14182
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If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read]
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Full Idea:
In 'A is taller than B, and B is taller than C, so A is taller than C' this can been seen as a matter of meaning - it is part of the meaning of 'taller' that it is transitive, but not of logic. Logic is now seen as the study of formal consequence.
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From:
Stephen Read (Formal and Material Consequence [1994], 'Reduct')
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A reaction:
I think I find this approach quite appealing. Obviously you can reason about taller-than relations, by putting the concepts together like jigsaw pieces, but I tend to think of logic as something which is necessarily implementable on a machine.
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14184
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In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read]
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Full Idea:
A puzzle about modus ponens is that the major premise is either false or unnecessary: A, If A then B / so B. If the major premise is true, then B follows from A, so the major premise is redundant. So it is false or not needed, and contributes nothing.
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From:
Stephen Read (Formal and Material Consequence [1994], 'Repres')
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A reaction:
Not sure which is the 'major premise' here, but it seems to be saying that the 'if A then B' is redundant. If I say 'it's raining so the grass is wet', it seems pointless to slip in the middle the remark that rain implies wet grass. Good point.
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14186
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Logical connectives contain no information, but just record combination relations between facts [Read]
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Full Idea:
The logical connectives are useful for bundling information, that B follows from A, or that one of A or B is true. ..They import no information of their own, but serve to record combinations of other facts.
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From:
Stephen Read (Formal and Material Consequence [1994], 'Repres')
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A reaction:
Anyone who suggests a link between logic and 'facts' gets my vote, so this sounds a promising idea. However, logical truths have a high degree of generality, which seems somehow above the 'facts'.
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17447
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Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
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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.
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From:
report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
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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'.
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