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11023
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The logical connectives are 'defined' by their introduction rules [Gentzen]
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Full Idea:
The introduction rules represent, as it were, the 'definitions' of the symbols concerned, and the elimination rules are no more, in the final analysis, than the consequences of these definitions.
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From:
Gerhard Gentzen (works [1938]), quoted by Stephen Read - Thinking About Logic Ch.8
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A reaction:
If an introduction-rule (or a truth table) were taken as fixed and beyond dispute, then it would have the status of a definition, since there would be nothing else to appeal to. So is there anything else to appeal to here?
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11213
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Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
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Full Idea:
To every logical symbol there belongs precisely one inference figure which 'introduces' the symbol ..and one which 'eliminates' it. The introductions represent the 'definitions' of the symbols concerned, and eliminations are consequences of these.
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From:
Gerhard Gentzen (works [1938], II.5.13), quoted by Ian Rumfitt - "Yes" and "No" III
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A reaction:
[1935 paper] This passage is famous, in laying down the basics of natural deduction systems of logic (ones using only rules, and avoiding axioms). Rumfitt questions whether Gentzen's account gives the sense of the connectives.
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6007
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If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
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Full Idea:
The 'undetected' or 'veiled' paradox of Eubulides says: if you know your father, and don't know the veiled person before you, but that person is your father, you both know and don't know the same person.
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From:
report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
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A reaction:
Essentially an uninteresting equivocation on two senses of "know", but this paradox comes into its own when we try to give an account of how linguistic reference works. Frege's distinction of sense and reference tried to sort it out (Idea 4976).
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6008
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Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
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Full Idea:
The 'sorites' paradox of Eubulides says: if you take one grain of sand from a heap (soros), what is left is still a heap; so no matter how many grains of sand you take one by one, the result is always a heap.
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From:
report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
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A reaction:
(also Cic. Acad. 2.49) This is a very nice paradox, which goes to the heart of our bewilderment when we try to fully understand reality. It homes in on problems of identity, as best exemplified in the Ship of Theseus (Ideas 1212 + 1213).
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