One needs to understand that Wittgenstein changed his views after the Tractatus. As I believe Toulmin pointed out in his book, Wittgenstein's Vienna, W. was trying to do for philosophy what Boltzmann had done for statistical physics and reduce philosophy to a set of rules. That is also consistent with the goals of Leibniz, Boole, Russell of course, and ultimately Turing. In fact, as mentioned in the book, Turing and W. offered courses on the foundations of mathematics at the same time in Cambridge. The mathematical world has ignored W for the most part and works along lines much closer to the ideas of Turing.
Wittgenstein (W hereafter) seems to be struggling with multiple issues: 1) How do humans learn a language? 2) In what sense do words have signification or meaning?.
The first problem is fraught with issues of modeling a human. This is exemplified in his inability to describe how a child understands the pronouns "this" and "that" via pointing. Humans do it via some unknown neurological mechanism that involves the structure of the brain the eye and probably the historical experience of the organism. I was reminded that William James wondered how humans could make sense of the "bloomin', buzzin' confusion" that surrounds us at every moment. As interesting and significant as this problem may be, I am going to assume that W's repeated struggle with this issue is irrelevant to the main issue of "meaning". At item 10 (on page 6), W asks, "Now what do the words of this language signify?"
Already, having considered the issue of a pronoun, it is clear that there is no fixed object that is signified by the word "this". It is context (and probably historically) dependent. But he notes at item 17 that he has suggested several different languages over the previous items and that different "kinds of word" complicate the issue. But the real issue seems to be whether or not it is possible to coherently believe that words ultimately relate to objects. The long series of examples is used to answer "No" to this question. His answer is that language is a kind game (with words and behaviors among humans) and that the significance of a word is its use in this language game.
One of the issues that intrigues me is that W seems to be unaware of Model Theory, which grew out of the Russell-Whitehead program. This seems to deal with the issue of interpretations of words in a very precise sense, at least for mathematics. In particular, the first results were published in 1915, seven years before the Tractatus. So the issue of multiple interpretations was already an important one in the mathematical world. I am unaware if W every commented on model theory, but I believe that Russell retained his interest in mathematical logic at least up to the first world war in 1917. So I would guess that Russell knew of some of these results and issues.
Let me quote a short comment on Model Theory from Wikipedia. (This reference is OK; I've read similar things in my mathematical logic books.)
"In mathematics, model theory is the study of (classes of) mathematical structures such as groups, fields, graphs, or even universes of set theory, using tools from mathematical logic. A structure that gives meaning to the sentences of a formal language is called a model for the language. If a model for a language moreover satisfies a particular sentence or theory (set of sentences), it is called a model of the sentence or theory. Model theory has close ties to algebra and universal algebra."
http://en.wikipedia.org/wiki/Model_theory
The point is that there are different ways to interpret the exact SAME set of symbols. This seemed to be a problem that was bothering W. It is surprising that he did not refer to this work.
I would like to read selections of philosphical investigations.
ReplyDeleteOne needs to understand that Wittgenstein changed his views after the Tractatus. As I believe Toulmin pointed out in his book, Wittgenstein's Vienna, W. was trying to do for philosophy what Boltzmann had done for statistical physics and reduce philosophy to a set of rules. That is also consistent with the goals of Leibniz, Boole, Russell of course, and ultimately Turing. In fact, as mentioned in the book, Turing and W. offered courses on the foundations of mathematics at the same time in Cambridge. The mathematical world has ignored W for the most part and works along lines much closer to the ideas of Turing.
ReplyDeleteWittgenstein (W hereafter) seems to be struggling with multiple issues: 1) How do humans learn a language? 2) In what sense do words have signification or meaning?.
ReplyDeleteThe first problem is fraught with issues of modeling a human. This is exemplified in his inability to describe how a child understands the pronouns "this" and "that" via pointing. Humans do it via some unknown neurological mechanism that involves the structure of the brain the eye and probably the historical experience of the organism. I was reminded that William James wondered how humans could make sense of the "bloomin', buzzin' confusion" that surrounds us at every moment. As interesting and significant as this problem may be, I am going to assume that W's repeated struggle with this issue is irrelevant to the main issue of "meaning". At item 10 (on page 6), W asks, "Now what do the words of this language signify?"
Already, having considered the issue of a pronoun, it is clear that there is no fixed object that is signified by the word "this". It is context (and probably historically) dependent. But he notes at item 17 that he has suggested several different languages over the previous items and that different "kinds of word" complicate the issue. But the real issue seems to be whether or not it is possible to coherently believe that words ultimately relate to objects. The long series of examples is used to answer "No" to this question. His answer is that language is a kind game (with words and behaviors among humans) and that the significance of a word is its use in this language game.
One of the issues that intrigues me is that W seems to be unaware of Model Theory, which grew out of the Russell-Whitehead program. This seems to deal with the issue of interpretations of words in a very precise sense, at least for mathematics. In particular, the first results were published in 1915, seven years before the Tractatus. So the issue of multiple interpretations was already an important one in the mathematical world. I am unaware if W every commented on model theory, but I believe that Russell retained his interest in mathematical logic at least up to the first world war in 1917. So I would guess that Russell knew of some of these results and issues.
Let me quote a short comment on Model Theory from Wikipedia. (This reference is OK; I've read similar things in my mathematical logic books.)
ReplyDelete"In mathematics, model theory is the study of (classes of) mathematical structures such as groups, fields, graphs, or even universes of set theory, using tools from mathematical logic. A structure that gives meaning to the sentences of a formal language is called a model for the language. If a model for a language moreover satisfies a particular sentence or theory (set of sentences), it is called a model of the sentence or theory. Model theory has close ties to algebra and universal algebra."
http://en.wikipedia.org/wiki/Model_theory
The point is that there are different ways to interpret the exact SAME set of symbols. This seemed to be a problem that was bothering W. It is surprising that he did not refer to this work.