PHILOSOPHY OF LANGUAGE

1. PHILOSOPHY OF LANGUAGE HOW TO TALK ABOUT TALK

2. WHY LANGUAGE? • QUESTION: How does language work? • ANSWER: We don’t really know! • How can we not know how something we ostensibly invented works?! • Think of the question (How does language work?) as a scientific one. Philosophy and science are sometimes indistinguishable, especially as regards undeveloped questions and answers. • A simple hypothesis: Language works solely by means of reference.

3. REVIEW • Each word or phrase has a sense and reference. • An expression expresses its sense and refers to its reference. • One difference between sense and reference is this: The reference of an expression can change while its sense remains the same. • For example: The reference of the definite description the King of France has changed over time. In the late 7th century, the reference was a guy named Clovis III. In the late 18th century it was Napoleon. Today, it has no reference because there is no king of France. • Other examples? • These are really just further instances of the fact that two expressions can have the same sense and yet differ in reference. The reference of the king of France in the late 7th century differs from its reference in the late 18th century. But the sense remains the same.

4. REVIEW • WHAT PROBLEMS DOES THE SENSE/REFERENCE DISTINCTION SOLVE? • THE PROBLEM OF THE COGNITIVE VALUE OF a = a VERSUS a = b. • THE PROBLEM OF “EMPTY” NAMES AND DESCRIPTIONS • THE SUBSTITUTION PROBLEM • VIEW THE PROBLEMS AS “SCIENTIFIC” AND “TECHNICAL”

5. REVIEW • THE PROBLEMS ARISE ON THE ASSUMPTION THAT THE ONLY THING THE SYMBOLS OF LANGUAGE DO IS REFER. • EXAMPLE: EMPTY NAMES • PROBLEMS 1 AND 3 ARE RELATED. • THE DIFFERENCE IN COGNITIVE VALUE OF a = a AND a = b MAY TRANSLATE INTO A DIFFERENCE IN TRUTH VALUE OF CERTAIN PAIRS OF SENTENCES. • FOR EXAMPLE: THE SENTENCE THE POLICE KNOW THAT THE MURDERER IS THE MURDERER MAY BE TRUE, BUT THE POLICE KNOW THAT JONES IS THE MURDERER MAY BE FALSE PRECISELY BECAUSE JONES = JONES AND JONES = THE MURDERER DIFFER IN COGNITIVE VALUE, THAT IS, BECAUSE THEY DIFFER IN THE VALUE OF THE INFORMATION THEY CONVEY.

6. THE SUBSTITUTION PROBLEM • IT’S REALLY NOT ENOUGH TO SAY THAT SINCE THE MURDERER AND JONES DIFFER IN SENSE (THOUGH NOT IN REFERENCE), THE TWO SENTENCES • THE POLICE BELIEVE THAT THE MURDERER IS THE MURDERER • THE POLICE BELIEVE THAT JONES IS THE MURDERER MAY DIFFER IN TRUTH VALUE (1 TRUE AND 2 FALSE). WHY? • WE HAVE THE FOLLOWING SOLID LOGICAL PRINCIPLE ABOUT IDENTITY: • IF a = b, THEN a AND b ARE ALWAYS INTERCHANGEABLE. (SUBSITUTION) • SO WE CAN REPLACE THE FIRST OCCURRENCE OF THE MURDERER IN 1 BY JONES AND GET 2!

7. THE SUBTITUTION PROBLEM • TO SAY “WELL, THE TWO EXPRESSIONS DIFFER IN SENSE” GIVES US NO DIRECTION. WHERE DO WE GO FROM HERE? • IT WON’T DO TO SAY “THE SUBSTITUTION PRINCIPLE ONLY WORKS IF THE TWO EXPRESSIONS a AND b HAVE THE SAME SENSE. WHY? • EXAMPLE: SINCE JONES = THE MURDERER AND THE MURDERER KNOWS HOW TO FLY AN AIRPLANE, JONES MUST KNOW HOW TO FLY AN AIRPLANE. HERE THE SUBSTITUTION WORKS. WHAT’S GOING ON? • OTHER EXAMPLES?

8. THE BOTTOM LINE • THESE THREE SCIENTIFIC/PHILOSOPHICAL PROBLEMS CONCERNING LANGUAGE, FIRST BROUGHT TO OUR ATTENTION BY FREGE, • THE PROBLEM OF COGNITIVE VALUE • THE PROBLEM OF EMPTY NAMES AND DESCRIPTIONS 3. THE SUBSTITUTION PROBLEM REMAIN UNSOLVED TODAY!

9. BERTAND RUSSELL (1872-1970) • CREATED MATHEMATICAL LOGIC • CREATED PHILOSOPHY OF LANGUAGE • CREATED ANALYTIC PHILOSOPHY • WON THE NOBEL PRIZE FOR LITERATURE • WROTE WHY I AM NOT A CHRISTIAN

10. RUSSELL’S “ON DENOTING” • RUSSELL’S THEORY OF DESCRIPTIONS AND HIS SOLUTIONS TO THE THREE PROBLEMS • Russell did not buy Frege’s distinction between sense and reference, and hence didn’t buy Frege’s solution to the three problems. • But despite his overt denial, Russell did recognize the sense/reference distinction, at least as applied to predicates. He says, for example, that ‘unicorn’ expresses a meaningful concept, even though there are no unicorns. But he claims that the distinction does not apply to proper names or definite descriptions. (See below.) • So, given that he would not appeal to the sense/reference distinction, what was Russell’s solution to the three problems?

11. RUSSELL’S THEORY OF DESCRIPTIONS • His solution comes in the form of his famous Theory of Descriptions. 5. Denoting phrases: a dog, some dog, every dog, the neighbor’s dog, (my dog, that dog), Oscar, the author of Waverly, the King of France, the center of mass of the earth. 6. The denoting phrases beginning with‘the’(or ‘my’ and ‘that’) are called “definite descriptions” because they describe only one object “unambiguously.” The others describe things “ambiguously.” Thus, ‘a dog’ or ‘some dog’ picks out a dog or two, but it doesn’t matter which.

12. RUSSELL’S THEORY OF DESCRIPTIONS 7. Russell argues that denoting phrases do not work like names. “Some dogs bark” does not describe any one particular dog, nor does the phrase ‘some dog’ pick out some special object. So the sentence “Some dogs bark” is not really a subject/predicate sentence at all, unlike “Fido barks.” Russell argues, for example, that “I met a man” does not mean the same as “I met Jones” even if it is Jones I met, since “I met a man, but it wasn’t Jones” is not contradictory. You will find a number of arguments along these lines in “Descriptions.” (def. descr.)

13. RUSSELL’S THEORY OF DESCRIPTIONS 8.Russell analyses “I met a man” as “x is a man and I met x” is sometimes true. A more modern statement of this is: “I met a man” means “There is an object x, such that (x is a man and I met x). Similarly “All dogs bark ”means “For any object x, (if x is a dog, then x barks). In more modern logical terminology, the denoting phrases “for any object x” and “there is an object x” (or “for some object x) are called quantifier phrases. Another example of a quantifier phrase is “most dogs” as in “Most dogs bark.”

14. THEORY OF DESCRIPTIONS 9. Quantifier phrases are not names. “Who did you pass on the road?" the King went on, holding out his hand to the Messenger for some more hay. "Nobody," said the Messenger. "Quite right," said the King: "this young lady saw him too.” • Definite descriptions are quantifier phrases • Ordinary proper names are disguised definite descriptions. VERY CONFUSING!

15. THEORY OF DESCRIPTIONS • LET’S PUT THIS ALL TOGETHER • QUANTIFIERS ARE NOT NAMES • DEFINITE DESCRIPTIONS ARE QUANTIFIER PHRASES • PROPER NAMES ARE DEFINITE DESCRIPTIONS • IT SEEMS TO FOLLOW FROM 2 AND 3 THAT NAMES ARE QUANTIFIER PHRASES--WHICH CONTRADICTS 1! • EXAMPLE: ARISTOTLE IS SHORT FOR PLATO’S BEST STUDENT, AND THE LATTER IS A DEFINITE DESCRIPTION WHICH IS ANALYSED AS A QUANTIFIER PHRASE. • FOR RUSSELL ONLY THIS AND THAT ARE REALLY NAMES. STRANGE!

16. THEORY OF DESCRIPTIONS • THE MAIN PROPOSITION OF THE THEORY OF DESCRIPTIONS: IF DEFINITE DESCRIPTIONS ARE QUANTIFIER PHRASES, AND IF ORDINARY PROPER NAMES ARE (ABBREVIATED) DEFINITE DESCRIPTIONS, THEN WE HAVE A SOLUTION TO ALL THREE PUZZLES. • THE THREE PROBLEMS ARE SEEN AS ARISING FROM A MISUNDERSTANDING OF BOTH THE LOGICAL GRAMMAR AND THE LOGICAL SEMANTICS OF DEFINITE DESCRIPTIONS. • AN ANALOGY: NOBODY IS IN THE ROOM; NOBODY IS A GHOST; THEREFORE, A GHOST IS IN THE ROOM. WHAT’S THE MISTAKE HERE?

17. THEORY OF DESCRIPTIONS: DETAILS • DEFINITE DESCRIPTIONS ARE QUANTIFIER PHRASES. HOW SO? • RUSSELL SPELLS OUT A PROCEDURE FOR REPLACING ANY SENTENCE CONTAINING A DEFINITE DESCRIPTION WITH AN ALLEGEDLY EQUIVALENT ONE THAT DOES NOT CONTAIN IT AND THAT CONTAINS ONLY A QUANTIFIER PHRASE INSTEAD. • FOR EXAMPLE: 1. THE POSITIVE SQUARE ROOT OF 4 IS EVEN. 2. THERE IS EXACTLY ONE POSITIVE SQUARE ROOT OF 4 AND IT IS EVEN THE RELEVANT DEFINITE DESCRIPTION IS THE POSITIVE SQUARE ROOT OF 4. WHAT HAS HAPPENED TO IT?

18. THEORY OF DESCRIPTIONS: DETAILS • WHAT DO WE HAVE IN 2? • THERE IS EXACTLY ONE POSITIVE SQUARE ROOT OF 4 AND IT IS EVEN. • WE HAVE THE TWO PREDICATES POSITIVE SQUARE ROOT OF 4 AND EVEN • THE LOGICAL OPERATOR, IN THIS CASE A QUANTIFIER PHRASE, THERE IS EXACTLY ONE • THE LOGICAL OPERATOR AND. NO DEFINITE DESCRIPTION! But most people can’t see much of a difference between 1 and 2. How does this move solve the three problems?

19. THE PROBLEM OF EMPTY DESCRIPTIONS 3. THE PRESENT KING OF FRANCE IS BALD. • THE PRESENT KING OF FRANCE IS NOT BALD. • THE TWO LISTS • THERE IS EXACTLY ONE KING OF FRANCE AND HE IS BALD. • THERE IS EXACTLY ONE KING OF FRANCE AND HE IS NOT BALD. • IT IS NOT THE CASE THAT THERE IS EXACTLY ONE KING OF FRANCE AND HE IS BALD. • SO FOR RUSSELL, POSITIVE SENTENCES WITH EMPTY DESCRIPTIONS WILL BE FALSE. • WHAT ABOUT NEGATIVE SENTENCES?

20. THEORY OF DESCRIPTIONS: DETAILS • NEGATIVE SENTENCES WITH EMPTY DESCRIPTIONS WILL BE TRUE OR FALSE DEPENDING ON THE SCOPE OF THE NEGATION. • CONTRAST WITH FREGE. • FOR FREGE, 3 AND 4 HAVE NO TRUTH VALUE AT ALL. AND FREGE’S DOCTRINE DOES NOT REVEAL THE AMBIGUITY IN 4. • DOES IT MATTER? • YES. THE PRESENT KING OF FRANCE DOES NOT EXIST. • THIS SENTENCE IS TRUE. BUT FOR FREGE IT LACKS ANY TRUTH VALUE. • ON RUSSELLS ACCOUNT, IT COMES OUT TRUE--OR DOES IT?

21. THE PROBLEM OF EMPTY DESCRIPTIONS • THE PRESENT KING OF FRANCE DOES NOT EXIST. • THERE IS EXACTLY ONE KING OF FRANCE AND HE DOES NOT EXIST. • IT IS NOT THE CASE THAT THERE IS EXACTLY ONE KING OF FRANCE. • NOT FAIR TO FREGE? • “LIGHT IS PROPAGATED IN THE LUMINIFEROUS ETHER.” • “AS REQUIRED BY MAXWELL’S EQUATIONS.” • FOR FREGE, THE FIRST STATEMENT IS A KIND OF NONSENSE; FOR RUSSELL IT IS FALSE.

22. THE SUBSTITUTION PROBLEM • GIV WISHED TO KNOW WHETHER SCOTT = SCOTT. • THE POLICE WISH TO KNOW WHETHER JONES = JONES. • GIV WISHED TO KNOW WHETHER SCOTT =THE AUTHOR OF WAVERLY. • THE POLICE WISH TO KNOW WHETHER JONES = THE MURDERER. • GIV WISHED TO KNOW WHETHER THERE IS EXACTLY ONE AUTHOR OF WAVERLY AND HE IS SCOTT. • THERE IS EXACTLY ONE AUTHOR OF WAVERLY AND GIV WISHED TO KNOW WHETHER HE IS SCOTT. • GIV WISHED TO KNOW WHETHER THERE IS EXACTLY ONE SCOTT AND HE IS SCOTT.

23. A SERIOUS LIMITATION • GIV WISHED TO KNOW WHETHER CREATURES WITH A HEART ARE CREATURES WITH A HEART. 2. GIV WISHED TO KNOW WHETHER CREATURES WITH A HEART ARE CREATURES WITH A KIDNEY • CREATURES WITH A HEART = CREATURES WITH A KIDNEY • SO THE THEORY OF DESCRIPTIONS CAN’T SOLVE THE SUBSTITUTION PROBLEM FOR PREDICATES.

24. THE PROBLEM OF COGNITIVE VALUE • RECALL WHAT FREGE SAYS ABOUT a = a versus a = b. • BUT RUSSELL SAYS THAT WHEN a IS A DEFINITE DESCRIPTION, a = a IS NOT AN INSTANCE OF THE “LAW OF IDENTITY.” • EXAMPLE: THE MURDERER = THE MURDERER/ THERE IS EXACTLY ONE MURDERER AND HE IS THE MURDERER. • THE RUSSELL SENTENCE HERE IS NOT ANALYTIC OR A PRIORI. • RUSSELL SOLVES THE PROBLEM AT THE LEVEL OF PREDICATES. DISTINCT DEFINITE DESCRIPTIONS GENERATE DISTINCT PREDICATES, POSSIBLY DIFFERING IN MEANING. • THE WHOLE NUMBER BETWEEN 1 AND 3 = THE UNIQUE EVEN AND PRIME NUMBER.

25. NAMES • ORDINARY NAMES: YOUR NAME, CHICAGO, ETC. • LOGICALLY PROPER NAMES: THIS, THAT, NUMERALS AND OTHER NAMES OF MATHEMATICAL OBJECTS (?) • ORDINARY NAMES ABBREVIATE DEFINITE DESCRIPTIONS. • LOGICALLY PROPER NAMES HAVE TO REFER.