Some Terminology

Some Terminology - is equal to 4 Finally consider a...

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Some Terminology (i) a sentence is a priori true if and only if (iff) it can be known independently of experience (contrast: a posteriori: can only be known by experience). (ii) a sentence is necessarily true iff it couldn’t be false, i.e. it is true in every possible world (contrast: contingent: false is some possible worlds, true in others) (iii) a sentence is analytically true iff it is true in virtue of its meaning (contrast: synthetic: neither true nor false in virtue of its meaning) Note: these aren’t obviously the same. So, for instance, ‘Bachelors are unmarried’ is analytic, a priori and necessary. Statements of arithmetic like ‘2 + 2 = 4’ are a priori and necessary; but it’s not obvious that they are analytic. (It’s not obvious that it’s part of the meaning of ‘2 + 2’ that it
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Unformatted text preview: is equal to 4.) Finally consider a sentence like ‘Goldbach’s conjecture is true’. Goldbach’s conjecture is the conjecture that every even number is the sum of two primes. No one has ever found a counter-example; but no one has ever given a proof. Perhaps the conjecture is true but there is no proof. Then ‘Goldbach’s conjecture is true’ will be necessary; but not a priori (since we cannot know that it is true, since we can give no proof of it) and not analytic (otherwise we could give a proof just by paying careful attention to the meanings of the words). Sometimes it is said that if egoism is a priori true, it would be trivial and uninteresting; but that is too quick. At most that would follow if it were analytic (though even that is controversial)....
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