Technical Reasoning/Structure of Arguments

Arguments Generally

edit

Notice that arguments are how we demonstrate the necessary truth of some conclusion, from a set of assumptions and accepted inferences rules. We will use the words "argument" and "proof" interchangeably.

In the above proof, we assumed the existence of two points A and B.

With the help of some other assumptions and inference rules, we were allowed to infer the existence of a circle centered at A and running through B.

After a long enough sequence of propositions like these, we eventually ended at the proposition "therefore   is equilateral". This was the conclusion, and it ended the argument for the theorem at the beginning.

In the abstract, this is always the structure of a proof:

  • A collection of basic assumptions, called the "premises" of the argument.
  • A sequence of propositions, such that every next one is a premise or inferred from earlier propositions (using an allowed inference rule, of course).
  • The last proposition in the sequence is the conclusion. The "goal" of the argument is to arrive in this way at the conclusion.