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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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5953
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For the Cyrenaics experience was not enough to give certainty about reality [Aristippus young, by Plutarch]
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Full Idea:
The Cyrenaics, placing all experience within themselves, thought such evidence was insufficient warrant for certainty about reality, and withdrew as in a siege from the world, admitting that objects 'appear', but refusing to pronounce the word 'are'.
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From:
report of Aristippus the younger (fragments/reports [c.335 BCE]) by Plutarch - 74: Reply to Colotes §1120
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A reaction:
This seems to be the most extreme position found in ancient thought. It accompanies their extreme hedonism, based on the reality of experience and lack of interest in anything external. A bit daft, really.
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19347
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Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
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Full Idea:
For individuation, substance needs three properties: independence, to separate it from other things; unity, to call it one thing, rather than an aggregate; and permanence or stability over time. Its other role is as subject for predicates.
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From:
Franklin Perkins (Leibniz: Guide for the Perplexed [2007], 3.1)
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A reaction:
Perkins is describing the Aristotelian view, which is taken up by Leibniz. 'Substance' is not a controversial idea, if we see that it only means that the world is full of 'things'. It is an unusual philosopher wholly totally denies that.
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3026
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Actions are influenced by circumstances, so Cyrenaics say felons should be reformed, not hated [Aristippus young, by Diog. Laertius]
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Full Idea:
Cyrenaics say errors should be pardoned, because men do not err intentionally but are influenced by circumstances; one should not hate a person, but only teach him better.
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From:
report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.9
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A reaction:
A very appealing suggestion, and rather wonderful for its time. There is still implied agreement about what is 'error', and what counts as 'better'.
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3024
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Cyrenaics teach that honour, justice and shame are all based on custom and fashion [Aristippus young, by Diog. Laertius]
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Full Idea:
The Cyrenaics taught that there was nothing naturally and intrinsically just, or honourable, or disgraceful; but that things were considered so because of law and fashion.
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From:
report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.8
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A reaction:
As we would say now, values and virtues are 'cultural constructs'. This obviously contains a lot of truth, but I don't think our opposition of genocide is just 'fashion'.
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