Logos is persuasion through reasoning and evidence — the appeal to the argument itself rather than to the speaker's standing or the audience's feelings. It is the third of Aristotle's modes, and the one the rest of this site is largely about.
Logos is not a guarantee of soundness. It is a mode, and a mode can be imitated.
Lincoln's Cooper Union address works almost entirely this way: he examines what each of the thirty-nine signers of the Constitution did and said on the question at issue, one by one, and builds the conclusion out of the count. The persuasion is the accumulation.
The three appeals are not alternatives to choose between. Most effective argument uses all three, and the question is which is carrying the load.
The most useful thing to understand about logos is that its appearance is itself persuasive, independently of whether the reasoning is any good. Numbers, citations, structured steps and the vocabulary of evidence all signal rigour, and readers relax their scrutiny in the presence of that signal — which is exactly when scrutiny is most needed.
This is why nearly every entry in the fallacy library describes something that looks like logos. A slippery slope has the shape of a causal chain. A base rate error has the shape of a statistical inference. Each borrows the authority of reasoning while failing at it, and each is far more effective than open emotional appeal would be against the same audience.
The practical consequence is that logos deserves more suspicion than the other two modes, not less. Pathos and ethos announce themselves; a reader notices being moved and notices being impressed. Reasoning that merely resembles reasoning announces nothing at all.
