8920
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Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]
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Full Idea:
A relation R on a non-empty set S is an equivalence relation if it is reflexive (for each member a, aRa), symmetric (if aRb, then bRa), and transitive (aRb and bRc, so aRc). It tries to classify objects that are in some way 'alike'.
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From:
Seymour Lipschutz (Set Theory and related topics (2nd ed) [1998], 3.9)
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A reaction:
So this is an attempt to formalise the common sense notion of seeing that two things have something in common. Presumably a 'way' of being alike is going to be a property or a part
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9160
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Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H]
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Full Idea:
Propositions such as 'People usually tell the truth' seem to count as default reasonable, but it is odd to count them as a priori. Empirical indefeasibility seems the obvious way to distinguish those default reasonable propositions that are a priori.
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From:
Hartry Field (Apriority as an Evaluative Notion [2000], 1)
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A reaction:
Sounds reasonable, but it would mean that all the uniformities of nature would then count as a priori. 'Every physical object exerts gravity' probably has no counterexamples, but doesn't seem a priori (even if it is necessary). See Idea 9164.
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9165
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Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H]
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Full Idea:
Reliability is not a 'factual property'; in calling a rule reasonable we are evaluating it, and all that makes sense to ask about is what we value. We place a high value on the reliability of our inductive and perceptual rules that lead to truth.
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From:
Hartry Field (Apriority as an Evaluative Notion [2000], 5)
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A reaction:
This doesn't seem to be a contradiction of reliabilism, since truth is a pretty widespread epistemological value. If you do value truth, then eyes are pretty reliable organs for attaining it. Reliabilism is still wrong, but not for this reason.
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9162
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Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H]
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Full Idea:
Reliability is not all we want in an inductive rule. Completely reliable methods are available, such as believing nothing, or only believing logical truths. But we don't value them, but value less reliable methods with other characteristics.
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From:
Hartry Field (Apriority as an Evaluative Notion [2000], 3)
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A reaction:
I would take this excellent point to be an advertisement for inference to the best explanation, which requires not only reliable inputs of information, but also a presiding rational judge to assess the mass of evidence.
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9163
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If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H]
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Full Idea:
If some inductive rule is basic for us, in the sense that we never assess it using any rules other than itself, then it must be one that we treat as empirically indefeasible (hence as fully a priori, given that it will surely have default status).
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From:
Hartry Field (Apriority as an Evaluative Notion [2000], 4)
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A reaction:
This follows on from Field's account of a priori knowledge. See Ideas 9160 and 9164. I think of induction as simply learning from experience, but if experience goes mad I will cease to trust it. (A rationalist view).
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