Classical: The standard kinds of logic that you learn in undergraduate logic classes are the best (or right) logics, the ones that best model (ETA: idealized versions of) our inferential processes. Examples of classical logics are Boolean logic and first-order predicate calculus. Classical logics are bivalent (sentences can only be true or false), obey the principle of the excluded middle (if a proposition is not true, its negation must be true) and obey the law of non-contradiction (a proposition and its negation cannot both be true).
Non-classical: The best logic is not classical. Non-classical logics usually reject the principle of the excluded middle or the law of non-contradiction. An example of a non-classical logic is dialetheism, according to which there are true contradictions (i.e. some sentences of the form “A and not A” are true). Proponents of non-classical logics argue that many of our scientific theories, if you probe deeply, involve inconsistencies, yet we don’t regard them as trivially false. So they claim that we need to revise the way we understand logic to accurately model our inferential processes.
Classical: The standard kinds of logic that you learn in undergraduate logic classes are the best (or right) logics, the ones that best model our inferential processes
Is that the right criterion? Or should it be: the ones that best model the correct inferential processes, whether or not we humans adhere to them?
I lean towards classical, but with the proviso that we have to be careful about what counts as a statement. Sneak in a statement with ambiguous truth values, and classical logic halts and catches fire. Personally I’m OK with rejecting such statemetns.
In my AI lessons, the “non-classical logic” course including all the probabilistic theories : fuzzy logic, Bayesian, … that’s why I voted “lean : non-classical”, but I guess it’s just a matter of vocabulary.
Classical: The standard kinds of logic that you learn in undergraduate logic classes are the best (or right) logics, the ones that best model (ETA: idealized versions of) our inferential processes. Examples of classical logics are Boolean logic and first-order predicate calculus. Classical logics are bivalent (sentences can only be true or false), obey the principle of the excluded middle (if a proposition is not true, its negation must be true) and obey the law of non-contradiction (a proposition and its negation cannot both be true).
Non-classical: The best logic is not classical. Non-classical logics usually reject the principle of the excluded middle or the law of non-contradiction. An example of a non-classical logic is dialetheism, according to which there are true contradictions (i.e. some sentences of the form “A and not A” are true). Proponents of non-classical logics argue that many of our scientific theories, if you probe deeply, involve inconsistencies, yet we don’t regard them as trivially false. So they claim that we need to revise the way we understand logic to accurately model our inferential processes.
Is that the right criterion? Or should it be: the ones that best model the correct inferential processes, whether or not we humans adhere to them?
Good point. I’ve edited to reflect this.
I lean towards classical, but with the proviso that we have to be careful about what counts as a statement. Sneak in a statement with ambiguous truth values, and classical logic halts and catches fire. Personally I’m OK with rejecting such statemetns.
What does Bayesian probability theory count as?
Bayesian probability is an extension of classical logic. I don’t think philosophers consider it to be non-classical.
In my AI lessons, the “non-classical logic” course including all the probabilistic theories : fuzzy logic, Bayesian, … that’s why I voted “lean : non-classical”, but I guess it’s just a matter of vocabulary.
Okay, so “Accept: classical” be it.