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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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9455
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Maybe proper names have the content of fixing a thing's category [Bealer]
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Full Idea:
Some say that proper names have no descriptive content, but others think that although a name does not have the right sort of descriptive content which fixes a unique referent, it has a content which fixes the sort or category to which it belongs.
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From:
George Bealer (Propositions [1998], §7)
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A reaction:
Presumably 'Mary', and 'Felix', and 'Rover', and 'Smallville' are cases in point. There is a well known journalist called 'Manchester', a famous man called 'Hilary', a village in Hertfordshire called 'Matching Tie'... Interesting, though.
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9454
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The four leading theories of definite descriptions are Frege's, Russell's, Evans's, and Prior's [Bealer]
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Full Idea:
The four leading theories of definite descriptions are Frege's, Russell's, Evans's, and Prior's, ...of which to many Frege's is the most intuitive of the four. Frege says they refer to the unique item (if it exists) which satisfies the predicate.
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From:
George Bealer (Propositions [1998], §5)
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A reaction:
He doesn't expound the other three, but I record this a corrective to the view that Russell has the only game in town.
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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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9452
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Propositions might be reduced to functions (worlds to truth values), or ordered sets of properties and relations [Bealer]
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Full Idea:
The reductionist view of propositions sees them as either extensional functions from possible worlds to truth values, or as ordered sets of properties, relations, and perhaps particulars.
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From:
George Bealer (Propositions [1998], §1)
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A reaction:
The usual problem of all functional accounts is 'what is it about x that enables it to have that function?' And if they are sets, where does the ordering come in? A proposition isn't just a list of items in some particular order. Both wrong.
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9451
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Modal logic and brain science have reaffirmed traditional belief in propositions [Bealer]
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Full Idea:
Philosophers have been skeptical about abstract objects, and so have been skeptical about propositions,..but with the rise of modal logic and metaphysics, and cognitive science's realism about intentional states, traditional propositions are now dominant.
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From:
George Bealer (Propositions [1998], §1)
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A reaction:
I personally strongly favour belief in propositions as brain states, which don't need a bizarre ontological status, but are essential to explain language, reasoning and communication.
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