Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Calculus Ratiocinator' and 'The Internalist Conception of Justification'

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3 ideas

2. Reason / A. Nature of Reason / 6. Coherence
If the only aim was consistent beliefs then new evidence and experiments would be irrelevant [Goldman]
     Full Idea: If mere consistency is our aim in achieving a coherent set of beliefs, then new evidence and experiments are irrelevant.
     From: Alvin I. Goldman (The Internalist Conception of Justification [1980], §VIII)
     A reaction: An important reminder. What epistemic duty requires us to attend to anomalous observations, instead of sweeping them under the carpet?
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
A whole is just its parts, but there are no smallest parts, so only minds and perceptions exist [Leibniz]
     Full Idea: The whole, if it is assumed to be body or matter, is nothing other than all of its parts; but this is absurd, since there aren't any smallest parts. Therefore there really exist only minds and their perceptions.
     From: Gottfried Leibniz (Calculus Ratiocinator [1679], A6.4.279), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7
     A reaction: Leibniz is sometimes labelled as an 'idealist', but this text is unusual in being so explicit, and he was mainly concerned to explain the reality of individual bodies. Monads were his final attempt to do this, not an attempt to escape into pure minds.