If pressed to supplement Tweedledee's ostensive definition of logic with a discursive definition of the same subject, I would say that logic is the systematic study of the logical truths. Pressed further, I would say that a sentence is logically true if all sentences with its grammatical structure are true. Pressed further still, I would say to read this book.
Willard Van Orman Quine... two men could be just alike in all their dispositions to verbal behavior under all possible sensory stimulations, and yet themeanings or ideas expressed in their identically triggered and identically sounding utterances could diverge radically, for the two men, in a wide range of cases.
Willard Van Orman QuineWe must not leap to the fatalistic conclusion that we are stuck with the conceptual scheme that we grew up in. We can change it, bit by bit, plank by plank, though meanwhile there is nothing to carry us along but the evolving conceptual scheme itself. The philosopher's task was well compared by Neurath to that of a mariner who must rebuild his ship on the open sea.
Willard Van Orman QuineTreating 'water' as a name of a single scattered object is not intended to enable us to dispense with general terms and plurality of reference. Scatter is in fact an inconsequential detail.
Willard Van Orman QuineThe totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.
Willard Van Orman Quine