PHIL 6 Symbolic Logic
December 2nd, 2014
There are many widely accepted theories of truth in the field of deductive logic. From
Paul Horwich to Gottlob Frege, the latter of whom is often considered the grandfather of modern logic, truth has many differing foundations, from semantic accounts to syntactical ones. No matter what the underlying structure of the truth may be, it is always provable with its own corresponding methodology. I discovered the semantic theory of truth while reading Logic,
Semantics, and Metamathematics by Alfred Tarski. This book is actually a collection of essays that were published by Alfred Tarski between 1923 and 1938 relating to the field of logic, semantics and mathematics. There is one essay in particular that I plan to respond to and that essay is entitled “The Concept of Truth in Formalized Languages.” This essay was chosen for the simple reason that it has completely dissected the semantic theory of truth that I have been researching for quite some time now. This paper will be divided into two sections. The first section will comprise my response to the different definitions of truth that Tarski proposes concerning colloquial language. The second section will be my response to an element of defining truth in formalized language, the truth predicate, T-schema, or Convention T.
Response to Semantic Definitions of Truth
In this first section, Tarski sets the discussion in motion with a semantic definition of truth in colloquial language:
A true sentence is one which says that the state of affairs is so and so, and the state of affairs is indeed so and so.1
Here, Tarski admits that this semantic definition leaves much room for ambiguity, but the actual intention of the definition is clear. In my response, the definition seeks to describe a sense in which something is true, and for that sentence to be true the intention of the sentence must match the underlying structure of that sentence. This interpretation of this aspect of Tarski’s theorem can best be illustrated by my example:
A.) I went to the store to get jellybeans.
B.) The store was closed, so I never wanted jellybeans anyway.
This example clearly proves the fact that line ‘B’ is not correct, because the speaker clearly intended to go to the store. This may be an overly vague example, but it proves how a sentence can be proven false by analyzing the underlying intention of the sentence.
On another note, this idea is accompanied in the essay by another that is a little more powerful and starts to put the theory in context. This was stated by Tarski also, but there are certain sentences than will suffice for a partial definition of truth.2 Tarski states that this
‘scheme’ of that kind of sentence can be illustrated in the following manner: x is a true sentence if and only if p.
Tarski explains the anatomy of this example as follows: if we are to derive a plausible definition of truth from this structure, then we substitute in place of P any sentence and in place of x we
Tarski, Alfred. Logic, Semantics, Metamathematics: Papers from 1923 to 1938. (Indianapolis: Hackett Publishing
Company, Inc, 1983). p. 155
Tarski, Alfred. Logic, Semantics, Metamathematics: Papers from 1923 to 1938. p. 155
substitute any name of a sentence.3 From this there is a reasonable definition of truth that can be constructed, and it is as follows:
‘it is snowing’ is a true sentence iff it is snowing.
This example corresponds with the discussion above, which explicates the name of a sentence, which in this case is the quotation-mark name of a sentence. Tarski attempts to define this quotation-mark sentence as the expressions found in a sentence that lie between quotation marks.4 I find this interesting for several reasons, but the sole reason is because this theory has actually taken a full predicate of a sentence and give it such a standard as to describe the function of the sentence as a whole, not just a sentence that can be…