I can clarify his thinking in the Tractatus with my notes, and have myself also interesting remarks to make.

Also, I started on it because I felt a bit better, and felt like doing it, mostly because what I have is good, but does not exist in a good html-edition.

P.P.S. It may be I have to stop Nederlog for a while. The reason is that I am physically not well at all. I don't know yet, but if there is no Nederlog, now you know the reason.

As to ME/CFS (that I prefer to call ME):

1. Anthony Komaroff

Ten discoveries about the biology of CFS (pdf)

3. Hillary Johnson

The Why

4. Consensus (many M.D.s) Canadian Consensus Government Report on ME (pdf)
5. Eleanor Stein

Clinical Guidelines for Psychiatrists (pdf)

6. William Clifford The Ethics of Belief
7. Paul Lutus

Is Psychology a Science?

8. Malcolm Hooper Magical Medicine (pdf)

Short descriptions:

1. Ten reasons why ME/CFS is a real disease by a professor of medicine of Harvard.
2. Long essay by a professor emeritus of medical chemistry about maltreatment of ME.
3. Explanation of what's happening around ME by an investigative journalist.
4. Report to Canadian Government on ME, by many medical experts.
5. Advice to psychiatrist by a psychiatrist who understands ME is an organic disease
6. English mathematical genius on one's responsibilities in the matter of one's beliefs:
   "it is wrong always, everywhere, and for anyone, to believe anything upon
     insufficient evidence
7. A space- and computer-scientist takes a look at psychology.
8. Malcolm Hooper puts things together status 2010.

    "Ah me! alas, pain, pain ever, forever!

No change, no pause, no hope! Yet I endure.
I ask the Earth, have not the mountains felt?
I ask yon Heaven, the all-beholding Sun,
Has it not seen? The Sea, in storm or calm,
Heaven's ever-changing Shadow, spread below,
Have its deaf waves not heard my agony?
Ah me! alas, pain, pain ever, forever!
     - (Shelley, "Prometheus Unbound") 

    "It was from this time that I developed my way of judging the Chinese by dividing them into two kinds: one humane and one not. "
     - (Jung Chang)


See also: ME -Documentation and ME - Resources

Maarten Maartensz

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