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What is the difference between mathematical logic and philosophical logic? Yes I know, one has more math than the other. Is Gödel's incompleteness in mathematical logic? Is modal logic in philosophical logic? Can you give other examples of different logics or questions each asks in order to distinguish the two?

Gödel's first incompleteness theorem says that, for any suitable formal theory which is consistent and includes enough arithmetic, there will be an arithmetical sentence -- a "Gödel sentence" -- which that theory can neither prove nor disprove. This theorem is a bit of mathematics: its proof is undoubtedly a sound mathematical proof. (That's why those obsessives who plague internet discussion groups with purported refutations of Gödel are so very annoying! -- they are refusing to follow, or are incapable of following, a relatively straightforward bit of purely mathematical reasoning.) The question of the significance of Gödel's theorem, however, is quite another matter. To investigate that , we need to engage in philosophical reflection. Some have held, for instance, that Gödel's theorem can be used to show that minds are not machines. Let's not worry here about why that's been said: the simple point we need now is just that, to decide the merits of this interpretative view, we need...

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