• Janus

    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".
  • Banno
    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.
  • Janus

    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."
  • apokrisis
    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.
  • Banno
    Indeed, he did use that term in his rules for scientific reasoning.
  • Moliere
    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.
  • apokrisis
    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.
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