W before the turn

This is a more fully fleshed out version of an earlier post on early W. Again I hear echoes of Scott Dodge for nobody, but it is great to re-engage.

Below are the 7 basic propositions on which Ludwig Wittgenstein's earliest work, known in English as the Tractatus Logico-Philosophicus, which he submitted as a dissertation at Cambridge University and on the basis of which he was awarded his doctorate, is based. The Latin title was suggested by G.E. Moore as the title for its publication in English. Moore was a friend of W's and a Cambridge University Philosophy professor. In naming the work Moore had in mind Baruch Spinoza's Tractatus Theologico Politicus.

The entire work is organized on the basis of these 7 propositions. Each proposition or sentence is numbered according to this system: 1; 1.1; 1.2; 1.2.3; 1.2.3.4- 2.1; 2.1.5, etc., all the way through to seven. Proposition 7 is unique in that it has no supporting propositions.

After being awarded his doctorate from Cambridge, W returned to his native Austria and trained to be an elementary school teacher. He taught school in lower Austria for several years. His turn began after the publication of the Tractatus and toward the end of his teaching career, during which we worked to develop, among other things, methods to teach kindergartners algebra. The structure, simplicity, and elegance of the Tractatus are obvious. Therein, as the saying goes, lies the rub. Is the world really reducible in that way? W came to see it was not.

Among the external factors in his turn, which resulted in his return to Cambridge and Philosophy, were the visits of F.P. Ramsey (brother of Michael Ramsey, who was Archbishop of Canterbury from 1961-1974). Ramsey was a genius who died at 26 and was a fellow of King's College Cambridge, who traveled to Austria to meet with W and discuss the Tractatus with him. A second identifiable external factor were his discussions and involvement with members of the Vienna Circle, a group of so-called logical positivists, chief among whom was Rudolf Carnap. Of particular note in these latter discussions was the verifiability principle, based on 4.024 of the Tractatus. Stated simply, W detected an inherent contradiction in this derived principle. Namely, what verified the principle of verifiability?

In any case, he ultimately returned to Cambridge and continued teaching Philosophy. Eventually he assumed the chair of Philosophy held by G.E. Moore upon Moore's retirement. While W's later phase began during the time between the publication of the Tractatus and his return to Cambridge, he continued wrestling with the fundamental issues engaged by these 7 propositions for the rest of his life, even rejecting proposition 2 , regarding atomic facts. In his later work he focused on the relationship between language and logic, a departure from his work leading up to and culminating with the Tractatus, which, taking its lead from Frege and Russell, explored the relationship of logic to mathematics.

The Seven Fundamental Propositions of the Tractatus

1. The world is everything that is the case.

2. What is the case, the fact, is the existence of atomic facts.

3. A logical picture of facts is a thought.

My comment: Thought and picturing (i.e., seeing) remains problematic for W.

4. A thought is a proposition with sense.

My comment: This smacks of Russelian empiricism. Russellian for Bertrand Russell , W's tutor at Cambridge and sometime mentor, with whom he had a complete falling out. Russell, along with Alfred North Whitehead, did some great work (i.e., Principia Mathematica) in the 1910s, but, unlike W who remained engaged in the rough-and-tumble of Philosophy until the end of his life, really faded as a serious thinker. But then Russell died in 1970 at age 97. Whereas, W died at age 62 (three days after his 62nd birthday) in 1951.

5. Propositions are truth-functions of elementary propositions. An elementary proposition is a truth function of itself.

My comment: An elementary proposition would be John has brown hair. The truth function of this elementary proposition consists solely in whether John actually has brown hair. Either he does or he does not (how one might verify if John has brown hair {i.e., looking at John to see if his hair is brown} introduces the problem of verifiability). Therefore, this elementary proposition is simply either true or false. In this way it is a truth function of itself.

6. The general form of a proposition is the general form of a truth-function.

My comment: An example of a general proposition, which is made up elementary propositions, is John has brown hair and blue eyes. This is a truth functional proposition. Let's call the proposition John has brown hair a and call the proposition John has blue eyes b. So, the conjunctive proposition a&b is truth functional because it is true just if a and b are true and it is false if either a or b is false. It is also false if both a and b are false. One can also detect a bit of the challenge presented to logic by language. John may have blue eyes, but have blonde hair. Nonetheless, logically, the initial general propositions a&b remains false. Disjunctions (i.e., Either John is a male or he is a female) are also truth functional. In this W is following the work of mathematician Gottlieb Frege, one of the founders of modern logic, who assigned truth values to propositions and derived truth functionality from these values in his explorations on the relationship between mathematics and logic. W's early concern was the same, but after his turn he began to focus, building on his early work as embodied in the Tractatus , on the relationship between logic and language and language and the world, which he came to see as being far more complex than these 7 propositions.

7. What we cannot speak about we must pass over in silence.

My comment: This statement, ends the Tractatus and is not elaborated on further.