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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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7399
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Even without religion, there are many guides to morality [Bacon]
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Full Idea:
Atheism leaves a man to sense, to philosophy, to natural piety, to laws, to reputation; all which may be guides to an outward moral virtue, though religion were not.
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From:
Francis Bacon (17: Of Superstition [1625], p.52)
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A reaction:
One might add to Bacon's list 'contracts', or 'rational consistency', or 'self-evident human excellence', or 'natural sympathy'. This is a striking idea, which clearly made churchmen uneasy when atheism began to spread.
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