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9226
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If mathematical theories conflict, it may just be that they have different subject matter [Field,H]
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Full Idea:
Unlike logic, in the case of mathematics there may be no genuine conflict between alternative theories: it is natural to think that different theories, if both consistent, are simply about different subjects.
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From:
Hartry Field (Recent Debates on the A Priori [2005], 7)
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A reaction:
For this reason Field places logic at the heart of questions about a priori knowledge, rather than mathematics. My intuitions make me doubt his proposal. Given the very simple basis of, say, arithmetic, I would expect all departments to connect.
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21500
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We rely on memory for empirical beliefs because they mutually support one another [Lewis,CI]
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Full Idea:
When the whole range of empirical beliefs is taken into account, all of them more or less dependent on memorial knowledge, we find that those which are most credible can be assured by their mutual support, or 'congruence'.
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From:
C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 334), quoted by Erik J. Olsson - Against Coherence 3.1
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A reaction:
Lewis may be over-confident about this, and is duly attacked by Olson, but it seems to me roughly correct. How do you assess whether some unusual element in your memory was a dream or a real experience?
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6556
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If anything is to be probable, then something must be certain [Lewis,CI]
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Full Idea:
If anything is to be probable, then something must be certain.
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From:
C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 186), quoted by Robert Fogelin - Walking the Tightrope of Reason Intro
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A reaction:
Lewis makes this comment when facing infinite regress problems. It is a very nice slogan for foundationalism, which embodies the slippery slope view. Personally I feel the emotional pull of foundations, but acknowledge the very strong doubts about them.
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21498
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Congruents assertions increase the probability of each individual assertion in the set [Lewis,CI]
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Full Idea:
A set of statements, or a set of supposed facts asserted, will be said to be congruent if and only if they are so related that the antecedent probability of any one of them will be increased if the remainder of the set can be assumed as given premises.
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From:
C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 338), quoted by Erik J. Olsson - Against Coherence 2.2
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A reaction:
This thesis is vigorously attacked by Erik Olson, who works through the probability calculations. There seems an obvious problem without that. How else do you assess 'congruence', other than by evidence of mutual strengthening?
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5828
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Extension is the class of things, intension is the correct definition of the thing, and intension determines extension [Lewis,CI]
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Full Idea:
"The denotation or extension of a term is the class of all actual or existent things which the term correctly applies to or names; the connotation or intension of a term is delimited by any correct definition of it." ..And intension determines extension.
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From:
C.I. Lewis (An Analysis of Knowledge and Valuation [1946]), quoted by Stephen P. Schwartz - Intro to Naming,Necessity and Natural Kinds §II
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A reaction:
The last part is one of the big ideas in philosophy of language, which was rejected by Putnam and co. If you were to reverse the slogan, though, (to extension determines intension) how would you identify the members of the extension?
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7903
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The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
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Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
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From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
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A reaction:
What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
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