Monday, June 9, 2008

Quotes from Intro to Methods of Logic

Nice quotations/passages:

"Logic, like any science has as its business the pursuit of truth. What are true are certain statements; and the pursuit of truth is the endeavor to sort out the true statements from the others, which are false."

"Truths are as plentiful as falsehoods, since each falsehood admits of a negation which is true. But scientific activity is not the indiscriminate amassing of truths; science is selective and seeks the truths that count for most, either in point of intrinsic interest or as instruments for coping with the world."

"Physical objects, if they did not exist, would (to transplant Voltaire's epigram) have had to be invented. They are indispensable as the public common denominators of private sense experience."

"Logic and mathematics were coupled as jointly enjoying a central position within the total system of discourse. Logic as commonly presented seems to differ from mathematics in that in logic we talk about statements and their interrelationships, notably implication, whereas in mathematics we talk about abstract nonlinguistic things: numbers, function and like. This contrast is in large part misleading. Logic truths, e.g., statements of the form 'If p and q then q', are not about statements; they may be about anything, depending on what we put in the blank 'p' and 'q'. When we talk about such logical truths, and when we expound implications, we are indeed talking about statements; but so are we when we talk about mathematical truths.
But it is indeed the case that the truths of mathematics treat explicitly of abstract nonlinguistic things, e.g., numbers and functions, whereas the truths of logic, in a reasonably limited sense of the word 'logic', have no such entities as specific subject matter. Despite this difference, however, logic in its higher reaches is found to bring us by natural stages into mathematics. For, it happens that certain unobtrusive extensions of logical theory carry us into a realm, sometimes also called 'logic' in a broad sense of the word, which does have abstract entities of a special kind as subject matter. These entities are classes; and the logical theory of classes, or set theory, proves to be the basic discipline of pure mathematics."

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