Foundations of Mathematics

Foundations and Logic

What is an argument?

In logic, an argument is not a “heated discussion,” although some mathematicians may argue over the validity of certain mathematical arguments. In this sense, an argument is a list of statements called premises, followed by a statement called the conclusion. Generally, an argument is valid if the conjunction of its premises implies its conclusion; stated differently, validity means that if all the premises are true, then so is the conclusion. But remember: The validity of an argument does not guarantee the truth of its premises, and thus it does not guarantee the truth of its conclusion. It only guarantees that if the premises are true, the conclusion will be true.


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