Foundations of Mathematics

Foundations and Logic

What is logic?

Although it closely resembles mathematics (and is sometimes used as a basis for it), logic is a branch of knowledge or inquiry that is separate from mathematics and the sciences, but is still used by both fields in various ways. Simply put, logic is described as the systematic study of well-founded inference, in which there is a definite distinction between logical validity (also known as the formal properties of the inference process) and truth. This also means that a true result may come from an invalid argument (see below for definition of an argument). For example, “all cats are cute; Fluffer is a cat; therefore, Fluffer is cute,” is a valid inference; whereas, “all cats are cute; Fluffer is cute; therefore, Fluffer is a cat,” is an invalid inference, even if Fluffer really is a cat.


A bust of the Greek philosopher Aristotle, whose work Organon is the earliest known to introduce systematic logic, the foundation of mathematical logic.


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