Logic and Mathematics
- Formal logic, logical argument based on form
- Formal cause, Aristotle's intrinsic, determining cause
- Formal power series, a generalization of power series without requiring convergence, used in combinatorics
- Formal calculation, a calculation which is systematic, but without a rigorous justification
- Formal set theory, as opposed to Naive set theory
- Formal derivative, an operation on elements of a polynomial ring which mimics the form of the derivative from calculus
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Famous quotes containing the words logic and/or mathematics:
“We want in every man a long logic; we cannot pardon the absence of it, but it must not be spoken. Logic is the procession or proportionate unfolding of the intuition; but its virtue is as silent method; the moment it would appear as propositions and have a separate value, it is worthless.”
—Ralph Waldo Emerson (1803–1882)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)