(5 years have passed since the previous post)
I don't think that deduction is less fundamental than induction; deductive reasoning seems to be at least as fundamental as inductive. But that doesn't mean that one can subsume the other. — SophistiCat
(I am just quoting the last post of an interesting conversation between
@SophistiCat and
@apokrisis. This topic is also somewhat related to a recent thread on intuition (
link).)
I don't know if either of your thoughts have changed on this in the last few years. It seems to me that SophistiCat's objections are weighty for anyone who doesn't accept the approach of pragmatism, but I think it is equally clear that there must be some
tertium quid that is being overlooked. I tend to think this
tertium quid is Aristotle's notion of induction which was then helped by the metaphysical justification that Christianity provided for it. In the Medieval period the genus was referred to as
intellection, a sort of direct knowing as opposed to discursive knowledge.
Usually when we think of induction we think of observing a series of regularities and then forming a probabilistic guess that the next event will also adhere to that regularity. For example,
calls induction "probable reasoning" as opposed to the "certain reasoning" of deduction. For Aristotle and the Medievals (and probably also Plato) it was different. There is a kind of certain knowledge in induction/intellection, distinct from probabilistic reasoning.
But there is a more recent and more accessible entry point to the topic, and it is found in the language acquisition of children. Walker Percy was a doctor, novelist, and semioticist:
Percy experienced [symbol acquisition] firsthand. His second daughter, Ann, was born deaf. Her language tutor and the whole family participated in her language education, and Percy saw her symbolic acquisition in process, in a much different and more conscious manner than the automatic attainment of the average toddler. — Walker Percy and the Magic of Naming, by Karey Perkins (English Dissertation)
A number of Percy's books relate to this subject, but especially
The Message in the Bottle and
Signposts in a Strange Land. Section 2 of that dissertation is a quick introduction to the topic, "2. The Children: The Magic and Mystery of Naming" (again, an
English dissertation). The standard case, which Percy also focused on, is Helen Keller.
In a nutshell the idea is that when you train a dog to sit you are doing something fundamentally different than when you train a child to use language. This is particularly obvious in cases like Helen Keller, where the transition from dyadic to triadic activity is so stark, beautiful, and hard-won.
Or rather, when Helen finally understood the
symbol 'water', something fundamentally different occurred than when the dog finally responded to the
sign 'sit', even though the stimuli presented were not overly different (children manage symbol acquisition even in spite of parents who approach the task the same way they might approach the training of a dog). At some point Helen crossed a mysterious threshold and understood that 'water' is a symbol, not a sign, and her mind was opened to the entirely new reality of symbols. This, I claim, is intellection (induction), or at least something very close to it. 'Water' changed from being a mere lever which was pulled whenever Helen was thirsty, to a symbolic reality that existed on a plane distinct from stimuli and conditioning and utility.
This is the sort of qualitative 'jump' that Aristotle means by induction. It is the act of seeing a truth in a way that is 'spiritual' and not merely mechanical (for lack of a better word). It also applies in a variety of different contexts. Sometimes we intellect/induct the nature of some reality from frequent exposure, like Helen. Sometimes we require a variety of different arguments before the truth of a conclusion finally "clicks" for us. But even the terms, propositions, inferential rules, and inferential steps of formal arguments require a sort of direct intellectual perception, similar to Helen's symbolic association between 'water' and the physical stuff she was so familiar with via her senses.
Helen's "jump" was not deductive reasoning; it was not abductive reasoning; it was not inductive reasoning (
a la Hume); so what was it? The "jump" doesn't occur with dogs or cats or llamas. It isn't predictable or controllable; Helen's teachers often despaired that it would ever occur. "Magical" is not a bad word for it, but in any case it is entirely foreign to our modern mechanistic approach to reality.
Whatever the case, it seems to me that
could be right in his claim that "helping ourselves" to inductive reasoning may not be a problem, so long as it is understood in this very rarefied sense. If intellection really is a
tertium quid, then it is not bound by the rules of deduction or Humean induction. The only reason we can't help ourselves to it is because it doesn't wait on our beck and call in the way that deduction or Humean induction do, but this is a rather different problem than the one that SophistiCat complained of.