Are there true contradictions?
>>16840849Anyone who denies the law of the excluded middle is either a grifter or a retard.
>>16840855UH OHUH OH SPAGHETIO
>>16840849Yes and no.
>>16840849There are no "truths" in formal logic. There are only axioms, assumptions, and deductions. You can assume a contradiction, but as shown any statement follows from it so it's rather pointless.
>>16840906>this is a valid deduction>this statement follows from these axioms
>>16840940Yeah, you can call that truth if you like.
>>16840855>https://plato.stanford.edu/entries/goedel-incompleteness/checkmate, shit4brain
>>16840906The premise of a contradiction rests on a contradiction which superficially invalidates it for disqualification. For a contradiction to be known, then it must be shown to exist. And if a contradiction exist, it precisely nullifies its exclusionary capability. Because there is a counterexample. So one could only say that a contradiction is merely highly unlikely and seek out further argumentation to find certainty.Erasing this requires revisiting the basis of the so-called laws of logic.
>>16840906The principle of explosion follows from disjunctive introduction. You can just restrict disjunctive clauses with a relevancy principle.
>>16840855The law of excluded weakens a system, and its exclusion has nothing to do with paraconsistency, its just intuitionistic logic.
If you can't say anything of substance without posting a meme that literally needed a meme template to even be made then you don't have anything of substance to say. At the very least, you should do it somewhere else. You're not gonna get nearly as many bites here as you would on another board so you're just denying yourself a far better dopamine drip. If it helps, I could try to turn that into a mathematical proof for you, but otherwise you'd probably be better off on /b/ or /tv/.
>>16840849Yes, it is true that zero is its own opposite number, its own additive annihilator, a valueless value that contradicts itself which is why it the origin number of the deductive explosion known as numerical arithmetic.
>>16840849We consider first order logic formulas build on a language (a collection of constants, function and relation symbols) and the logical connectors -> and forall only. In the following let be O any fixed formula without free variables (it could be a constant). We define a "proof" to be any sequence (A_1,...,A_n) where for every i in {1,...,n} either:(1) A_i has one of the following forms: A -> (B -> A), (A -> (B -> C) -> ((A -> B) -> (A -> C)) or (forall x A) -> (A[x:= t])(2) there are integers j,k such that j < i, k < i and A_j = A_k -> A_i(3) there is an integer j such that j < i and formulas B,C and a letter y not having any free occurrence in B such that A_j = B -> C and A_i = B -> (forall y C)Note for further concerns that this system doesn't have any "non contradiction principle"; in fact it doesn't even expresses negations (it is a fragment of intuitionistic logic with only implications). But notice as well that if we had a constant "false" in the language and had the exra axioms "((A -> false) -> false) ->A" we could express and prove with the rules above, all classical first order logic theorems.We say a formula F is regular (remember we have fixed a formula O without free variables) if there is a proof of (((F -> O) -> O) -> F). It is routine to check that O is itself regular and that the set of regular formulas is stable by implication (in fact for every formula S and every regular formula R, (S -> R) is regular) and forall. Also, for every regular formula A, there is a proof of (O -> A) in the above sense. So we define, for any first order formula P (with the added constant false this time), the translation P* (which will always be regular) by induction:-if P is atomic, P* is P->O;-if P = A -> B, P*:= (A*) -> (B*);-if P:= forall x A, P*:= forall x (A*). This translation interprets all classical reasoning in our base system. So the non contradiction is obtained and paraconsistent logic is this a meme.
>>16840849>>are there any true contradictions?Yes, Paradoxes
>>16842688What is the specific logical expansion for the impossibility of contradiction?
The paradox of tolerance
