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Saturday, April 25, 2015

Underdetermination

One hears much that scientific theories are underdetermined; that through any finite collection of facts, one may draws countless explanatory theories. The existence of at least four or five theories of quantum mechanics to explain the same body of facts is an illustration, even if one of them is more popular than the others.¹ ² The Copenhagen Interpretation insists that all potencies exist until the particle is actualized by measurement. The equations don't tell us how a particle’s properties "solidify" at that moment of measurement, or "how reality picks which form to take. But the calculations work."

Although in matters of religion the existence of multiple interpretations is said to prove that there is no "there" there, it does not do so in matters of Science!™ because Invisible Sky Fairies! It is simply in the nature of theories that there can always be more than one for any given set of data. Recall how, at the dawn of the modern age there were multiple theories explaining the motions of the heavens, with the Ptolemaic theory being the most popular, the "consensus science." The calculations worked, but they did not tell us how the planets moved as they did.

But "the quanta are a hopeless mess" and it is useful to have a more homey example of underdetermination. Detective fiction is good at this: maintaining multiple theories of whodunnit until the end, when a new fact or a new arrangement of the facts collapses the potencies into an actual. The new fact may be the discovery of stellar aberration or the Afshar Experiment.

But here is an example of how a fact may support multiple theories:

Matt Briggs, the Statistician to the Stars, recently noted a kerfuffle in the rarefied world of chess.
Chess Grandmaster Nigel Short caused a stink, reaching oooo-weee! but not quite burn-him! levels, when he said that men and women are different and that men are better at chess than women.

Female chess player Amanda Ross said in response that, it is “incredibly damaging when someone so respected basically endorses sexism”. Sexism is when a disparity of any kind exists between males and females.
Let's call these the Short Theory and the Ross Theory.
So let us appeal to the Facts! In a list of living Grandmasters, there are:
  • 1413 men 
  • 33 women.
This fact supports Short's theory that men are better at chess.

It also supports Ross's theory that sexism in chess suppresses women's achievement.

This is why proponents of a theory are seldom swayed by the facts. Facts alone have no swaying power, since they will (and must) be interpreted in the light of some theory.


Notes:
1. Further confused by the fact that the mathematical formalism common to them all is also referred to broadly as "quantum theory." But "quantum theory" as such is not a theory. 
2. For the record, four that come trippingly to mind are:
a) Copenhagen (Bohr, Heisenberg), which reifies Aristotelian potencies until measurement collapses reality onto one of them.
b) Standing Wave (deBroglie, Bohm), in which the particle rides on the wave.
c) Many Worlds (Wheeler) in which all potencies are actualized, but in different worlds.
d) Transactional (Cramer) in which the wave travels backward as well as forward in time, thus reifying final cause.

30 comments:

  1. Does anyone notice how many atheists today are terrible at generalizations? On this one Blog, I told an atheist in general, that Medieval science was more about knowledge for knowledge's sake, while modern science is more about technology.

    And he told me that this is a misunderstanding of enlightenment philosophers.

    Can they not look at the big picture at all?

    Christi pax.

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    1. Your interlocutor may not have been familiar with Francis Bacon or Rene Descartes. Their specific program was to move the study of nature from knowledge for knowledge's sake to knowledge for the sake of making useful stuff. Ask anyone even today about the results of science and you're likely to hear about technological advances.

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    2. Another point he brings up is that in quantum physics, the difference is not between "theories" but between "interpretations." I think he just using a different word for the same thing.

      Christi pax.

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    3. Yes. He is using "theory" to mean the mathematical formalism rather than the physical theory itself. There are cases where different theories involve not only the same facts, but even the same equations.

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    4. How do you discuss truth with those who laugh at metaphysics?

      When do you realize that their harden heart is not to be broken by you?

      Christi pax.

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    5. People who laugh at metaphysics are usually following a deficient version of it.

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    6. I quit replying to them. It's just a fruitless endeavor.

      The interesting thing is that the man claimed to have a PHD in Physics, which is why I just thought we were talking pass each other with different terms. Don't really know.

      Christi pax.

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  2. The response from Ross should have been, "In general, men are better than women at chess. In particular, I will beat almost any man at chess."

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  3. http://outshine-the-sun.blogspot.com/2015/03/estranged-notions-why-something-rather.html#comment-1989524841

    How would you respond to such a person? Or would you just ignore him?

    Christi pax.

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    1. Sweet Mercy, I'm not sure there's anything that *can* be done with those folks. I for one wouldn't even know where to begin. Though I am distressed to note that more than a few of them are making arguments to the tune of "yeah, well, all this *metaphysics* stuff is just putting a respectable face on unscientific mumbo-jumbo. Christianity is SUPPOSED to be about REAL EXPERIENCES! But they just can't FIND any, so they resort to this nonsense! Poo!" Well, whatever they want to believe.

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    2. One of the reasons I came here is that they compared me to YOS quite a bit, and brought him up a couple of times.

      For example, before I made an account on disque, I used the guest account "Socrates," but then chaned it to "Lucretius," and that reminded them of YOS apparently. I also have similar mannerisms in my writing, according to them. Am I a long lost relative or something? :shrug:

      Christi pax.

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  4. The QM probabilities are not potencies in the philosophic usage of the term since QM belies the realism of the classical philosophy. That reality is observer-dependent --the central tenet of all QM interpretations sits very uneasily with realism of the perennial philosophy hence
    the QM measurement can not be described as "actualization of a potency" since the potency and actualization depend upon a realistic world view.

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    1. Mortimer Adler and Jacques Maritain—the Paul McCartney and John Lennon of 20th century Thomism—don't appear to agree. (At least, I think Maritain didn't. I know Adler didn't.)

      Adler seems to have held (if I read him right) that QM poses no problem for Aristotelian (mitigated) realism because quanta are parts of wholes, or even discrete degrees of qualities—and in Aristotelian metaphysics, parts are less real than wholes, and qualities are less real than the things they're the qualities of.

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    2. Adler and Maritain were not physicists. Fr Jaki who had a doctorate in physics always held to a belief in the essential non-realism of Copenhagen interpretation.

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    3. And Jaki was not a philosopher, so which person talking about how the field he's qualified in relates to a field he isn't qualified in do you trust?

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  5. Can you help me better understand this response please:

    "No, your usages of 'theory' in your comment above is incorrect.
    Referring to a 'physical theory' means that you are using the word 'theory' in the strict scientific sense of a well-substantiated explanation of a large body of facts, and can make predictions.
    Referring to various interpretations of quantum mechanics, the word 'theory' is only applicable in its common-parlance sense, with the appropriate tentativeness of a hypothesis or idea or proposal. The interpretations of QM are not 'physical theories.'
    It is as if you had said 'All feathers are light. Nothing light can be dark. Therefore no feathers can be dark.' This is an equivocation fallacy, using two different meanings.
    Maybe you would like the world to use different words so it wouldn't be so complicated for you. Get over it.
    Several of us have explained this same thing to you several times. Please stop doing it."

    Christi pax.

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    1. Your friend is using the word "theory" to refer to the mathematical formalism that the theories have in common. This is like talking about the "theory" of evolution instead of the theory of natural selection, although in this case "evolution" is the facts that are in search of the theory. (Unlike other sciences, there is no mathematical formalism in evolution.) He is using "theory" in a more colloquial sense.

      The logical positivists took science as a three-later cake: the bottom layer was observations/facts; the middle layer were the mathematical laws/regularities; and the top layer consisted of the physical theories, that is, stories told about the physics that made real the mathematics. Now, this came under attack by Popper, and later by Quine, but the so-called "Received View" has persisted with retreats into the stance by your friend whenever it is perceived that the class enemy is discussing the matter.

      Some discussion here:
      http://www.brlsi.org/events-proceedings/proceedings/24924

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  6. Can you please provide some recourses on qualitative vs quantitative, in response to this:

    "Part of the issue here, I think, is that Flynn's concept of "abstraction" is itself an abstraction, and doesn't bear any real relationship to the way we think.
    The underlying mechanism is more like "associating similar things together" and/or "treating some parts of an experience as more salient than others". Looked at this way, it's much more understandable how it can develop gradually.

    So, the brain doesn't store experiences with precision (there's no reason why it should develop the ability to be able to). Therefore any association between experiences will capture some space of similar experiences too. That gives us categories with central and noncentral membership; treating some parts of experience as more salient gives us "essential" vs "accidental" properties.

    Then there's the fact that some fairly advanced cognitive abilities (such as the ability to use deception against conspecifics as part of a planned strategy) are found throughout the great apes (humans, chimps, gorillas, and orangutans), and the fact that the great apes (excluding humans) consistently outperform other primates on a variety of tests intended to study domain-general cognitive abilities.

    It's very easy for a large enough quantitative difference to look like a qualitative difference even when it is not (to the extent that "qualitative difference" even means anything)."

    Thank you.

    Christi pax.

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    1. Your friend does not understand "abstraction" and seems to believe it is "my" concept. He confuses it with "association." He also does not understand the distinction between "essential" and "accidental" and seems to feel that it is the same as "central" and "non-central." (How one identifies the "center" in order to make such a judgment is wonderful to contemplate. Do we use Euclidean geometry?) I love terms like "domain-general cognitive abilities." They sound almost like science. Obviously, cognitive abilities do exist at different levels -- digestion in plants, perception in animals -- and one may serve as a material cause for the other. Animal prudence (or "estimation") is certainly a precursor for intellection, although it operates by instinct, not intellect.

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    2. Yes, I thought it was just an emotional dislike of Catholic philosophy disguised as rational thought. However, I was asking if you had some writing recommendations on this topic. I do already own Professor Feser's books, and I was looking for more.

      Thank you.

      Christi pax.

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    3. @Daniel D. D.: It's not just an emotional dislike of Catholic philosophy disguised as rational thought. It's an emotional dislike of Catholic philosophy disguised as rational thought by wrapping it in prestigious-sounding science-esque but ultimately non-scientific jargon.

      Basically, because your interlocutor had no argument, they tried to baffle you with Dog Latin, as the Protestant caricature held medieval priests would do. (Of course, if you were from the continent and didn't live in the Holy Roman Empire, the medieval form of your daily language and Church Latin were almost mutually intelligible—much closer, for example, than the Modern and Classical forms of Chinese or Japanese.)

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  7. Hello,

    Do I got this right?:

    Facts: recorded observations, preferably measured mathematically

    Laws: regularities and patterns in the facts, also preferably stated in equation form

    Theories: stories we tell ourselves in order to make senses of the facts. Theories make the Laws from mathematical formulas to descriptions of nature.

    Christi pax.

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    1. Yeah, that was the old logical positivist notion. Popper and rest tried to undermine the distinction, and even showed that theories were not needed. As long as you knew the laws and formulas, things would work out. E.g., you can use the law of gravity without worrying whether gravity is a spooky invisible "force" acting at a distance or is a warp in spacetime caused by the presence of matter.

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    2. Well, thank you for your help.

      At first, since he claimed to be a Physicist, I thought that I might be in the wrong. But, he then said that what I wrote above was complete trash, so I suspect that those who study the metric properties of physical bodies don't necessarily have any understanding of the study of science.

      Christi pax.

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    3. Tell him to take the matter up with Poincare, Mach, and the others. Rumor has it that they too were physicists.

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    4. Just as expertise in engineering doesn't automatically equal understanding of the physics principles that make engineering work—few indeed are the electrical engineers who could teach Quantum Electrodynamics—expertise in physics doesn't automatically equal understanding of the epistemological principles that make physics work.

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  8. Does this make things clear, in your opinion:

    " 'Physicists call them interpretations, should we not use the conventional language?'

    I was never concerned with what physicist call them. What I was explaining is that each interpretation, in the context of philosophy of science, would be a theory on its own right. I think the use of the term interpretation is just a way to separate the differences between each theory/interpretation and their similarities. For example, epeeist correctly pointed out along with Andrew that each interpretation share the same formalisms.

    So, put it another way, it just a difference in emphasis, probably due to the type of work a physicist is doing compared to a philosopher of science. Physicist use "theory" in the context of quantum physics to refer to what all interpretations/theories have in common, and "interpretation" to refer to the differences, which is why epeeist probably referred to them as "meta-theory."

    Philosophers of science, on the other hand, might feel more comfortable, in order to keep a similar definition of theory for all the sciences, to use "theory" to refer to both what the theories have in common and what they have in difference. I use theory this way.

    "Theory" for epeeist refers to what I would say are the shared aspects of each quantum theory, while "interpretation" for epeeist refers to what I would say are the aspects of each quantum theory where they differ from each other. For me, when I speak of the Copenhagen theory, I mean both what all the quantum theories/interpretation have in common and what makes the Copenhagen theory different from the others.

    To me, epeeist's use of "theory" refers to the theoretical overlap between each theory/interpretation, while "interpretation" refers to the theoretical differences between each.

    "Theory" to epeeist includes the mathematical formalism, while "theory" to Lucretius includes both the formalisms and the interpretations.

    I prefer my terms because "theory" when used in different branch of science would be defined differently under epeeist's definitions, while under my view they are the same. For example, since "theory" in epeeist's usage refers to the math, theory would be defined differently in biology, since the theory of natural selection doesn't use any mathematical formulas. Natural selection would be a interpretation, if we used epeeist's definitions. Under my definitions, theory would be the same in both sciences, making things simpler for the philosopher.

    Hopefully I cleared the air with this one :-)"

    Christi pax.

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    1. There is a colloquial usage of "theory" which means collectively all theories regarding a subject. We might even make a distinction between (e.g.) "theory of evolution" and an "evolutionary theory." Examples of the latter would be Darwin's "natural selection," Kimura's "neutral selection," Shapiro's "information-theory approach." The former would include all of these as a common ground in which theorists interact, exchange views, weight the pros and cons of each theory. To mix these two kinds of discourse -- one technical, the other social -- risks confusing a fact (evolution) with a possible physical explanation of that fact (natural selection).

      It is possible to call these various physical theories "interpretations of the facts of the subject area" but "interpretations" seems too weak or dismissive. Everyone seems to agree on the facts of quantum mechanics, but the physical theory that explains these facts is open. Copenhagen, the most popular, claims that the probabilities that result from the formalism are real facets of the physical world, not just convenient calculations. The many-worlds theory holds that there really are physically many worlds in each of which a different outcome of the probability holds. Cramer's transactional theory holds that there is a really-truly advanced and retarded wave traveling forward and backward in time and their handshake is what realized the outcome.
      One approach to theory is Duhem, who is something of an instrumentalist:
      http://www.amazon.com/Structure-Physical-Princeton-Science-Library/dp/069102524X/ref=sr_1_3?s=books&ie=UTF8&qid=1430690593&sr=1-3&keywords=pierre+duhem
      Another is Nancy Cartwright's, which makes a distinction between phenomenological laws (laws) and theoretical laws (theories).
      http://joelvelasco.net/teaching/120/cartwright-How_the_Laws_of_Physics_Lie.pdf

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    2. Thank you.

      Christi pax.

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  9. Do you know of any resources that defend the Exodus event as historical?

    Christi pax.

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