Philosophy Discussion4

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What is Philosophical Analysis?

Five conditions of philosophical analysis:

• An analysis has the logical form of a universally quantified

biconditional

• An analysis is necessarily true

• An analysis is informative

• An analysis is knowable a priori

• An analysis is testable by the method of counterexample

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Informative Analyses

1. A brother is a male sibling

2. A brother is a brother

• For (1) to qualify as a meaning analysis it must be necessarily

true and knowable a priori. This is only the case if “brother“ and

“male sibling“ are synonymous.

• “Brother“ and “brother“ in (2) are synonymous. What then

distinguishes the informative analysis (1) from the uninformative

claim (2)?

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Paradox of Analysis

• Either I don‘t know what a given concept means, in which case I cannot

judge that a proposed meaning analysis is correct. Or I do know what a

given concept means, but then the analysis is uninformative.

• I judge a proposed analysis as correct by reference to the concept I

already understand, in which case the analysis must be identical to the

concept and thus uninformative. But if it is not identical, how can I judge

the analysis as correct?

• For a philosophical analysis to be informative, it must be incorrect; and

to be correct, it must be uninformative.

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The paradox of analysis goes back to Plato (Meno 80e). The 20th

century formulation of the paradox is due to C.H. Langford (1895-1964)

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“Let us call what is to be analyzed the analysandum, and let us call

that which does the analyzing the analysans. The analysis then

states an appropriate relation of equivalence between the

analysandum and the analysans. And the paradox of analysis is to

the effect that, if the verbal expression representing the analysandum

has the same meaning as the verbal expression representing the

analysans, the analysis states a bare identity and is trivial, but if the

two verbal expressions do not have the same meaning, the analysis

is incorrect“ (Langford 1942: 323).

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Reconstruction of the paradox of analysis:

1) An meaning analysis of a concept, F, should say what F is identical to.

2) Suppose that a given analysis of the concept F says that it is identical to the

concept G.

3) So if the concepts F and G are not identical, the analysis is false. (1, 2)

4) Alternatively, if the concepts F and G are identical, then what the analysis says

(namely that F = G) has the same content as the claim that the concept F is

identical to the concept F.

5) But it is uninformative (“trivial“) that the concept F is identical to the concept F.

6) So if the concepts F and G are identical, what the analysis says is uninformative.

(4, 5)

C) Therefore, the analysis is either false or uninformative. (3, 6)

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The paradox of analysis is doubly

paradoxical because the paradox is an

informative result derived from an

analysis of the concept of analysis.

Solutions to the Paradox of Analysis

• Solutions to the paradox of analysis:

– Sense and Reference (Gottlob Frege)

– Family resemblance (Ludwig Wittgenstein)

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Gottlob Frege (1848–1925). A

German mathematician, logician

and philosopher. He is considered

to be one of the founders of

modern logic, made major

contributions to the foundations of

mathematics, and is the father of

analytic philosophy.

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Ludwig Wittgenstein (1889 –

1951). Austrian philosopher who

worked primarily in logic, the

philosophy of mathematics, the

philosophy of mind, and the

philosophy of language. He

taught at the University of

Cambridge.

Sense and Reference

• Proposal: the paradox of analysis dissolves once we distinguish

between the sense and the reference of a word or phrase (Gottlob

Frege 1848–1925).

Reference

The object denoted by a word or phrase

Sense

The mode of presentation of the object denoted by the word or phrase.

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• If two expressions have the same sense, then they have the

same referent (if they have a referent at all)

• Two expressions with the same referent need not have the

same sense. E.g., “Mary’s brother” and “John”

• Senses are rules for finding the reference. The sense states a

definite description states a property that only a single object

has.

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More examples for expressions with the same reference but different

senses:

• “Mark Twain is Samuel Clemens“ vs. “Mark Twain is Mark Twain“

• “Lines have the same direction if and only if they are parallel to one

another“ vs. “Lines have the same direction if they have the same

direction“

• “Alvin believes that the greatest student of Plato was a philosopher”

vs. “Alvin believes that the greatest teacher of Alexander the Great

was a philosopher”

• “Alvin believes that 2 + 2 = 4” vs. “Alvin believes that 2 + 2 = the

positive cube root of 64”

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• “John” and “Mary’s brother“ have the same reference but

different senses. This is why “John = Mary‘s brother“ is

informative but “John = John“ is not.

1. John is Mary‘s brother

2. John is John

• (2) is trivially true. (1), however, is informative because

someone might learn something new upon reading (1). Hence

(1) and (2) differ in cognitive value.

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• “Brother” and “male sibling“ have the same reference but

different senses. This is why “brother = male sibling“ is

informative but “brother = brother“ is not.

1. A brother is a male sibling

2. A brother is a brother

• (2) is trivially true. (1), however, is informative because

someone might learn something new upon reading (1). Hence

(1) and (2) differ in cognitive value.

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Family Resemblance

• Proposal: Abandon the search for necessary and sufficient conditions for

philosophical concepts and instead look for family resemblances (Ludwig

Wittgenstein).

• Example: What are necessary and sufficient conditions for something being

a game?

– Not all games involve competition (e.g., patience)

– Not all games are fun for the participants (e.g., gladiatorial games)

– Not only games are governed by rules (e.g., political debates)

– Not only games have objectives (e.g., initiation ceremonies)

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• Pairs of games resemble each other in certain respects, but

what respects these are, differ between different pairs of

games.

• Analogy: faces of pairs of people from the same family may

resemble each other in certain respects but what these

respects are differ from pair to pair.

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