William Nestle’s Vom Mythos zum Logos (1940) is the classical statement of this reading. On the opening page, Nestle claims mythos and logos are “the two poles between which man’s mental life oscillates. Mythic imagination and logical thought are opposites,” the former being “imagistic and involuntary,” rooted in the unconscious, while the latter is “conceptual and intentional, and analyzes and synthesizes by means of consciousness” (quoted in Glenn Most, “From Logos to Mythos,” in From Myth to Reason?, 27).

Apollo represents harmony, progress, clarity, logic and the principle of individuation, whereas Dionysus represents disorder, intoxication, emotion, ecstasy and unity (hence the omission of the principle of individuation). Nietzsche used these two forces because, for him, the world of mind and order on one side, and passion and chaos on the other, formed principles that were fundamental to the Greek culture:[3][4] the Apollonian a dreaming state, full of illusions; and Dionysian a state of intoxication, representing the liberations of instinct and dissolution of boundaries. In this mould, a man appears as the satyr

My freely downloadable Beginning Mathematical Logic is a Study Guide, suggesting introductory readings beginning at sub-Masters level. Take a look at the main introductory suggestions on First-Order Logic, Computability, Set Theory as useful preparation. Tackling mid-level books will help develop your appreciation of mathematical approaches to logic.

Though rarer in computer science, one can use category theory directly, which defines a monad as a functor with two additional natural transformations. So to begin, a structure requires a higher-order function (or "functional") named map to qualify as a functor:

It's hard to say why people think so because you certainly don't need to know category theory for using them, just like you don't need it for, say, using functions.

Willard Van Orman Quine insisted on classical, first-order logic as the true logic, saying higher-order logic was "set theory in disguise".

Remark1.73.IfPandQare total orders andf:P!Qand1:Q!Pare drawn witharrows bending as in Exercise 1.72, we believe thatfis left adjoint to1iff the arrows donot cross. But we have not proved this, mainly because it is difficult to state precisely,and the total order case is not particularly general