How mathematicians define the concept of logic for the purposes of Classical Logic?
Also, how do philosophers and mathematicians at different period in history defined the word "logic", if they did?
What is logic for academics?
I put here various claims about Classical Logic which can be found on this forum:
The convention about the material conditional is one of the things that makes classical logic classical.
"By the convention about the material conditional, when the premise is false the conditional is true." It is not merely a convention; it is a provable fact of classical logic.
What is generally now called Classical logic is the framework that is thought to encapsulate both the Predicate calculus formalism and the compositional aspect that a structured, two-valued algebra of logic gave us in the propositional case.
LEM (Law of Excluded Middle) (...) is central to classical logic
in Classical Propositional Logic, True and False are understood as forming a two-valued Boolean Algebra
Also, Wikipedia says that Classical logic is also called “standard logic” and that it is the one formal system which is the most studied and used. It gives its defining characteristics as follows:
- Law of excluded middle (LEM)
- Double-negation elimination
- Law of non-contradiction (LNC)
- Principle of Explosion (PoE)
- Monotonicity of entailment (MoE)
- Idempotency of entailment (IoE)
- Commutativity of conjunction
- De Morgan’s Laws
MoE says that if a sentence follows from a set of sentences, then it also follows from any superset of these sentences. A corollary is that a valid argument cannot become invalid by the addition of new premises.
IoE says that if a consequence follows, it also follows when any number of instances of an existing premise are added.