Respond to one of these prompts and be clear about which one you are referring to: PROMPT #1: PARADOX OF ANALYSIS. Analyze the concept of philosophical (conceptual) analysis. Is every concept in need
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Phil 2: Puzzles and Paradoxes
Prof. Sven Bernecker
University of California, Irvine
Paradox of Analysis
Three paradoxes of understanding:
•Paradox of Analysis
•Problem of the Criterion
•Hermeneutic Circle
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•Plato (428/427 or 424/423 – 348/347 BC) .Philosopher and mathematician in Classical Greece.
•George Edward "G.E.“ Moore (1873 –1958). British philosopher who taught at the University of Cambridge. He worked in ethics, epistemology, and metaphysics.
•Cooper Harold “C.H.” Langford (1895 -1964). An Irish philosopher and mathematical logician who taught at the University of Michigan 3
Necessary/Sufficient Conditions
•To say that X is a necessary condition for Y is to say that it is impossible to have Y without X. In other words, the absence of X guarantees the absence of Y. Example: Having four sides is necessary for being a square.
•To say that X is a sufficient condition for Y is to say that the presence of X guarantees the presence of Y. In other words, it is impossible to have X without Y. Example: Being a square is sufficient for having four sides.
•See lecture 1.4, slide #7
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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 isa male sibling 2. A brother isa brother
•For (1) to qualify as a meaning analysis it must benecessarily true and knowable a priori . This isonly 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 toPlato ( Meno 80e). The 20 th century formulation of the paradox isdue toC.H. Langford ( 1895 -1964)
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“Let uscall what istobeanalyzed the analysandum ,and letuscall 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 ofanalysis isto the effect that ,ifthe verbal expression representing the analysandum has the same meaning asthe verbal expression representing the analysans ,the analysis states abare identity and istrivial, but ifthe two verbal expressions donot have the same meaning ,the analysis isincorrect “(Langford 1942 :323 ). 2/10/2018
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Reconstruction of theparadox of analysis :
1) An meaning analysis of a concept , F, should say what F isidentical to. 2) Suppose that a given analysis of theconcept F says that itisidentical tothe concept G. 3) So iftheconcepts F and G arenot identical , theanalysis isfalse . (1, 2) 4) Alternatively , iftheconcepts F and G areidentical , then what theanalysis says (namely that F = G) has thesame content astheclaim that theconcept F is identical totheconcept F. 5) But itisuninformative (“trivial“) that theconcept F isidentical totheconcept F. 6) So iftheconcepts F and G areidentical , what theanalysis says isuninformative . (4, 5) C) Therefore , theanalysis iseither false oruninformative . (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).
ReferenceThe object denoted by a word or phrase SenseThe 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 forexpressions with the same reference but different senses :
•“Mark Twain isSamuel Clemens“ vs. “Mark Twain isMark Twain“ •“Lines have the same direction ifand only ifthey are parallel toone another “ vs. “Lines have the same direction ifthey 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 iswhy “John = Mary‘s brother “ is informative but “John = John“ isnot.
1. John isMary‘s brother 2. John isJohn
•(2) istrivially true . (1), however , isinformative 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 iswhy “brother = male sibling “ is informative but “brother = brother “ isnot.
1. A brother isa male sibling 2. A brother isa brother
•(2) istrivially true . (1), however , isinformative 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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