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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5060
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All substances analyse down to simple substances, which are souls, or 'monads' [Leibniz]
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Full Idea:
What (in the analysis of substances) exist ultimately are simple substances - namely, souls, or, if you prefer a more general terms, 'monads', which are without parts.
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From:
Gottfried Leibniz (Metaphysical conseqs of principle of reason [1712], §7)
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A reaction:
This seems to me to be atomistic panpsychism. He is opposed to physical atomism, because infinite divisibility seems obvious, but unity is claimed to be equally obvious in the world of the mental. Does this mean bricks are made of souls? Odd.
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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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5059
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Power rules in efficient causes, but wisdom rules in connecting them to final causes [Leibniz]
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Full Idea:
In all of nature efficient causes correspond to final causes, because everything proceeds from a cause which is not only powerful, but wise; and with the rule of power through efficient causes, there is involved the rule of wisdom through final causes.
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From:
Gottfried Leibniz (Metaphysical conseqs of principle of reason [1712], §5)
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A reaction:
Nowadays this carrot-and-stick view of causation is unfashionable, but I won't rule it out. The deepest 'why?' we can ask won't just go away. This unity by a divine mind strikes me as too simple, but Leibniz is right to try to unify Aristotelian causes.
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