• Pfhorrest
    4.6k
    In a previous thread I wrote:

    beliefs that are more specific and detailed, having higher information content, are inherently less likely to be true — or conversely put, a belief that is so broad and general that it could not possibly be false accomplishes that by claiming nothing of substance at all, leaving no claims open to falsify — so such unlikely, high-information beliefs that, nevertheless, still have not been falsified, have withstood much more testing than those that put forward nothing to testPfhorrest

    This notion of the information density of beliefs dovetails into another prominent principle of belief-formation: the principle of parsimony, commonly called Occam's Razor, after William of Occam who coined a well-known formulation of it. This principle states that if given multiple beliefs or theories or abstract models that all concord equally well with the evidence at hand, the simplest of them should be preferred. I agree with this principle in general, and find that it relates in more detail to what Thomas Kuhn described as the structure of scientific revolutions.

    Kuhn's account was a sociological description of how he observed scientific revolutions to have actually occurred in practice, which he attributed to non-rational social and personal factors more than to adherence to any kind of rational principles. But I think it can be adapted into a more advanced version of the principle of parsimony and used as a normative epistemological rule for how science, and belief-formation more generally, should rightly be conducted.

    Kuhn observed science to advance in phases. The process begins with what he called "pre-science" where there are no prevailing theoretical frameworks or approaches, or "paradigms", uniting the research efforts, but rather many different competing approaches. Then it proceeds into what he called "normal science" once such a paradigm has been established by the widespread success of some theory. And then, as new evidence that cannot successfully be incorporated into that paradigm builds up, a period of what he called "revolutionary science" occurs wherein once again many different approaches compete in the effort to reconcile all those anomalies together with all of the older evidence into a new paradigm, re-establishing a new period of normal science.

    I think that this general process can be turned into a normative principle for belief-formation by formulating it in terms of parsimony, or in terms of how complex a theory needs to be to account for the evidence at hand; because the entire point of coming up with theories, abstract models to believe, is to have an easier, simpler representation of reality to work with than just the whole body of raw observational evidence thus far accumulated.

    On my normative account, the period of pre-science is one in which no single theory has yet been devised that can account for all of the evidence at hand, and so there is no better, easier, simpler, more parsimonious way of describing all the evidence than many different theories used in a patchwork to account for each of the disjointed areas of evidence. Once a theory is devised that can account for all of that evidence, that then becomes the better, easier, simpler, more parsimonious way of describing it all, and so the patchwork of other theories are rationally, pragmatically discarded in favor of it. There may still be other theories that also account for all of that evidence, and so are equally unfalsified, but unless they are in turn even more parsimonious, there is no reason to use them instead, and pragmatic reason not to.

    But as new evidence accumulates that cannot be reconciled with the existing paradigmatic theory, the best way to describe all the evidence at hand begins to grow again into an unwieldy patchwork of the main paradigmatic theory and all of the exceptions and special cases needed to be made and used to handle the anomalous evidence, until at some point that patchwork becomes so complex that other competing theories, previously rejected as less parsimonious than the paradigmatic one, are now more parsimonious than the old paradigm plus all of its exceptions, and it becomes rational to adopt the best of them instead of trying to cling to the old paradigm and its mess of special exceptions.
  • norm
    168

    What comes to my mind is algorithmic information theory, not the gritty details but the philosphical inspiration from Leibniz. The best theory best compresses the data. Given the imperfection of measurements and other factors, the compression tends to be lossy, but obviously good enough for me to post this with the expectation that it'll become readable around the world within seconds.

    In this context, it's thinkable that a patchwork could still require less bits than one grand theory. In that case, we might shift from parsimony to aesthetics. Unification might just deeply please us, even if it costs more.
  • Pfhorrest
    4.6k
    The best theory best compresses the datanorm

    :100: :up:
  • Enrique
    842
    But as new evidence accumulates that cannot be reconciled with the existing paradigmatic theory, the best way to describe all the evidence at hand begins to grow again into an unwieldy patchwork of the main paradigmatic theory and all of the exceptions and special cases needed to be made and used to handle the anomalous evidence, until at some point that patchwork becomes so complex that other competing theories, previously rejected as less parsimonious than the paradigmatic one, are now more parsimonious than the old paradigm plus all of its exceptions, and it becomes rational to adopt the best of them instead of trying to cling to the old paradigm and its mess of special exceptions.Pfhorrest

    The rivalry between geocentrism and heliocentrism is a perfect example of this. Heliocentric models existed pre-Aristotle, but it seemed more parsimonious to most ancients that what was not known from the vantage point of Earth should be regarded in practical principle as fundamentally oriented to it, though this view required some convoluted notions to explain retrograde motion etc. As Western religion and the idea that the cosmos was designed came to increasing predominance, it made sense to view the planet as located within an enigmatic empyrium: what was not knowable at the time was not intended to be known, and the geocentric model also prevailed. Then telescopes came along and it was proven by direct observation that the planets revolve around the sun in a vast universe of analogous composition. It turned out that our sense of conceptual aesthetism and economy was flawed, totally reconfiguring humanity's intuitions about nature. Theoretical contemplation always has a rationale, but it can be radically in error.
  • TheMadFool
    13.8k


    The simplest hypothesis is that the clock is broken. Occam's razor could obscure the truth.
  • Pfhorrest
    4.6k
    The rivalry between geocentrism and heliocentrism is a perfect example of this.Enrique

    :up: :100:

    I don't get it.
  • TheMadFool
    13.8k
    I don't get it.Pfhorrest

    You do. The clock hands start at 12:00 and after 12 hours it returns to 12:00. If I had checked the clock at 12:00 and come back after 12 hours the hands of the clock would be exactly where they were, at 12:00.

    The simplest explanation: the clock hands haven't moved i.e. the clock is broken

    True explanation: 12 hours have passed since you last checked the clock.
  • 180 Proof
    14.1k
    The best theory best compresses the data.norm
    :100:
    The rivalry between geocentrism and heliocentrism is a perfect example of this.Enrique
    :clap:

    The simplest explanation: the clock hands haven't moved i.e. the clock is broken

    True explanation: 12 hours have passed since you last checked the clock.
    TheMadFool
    Viewed on end one sees a large metal ring but when viewed laterally one sees a length of coils of a large metal spring. The latter is a more complete description than the more parsimonious former description. Neither, however, are "wrong".
  • TheMadFool
    13.8k
    Viewed on end one sees a large metal ring but when viewed laterally one sees a length of coils of a large metal spring. The latter is a more complete description than the more parsimonious former description. Neither, however, are "wrong".180 Proof

    :ok: :up:

    I think parsimony isn't the only game in town though. Explanatory power which would include completeness also matters, right?
  • norm
    168
    and it becomes rational to adopt the best of them instead of trying to cling to the old paradigm and its mess of special exceptions.Pfhorrest

    Why is the most compressed the most rational theory? Are we equating rationality with efficiency here? In other words, is it just manifestly rational to get a good deal?
  • Pfhorrest
    4.6k
    I think parsimony isn't the only game in town though. Explanatory power which would include completeness also matters, right?TheMadFool

    Yes, absolutely. That's why all of this discussion of parsimony is couched only in terms of "multiple beliefs or theories or abstract models that all concord equally well with the evidence at hand". If you have made so few observations that you don't even know that the hands of the clock move (or that the spring inside of it unwinds, cf @180 Proof), then yes, the theory that it's just a stationary object with the hands always pointing the same way is more parsimonious and so preferable. But if we then make some observations of the hands in a different positions, we would very quickly have to rack up so very very many exceptions to that theory to maintain concordance with the evidence that in almost no time the theory that the hands move the way clock hands normally do would become far more parsimonious than the stationary theory plus 719 exceptions.

    In other words, is it just manifestly rational to get a good deal?norm

    Yes, though I wouldn't say I'm completely equating rationality with efficiency, but rather just saying that efficiency constitutes one type of reason to prefer one option over another (it gets us at least as much of something preferable in exchange for less of something unpreferable), and thus in absence of reasons to the contrary going with that reason is the rational (i.e. reasonable) thing to do.
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