[2.2.8.] Substitutivity and Intensional Contexts.

 

 

[2.2.8.1.] The Principle of Substitutivity.

 

Like many philosophers, Frege accepts the following principle about language:

 

The Principle of Substitutivity[1] (df.): Co-referring expressions (i.e., expressions that have the same reference) can be substituted for one another without changing the truth-value of the sentence in which the substitution is made.

 

For example, “Barack Obama” and “The 44^th US President” are co-referring expressions, i.e., they have the same reference (namely, the man Barack Obama). Suppose we take the sentence...

 

(A) “Barack Obama was a Senator from Illinois.”

 

and replace “Barack Obama” with “The 44^th US President,” to get the sentence

 

(B) “The 44^th US President was a Senator from Illinois.”

 

According to the Principle of Substitutivity, by replacing one expression with a co-referring expression, we do not change the truth value of the sentence itself. So if (A) is true, then (B) is as well. And if (A) is false, then so is (B).

 

Leibniz’s formulation (quoted approvingly by Frege by p.25): “Eadem sunt, quae sibi mutuo substituti possunt, salva veritate”: “Those things are the same which may be substituted mutually everywhere without change of truth value.” This formulation makes it sound like it is the substitution of things, rather than linguistic expressions, which is at issue. For this reason, the modern statement of the law given above is preferable.

 

 

[2.2.8.2.] Extensional vs. Intensional Contexts.

 

The standard view among philosophers is that the Principle of Substitutivity is not true about every linguistic context.

 

Most philosophers distinguish contexts about which it is true from those about which it is not:

 

extensional context (df.): a linguistic context, e.g., a sentence, in which you can exchange co-referring expressions and not change the truth value; in other words, it is a context for which the Principle of Substitutivity holds.

 

intensional context (df.): a linguistic context, e.g., a sentence, in which you cannot always exchange co-referring expressions without change of truth value; i.e., it is a context for which the Principle of Substitutivity does not hold. [Such contexts are also called opaque contexts and oblique contexts.]

 

 

[2.2.8.3.] Propositional Attitudes.

 

Most philosophers believe that reports of propositional attitudes create intensional contexts.

 

propositional attitude (df.): a psychological relationship that a person can have with a proposition (e.g., believing that, knowing that, hoping that, wishing that, desiring that, fearing that...)

 

For example, each of the sentences

·         “Scarlett believes that tomorrow is another day.”

·         “Mike hopes that the killer will be caught.”

·          “Lois suspects that Clark is Superman.”

·         “Bill believes that the Unabomber is in prison.”

reports on a propositional attitude; in other words, it ascribes a propositional attitude to some person.

 

 

[2.2.8.4] The Standard View.

 

The standard view is that the Principle of Substitutivity fails for reports of propositional attitudes.

 

Suppose that Bill believes that the Unabomber is in prison. So the sentence

 

“Bill believes that the Unabomber is in prison.”

 

is true. According to the Principle of Substitutivity, we ought to be able to substitute the name “Ted Kaczynski” for “the Unabomber” without changing the sentence’s truth value. This is because “Ted Kaczynski” and “the Unabomber” refer to the same individual.

 

But suppose that Bill does not know that Ted Kaczynski is the Unabomber. In fact, he thinks they are different people.

 

So the sentence

 

“Bill believes that Ted Kaczynski is in prison.”

 

is false.

 

Because of this, the standard view is that in reports of propositional attitudes, the Principle of Substitutivity fails.

 

 

 

 

[2.2.8.5.] Frege’s View.

 

Frege was one of the first philosophers to weigh-in on this phenomenon. In fact, the attempt to explain what is going on when the Principle of Substitutivity apparently fails in reports of propositional attitudes is sometimes called Frege’s Puzzle About Propositional Attitude Reports. [2]

 

Frege’s explanation is very different from what has come to be the standard view. It relies on his distinction between customary reference and indirect reference. Recall:

 

In reported speech, e.g., the italicized words in

·         “Hannity said that G. W. Bush is a great President.”

·         “Smith shouted that the house is on fire.”

·         “CNN reported that the economy is in trouble.”

an expression (either a name or an entire sentence) does not have its customary reference.

 

Instead it has an indirect reference, which is the customary sense of the expression (the sense that the expression normally has).[3] E.g., in “Hannity said that G. W. Bush is a great President”...

·         “G. W. Bush” does not have its customary reference, viz. the man G. W. Bush;

·         rather, it has an indirect reference, namely, the customary sense of “G. W. Bush,” which is something like “The 43^rd President of the United States who was once Governor of Texas and who is the husband on Laura Bush.”

 

 

The Fregean solution to this problem is this:

 

In reports of propositional attitudes, words (including names) do not have their customary reference.

 

Rather, they have an indirect reference, which is their customary sense.

 

So in

 

“Bill believes that the Unabomber is in prison.”

 

the name “the Unabomber” does not refer to a person. Rather, it refers to the customary sense of that name (the sense conveyed by a long definite description, something like “The American domestic terrorist who, between 1978 and 1995, sent 16 mail-bombs that killed three people and injured 23 others.”)

 

And in the sentence

 

“Bill believes that Ted Kaczynski is in prison.”

 

the name “Ted Kaczynski” does not refer to a person. Rather, it refers to the customary sense of that name (conveyed by a long definite description, something like “The son of Theodore and Wanda Kaczynski who has mathematics degrees from Harvard and the University of Michigan”).

 

So in those two sentences, “Ted Kaczynski” and “the Unabomber” are not really co-referring expressions.

 

So the fact that those sentences have different truth values does not violate the Principle of Substitutivity.

 

 

Almost the last 2/3 of the “On Sense and Reference,” from the second column on p.25 to the end, is dedicated to defending the view that all true sentences have the same reference (“the True”) and all false ones the same reference (“the False”). It is taken up by detailed considerations of apparent counterexamples to the Principle of Substitutivity, which, if they were not just apparent counterexamples but actual ones, would show Frege’s view about sentence reference to be incorrect.

 

Stopping point for Friday January 23. For next time, begin reading Frege’s “The Thought: A Logical Inquiry” (pp.93-95, stopping at the end of the first paragraph on p.95).