Month: September 2019

Why Mathematical Platonism Is Silly

Basically, mathematical Platonists feel that, because there is so much complexity to math, it must be something “discovered,” as if from some Platonic mathematical realm. The problem with that is that the derivations in math cannot be any other way; they are what they are out of necessity (given math’s fundamental axioms, at least). That means that, even if there is some Platonic mathematical realm, the “discoveries” of math can’t come from it because that would imply that, were the realm somehow any different, the discoveries of math could be somehow different—that just working out the logic in our minds or by hand or on computer we’d come up with different results. But that would be incogent. The reason we get the results we get is that they’re the only results that are cogent. So, even if there were such thing as some Platonic realm containing all mathematical objects and relations, it would be completely superfluous because the discoveries of math can’t “come from” it, and therefore, given Occam’s razor, it makes little sense to assume its existence.

Another way to tackle the issue starts with an analysis of the meaning of the term “exists”. In order to coherently claim something exists, you must imply that it’s in some way, at least in principle, detectable or otherwise noticeable. If something is not noticeable under any potential circumstances, then what does it mean to say that it exists? To claim that something exists includes defining what the basic form is of the thing that exists; otherwise, you’re not saying what it is that exists, and it might as well be the most contentless thing imaginable, with the limit being nothingness. And how can you imagine the form of something without imagining interacting with it in some way to see the form? (See my argument for “form is function” in my previous essay and here.) And if the thing you posit exists can’t be interacted with (or, more specifically, can’t affect you) even in principle then imagining this observation of it is self-contradictory when you take the whole context into account, i.e., the whole world, from you to the claimed extant. Not to mention that the idea that something that exists that doesn’t affect us is a) unfalsifiable, and b) in violation of Occam’s razor.

So, if to say that something exists is to imply that it can affect us, then it makes no sense to say that mathematical “objects” (or whatever they are) are “exist” in some Platonic mathematical realm, because if they actually affected us then it would be hypothetically possible for them to affect us in some other way, thus implying some other hypothetical nature in which they exist. Instead, mathematics is all tautology, as it all necessarily follows from its fundamental axioms. Interaction/affecting is a process of action in time, and the objects of mathematics are timeless and unchangeable, so they can’t affect us in order for us to observe them.

In his book The Emperor’s New Mind, Roger Penrose argues for mathematical Platonism on the grounds that a given point is or is not in the Mandelbrot set independently of what mathematician or computer is examining it. By “examining it”, of course, he means executing the algorithm that determines whether a point is in the Mandelbrot set. I would say that, since there’s no way for an independent truth of which points are in the Mandelbrot set to “make its way into” the results of a completely deterministic algorithm, that truth must be an aspect of, or an indirect reflection of, the algorithm itself (including the rules for multiplication of complex numbers). It is simply illustrated in a way by which it appears very complicated, while its abundant self-similarity across place and scale is one sign of its actual underlying simplicity. Basically, humans are not smart enough to see “through” the imagery to its underlying simplicity, so our minds are tricked.

Let’s now tackle this problem from the opposite direction, starting with the fractal image and then deriving the algorithm. Let’s consider two reasonable suppositions: 1) The greatest measure of compressibility of a set of data is the smallest algorithm that can recreate that data, and 2) A set of data only actually contains as much information as its most compressed state; the rest is redundancy. If you made a program that could read a set of data and return the smallest algorithm that creates that data (though it might take a quintillion years to do that) and you fed it a Mandelbrot image, it would certainly (eventually) spit out the algorithm that created the image in the first place. Therefore, a Mandelbrot image actually, on a fundamental level, contains no more information than the algorithm that created it.

This thought experiment brings us to another interesting point: Penrose could have used for his argument any algorithm that produces an apparently complex set of data. For example, a pseudo-random number generator would generate an image with much more apparent complexity than a Mandelbrot image (in that it appears to be way less compressible, hence it appears to contain more information), yet Penrose doesn’t use a pseudo-RNG for his argument because it’s more obvious in that case that the only meaning in the data is in the algorithm that produces it. Yet the obvious structure of a Mandelbrot image is not any more evidence that the information exists in some Platonic realm than a pseudo-RNG-generated image is, because it’s no surprise that a simple algorithm could produce a structured image, since the image, being wholly a reflection of the originating algorithm, must therefore be a manifestation of complexity in simplicity. So, it’s apparent that Penrose was duped in this case by the mere interestingness (or whatever) of the patterns composing the Mandelbrot image.

Another argument for mathematical Platonism I’ve come across goes something like this: Math must exist prior to matter logically, if not chronologically, in order for matter to even exist because matter’s existence as such is wholly dependent upon mathematical laws. To this I have to say that mathematical laws aren’t something matter requires, as if they’re a separate thing from matter—the mathematical “laws” characterizing matter’s behavior are only ways to formally describe the behavior, and they’re merely abstractions. Reifying abstractions as something objectively existing is silly. In what form could they possibly exist?

A mathematical model of matter is basically a reduced simulation of matter. The math is merely a way of representing the matter’s behavior, and the matter is not separate from its behavior. Again, form is function. As I said in my previous essay, how can you know the form of something other than through how it interacts with the observer? And how it interacts with the observes is its function. And the functionality of matter and energy is the physics of it.

The degree to which matter behaves according to mathematical principles is the degree to which matter behaves both consistently and cogently (i.e. self-consistently). Of course matter behaves consistently, because it’s still the same stuff from one moment to the next, and the nature of its composition determines how it behaves. And to imagine that matter behaves in any way but cogently would be an incogent imagining, and thinking incogently is useless and irrelevant to reality, so of course matter behaves cogently.

Mathematical laws aren’t detectable even in principle except indirectly via the behavior of matter, so it’s unwarranted to assume that they have an existence independent of matter. And they’re not really even detectable via the behavior of matter because they could hardly have been anything different; they’re merely cogent or self-consistent thinking, codified.

Another argument (or perhaps merely a description) of mathematical Platonism I’ve seen briefly describes Platonism in general and then adds math to that realm in terms of some kind of basic or archetypal mathematical forms. The exact nature of these forms is irrelevant, because the premise of Platonism itself is silly.

Some Platonic forms, such as beauty, are merely abstractions derived from what many objects seem to have in common and then apparently reified as things-in-themselves by way of language. “Beauty” as being independent of anything beautiful exists only as a linguistic construct.

Other, more concrete Platonic forms, such as the ideal horse, are simply categories people hold in their minds as a result of seeing many similar objects which are given a common name, especially where there is not a smooth continuum of objects’ forms ranging from the ideal in question to completely different forms. There are many different reasons objects would take common forms in islands of similarity, and none of them is because there exists some Platonic form somehow supernaturally dictating their manifestations. For example, all horses are relatively similar to all other horses (and thus categorizable under one name) because of the evolutionary mechanics of speciation.

What’s more likely: That forms exist as templates in our minds used to categorize objects, created largely without our noticing over time through observation and teaching, especially in the early stages of learning; or that they exist in some unobservable, independent realm of abstractions without any conceivable sort of grounding, and that we psychically access a form in this realm every time we identify something? Especially considering how pragmatically useful it is to employ these categorizations, thus implying their likely arising from natural processes of cognition, and considering how naturalistically the islands of similarity in objects arise, thus making their definitions in an independent realm superfluous. And to say nothing of the areas of object differentiation where there are no islands of similarity, only continuums of object forms ranging between objects of completely different configurations, and also to say nothing of the ubiquitous continuums between areas of object forms where there are distinct islands of similarity and areas where there aren’t; for example, extruding from the island of horse forms are forms such as the zorse, a zebra/horse cross, a horse that just lost one of its limbs, horses with some sort of obvious genetic mutation, etc., horses still in the womb ranging through all the phases of ontogeny, etc.

Platonism is obviously a very naive and antiquated way of thinking characterized by a lack of self-reflection regarding language, abstraction and the process of identification, and mathematical Platonism is an even more problematic extension of that.

This essay was loosely based on a much more awkward and obtuse essay I wrote 21 years ago that can be found here:

I wrote a little bit more about mathematical Platonism, particularly about why it’s not true that “pi is infinite,” here:

Why the Speed of Light Probably Isn’t a Constant

All matter and energy is constantly in flux. What appears to be solid, such as a desk, is actually made of trillions of tiny atoms, each one vibrating in place, and each one made up of waves of electron fields around nuclei that are made of vibrating protons and neutrons which are in turn made of moving quarks. Force fields are in flux because they emanate from matter which is in flux, and force fields aren’t matter or energy anyway—they’re just mathematically defined causal relationships between physically existing things.

The laws of physics appear to be static, but they all boil down to two aspects: 1) the aspect of it that is necessarily true just because it’s logically consistent with the of physics. This aspect is why we’re able to do derivations in physics; and 2) the aspect of it that comes purely from observations. The first aspect is necessarily static just because logic itself can’t logically be any different, but there’s no justification to assume the other is static just because the observations seem consistent over time. Since everything else we observe is in flux, chances are that those things are in flux as well—they just change too slowly to be noticed.

Add to this the fact that there’s no ultimate way to distinguish between the physics of matter and energy and the physicality of it. The so-called “laws” of physics are not a separate thing “acting on” matter and energy. The closer you look, the more these two things blend together. One way of saying this is that form is function. How can you know the form of something other than through how it interacts with the observer? And how it interacts with the observer is its function. And the functionality of matter and energy is the physics of it.

All of physicality boils down to matter, energy and fields. Matter is in turn a pattern of seething energy, and fields. Can’t, even in principle, be defined or observed in any way other than as causal relationships between matter, so it’s safe to say that fields are merely an aspect of physics. And what is energy other than behavior patterns, and what determines its behavior if not the internal logic and mechanics of it which is what physics reveals? Also, as I mentioned in my last essay, Emmy Noether proved that the conservation of energy logically follows from the consistency through time of the laws of physics. And what is the concept of energy other than an invariant? What sense would energy make if it weren’t conserved?

So, everything physical is in flux, and there’s no ultimate way of distinguishing between physics and the physical. And physics is derived from only from a combination of observations and pure logic, while we can only observe the physical and most of what we observe seems to change constantly. So all of this would seem to suggest that the constants in physics, such as the speed of light and the gravitational constant for example, aren’t actually constants but are only assumed to be because they’re so slow to change. They’re part of a cascade of change that makes up the physical world, from the most universal and slowest to the most local and fastest.

I wrote a longer, more elaborate version of this same basic concept here and a briefer version of that one here.

A Possibly Specious Argument for Immortality of the Mind

  1. Energy is always conserved. This is a fundamental law of physics. It was even proven by Emmy Noether in 1915 that the law of conservation of energy necessarily follows from the fact that the laws of physics do not change over time. Of course, it’s known that matter and energy are interchangeable (hence E=mc2 and the atomic bomb), so that means matter is conserved too except when it’s converted to or from energy, in which case its constituent energy is still conserved.
  2. Everything is, theoretically, made up of matter and energy.
  3. Therefore, when we say that something—any physical thing—has been created or ceased to exist, it must merely mean that its constituent matter and energy has been transformed into some other configuration, which we then call something else.
  4. Therefore, the “things” that we observe to come into existence or cease to exist must only amount to perceptual categories. Sure, these things “exist” inasmuch as they are made up of matter and energy, but since this matter and energy cannot be created or destroyed (the big bang and quantum fluctuations not withstanding), these things do not exist independently of our perceptual categories inasmuch as they can be created or cease to exist.

    (The rest of #4 you can skip if you like.)

    This is not to say that Eastern Airlines or the library at Alexandria still exists, but that, exactly inasmuch as they have ceased to exist, they amount to an abstraction or concept in mere reference to a particular part or aspect of what is or was.

    For example, let’s take a wooden chair. Over a very long period of time, this chair will slowly rot into oblivion. Or it might burn up in a fire.

    During this process, there is no definitive point in time at which the chair, as such, ceases to exist. At the end of this process, you may unequivocally state that the chair no longer exists, but choosing the exact point at which its constituent matter and energy is no longer a “chair” is a complete judgment call! It is arbitrary, hazy, and what it shows is that we do not have actual objects that are created and cease to exist, but rather, actual matter and energy whose state is continually shifting into and out of our relatively arbitrary categories like “chair” or eves “wood” versus “dirt” or perhaps “light” and “heat.”

    (Even the transformation of energy in a chemical bond into light and or heat form, as well as the material separation of the atoms, is a process or event, taking some amount of time, so there is a continuum of state that ranges from fitting into one label (such as “wood) and another label (such as “light”), even on the level of individual molecules. The same applies even to the nuclear transformation of matter into energy.)

    So all we really have is eternal actuality versus transient perceptual categories.

    To go on a tangent and make another point along the way, this means that nothing in our human experience truly has every been created or destroyed. So to extrapolate that, because everything we know of has been created and will cease to exist, the universe itself must have been created and must cease to exist at some time (as opposed to being eternal, which is something we have trouble comprehending), is a blatant intuitional error.

    The universe itself contains all transient states of matter and energy which we categorize as this thing or the other thing that we think has been destroyed when its matter and energy has transformed into another thing. That energy itself, which can take the form of anything we know of, has never been known to be created or destroyed, and obviously any possible state of that energy could be said to constitute “the universe”.

    Therefore, the universe is, in all likelihood, eternal.

    (Since all our physics breaks down when extrapolated backward to the point of the big bang, it’s pure presumption to say that the big bang was the beginning of existence or the beginning of time. We don’t know what may have existed before it and caused it.)
  5. The mind precedes, and is primary to, all of its conceptual categorizations. Your mind necessarily exists, both chronologically and logically, before it can classify the stuff it observes.

    So, we have shown that..
    1. The existence of a mind is primary to its representation (or conceptualization) of all other “things”‘ existence. Specifically, the creation and destruction or cessation of things happens strictly with respect to the mind’s representations of those things.
  6. Therefore, the mind itself is never destroyed in actuality.

This argument is a rewrite of essentially the same argument I made in 2001 that can be found here. Its style is highly awkward, and it’s too terse for even me to follow some of it now, but it contains a little bit of stuff not presented here. Also, it begins to make a completely different point at the end that I didn’t include here because I seem to have found a non sequitur in it and not to mention because it ends mid-sentence and mid-thought. (How I was planning on finishing that thought I have no idea now.)

How We’re Looking at “Instinct” Wrong

As with many, many things in life, looking at the concept of instinct through scientism-colored glasses blinds us to seeing half the nature and wonder of the subject in question—in this case all the organisms in the animal kingdom. The observation of instinct is one more potential path to the understanding of the underlying magic in life and living beings—one more path thwarted by the overlay of the scientistic mindset upon everything we perceive.

The prevailing physicalist, mechanistic worldview of our times causes us to assume that “instinct” is just a kind of programming or hard-wiring of the brain that dictates the animal’s actions, presumably somehow excluding or subverting the animal’s free will exactly where it needs to. We think of it in a mechanistic way, like it’s just neurological wiring which makes animals do things they can’t help but do.

I’ve seen one person describe/define instinct as “behaviors constrained by genetics in response to environmental events.” This assumption is inadequate, for two reasons. One, we can’t be sure they’re genetic. Some behaviors have been known to be passed down neither by genes nor by nurture, in controlled conditions. We just assume everything passed down by means other than nurture is genetic because that’s the only mechanism (we think) we understand.

Two, it’s a rather behavioristic framing, ignoring that what we call instinctual behavior tends to require dynamic intelligence to be applied to it, hence it’s mediated by the organism’s consciousness. It’s paradoxical to try to imagine how an organism can be influenced to do something and apply intelligence to that directive (which also requires directing consciousness to it) while it has no understanding of why it wants to do that thing. Does it come as some kind of feeling, or what? (When I say, in other words, that intelligence is applied to the execution of the instinct, what I mean is, for example, when a spider makes its web, it doesn’t make it the same way every time. It dynamically adapts its web weaving to the particulars of its environment, sometimes even in clever ways.)

The truth, I think, is that there’s a spectrum of consciousness and drives in animals going from pure self-awareness (or at least plain awareness) and conscious decision-making to more primal levels of consciousness (or the subconscious) and drives which we call instinct. Instinct is very much a part of their mind, intelligence and emotions.

It’s still fascinating, though, how the animal mind can be driven by instinct to perform behaviors of its own free will that are too complex and crafty for it to have any kind of coherent reasoning about. But I suppose it’s only slightly more fascinating than the idea that we humans, as conscious and free-choosing as we are, can be driven by instinct to, say, desire sex, or suckle on a bosom, or even that we can be influenced to want to avoid a certain situation by means of the sensation we call pain.

By saying that instinct isn’t “hard-wired” in the brain, I’m not necessarily saying that it doesn’t ultimately exist as an aspect of the central nervous system, or that it’s not determined by one’s DNA, or whatever; I’m just characterizing the phenomenological nature of it vis-à-vis consciousness.

But I’m not saying it is necessarily contained by the brain either. I’m partial to a theory of mine that instinct works by means of Sheldrakian morphic resonance: That is to say, the spider spins its web because the spider falls within the morphic field of its species, and that field contains, among many other things, the instinctive pattern of web-spinning for that species. And the morphic field of the species must have evolved alongside its genetic evolution, in a sort of “symbiotic” relationship.

In other words, as spiders figure out how to do certain things (or do certain things randomly that happen to be propitious for survival), those behavior patterns get embedded into the morphic field for the species so that further members of the species tend to perform the same habit. Thus genetic evolution can progress within the context of that existing habit, along with whatever else is affected and effected by the morphic field. And, of course, conversely, the morphic field changes according to the context of the physical definition of the species as genetically determined.

Some of those “other things” influenced by the species’ morphic field could be the very chemical processes that allow the body to function. After all, Sheldrake claims that after a certain type of crystal was grown in a lab in one place in the world, it suddenly would grow a lot faster in labs in other places of the world. We don’t really know enough about how things work to say for certain that the workings of some chemical processes aren’t undertermined WRT the physics we know; some of it could be up to morphic fields. Indeed, some (or possibly all?) of what we call the rules of physics themselves could actually be due to morphic resonance.

(BTW, this should go without saying, but when I say that a morphic field belongs to the particular species, I don’t necessarily mean that there’s exactly one morphic field for each species in some kind of discrete way. The delineations between morphic fields for sibling species are most likely blurry. The divisions between hierarchies of morphic fields corresponding to hierarchies of animalia are also probably blurry.)

(Also BTW, I know it’s a little late in the game to explain this, but in case you don’t know already, the idea of morphic resonance and morphic fields is an idea that when some manner of thing/process behaves in a particular way it’ll be more likely to behave in the same way in future instantiations of it, even if they’re in a completely different place. Hope that helps clear up the last four paragraphs.)

Another alternative to the idea that instincts are stored in the brain—and this isn’t incompatible with the idea that they operate via morphic resonance at all—is that they’re stored in the whole body. I don’t think all aspects of mind are necessarily in the head. (I don’t think all aspects of mind are necessarily in the body at all, but that’s another issue.)

You feel emotions in places in the rest of your body, so the natural conclusion is that emotions can reside within other parts of the body. Assuming that they’re completely generated in the brain and that feeling them extended to the rest of the body is therefore an illusion is tendentiously scientistic.

Also, I once read a story of a man who had had a heart transplant from another guy who had died in a car crash. For a while after receiving the new heart the man would hear (or maybe he would dream he heard? I don’t remember) a mysterious ticking sound. It was later concluded that the ticking sound he heard was the sound of the turn signal that was still ticking for a while after the car had crashed.

But more to the point, the story also said that the heart recipient’s tastes in food and other things started to change, and, if I remember correctly, upon conferring with the relatives of the heart donor it was found out his tastes were changing to be more like those of the donor. So, if personality can be housed in the rest of the body, then maybe instinct can be, too. After all, it’s all interconnected.

I shouldn’t have written so many paragraphs about where the instincts might be stored, though. The main takeaway from this essay should be that instinct is just as much a part of mind as free will and emotion are, and that looking at it in a scientistic or mechanistic way bars us from seeing the magic in life that instincts intimate.