Blacknight:
It’s entirely possible that terms have evolved since I taught formal logic to computer programmers way back when. I won’t quibble with you over your terms.
As a matter of interest, here’s how I learned it. A compound proposition (a proposition being a statement that is either true or false, but not both true and false, nor neither true nor false) is a tautology if it is true regardless of the truth value of its component propositions. For example, “Either Shakespeare wrote Hamlet, or he didn’t.” That is (or was) a tautological compound proposition.
A syllogism, however, which strictly comprises (or did comprise) two propositions and a conclusion, is tautological if the conclusion is a restatement of the first proposition, which is called (or was called) the axiom, i.e., the initial premise. In other words, the conclusion would have to be true because it is the same as its axiom, and all axioms are true. An axiom is simply a premise that is offered without proof, and is taken as true on its face.
In my day, rigid logical proofs followed a specific format, beginning with definitions, which are themselves tautologies. Then the writer would offer his axiom set. In almost every case, the very first axiom, after a definition of A as any arbitrary abstraction, was “A is A”. This very obvious proposition was quite necessary because, without it, the definitions would not hold a one-to-one correspondence with the items they defined. After the axioms would follow the premises, each of which was required to follow from its predecesor. The proof ended with its conclusion, which was, in effect, the last premise.
Ayn Rand, of course, was so fetishly fond of “A is A”, appropriating it for her famous Objectivism philosophy, that these days, it is practically identified with her, although she was most certainly not its inventor by any means. She did, however, contribute one thing new in her (vain) attempt to validate what she considered to be objective reality. Her first axiom, even before “A is A” was “Existence exists”. Her disciples thought it was wonderful; I thought it was banal.
But there you go. Anyway, thanks for the updates on the modern terminology and its usage.
Arnold:
If there is a supernatural god who exists outside you, I can’t offer any advice on how to find him. But the God I found was within me. According to Him, He is within you, too. Search there.