Our old friend Piercello, whom some of you may remember for his
three-factor theory of human nature and his theory of aesthetics, dropped by to ask for some thoughts on a new theory that
successful argumentation depends on consensus. It's a short argument if you want to read it.
I have some things to say about it.
1) The kind of argument he is describing is deductive logic. There are other kinds of arguments, but I think they are even more susceptible to the charge he is bringing. Non-logical forms of argument, for example persuasion by appeal to emotion, are even more dependent on 'a consensus about how things should be done' than deduction. I don't actually have to share your feelings -- certainly I don't have to experience them -- to appeal to them. But I do have to understand
how you feel in order to frame an argument that will successfully motivate you to action in the way I desire. Induction is already a problematic form of argument, really more a form of guesswork than a proper proof, but that makes it also more subject to consensus about what kinds of guesses we're allowed to make. (Usually: "It's a proper inductive proof if and only if it is based on a random sample from a proper set; if and only if it is repeatable from a number of randomly selected elements from the set," etc. But this still depends on a consensus idea of what 'a proper set' entails, a question that is easy in mathematics or strict logic, but quite hard in practical reality.)
2) Deduction is a limited form of argument, though, because it is incapable of discovering anything. What deduction allows you to do is to prove that since you know X, you also know Y. It's a form of realization, in other words, rather than discovery of new facts about reality. The most classic example of a deductive proof is this one:
Assumption: Socrates is a man.
Assumption: All men are mortal.
∴ Socrates is mortal.
If the assumptions are true, the conclusion follows. The reason it follows isn't actually the one, Piercello, that you're suggesting. It's not that I have chosen a methodology that you agree is valid, based on a standard that you agree is reasonable, which was chosen by method... etc. The reason it follows is that the truth is contained in the assumptions. What the deduction is doing is helping us realize that we know the conclusion
because we know the facts in the assumptions. Nothing new is really being added. Something new is being recognized.
Now if your point is
rhetorical, it may be that you're correct about the necessity of consensus. In other words, if the argument is that
I can only convince you of the conclusion if you agree to the methodology of deductive logic, that might be right. If the point is not rhetorical but logical, however, it is not right. Because deduction is only recognition of the truths I also know from what I already know, the argument is valid whether or not I like it or agree to it.
Notice by the way that the classic syllogism isn't really subject to the third line of attack you mention ("You've cherry-picked your evidence"). Assuming those two assumptions turn out to be factually accurate, the conclusion follows no matter what new assumptions you add to the pot. The only new information that could alter the conclusion is information that invalidates one of the assumptions (e.g., "Socrates is not a man but a god"). Otherwise, the conclusion holds whatever else you add ("All ravens are black"; "Some men are very long-lived"; etc).
There you go.