Timeline for answer to Classical vs relevance and intuitionistic logics by Mauro ALLEGRANZA
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| 2 days ago | history | edited | Mauro ALLEGRANZA | CC BY-SA 4.0 |
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| 2 days ago | comment | added | Mauro ALLEGRANZA | Thus, the interesting fact, for me, is not that they a based on different points of view, but the fact that they are "comparable". | |
| 2 days ago | comment | added | Mauro ALLEGRANZA | @mudskipper agreed, but if you want to count theorems... the issue become misleading. Classical logic proves LEM: thus, it "wins". But for IL LEM is not valid, that means that CL is not sound... | |
| 2 days ago | comment | added | mudskipper | +1 But this answer is extremely succinct! If "stronger" in the question also refers to "being able to prove this-or-that theorem", then that part of the question is not touched on. Right? CL and IL are equivalent under translation, but this works by weakening what is claimed. So, not everything provable in CL is provable in IL (and proofs in IL, if they are found, for the same theorem are usually quite a bit more involved). In this last respect CL versus IL is not just a philosophical issue without importance for math itself. | |
| 2 days ago | comment | added | J D | +1 "This means that the issue about the "right" logic is not a "issue of logic". It is a philosopical issue". (I'd say "philosophy of logic" to split the difference.) @Keshlam might be interested to see that the development of theses in IL/CL, positions on pluralism, and also those that look to hybridize psychologism/anti-psychologism are arguably current contributions that have implications relevant to the exploration of AI and AGI. | |
| 2 days ago | history | edited | Mauro ALLEGRANZA | CC BY-SA 4.0 |
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| 2 days ago | history | answered | Mauro ALLEGRANZA | CC BY-SA 4.0 |