17 ideas
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
4261 | The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
17806 | It is untenable that mathematics is general physical truths, because it needs infinity [Curry] |
17808 | Saying mathematics is logic is merely replacing one undefined term by another [Curry] |
4255 | Externalist theories of knowledge are one species of foundationalism [Bonjour] |
4257 | The big problem for foundationalism is to explain how basic beliefs are possible [Bonjour] |
4256 | The main argument for foundationalism is that all other theories involve a regress leading to scepticism [Bonjour] |
4258 | Extreme externalism says no more justification is required than the truth of the belief [Bonjour] |
4259 | External reliability is not enough, if the internal state of the believer is known to be irrational [Bonjour] |
4260 | Even if there is no obvious irrationality, it may be irrational to base knowledge entirely on external criteria [Bonjour] |