Quick comment on David Miller, Do We Reason When We Think We Reason, or Do We Think?, Learning for Democracy 1, 3, 2005, 57-71.

Miller’s central conjecture is that it is not logical thinking or reasoning which drives intelligent thinking forward, but rather blind guessing, intuitive thinking. Conjectures don’t come from reasoning, and conjectures are what allow us to make progress. This is contrary to the doctrine of followers of critical thinking who ignore conjecture formation and argue that reasoning is all about justification and trying to persuade, “an attitude,” Miller suggests, “that reeks of authority, of the attitude of a person who wants to teach rather than to learn” (p. 62); they also hold that critical thinking is about finding flaws in arguments – Miller argues that it should be about finding flawed guesses.

I agree, with some caveats.

Miller makes the assumption that since a conclusion of a deductive inference is “implicitly or explicitly” included within its premises, that nothing new is discovered by drawing the conclusion. Every deductive argument, says Miller, is “question begging”. This can be defeated with a mathematical example. Given some set of axioms, e.g. Dedekind-Peano arithmetic, it is very difficult to prove anything that’s not trivially true. In fact many trivially true statements are difficult to prove! Drawing “question begging” inferences can be tricky and informative. However even in purely deductive mathematical reasoning, conjecture forming is crucial, so requires some sort of guessing of the flavour suggested by Miller. Proving statements in theories which include mathematical induction, for instance, often requires the proof of lemmas which need to be speculated somehow.

It is clear the premises of a deductive argument have to come from somewhere. This is the easiest way to attack deduction and show that it is not identical to “thinking”. A valid argument from a set of premises which are not true is useless. The moon is provably made from brie if we slip a contradiction into our premises (and use a logic in which B follows from A and ~A). But drawing inferences from a set of premises allows us to understand more about what they mean, how the different bits of knowledge we have relate to each other.

Also logic consists of more than rules of inference, premises, and conclusion to prove. Somehow the bits have to be glued together, often with a search mechanism of some kind, to draw the conclusions.

I don’t think it’s accurate to say that we don’t reason when we generate new conjectures. It may not feel like reasoning as a book on logic or probability describes it but the brain could very well still be doing something which can be accurately modelled using logic or probability. The missing ingredient is perception (a big chunk of which is top-down, dare I suggest deductive?), how we modify according to the environment we’re in. This, I reckon, allows us to grow new deductive machinery.

Now could it be that the search mechanism isÂ what does the guessing for us, generates the conjectures?

The reasoning MillerÂ discusses seems to be of the very conscious flavour, i.e. our culturally evolved reasoning technology. In a deductive calculus perhaps? We’re “reasoning” if and only if we’re consciously aware of doing something which resembles reasoning. So given this viewpoint on reasoning, a valid question to ask could be, would learning logic/probability help us to be more creative, say? Help us in our conversations? But I think reasoning systems developed by mathematicians and others can also be useful to analyse what we’re doing when it doesn’t feel like we’re reasoning.

Bah. You suggested a search mechanism already. But I was going to suggest that this seems like a plausible model of human “conjecture.”

The scenario might go something like this: Assume that a mental state m, for example, has as members a number of propositions p, q, r, etc. – all of rank n. While I am not a cognitive scientist, I find it not unreasonable to think that a person at m, who is interested in achieving mental state m+i, initiates a “search” through propositions of rank n+1 (and others?) to find “possible conjectures.” Those members of the n+1-ranked set that are obviously in contradiction with members of the n-ranked set are rejected out of hand. At this point, it’s plausible that desires come into mind. For instance, I might have some terrible aversion to (p ^ q), so I conjecture that ~(p ^ q). The search process, then, might be looping – because ~(p ^ q) is actually of rank n + 2 – but if it incorporates things like F-L closure, it wouldn’t have to be infinite. We may finally settle on a set of conjectures that appeal to us and then attempt to deduce from the set of propositions m to the set of appropriate propositions of rank n+1 and on to mental state m+i.

This is a bit telegraphic, but my point is that search mechanisms may be at least a viable area of research for what you’re talking about here. Really fascinating stuff.