Timeline for Why should I not believe there are true contradictions?
Current License: CC BY-SA 4.0
11 events
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| May 8 at 17:22 | comment | added | Kaia | @Jay I think the contradictory-definitions interpretation is the intended one. It's the only one that makes sense with the non-contradiction/paraconsistency that the question talks about in its second half. Like you say, if it's the element-wise AND, it's just a properly defined set that does not include Delia. | |
| May 8 at 16:19 | comment | added | Corbin | @Jay: Modern logic is formalized and can be analyzed with maths. Additionally, maths is formalized with logics. Your view is pre-Cantorian; it use to be not wrong, but mathematicians have moved past it. We no longer rely solely on intuition, and as a result, we now have constructive logics, linear logics, and many other non-intuitive deductive systems. These matter in "the real world"; computers run on constructive logic, logistics and stoichiometry are linear logics, etc. | |
| May 8 at 15:37 | comment | added | Jay | @corbin Hmm. The fact that people can and have constructed complex axioms and proven that there are relationships between them, doesn't really change the fact that at some point you have to start with, "let's just agree that this makes sense". And in any case I was talking about laws of logic, not mathematical axioms. One could, perhaps, prove that a mathematical axiom describes the real world experimentally. But that's not the same things as proving that "contradictions are not allowed" is valid. As to "sometimes intuition is wrong" ... of course. I don't deny that. | |
| May 8 at 15:22 | comment | added | Jay | ... the fact that a contradictory premise leads to contradictory conclusions is exactly what we would expect. It does not shake the laws of logic or force us to rethink our understanding of those laws. it's more like, "duh, so what?" | |
| May 8 at 15:21 | comment | added | Jay | @Kaia I haven't gone back to the original source. Just based on the OP, I guess it's a matter of interpretation. If what he meant is that the definition of "wulture" is "is a vulture and is not white", than that's a perfectly good definition and the fact that it excludes a certain creature, in this case a white vulture, is perfectly reasonable. If what he meant is that he has two contradictory definitions of "wulture", one definition is "is a vulture" and the other definition is "is not white", then yeah, you have a contradiction right there, and ... | |
| May 7 at 18:02 | comment | added | Kaia | "But the original post said that the definition of "wulture" is "is a vulture" AND "is not white"" It's not an object-wise AND, it's a contradictory definition. | |
| May 7 at 17:57 | comment | added | Corbin | One missing nuance: most modern axioms of logic are not accepted purely from intuition. Some axioms, particularly combinators like S and K, are synthetic and chosen for power and parsimony. Others, like quantifier introduction/elimination, are justified by topos theory; see e.g. this answer. The axioms of first-order logic are crafted to satisfy Gödel's completeness theorem. Sometimes intuition is wrong; consider LEM. | |
| May 7 at 13:01 | comment | added | Jay | @edelex If you can show that following a rule leads to nonsense, then sure, that's an argument that the rule is not valid. But to say that if I break this rule, this leads to nonsense, that certainly does not prove that the rule is invalid. If anything it is an argument that the rule is valid, because breaking it leads to problems. | |
| May 7 at 13:00 | comment | added | Jay | @edelex But the original post said that the definition of "wulture" is "is a vulture" AND "is not white". So by definition it does NOT include all vultures, only those that are not white. If you interpret the definition to mean "includes all vultures", period end of sentence, and also "does not include anything that is white", then the definition is self-contradictory to begin with. Maybe that's the point, but to say, "I invented this definition that makes no sense, and when I try to apply it the results make no sense" ... that's not a very interesting line of thought. | |
| May 7 at 8:08 | comment | added | edelex | But if 'wulture' includes all vultures then she also must be in the set. | |
| May 6 at 18:44 | history | answered | Jay | CC BY-SA 4.0 |