17896
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We need to know the meaning of 'and', prior to its role in reasoning [Prior,AN, by Belnap]
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Full Idea:
For Prior, so the moral goes, we must first have a notion of what 'and' means, independently of the role it plays as premise and as conclusion.
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From:
report of Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.132
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A reaction:
The meaning would be given by the truth tables (the truth-conditions), whereas the role would be given by the natural deduction introduction and elimination rules. This seems to be the basic debate about logical connectives.
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17898
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Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B [Belnap on Prior,AN]
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Full Idea:
Prior's definition of 'tonk' is inconsistent. It gives us an extension of our original characterisation of deducibility which is not conservative, since in the extension (but not the original) we have, for arbitrary A and B, A |- B.
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From:
comment on Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.135
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A reaction:
Belnap's idea is that connectives don't just rest on their rules, but also on the going concern of normal deduction.
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22308
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Only the actual exists, so possibilities always reduce to actuality after full analysis [Russell]
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Full Idea:
Possibility always marks insufficient analysis: when analysis is completed, only the actual can be relevant, for the simple reason that there is only the actual, and that the mere possibility is nothing.
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From:
Bertrand Russell (Papers of 1913 [1913], VII.26), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 42 'Logic'
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A reaction:
Quine agreed with Russell on this. You won't get far in life if you deny possibilities. The answer is to recognise that the actual is dynamic, and not passive.
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