# 1.5: Deduction

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Logic can be applied to draw conclusions from a set of **premises**. A premise is just a proposition that is known to be true or that has been accepted to be true for the sake of argument, and a conclusion is a proposition that can be deduced logically from the premises. The idea is that if you believe that the premises are true, then logic forces you to accept that the conclusion is true. An **argument** is a claim that a certain conclusion follows from a given set of premises. Here is an argument laid out in a traditional format:

If today is Tuesday, then this is Belgium Today is Tuesday

∴ This is Belgium

The premises of the argument are shown above the line, and the conclusion below. The symbol ∴ is read ‘therefore’. The claim is that the conclusion, “This is Belgium”, can be deduced logically from the two premises, “If today is Tuesday, then this is Belgium” and “Today is Tuesday”. In fact, this claim is true. Logic forces you to accept this argument. Why is that?