Group:
philosophy of mathematics
Topic:
analytic truth
Topic:
empirical truth
Topic:
limitations of formalism
Topic:
mathematical proof as a social process
Topic:
mathematics as a formal system
Topic:
mathematics by proofs and refutations
Topic:
metaphysics and epistemology
Topic:
number and arithmetic as part of language
Topic:
problems with empirical truth
Topic:
skepticism about knowledge
Topic:
what is truth
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Summary
Although analytic truth is a useful distinction, it is not as absolute as one might think. The domain of analytical truths, mathematics, is a fluid one. The idea of absolute, or final truths hasn't worked historical. It's hard to define analyticity without assuming it in the first place.
Quine argues that the whole distinction between analytic and synthetic is an artificial one; that all truth is "a man-made fabric which impinges on experience only along the edges. Even such statements as "x=x" could be otherwise.
Analyticity is really about what is certain and what could be otherwise. Quine is saying that nothing is certain. This is perhaps too strong a statement. A better approach is a basic faith that allows certainty and hence a path to knowledge. Wittgenstein says it well. "But, if you are certain, isn't it that you are shutting your eyes in face of doubt?--They are shut. Am I less certain that this man is in pain than that twice two is four?" The scientific approach assumes a similar faith. (cbb 4/94)
Subtopic: knowledge is fallible 
| Quote: human reason regards all knowledge as parts of a possible system and hence resists contradiction; but there is no system [»kantI_1781, OK]
| | Quote: everything in existence is conditioned, and still not dependent on an unconditioned and primal existence
| | Quote: the faculty of reason has a natural desire to build a self-subsistent systematic whole by ideas alone [»kantI_1781, OK]
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Subtopic: mathematics is fallible
| Quote: even though formalism, platonism, and constructivism treat mathematics as indubitable truth, mathematical truth is fallible and corrigible [»daviPJ_1981]
| | Quote: the process of lemma-incorporation yields an infinite regress unless proof is a game or there are trivially true lemmas [»lakaI_1976]
| | Quote: the calculi of mathematics was invented to suit experience and then made independent of experience [»wittL_1939]
|
Subtopic: science is fallible
| Quote: Pappian heuristic--derive consequences of a conjecture; if true, rederive the original conjecture, thus yielding a final truth; failed for science [»lakaI_1976]
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Subtopic: analytical truth
| Note: can teach the concept of analytical truth just as one can describe a 'dog' even though can't give a rigorous definition [»quinWV1_1951, OK]
| | Quote: a priori knowledge may be know empirically; e.g., a computer says a number is prime [»kripSA_1980]
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Subtopic: experience is necessary
| Quote: possible experience can alone give reality to our concepts; without it a concept is merely an idea, without truth or relation to an object [»kantI_1781, OK]
|
Subtopic: linguistic truth
| Quote: an artificial language could specify its analytic statements but this assumes a notion of analytic already [»quinWV1_1951]
| | Quote: if a language contains intension adverbs (necessarily) then interchanging equivalent predicates can demonstrate cognitive synonymy; analytic already [»quinWV1_1951]
| | Quote: it is nonsense to distinguish between a linguistic and a factual component to the truth of any one statement
| | Quote: truth depends on both language and extralinguistic fact; but can not distinguish analytic statements as not based on fact; act of faith [»quinWV1_1951]
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Subtopic: checking vs. creating a proof
| Quote: logic teaches how to know whether or not reasoning is conclusive but it does not teach how to find conclusive reasonings or demonstrations [»galiG_1638]
| | Quote: our mathematical knowledge is the same as Divine wisdom but we reason by steps while His is one of simple intuition [»galiG_1632]
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Subtopic: certainty
| Quote: am I less certain that this man is in pain than that twice two is four? different kinds of certainty [»wittL_1958a]
| | Quote: if you are certain, isn't it that you are shutting your eyes in face of doubt? They are shut
|
Subtopic: x=x
| Quote: although x=x is always true for names, it is not always true for definite descriptions; e.g., 'the present King of France' [»russB_1919, OK]
| | Quote: that a mark refers to the same object on two occasions is a convenient but contingent usage; e.g., a language in which "x=y" is analytic [»searJR_1958]
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Related Topics
Group: philosophy of mathematics (11 topics, 330 quotes)
Topic: analytic truth (51 items)
Topic: empirical truth (47 items)
Topic: limitations of formalism (93 items)
Topic: mathematical proof as a social process (14 items)
Topic: mathematics as a formal system (30 items)
Topic: mathematics by proofs and refutations (31 items)
Topic: metaphysics and epistemology (99 items)
Topic: number and arithmetic as part of language (30 items)
Topic: problems with empirical truth (21 items)
Topic: skepticism about knowledge (34 items)
Topic: what is truth
(67 items)
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