Frege’s Begriffsschritp (1879) overturned views of logic that held firm for more than two thousand years. He argued that logic is objective and universal, with no connection to our thoughts about what we call logic. Logic is the study of how statements relate to each other, and whether they are true or false. There are various kinds of logical statements, including mathematical and scientific ones. Propositions are said to be true if they correspond to reality or facts, and false when they do not. Some propositions cannot be proved to be true or false because they are self-evident, meaning they are obvious. For example, “All bachelors are unmarried men” is an instance of a tautology – a proposition that always holds true, regardless of any circumstance. Mathematical axioms are basic truth statements that are assumed to hold true until proven otherwise. A mathematical proof shows how one theorem leads logically to another, just as a chain of reasoning leads to a conclusion.

Frege’s argument about mathematics showing an objective basis is similar to what he argues about logic. He says that math is objective because we discover it through reasoning and demonstration. We don’t create it but discover its existence through analysis of the world. Mathematics is linked to logic because both are tools for reasoning. His works suggested that there was more to logic and syllogism making it an immensely powerful concept in philosophy.