Analysis works in the virtual domain of abstraction. It can typically be done anywhere, by anyone, with a lot of rational thinking and scratch paper (or a computer). Example disciplines include mathematics, (some) philosophy, and computer science.
Analysis typically starts from a set of initial propositions, calledaxioms and rules that allow the scientist to derive new propositions from existing ones. Analytical claims are statements, and the proof of a proposition is the sequence of rules thatderive the conclusion from the axioms.
This is the way that truth operates in analysis:
The initial axioms and any other assumptions are by definition true.
If the input statements to any rule are all true, then the output statement of that rule is also true.
Therefore, the conclusion of a proof must be true because it was derived by rules from a set of true statements.
A valid proof is one in which if the assumptions are true, the conclusion must necessarily be true [1]. A sound proof is a valid proof assumptions are true [2].
[1]The converse is NOT true: if a proof is invalid, it does NOT mean that the conclusion is false. Thinking so is one version of the'fallacy fallacy' [1-1].
[1-1]The other version of the `fallacy fallacy` is mistaking a weak fallacy for a strong one. This version is rampant in human reasoning [1-1-1].
[1-1-1]
I've noticed that very rational individuals often go through a phase of arguing on the internet where they throw around the names of fallacies as though citing a fallacy is a valid counter-argument. My experience is that this is not an effective strategy:
It comes off as pretentious or dismissive, and so is not likely to persuade anyone to change their mind.
(As mentioned above,) the presence of a weak fallacy does not invalidate an analytical argument.
It's usually more effective to explain the fallacy directly. For example, instead of declaring something a strawman, explain why you think that the argument being challenged isn't equivalent to the argument being made.
[2]Most analysis treats truth as binary: a thing is either true (conditional on its assumptions) or it isn't. Some more complicated branches of analysis expand upon this, allowing statements with fuzzy or non-binary truthiness.
Logical fallacies [3] derive from analysis. A strong (or formal) fallacy is one which renders a proof invalid. A weak (or informal) fallacy doesn't invalidate a proof, but it suggests that the proof may not be sound.
[3]I'm not going to include an (in)exhaustive list of fallacies here, because they can be readily found online, like on Wikipedia's list of fallacies ⬈.
Most analysis is not rigorous, and consists of the scientist using logic to reason rationally about a situation. For most practical purposes, this is sufficient; the logic can be followed by other scientists, and does a reasonable job of convincing them of its conclusions. However, if a higher bar of rigor is required, analysis can be formalized by writing unambiguous proofs that can be checked by a theorem-prover, or other piece of software that verifies that each derivation in the proof is valid.