Thursday, August 3, 2017

Are Mathematical Objects Real?

There has been a really bizarre idea, or, really, more of an attitude that has developed on the left that if you disagree with someone about something that is important, or even something that is relatively unimportant, that you're not supposed to have any respect for them.  Such a attitude is as stupid as it is snobbish.  There are people who have removed themselves from consideration as a decent person but there are people who certainly haven't totally left the realm of those you can learn from even when you disagree with them..

On matters of religion, I have some profound disagreements with William Lane Craig, though there are some areas of agreement, too.  Some of our disagreements are on very important issues but he is absolutely brilliant, especially in those areas of philosophy which he has specialized in.  Even when we might not see exactly eye-to-eye on those things, what he says on them is worth listening to and thinking about.  That's the reason I have listened to a number of his debates, his lectures and his interviews, especially on such issues as the interview he posted yesterday in which he went over an interview the eminent mathematical physicist, Roger Penrose gave to Robert Kuhn, on Closer To Truth.   I am going to listen to the Penrose interview a few more times and might say something about that later.   But I think Craig's critique of what Penrose says, especially on such things as mind-body dualism and what Penrose calls his "trialism" and the issues involved in materialist monism, mind-body dualism and Penroses introduction of mathematical objects and properties as a third realm of reality are worth listening to several times as well.

In light of the hackneyed and rote recital of the old argument against mind-body dualism, that an immaterial mind couldn't have any way to interact with a physical body (which is wrong*) it is interesting to think of why so many materialists who reject that possibility have no problem with such a proposed mathematical realm of reality having an even less explainable connection to materialism.  It seems to me that a materialist having to explain everything in terms of the crudest and most basic of defined properties of material objects and forces is at a total loss to explain both the possibility of other entities having other properties and, in the case of minds, abilities, that aren't so limited, which aren't definable in terms of physical properties and laws.

Penrose seems to have no problem with understanding that problem in terms of the interaction of mathematics and the material realm, which he takes as separate realms but he doesn't seem to understand that minds, which he implies are real, may have abilities that make the obvious understanding of his mathematical realm unsurprising.

I don't agree with everything that William Lane Craig says in this video and our interests in the issue don't exactly match, his is obviously primarily as a support of theism (which is interesting and perhaps persuasive, though I'm reticent to go there) mine is obviously political, as well.  But his analysis and criticism and agreement with Roger Penrose is worth considering.   I'll be considering both of these recordings for a long time to come.

*  I've been through that before,  if there is a non-material mental realm then the entities in that realm would not be rationally expected to have the same limits as that of unconscious matter because if those minds had the same limits they would not be different than physical objects.  And our experience of the mind is not explainable by physical or material laws.  Including our understanding and perception of and consciousness of any external reality.

Mind-body dualism was never, actually, refuted, it was merely made unfashionable.  As Craig points out someone as sophisticated in terms of material understanding implicitly accepts the validity of dualism which he wants to extend to a third realm of reality.  I'm not sure, from what I've heard, that Penrose is entirely comfortable with that implication of his statements, though he is certainly aware of the inadequacy of the materialist, brain-only dogma that has a hegemonistic hold on the culture of academia.

Update:  I just noticed that I linked to the wrong thing, above, here is what I'd meant to link to.

I started watching the video in the series where Kuhn talks to a younger William Lane Craig, I have to admit I was distracted by the vase on a piano in the background.  If there's one thing that drives me nuts it's seeing people putting any liquid near a piano, knowing what water can do to, for example, a well working keyboard.  Pianos aren't furniture. I'd dope slap anyone who put a vase of flowers or a glass of water or a drink on one.

Update 2:  Nope, that wasn't the right link either.  I can't find it, now.  You'll just have to listen to it as WLC has it on the Youtube.


  1. Most mathematicians are Platonists, which makes their denial of dualism even funnier.

    1. I would say that Roger Penrose, in mathematics, makes the same mistake Sean Carroll and other physicists who claim we're on the verge of a Theory of Everything which will explain everything about the physical universe (in Carroll's materialist ideology, of everything) that assumes we even know the general outline in which the objectively existing things they use to make their claims about are known to us, today or will be in the future, when there is no reason at all to believe that is possible. While that culture of temporally parochial arrogance isn't that surprising to me in a physicist, I'm kind of shocked to have to suspect that a mathematician would ever believe that all of the properties of even the lowest natural numbers is known to mathematics or that mathematics can, in any way, be separable from the only minds we know of which seem to deal in them, human beings and, arguably, parrots and, if I recall correctly, some of the apes which can articulate knowledge of them to us. And we don't even know if those animals really have a human understanding of them because their articulations of them aren't complex enough to know that.

      I suspect that the realm in which mathematics might be true is vaster than human beings can comprehend and that our mathematics is merely a limited view of that realm which we are capable of grasping. But, if that's the truth, that vast areas of that realm are unopen to us, then, like those imagined other universes people like Carroll invent, they would be forever inaccessible to us.

      We can only know what we can know and to pretend that we can know more than that, especially when you limit your rules of evidence to those of physics or mathematics, there is every reason to admit the role that belief plays in what you say about those or the reality you express in those terms. And there is every reason to believe that the reality you do express with those is not the entire realm of reality. And that, so long as we are limited in the way human beings are, that we don't have access to all of reality.

    2. I found this summary at the Stanford Encyclopedia of Philosophy. It nicely states Wittgenstein's thoughts on mathematics (he wrote an entire work on the philosophy of mathematics):

      "Wittgenstein maintains that “mathematical propositions” are not real propositions and that “mathematical truth” is essentially non-referential and purely syntactical in nature. On Wittgenstein's view, we invent mathematical calculi and we expand mathematics by calculation and proof, and though we learn from a proof that a theorem can be derived from axioms by means of certain rules in a particular way, it is not the case that this proof-path pre-exists our construction of it."

      Which is why I am so dubious about math describing the universe. Wittgenstein is approaching that from Hume's empiricism, basically. Mathematicians, as I say, tend to be Platonists. In Wittgenstein's terms, the two are engaged in different language games.

      And W. was all about the connections between language and reality. To put it simply, we know what calling an object a "tree" does not express the essence of that object (or give us control over it, which is the whole idea of "magic" in European thought, and why "spell" is both an incantation of power, and what letters are actually used for what word). The old idea is essentially Platonic, as all things have an "essence." Give that up, at least in Western thought, and you're left with empiricism (where Wittgenstein starts).

      Mathematicians are, in general, poor philosophers. They often sound more like medieval priests to me, than anything else. Pre-Thomistic, in fact (not that Aquinas was that close to empiricism, but he was far removed from the Scholastics, our stereotype for medieval thought.).

    3. I have to correct my previous comment, an error based on misreading the Stanford article I mentioned (found here: W. wrote no particular book on mathematics, but it was a major concern. The article has a nice reference to W.'s expectations of the result of his thoughts:

      "In his middle and later periods, Wittgenstein believes he is providing philosophical clarity on aspects and parts of mathematics, on mathematical conceptions, and on philosophical conceptions of mathematics. Lacking such clarity and not aiming for absolute clarity, mathematicians construct new games, sometimes because of a misconception of the meaning of their mathematical propositions and mathematical terms. Education and especially advanced education in mathematics does not encourage clarity but rather represses it—questions that deserve answers are either not asked or are dismissed. Mathematicians of the future, however, will be more sensitive and this will (repeatedly) prune mathematical extensions and inventions, since mathematicians will come to recognize that new extensions and creations (e.g., propositions of transfinite cardinal arithmetic) are not well-connected with the solid core of mathematics or with real-world applications. Philosophical clarity will, eventually, enable mathematicians and philosophers to “get down to brass tacks” (PG 467)."

      Sadly, that future is yet to be.

    4. Since I started taking the scriptures seriously, again, really seriously, I've been amazed, over and over again, to find that some of them, Paul certainly, the Prophets, the Psalmists, all through the collection, really, had a far deeper understanding of the problems of human minds addressing reality and the world than you generally find among even truly educated people, today. Certainly more than the typical blog babble and the kind of people who regularly get on programs like "Fresh Air".

      I really think that the atheist-materialist-scientistic dictatorship that arose in the so-called Enlightenment cut off Western culture from one of the most profound sources of inspiration and insight available to it. Though certainly not one that has the linear and narrow or even unambiguous character of mathematical or physical scientific discourse.

      I think people tend to think out of and talk out of what they're familiar with and what they feel comfortable with. You can learn things from all kinds of people but you shouldn't expect to take their program of thinking over and adopt it whole hog.

      I think one of the most obvious symptoms of an intellectual culture gone to decay is how giving a person or an idea cooties on the basis of fashion and that such are unmentionable and untouchable has gained sway I've had pseudo-lefties slang against me for posting WLC before. Oddly, he never killed anyone I'm aware of, they wouldn't fault me for citing Mao or Lenin or, probably more stylishly, Trotsky even as he was guilty of the murders in the Kronstadt rebellion and his defense of state terrorism in an entire book. Somehow, someone actually being a murderer and an apologist of terrorism seems more discreditable acts than having the ideological cooties over these things.

    5. Those cooties being reflective of gross ignorance. I'm not that familiar with WLC's thought, and what I know of it I disagree with in some measure; but I respect his efforts, if not his conclusions.

      He certainly doesn't have "cooties." Not to me, anyway.