18073
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Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
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Full Idea:
Dummett argues that classical logic depends on the choice of the concept of truth as central to the theory of meaning, while for the intuitionist the concept of assertability occupies this position.
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From:
report of Michael Dummett (The philosophical basis of intuitionist logic [1973]) by Philip Kitcher - The Nature of Mathematical Knowledge 06.5
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A reaction:
Since I can assert any nonsense I choose, this presumably means 'warranted' assertability, which is tied to the concept of proof in mathematics. You can reason about falsehoods, or about uninterpreted variables. Can you 'assert' 'Fx'?
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12714
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The substantial form is the principle of action or the primitive force of acting [Leibniz]
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Full Idea:
The substantial form is the principle of action or the primitive force of acting.
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From:
Gottfried Leibniz (De Mundo Praesenti [1686], A6.4.1507-8), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3
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A reaction:
The clearest statement of the modification of Aristotle's hylomorphism which Leibniz preferred in his middle period, and which strikes me as an improvement, and about right. Shame that monads got too much of a grip on him, but he was trying to dig deeper.
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12743
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A true being must (unlike a chain) have united parts, with a substantial form as its subject [Leibniz]
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Full Idea:
In a Being one per se a real union is required consisting not in the situation or motion of parts, as in a chain or a house, but in a unique individual principle and subject of attributes and operations, in us a soul and in a body a substantial form.
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From:
Gottfried Leibniz (De Mundo Praesenti [1686], A6.4.1506), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7
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A reaction:
Leibniz is said not to be an essentialist, by making all properties essential, but he is certainly committed to substance, and it sounds like essence here (or one view of essence), when it makes identity possible. This idea is pure Aristotle.
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19056
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If a sentence is effectively undecidable, we can never know its truth conditions [Dummett]
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Full Idea:
If a sentence is effectively undecidable, the condition which must obtain for it to be true is not one which we are capable of recognising whenever it obtains, or of getting ourselves in a position to do so.
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From:
Michael Dummett (The philosophical basis of intuitionist logic [1973], p.225)
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A reaction:
The instances of 'undecidable' sentences are most clearly seen in mathematics, such as the Continuum Hypothesis or Goldbach's Conjecture, or anything involving vast infinite cardinals. But do you need precise truth-conditions for meaning?
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