Am also looking to see what might be of interest around The Ancient Greek Philosophy niche too.
Ok back to Philosophy in Minutes and we're looking at Logic.
What Marcus Weeks says about Logic in the book is that it is used to check the validity (or not) of conclusions that are made.
This can be in the form of inductive reasoning that is is reasoning in which the premises* seek to supply strong evidence for but not absolute proof of the truth of the conclusion. The other typre is deductive reasoning, this links 'premises' with 'conclusions'. If all premises are true along with the terms being clear, and the rules of deductive logic are used then the conclusion reached is therefore necessarily true.
(*A Premise is a statement that an argument claims will induce or justify a conclusion.)