But it's not the way most thinking happens. For one, it doesn't capture inductive thinking, where the conclusions don't follow necessarily, or "abductive" thinking, inference to the best explanation, or reasoning by analogy, or the back-and-forth of "reflective equilibrium," where we try to adjust our general principles to fir particular conclsuions we like, or narrative thinking, where we try to tell a story that "makes sense". . . Or lots of other kinds of thinking.
You ask, what if my dissertation advisor, Allan Gibbard, uses axiomatic reasoning and I don't, how do we avoid talking past each other? Allan is a distinguished decision theorist, so he often does use strictly axiomatic reasoning. Decision theory is a branch of mathematics and its results are theorems. If I want to do or talk decision theory, I use it too. But often, as in Allen's book on ethics or his papers on metaphysics, we doesn't. He argues from intuitions we want to accept, using reflective equilibrium, or uses deductive reasoning that doesn't involved a closed set of axioms, or appeals to analogies. Just like you or me. Then we play those games. If someone uses axiomatic reasoning where it doesn't belong, you try to show this to him in various ways. ("Showing" is another kind of reasoning.)
Reasoning is not an "alternative" to the rules of inference, but the use of those rules. However, there is debate about what the rules of inference are. The deductive reasoning that goes on in axiomatic systems involves logic, but there are various logics. For example, "intuitionsitic" logic treats unprovable statements as neither true nor false. Susan Haack hasa fine book on Deviant Logics. And not all reasoning is deductive, as I have said.
I don't recall Yoshie's comment about "mysteries."
As for mystics who have nonrational means of "knowing" truth, who knows. What they "know" isn't what we notmally think of as knowledge, since the beliefs thus produced cannot be justified by reasoning, and knowledge is, at first approximation, justified true belief.
--jks
n a message dated 9/22/00 8:22:21 PM Eastern Daylight Time, MikalacNS at NAVSEA.NAVY.MIL writes:
<< Thanks for comments, justin.
> can i say that my axiomatic method is itself an axiom? however, if you
don't want to use the axiomatic approach, then how do people agree on "basic
assumptions" in discussions? otherwise, the discussants talk past each
other from that point, don't they? using your mentor professor as an
example, if he takes the axiomatic approach and you reject it, then how can
you discuss anything with him?
> here's another point: the axiomatic method is THE method for arriving at
formal (deductive) and factual (inductive) truth in mathematics and logic,
so why can't it be used for other language concepts too?
----------------
> i always considered the rules of inference as part of the reasoning process,
but i'd have to think about it some more before attempting to clarify my
position. apparently, you think of reasoning as an "alternative" to rules
of inference and vice versa. that confuses me, so can you explain the
dichotomy?
however if they are alternatives, as you say, then people have to agree on
which to use, don't they? IOW, they have to agree on either to use
reasoning or the rules of inference, right?
also, how would you answer yoshie's concerns about "mysteries" in contrast
to mine?
BTW, when i said that some people reject "reasoning" (and the rules of
reason), i was thinking of people we call "mystics" who arrive at "truths"
in other ways.
norm
>>