[2.2.8.6.] Why Frege Cannot Accept the Standard View.

 

Frege accepts each of the following ideas:

 

1.      The Principle of Compositionality: the reference of an entire sentence depends on nothing but what the words in that sentence refer to; so if the sentences “p” and “q” do not differ in the references of their constituent words, then “p” and “q” cannot have different references. For example:

 

(A)  Mark Twain wrote Tom Sawyer.

(B)  Samuel Clemens wrote Tom Sawyer.

 

The only difference between (A) and (B) are the names “Mark Twain” and “Samuel Clemens.” Since these names have the same reference (they both refer to the same individual), the sentences (A) and (B) must have the same reference.

 

2.      The reference of a sentence is its truth value. So all true sentences have the same reference, namely, the true; and all false sentences have the same reference, namely, the false.

 

According to the Standard View, in the sentences

 

(C)  “Bill believes that the Unabomber is in prison.” (T)

 

and

 

(D)  “Bill believes that Ted Kaczynski is in prison.” (F)

 

the names “the Unabomber” and “Ted Kaczynski” have the same reference.  Frege cannot agree to this, because (given the Principle of Compositionality and his view about sentence reference) it implies that C and D have the same truth value. If there is no difference between the two sentences regarding what their constituent terms refer to, then the two sentences must have the same reference, and for Frege that means they have the same truth value.

 

But they do not have the same truth value. So Frege cannot add the standard view (that “the Unabomber” and “Ted Kaczynski” are co-referring expressions in C and D) to his assumptions about compositionality and sentence reference; together those three ideas yield a contradiction.

 

 

[2.2.9.] The “Laws of Truth.”

 

“The Thought: A Logical Inquiry” (1918) is one of three papers Frege wrote late in his life. Collectively, the papers are known as Logical Investigations.[1] These papers were the beginning of Frege’s attempt to write a non-technical introduction to his system of logic.

 

“The Thought” opens as follows:

 

The word “true” indicates the aim of logic as does “beautiful” that of aesthetics or “good” that of ethics. All sciences have truth as their goal; but logic is also concerned with it in a quite different way from this. It has much the same relation to truth as physics has to weight or heat. To discover truths is the task of all sciences; it falls to logic to discern the laws of truth. (93)

 

Here Frege makes the following claims:

·         All sciences aim to discover truths, i.e., they all engage in inquiry, truth-seeking,

·         But logic is different, in that it aims to discover the laws of truth; i.e., logic investigates truth itself.

 

He goes on to explain this claim by distinguishing two types of law:

1.      laws that ought to be obeyed but which sometimes are not, e.g., “laws of morals or the state” (93) (these are known as normative or prescriptive laws); and

2.      laws that are always conformed to, e.g. laws of nature, which are very broad descriptions of things as they actually occur in the natural world (these are known as descriptive laws).

 

The “laws of truth” that are investigated by logic are descriptive. They do not prescribe how anything should be, but instead describe how something actually is. But what is it that they describe?

 

Frege’s answer seems to be that they describe what truth itself is: “The meaning of the word ‘true’ is explained by the laws of truth.” (93)[2]

 

Frege notes that the word “true” is used in many different ways, and he wants to make it clear what he means when he uses that word.

 

He notes that he is interested in “that kind of truth ... whose recognition is the goal of science.” (93) So he is concerned with “truth” in the sense in which ordinary scientific or factual claims can be true.

 

So the question is: what is it for an ordinary scientific or factual claim to be true? This is the question that the “laws of truth,” once identified, will answer. Those laws will explain this sense of the word “true.”

 

 

[2.2.10.] The Correspondence Theory.

 

Frege rejects a theory of truth that has been around since at least the time of Plato:

 

the correspondence theory of truth (df.): truth is a relation of correspondence between propositions (or sentences, or beliefs), on one hand, and the world, on the other; for a proposition (etc.) to be true is for it to correspond to the way things are. [This way of thinking about truth was held by Russell and the early Wittgenstein.][3]

 

Frege says a number of critical things about this theory. One of them is as follows:

 

Can it not be laid down that truth exists when there is correspondence in a certain respect? But in which? For what would we then have to do to decide whether something were true? We should have to inquire whether it were true that an idea and a reality, perhaps, corresponded in the laid-down respect. And then we should be confronted by a question of the same kind and the game could begin again. So the attempt to explain truth as correspondence collapses. (94)

 

Frege’s reasoning here can be formalized as follows...

 

Frege’s Argument Against the Correspondence Theory

 

1.      Assume that truth is a relation of correspondence with the world. Then...

2.      In order to discover whether “p” is true, we would need to discover whether “‘p’ corresponds to the world” is true.

3.      In order to discover whether “‘p’ corresponds to the world” is true, we would need to discover whether “‘“p” corresponds to the world’ is true” is true... and so on, without end.

4.      So, if we assume that truth is a relation of correspondence with the world, we can never discover whether a given proposition is true.

5.      [implicit] But we can in fact discover whether a given proposition is true.

6.      So, truth is not a relation of correspondence.

 

 

Stopping point for Monday January 26. For next time, read pp.95-99 of Frege’s “The Thought: A Logical Inquiry” (stop at the end of the last full paragraph; we will not discuss the rest of the article in class, but you can of course read it if you wish).