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What are some good arguments against taking plural logic, a slight extension of first order logic with plural quantification as a foundational logic? … The SEP article also mentions some results like the equi-interpretability of monadic second order logic and plural logic as justification for the ontological innocence of plural logic. …

Your argument in (1) that all logics have to be closed under negation seems to rest on the assumption that a logic should consist of all meaningful expressions in some context. …

Let's call the resulting proof in our refinement logic-inspired system H. …

In fact, you may think what we are doing isn’t really "logic" at all, but more philosophy of language, or even philosophy of mind or epistemology. Why then call it logic? … It suggests but does not directly claim that conflating an application of logic and logic itself obscures some important and interesting ideas. …

Have disjoint and non-disjoint flavors of higher-order logic with plural quantifiers both been studied? …

The single, most important logic is classical first-order logic (henceforth FOL). … , dependence logic. …

What kind of manipulation is valid formally changes from system to system (e.g. in intuitionistic logic vs classical logic). … Classical logic, however, doesn't give us the ability to talk about causality. …

I'm interested in nonclassical logic, particularly propositional logics because you only have one type of non-logical symbol. … The most powerful for propositional logics, in my opinion, is just translating formulas inductively into a classical first order logic with a single sort. …

(c≠d)∧(P(c)↔P(d)) Are there any go-to paradoxes / counterintuitive results if we take (3) as an axiom in a second-order logic system? …

Here's a somewhat artificial example of a three-valued logic constructed not to admit disjunction introduction while still having fairly symmetrical truth tables and agreeing with classical logic when … Here's a three-valued logic that doesn't admit disjunction introduction, and has the connectives K (conjunction/koniunkcja), A (disjunction/alternatywa), and C (implication/implikacja). …

In traditional logic, the following inference is valid All As are Bs. AaB ----------------- ----- Some As are Bs. …

I'll discuss classical propositional logic. Let M (for "model") be an intepretation. We can make M just a set of variables that are true, e.g. {A, B, C} or similar. … This is a specialized topic within logic, but people do study systems of logic that are specifically designed to avoid certain paradoxes or counterintuitive behavior like consequences following from contradictory …

So, the conditional theorem below is correct. P ⊢ S Q ⊢ S --------- P∨Q ⊢ S The conditional theorem is only false if there's a case where the premises are true and conclusion is false. And simi …

The variant of free logic that permits domains to be empty, but rejects non-referring terms is simply first-order logic. … Some presentations of first-order logic allow the domain to be empty, others require it to be non-empty. …

So, we want to encode the following sentence fragment in first-order logic: nor may any true gentlemen be punished with shipping, unless his crime be very shameful, and his course of life vicious and …