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I 43
Def Liberal Platonism/LP/terminology/Stalnaker: (early thesis): if the practice is legitimate (inferences, etc.) then we really make assertions and the semantics really tells us what the statements say.
Reference/liberal Platonism: a causal connection as a condition of reference is then superfluous.
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Reference .
Problem: the existence of numbers cannot be constituted by a practice.
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Numbers .
I 45
Liberal Platonism/Stalnaker: Solution: the commitment to numbers is constituted by the endorsement of the practice.
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Practise .
I 48
Liberal Platonism: in contrast to the modal realism it is still verificationistic.
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Verificationism , >
Realism .
I 54
Platonism/Mathematics/Stalnaker: Mathematical Platonism suggests an image according to which mathematical propositions are contingent.
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Mathematical entities , >
Hartry Field .
Ontological commitment/Mathematics/Platonism/Stalnaker: Since the Platonist claims at the end that realm of mathematical entities exists necessarily, he has not made any ontological commitment at all.
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Ontological commitment .
Liberal Platonism/Stalnaker: Liberal Platonism says that since ontological commitment is not a commitment to exclude a possibility, one does not need an external relation (causal connection).
If true mathematical propositions are necessarily true, one does not need facts to make the propositions true.
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Truthmakers , >
Nonfactualism .
Knowledge/Consequences/Stalnaker: Nevertheless, it could still be that one does not know all true consequences of necessary sentences.
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Omniscience .
Solution/Stalnaker: Here we should introduce the concepts of proof, calculation, construction, etc.
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Proofs , >
Mathematics .