It is - or rather, it isn't, in DL. See Aristotle, Rhetoric, or any many modern versions such as Corbet'sLaw of Noncontradiction, viz. ~(A & ~A) should be a theorem of a Dialectical Logic (DL). — Alvin Capello
Some logic, some sentences. Sample? And what of the fact that in a logic in which both sides of a contradiction can stand, anything is provable?logic in which some sentences are both True and False at the same time and in the same respect. — Alvin Capello
in which sentences can be both true and false at the same time and in the same respect. Priest likes to use the Liar Sentence as an example of one such, viz. "This sentence is false." — Alvin Capello
Presumably according to some paraconsistent rule, but how would that work? (New to me; please educate.) Perhaps the question is, if you're going to be both consistent and inconsistent, then how is that decided?in a Paraconsistent Logic, you can have a sentence of the form A & ~A, but it will not follow that some arbitrary sentence B can be proved from this. — Alvin Capello
Perhaps the question is, if you're going to be both consistent and inconsistent, then how is that decided?
My origami skills are not great, but I'm pretty good at unfolding. It appears, on unfolding, that 1) any argument with designated premises and a false conclusion is not-valid in LP. How about otherwise?In LP, an argument is considered valid if and only if there is no semantic interpretation wherein all the premises are designated and the conclusion is undesignated. — Alvin Capello
1. what does negation mean in paraconsistent logic?
2. If negation has an altogether different meaning than its meaning in classical logic then (A & ~A) in paraconsistent logic is NOT a violation of the law of noncontradiction.
It seems to me then that at least by the light of regular logic that LP is not sound, and only valid under its own rules. Yes? — tim wood
I don’t think it’s correct to say that a logic is either valid or sound. To be sure, most logics do have valid arguments in them, but the logic itself is not valid. — Alvin Capello
Other paraconsistent logics understand negation to be a contradictory-forming operator (contradictories are pairs of propositions that cannot both be true or both be false). — Alvin Capello
Well, one good reason to use it is that LP can deal with contradictory theories. Classical and other non-paraconsistent logics cannot do this. — Alvin Capello
Is there anything within that Plato and Aristotle did not cover?
Now suppose we have another object that is both round all over and it is not the case that it is round all over. This new object is both round and not round at the same time and in the same respect. This is because it is the entire object that is both round and not round. Therefore, this second object is truly contradictory. — Alvin Capello
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.