Cool, it's a very interesting thought experiment. From any possible viewpoint it would still be larger (and more enduring and endurant) than an apple, though, it seems.

Yes, it's hard to imagine Uluru slowly emerging out of some very different milieu, and where in that process we would locate the "initial conditions".

Have a look a the wiki article.

It is hard to find in that description events that take the inductive form. So again I suggest that induction is a post hoc account. As such I do not agree that it takes a centra place in science.

What exactly do you mean "events that take the inductive form" and which description are you referring to?

I would say that all accounts of human activities and thought processes are "post hoc" so I'm not sure what point you are trying to make in pointing that out in this particular case.

Apparently Newton thought he was doing inductive reasoning. From the Wiki article you linked:

"This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning."

It is hard to find in that description events that take the inductive form. So again I suggest that induction is a post hoc account. As such I do not agree that it takes a centra place in science. — Banno

So does that account instead describe deduction as being central to the development of the thinking involved? I think not.

Newton's theory of universal gravitation has of course become a classic test case for philosophy of science. Newton himself rejected a simple hypothetico-deductive model in favour of "the Newtonian style" which endorsed an abductive approach able to take the leap from complex particulars to simple generalities.

Inference to the best explanation involves a back and forth where the world as it is seen, and the laws that might explain that, swim into view together as the two halves a modelling relation. So the particular is extrapolated to discover some general - motivated by the reasonable metaphysical principle that lawful simplicity underlies all the messy real world complexity. And then the truth of that generality is checked against what it then predicts. It is tested by whether it seems to predict the particulars that were used to predict it.

So abduction is a mix of the inductive and deductive - but at a still vague level. All it needs is the start of what feels like it is going to become a good fit. Things are starting to snap together. A pattern is beginning to emerge.

You can try to formalise abduction as an if-then habit of thought. It is a species of induction in attempting the "invalid" thing of going from the particular to the general. And it is also "invalid" in that it accepts vagueness as a suitable grounding. Nothing actually has to be crisply or definitely stated at the beginning. That is instead the desired destination. Meanwhile a loose fit is good enough if it is a fit that seems to be growing tighter as work is done to clarify the direction being revealed.

Anyway, it is if-then reasoning. If this general rule were the case, these kinds of particular results would not look surprising. These kinds of particular results do exist. Therefore the general rule is probably the case. And historians show that this is the way Newton moved in his reasoning to develop a mathematically-definite theory.

So all reasoning involves this two-way interaction. We need to go from the particular to the general, and from the general to the particular, in as secure a way as possible. Obviously, deduction is more secure than induction because it introduces no new semantics. But then the cost of that is that deduction can introduce no new semantics.

Then the sense that this is a real jump, not some gradual change, is explained by the complex world of messy particulars being the state of broken symmetry in nature. And what we are trying to recover - as the trick that makes scientific models work - is the deeper symmetry that got broke.

We have a smashed up lot of glass bits on the floor. And a lot of bits are probably missing. We theb want to know whether it was once a glass vase or a glass dish, or whatever.

So the move from the particular to the general is seeking a hidden symmetry that is believed to lurk behind a messy complexity. We can't see that symmetry directly as a further thing to observe - symmetry-breakings tend to be thermally irreversible and so the past is gone. But we can imagine it mathematically. We can recover it as a mathematical idea.

Any amount of observables can't add up inductively to reveal the hidden whole. What's broke is broke when it comes to our available view of reality. But we can leap imaginatively to the kind of symmetry that could be broken to yield the kind of fragments we see all around.

So reasoning itself is an irreducible coupling of the inductive and deductive directions of thought. And then abduction goes to the fact that this self-organising loop has to start off as a seed and then grow into full and definite flower.

Abduction has both flavours of thought coupled together - as it must to be capable of growth towards a definite understanding. But it is that possibly successful thought still in its tentative stage - one where a loose fit is still acceptable. We are in a state of mind where we are allowing ourselves to be guided by some general principles - like that simple symmetries lie behind every messy and complex broken symmetry - and then looking backwards retroductively to see what generalisation can in fact predict the particulars we seem to identify as being suggestive or significant.

The peculiarity of an elliptical orbit could be explained if it were composed of an inertial straightline motion coupled to a centripetal accelerative force. The inertia is a symmetry, so falls out of the story. You now just have to account for the symmetry breaking which is the centripetal force exerted by a planetary body.

But why should only planets have gravity? Right, let's again find the symmetry. All masses attract. It is not something special but something which is the same for all. The symmetry of the force is broken only by the accident of the locally differing quantities of mass involved. There is the universal principle - the further inductive leap of imagination - needed to get a proper theory going.

And so a sharp picture of this thing called gravity swims into theoretical view. Eventually we can crank out predictions and begin to support the theory's newly acquired, strictly deductive, form with a sufficient weight of inductive confirmation.

Induction and deduction are initially entwined so closely as an if-then inference to the best explanation that the lines are blurred. The mind abductively has to juggle both at once in loose fashion.

But the goal - as a scientist - is to arrive at a clean separation between a theory and its truth. In the end, you want the deductive bit to stand alone as some mathematical grammar that encodes a symmetry and its symmetry breaking. And then the inductive bit becomes the evidence that supports that theoretical structure in terms of the observables that are close enough to whatever was predicted not to count as an unwanted surprise.

Indeed, he did use that term in his rules for scientific reasoning.

A bit late but I do want to say I didn't want to "out" you in speaking to Banno. I have liked his exchanges with you because it's helped me get a better grasp of your philosophical orientation -- and, even if it may be frustrating for you -- I enjoy that fact.

I do not think of you as "outsider"; just thought that was worth mentioning with some of your posts I read here.

Hey, that's fine. I don't take things personally. It's all about the cut and thrust of ideas. But thanks for saying that.

(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.