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Free Will
Mental Causation
James Symposium
Ludwig Wittgenstein

Wittgenstein's Picture Theory of Language
For Norman Malcolm's Ludwig Wittgenstein: A Memoir, G.H. von Wright wrote a biographical sketch recalling Wittgenstein's inspiration for his idea about language, that a proposition is a picture or model or mirror of reality.
Later he became engrossed in a new problem. It was the question of the nature of the significant proposition. There is a story of how the idea of language as a picture of reality occurred to Wittgenstein. It was in the autumn of 1914 on the Eastern Front, Wittgenstein was reading, in a magazine about a lawsuit in Paris concerning an automobile accident. At the trial a miniature model of the accident was presented before the court. The model here served as a proposition, that is, as a description of a possible state of affairs. It has this function owing to a correspondence between the parts of the model (the miniature-houses, -cars, -people) and things (houses, cars, people) in reality. It now occurred to Wittgenstein that one might reverse the analogy and say that a proposition serves as a model or picture, by virtue of a similar correspondence between its parts and the world. The way in which the parts of the proposition are combined – the structure of the proposition – depicts a possible combination oi elements in reality, a possible state of affairs.

Wittgenstein's Tractatus may be called a synthesis of the theory of truth-functions and the idea that language is a picture of reality.

In his Notebooks entry for September 30, 1914, he wrote

The general concept of the proposition carries with it a quite general concept of the co-ordination of proposition and situation: The solution to all my questions must be extremely simple.

In the proposition a world is as it were put together experimentally. (As when in the law-court in Paris a motor-car accident is represented by means of dolls, etc.1) [Cf. 4.031.]

This must yield the nature of truth straight away (if I were not blind).

Let us think of hieroglyphic writing in which each word is a representation of what it stands for. Let us think also of the fact that actual pictures of situations can be right and wrong. [Cf. 4.016.]

We can compare W's picture-writing Bilderschrift to Frege's concept-writing Begriffsschrift
" " : If the right-hand figure in this picture represents the man A, and the left-hand one stands for the man B, then the whole might assert, e.g.: "A is fencing with B". The proposition in picture-writing can be true and false. It has a sense independent of its truth or falsehood. It must be possible to demonstrate everything essential by considering this case.

It can be said that, while we are not certain of being able to turn all situations into pictures on paper, still we are certain that we can portray all logical properties of situations in a two-dimensional script.

This is still very much on the surface, but we are on good ground.


It can be said that in our picture the right-hand figure is a representation of something and also the left-hand one, but even if this were not the case, their relative position could be a representation of something. (Namely a relation.)


Wittgenstein's was not the first claim that a set of true propositions can contain knowledge of the physical world, that words can describe objects, but his Tractatus was surely the boldest:

Here Wittgenstein imagines a "model" theory, but language does not have a subset of the information in an object
4.01 The proposition is a picture of reality.
        The proposition is a model of the reality as we think it is.

4.11 The totality of true propositions is the whole of natural science
        (or the whole corpus of the natural sciences)

Although language is an excellent tool for human communication, its arbitrary and ambiguous nature makes it ill-suited to represent the world directly. What Wittgenstein saw in the miniature model of the accident at the Paris trial was a dynamic information structure that was partially isomorphic with the information structure of the original accident. Such a model is completely language independent!

It is sad that Wittgenstein proposed a picture theory of language, of language as a mirror of nature. As an excellent aeronautical engineer and architect, he knew that a working model is much more than a picture. He was very impressed by Heinrich Hertz's classic textbook The Principles of Mechanics, in which dynamical models played a large part.

Wittgenstein might have anticipated our information philosophy, which is a model theory of information structures. Today our best models are interactive dynamic computational models visualizable as 3-dimensional animations of physical objects and living beings.

Here Wittgenstein sees that the model must have the same "mathematical multiplicity" or complexity as the state of affairs,
viz., similar information
4.04 In the proposition there must be exactly as many things distinguishable as there are in the state of affairs, which it represents.

They must both possess the same logical (mathematical) multiplicity (cf. Hertz's Mechanics, on Dynamic Models).

But there is no mapping, no isomorphism of information between words (propositions) and objects (states of affairs). The extraordinarily sophisticated connection between a word and object is made in human minds, mediated by the experience recorder and reproducer (ERR) in the mind/brain. Words stimulate some neurons to start firing and to play back relevant experiences including the object. By contrast, a dynamic information model of a part of the world is presented immediately to the mind as a look-alike and act-alike simulation.

Without relevant experience recorded in the mind's ERR, words are mere noise.


By comparison, a photograph or a moving picture with sound can be seen and mostly understood by any human being, independent of their native tongue. The core elements of our information philosophy, models of information structures, go far beyond logic and language as a representation of the fundamental nature of reality.

Computer simulations must of course incorporate all the laws of nature, from the differential equations of quantum physics to the myriad processes of biophysics. At their best, simulations are not only our most accurate knowledge of the world, they are the best teaching tools ever devised. We must use them to transfer that knowledge to the next generation and to most of the world's population via the Internet and our ubiquitous smartphones.

What is knowledge? A subset of the information in information structures.

How do we know it? Information is stored in our minds when our life experiences are recorded by the ERR.

Where is the best knowledge? It used to be in books and the minds of our best teachers. Now it is being spread around the world, accessible from any computer or smartphone. The I-Phi website is a modest contribution.

David Marans' Logic Gallery
See more philosopher profiles at the Logic Gallery by David Marans

For decades, Anglo-American analytic philosophers and ordinary language philosophers have thought that the major problems of philosophy are problems of language and logic, that complete understanding of the natural world could be obtained through a complete set of logical propositions.
The aging Bertand Russell, worried about the failure of his Principia Mathematica project to derive mathematics from logic, saw in Wittgenstein the young, bright, scientifically-trained mind that might be able to establish a logical foundation, not only for mathematics but for all science as well.

Over an agonizing seven-year period that included his military service in World War I, Wittgenstein wrote his brief Logische-Philosophische Abhandlung, named Tractatus Logico-Philosophicus by G. E. Moore. In it Wittgenstein claimed to have solved all the problems of philosophy (at least all that could be shown in logic).

Wittgenstein also claimed that such problems could not be said or thought (only shown), and so everything written in the Tractatus was strictly speaking nonsense (unsinnung). Everything that had not been said in the Tractatus, Wittgenstein claimed was his truly important work on ethics and the meaning of life.

Despite the negative result for logic, Russell used some of Wittgenstein's work to rewrite Principia Mathematica. It was published as revised by Russell and Whitehead, but shortly thereafter Whitehead disavowed the changes, all actually made by Russell alone. To add to Russell's difficulties, Wittgenstein accused him of misunderstanding the Tractatus and misusing it.

Nevertheless, there grew up around Wittgenstein and Russell (now not talking to one another) a school of philosophy that attracted a diverse group of European science-minded philosophers like Moritz Schlick and his Vienna Circle.

Although Wittgenstein saw his logical philosophy as a failure and turned his interest to the therapeutic use of language – language as a game, this school of logical positivism (based on Wittgenstein's logical atoms) and logical empiricism (based on verification of atomic facts) grew to dominate Anglo-American Analytic philosophy for several decades.

Wittgenstein and Free Will

Ludwig Wittgenstein may have done more to inhibit discussion of free will than any other 20th-century philosopher. He declared the problem of free will and the mind-body problem to be "pseudo-problems," which were to be "dis-solved" by careful attention to actual language use.

In section 5 of the Tractatus, Wittgenstein makes a number of statements that purport to describe the world, its future, and freedom of the will, all of them the consequence of propositions and what we can deduce or infer from them.

5. A proposition is a truth-function of elementary propositions.

5.1 Truth functions can be arranged in series.
      That is the foundation of the theory of probability.

5.12 In particular, the truth of a proposition 'p' follows from the truth of another proposition 'q' if all the truth-grounds of the latter are truth-grounds of the former.

5.123 If a god creates a world in which certain propositions are true, then by that very act he also creates a world in which all the propositions that follow from them come true. And similarly he could not create a world in which the proposition 'p' was true without creating all its objects.

5.13 When the truth of one proposition follows from the truth of others, we can see this from the structure of the propositions.

5.131 If the truth of one proposition follows from the truth of others, this finds expression in relations in which the forms of the propositions stand to one another: nor is it necessary for us to set up these relations between them, by combining them with one another in a single proposition; on the contrary, the relations are internal, and their existence is an immediate result of the existence of the propositions.

5.132 If p follows from q, I can make an inference from q to p, deduce p from q.
          The nature of the inference can be gathered only from the two propositions.
          They themselves are the only possible justification of the inference.
          'Laws of inference', which are supposed to justify inferences, as in the works of Frege and Russell, have no sense, and would be superfluous.

5.133 All deductions are made a priori.

5.134 One elementary proposition cannot be deduced from another.

5.135 There is no possible way of making an inference from the existence of one situation to the existence of another, entirely different situation.

5.136 There is no causal nexus to justify such an inference.

5.1361 We cannot infer the events of the future from those of the present.             Superstition is nothing but belief in the causal nexus.

5.1362 The freedom of the will consists in the impossibility of knowing actions that still lie in the future. We could know them only if causality were an inner necessity like that of logical inference. The connexion between knowledge and what is known is that of logical necessity.
             ('A knows that p is the case', has no sense if p is a tautology.)

Wittgenstein asserts that truth-functions in a series are the basis of probability.
5.15 If Tr is the number of the truth-grounds of a proposition 'r', and if Trs is the number of the truth-grounds of a proposition 's' that are at the same time truth-grounds of 'r', then we call the ratio Trs : Tr the degree of probability that the proposition 'r' gives to the proposition s.

5.1511 There is no special object peculiar to probability propositions.

5.152 When propositions have no truth-arguments in common with one another, we call them independent of one another.
           Two elementary propositions give one another the probability 1/2.
           If p follows from q, then the proposition 'q' gives to the proposition p' the probability 1. The certainty of logical inference is a limiting case of probability.
           (Application of this to tautology and contradiction.)

5.153 In itself, a proposition is neither probable nor improbable. Either an event occurs or it does not: there is no middle way.

5.154 Suppose that an urn contains black and white balls in equal numbers (and none of any other kind). I draw one ball after another, putting them back into the urn. By this experiment I can establish that the number of black balls drawn and the number of white balls drawn approximate to one another as the draw continues.

           So this is not a mathematical truth.

           Now, if I say, 'The probability of my drawing a white ball is equal to the probability of my drawing a black one', this means that all the circumstances that I know of (including the laws of nature assumed as hypotheses) give no more probability to the occurrence of the one event than to that of the other. That is to say, they give each the probability 1/2, as can easily be gathered from the above 2 definitions.            What I confirm by the experiment is that the occurrence of the two events is independent of the circumstances of which I have no more detailed knowledge.

Wittgenstein On Identity
5.53 Identity of the object I express by identity of the sign and not by means of a sign of identity. Difference of the objects by difference of the signs.

5.5301 That identity is not a relation between objects is obvious. This becomes very clear if, for example, one considers the proposition "(x) : fx . HOOK . x=a". What this proposition says is simply that only a satisfies the function f, and not that only such things satisfy the function f which have a certain relation to a.

One could of course say that in fact only a has this relation to a, but in order to express this we should need the sign of identity itself.

5.5302 Russell's definition of "=" won't do; because according to it one cannot say that two objects have all their properties in common. (Even if this proposition is never true, it is nevertheless significant.)

5.5303 Roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing.

5.532 And analogously: not "( EXISTS x, y) . f(x, y) . x=y", but "( EXISTS x) . f(x, x)"; and not
"( EXISTS x, y) . f(x, y) . ~x=y", but "( EXISTS x, y) . f(x, y)".

Therefore instead of Russell's "( EXISTS x, y) . f(x, y)" : "( EXISTS x, y) . f(x, y) .v. ( EXISTS x) . f(x, x)".)

5.533 The identity sign is therefore not an essential constituent of logical notation.

5.534 And we see that the apparent propositions like: "a=a", "a=b . b=c . HOOK a=c", "(x) . x=x". "( EXISTS x) . x=a", etc. cannot be written in a correct logical notation at all.

5.535 So all problems disappear which are connected with such pseudo-propositions.

This is the place to solve all the problems with arise through Russell's "Axiom of Infinity".

What the axiom of infinity is meant to say would be expressed in language by the fact that there is an infinite number of names with different meanings.

Hypertext edition of the Tractatus Logico-Philosophicus in English and German (C.K. Ogden translation, with Russell introduction)

See also our growing bilingual translation of the Tractatus with annotations.

Wittgenstein On the Good
"What is good is also divine. Queer as it sounds, that sums up my ethics", Monk, p.278)
Information philosophy has discovered the cosmic creation process, which is the "divine providence" mistakenly and childishly attributed to a supernatural being. For those who like to anthropomorphize, we call it the Ergod, but it is a purely natural, if supremely benevolent, process

But Wittgenstein is quite correct. That "divine" process is the source of all that is good in the universe.

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