Against Metaphysical Continua

Actually written JANUARY 29, 2018

Here I present my reasoning against the existence of metaphysical continua.

Preface: What is a metaphysical continua?

-WHAT IS A METAPHYSICAL CONTINUA?-

First I will explain continua. An example of a continua is a number line representing the real numbers. Each point on the line represents a real number. Between any two of these real numbers there are more real numbers that can be represented by points and labeled. Real numbers can be found between any two real numbers infinitely. No matter how much we zoom in between two neighboring real number points, we can find more real number points between them, infinitely. We will never zoom into the space between two neighboring real number points and find a gap in the real numbers. Continua have no gaps. They are infinitely micro-scaleable. Real numbers, that we represent on number lines, are abstract continua that we grasp with the conceptual level of our consciousness. Space and time are examples of continua that we experience naturally at our basic perceptual level of consciousness.

A metaphysical continuum is a continuum that exists independently of consciousness. That is, such a continuum exists even when we don’t observe it. The reason I bother talking about such metaphysical continua is that I often ponder whether the continua of space and time would exist without we conscious beings who experience space and time.

Anyway, I have come to a point in my thinking where I suggest that metaphysical continua do not exist. Space and time, because they are continua, do not exist metaphysically. They are mental constructs (which is not to say they are completely subjective). They are constructed by the mind as ways to experience metaphysical difference, i.e. the fact that existence is not all one singular thing.

What follows is my argument for this.

-GAPS IN EXISTENCE CANNOT EXIST-

As a neo-Randian, I begin with the philosophical axiom of existence. Existence exists. And only existence exists. There is no such thing as a “nothing”, a “gap” in existence.

-PLURALITY / DIFFERENCE IS UNDENIABLE-

I continue by observing that difference is also a philosophical axiom. Existence has differences, different parts. Difference, parts, and plurality, are all correlates of this basic fact about existence. And like the axiom of existence itself, denying the axiom of difference leads to contradiction. To deny difference, one would have to either…

1) deny that anyone even experiences difference – in which case one is simply lying – because I know for a fact that I sure do experience difference. And so do you, you who are different from me, who experience each word you are reading as different from any other words here.

Or

2) claim that the experience of difference is an illusion. Difference does not really exist. But this claim insists there is a difference between the illusion we experience and what really exists. And this claim is therefore a claim that relies on difference. It attempts to invalidate difference by relying on difference.

Hence I maintain that difference is a philosophical axiom.

-CONTINUA ARE HOW WE EXPERIENCE DIFFERENCE-

We experience difference through the structure of continua. In fact, it seems we can’t even imagine difference without imagining the different things occupying different positions on some kind of continuum.

-- CONTINUATION JANUARY 6, 2023 --

But now we face a serious problem. We cannot imagine difference without imagining the different things in a continuum. But continua are infinite. And infinity is a problem.

-PROBLEM OF METAPHYSICAL ADJACENCY-

Infinity is a problem because it makes metaphysical adjacency impossible. I will call this the “problem of metaphysical adjacency”. It is basically the problem of Zeno’s arrow, but in a form I think shows the logical bind more plainly.

So, here is the problem of metaphysical adjacency [See also this poem about the problem]:

Any given thing that exists must be surrounded by other things. And these surrounding things must be directly adjacent to the given thing. By “directly adjacent” here I mean that they must be right next to one another, with no gaps between them.

There must be no gaps because such gaps would have nothing in them, which is to say that they are gaps in existence itself. Nothing would exist in the gaps. The gaps would be occupied by non-existence. And this is impossible. The existence of non-existence is a contradiction (and a fallacy that Rand called “reification to the zero” - making non-existence into a special kind of existing thing).

Thus there cannot be any gaps between directly adjacent things.

But if there are no gaps between existing things, there can be no distance between existing things. But if there is no distance between existing things, then things cannot actually be adjacent on the continuum, but must instead be at exactly the same position on the continuum. And that would make them identical - literally the same thing, not different things - which would violate the axiom of difference/plurality.

So the other alternative is to fill the gaps with an infinity of other things. Between any directly adjacent things there must be infinitely more things. But this is contradictory. It renders the very idea of “direct adjacency” meaningless. Pick any given thing. Now show me another thing that is directly adjacent to it. You can’t. Anything you show me has more things between the two things. It is impossible to show me the final directly adjacent thing. There’s always more between them, infinitely. Direct adjacency is impossible.

Direct adjacency is impossible, yet absolutely necessary to avoid equally impossible gaps filled with impossible non-existence.

Stuck between two impossibilities, we are.

-CONTINUA ARE IMPOSSIBLE-

But this is what we get with continua. Continua are literally impossible.

This means the continua of space and time are literally impossible.

They are impossible, yet we experience them.

-HOW CAN WE EXPERIENCE THE IMPOSSIBLE?-

How is it that we can experience what is logically impossible?

Super important question, this is.

-FORM VERSUS OBJECT DISTINCTION-

The best answer I have for this relies on what Objectivist philosopher David Kelley calls the distinction between form and object.

We perceive objects. And our awareness of objects is direct and infallible. But, we also must perceive objects in a particular way that generates the way objects appear to us. The appearance is the form, the form in which we perceive the object. The existence of the object is absolute; but the relativistic way we experience the object, the relativistic appearance of the object, is relative - generated by our consciousness.

More precisely, the form/appearance is what Kelley calls “relational”, instead of “relative”, to avoid getting this confused with general epistemic relativism. And it is crucial to understand that consciousness does not generate the form/appearance on its own, but so generates in causal connection with the object. Direct, infallible awareness of the object is necessary for awareness to generate the form/appearance for that object. Neither the form/appearance nor awareness of the object can exist without the other.

An interesting question pops up for me here. How accurate are our forms of awareness? When I look at a cube, it appears shaped like a cube. But does the object really look like a cube? - does it still have that cube shape even when nobody is looking at it?

Near as I can tell, Objectivists leave this an open question, the answer subject to never-ending scientific investigation and revision.

-SUPER DEEP RELATIONALISM-

Personally, I lean toward answering the question with “not accurate at all”. It seems likely to me that all forms/appearances are inaccurate, that indeed the cube does not look like a cube when nobody is perceiving it. More precisely, I lean toward the idea that, when nobody is perceiving the cube, it has no appearance at all. It does not have that cube shape, but it does not have any other shape either. It has no shape of any kind at all. Our consciousness generates the cube appearance. The cube shape is part of the form of our perceiving it. In fact, I take this to a total extreme: that the cube has no appearance of any sort at all, but that our consciousness generates every aspect of its appearance - including extension in time and space. I call this “super deep relationalism”.

-APPEARANCE/FORM EXISTING OUTSIDE THE MIND IS LOGICALLY IMPOSSIBLE-

This reasoning becomes a convenient way for me to explain away the fact that our minds experience impossible things, like the continua of time and space. If it is impossible, yet an undeniable part of our experience, it must be something generated by the mind, such as, in this case, relational forms of experiencing difference. Time and space are relational forms of experiencing difference.

Banishing time and space to the realm of mere appearance is pretty radical (super deep relationalism). Whereas banishing color qualia to that realm is less radical. The green color qualia of the grass is generated by my mind as part of the form/appearance of the grass, but not intrinsic to the grass. The grass does not look green when nobody is looking at it.

Ok, so one “banishment” is more radical than the other. But both banishments also reflect that what is banished is some impossible thing. Color qualia are no more possible than time and space. It is no more possible for grass to have that green color qualia than it is for anything to have space and time. All aspects of the form/appearance are impossible because they don’t exist in the objects. Our minds had to generate them in the process of being aware of the objects.

Well, this is my speculation about how the form versus object distinction can explain away how the mind can experience what is otherwise impossible - including how it can experience continua like time and space.

But, how valid is my speculation?

I mean, space and time are logically impossible. How can we experience what is logically impossible? While it is convenient to rely on the form versus object distinction, does such reliance really apply here?

-A PRECEDENT FOR EXPERIENCING THE LOGICALLY IMPOSSIBLE-

I have a bit more speculation on this issue. I summon the fact that the mind already does grasp logically impossible things at the abstract conceptual level. We have concepts such as “nothing” which are logically impossible. We are able to talk about “nothing” and understand what it means even if the existence of an actual “nothing” is logically impossible. Using abstraction, our minds can somehow imagine what is logically impossible. (See my writing in this book [blog] called “Meaning of Impossible Things”.) I can only suggest that this sets a precedent for our minds’ ability to experience the logically impossible, and then generalize that ability to other levels of consciousness as well, saying “if minds can do this at the abstract, conceptual level, why can’t they do this at the perceptual level as well?” Without a solid answer to this question, my speculation survives better. So, is there a solid answer to this question? Not a clue, for me anyway.

-INFINITY VIOLATES A PATTERN OF MIND SHUT DOWN-

And there’s yet another aspect of bizarreness afoot here. Infinity just seems to violate a pattern I was hoping there was some consistency in. The pattern is: The closer one comes to imagining a perceptually vivid experience of a logical impossibility, the more the mind shuts down. Imaginary concepts like “nothing” and “self-contradiction” are like this. The more one tries to imagine the concrete perceptual experience of actual “nothing”, the more the minds goes blank. Same with instances of self-contradiction, like omnipotence opposing itself. The experience of these imaginary concepts, even if experienced only in imagination, are like asymptotes that one can only approach but never reach. At the instant before reaching the experience, the mind just turns off. But infinity is completely the reverse of this pattern. Infinity is just as logically impossible as “nothing” and self-contradiction. But while the mind cannot experience “nothing” and “self-contradiction”, the mind does experience infinity. It’s more extreme than that even. The mind cannot experience any alternative to infinity. Completely backwards from the pattern.

-BROADENING THE PATTERN’S PRECONDITIONS-

Well, perhaps not entirely. I suspect maybe infinity becomes impossible to imagine when we try to imagine it in terms of the problem of metaphysical adjacency, by imagining trying to show someone the true and final metaphysically adjacent neighbor for any given thing. As one gets closer to finding that metaphysical neighbor, it’s very status as the final neighbor vanishes as more things appear between it and the given thing. So here maybe the mind does not shut down, like it does for “nothing”, but rather exhausts itself, chasing a goal that keeps outpacing it. But in either case, the mind cannot achieve the concrete perceptual experience of either “nothing” or “metaphysical adjacency”. They are impossible to experience for different reasons, but the result is the same: such an experience is a limit that can be approached but never achieved.

But then, we merely glance at the world and there it is: infinity.

-SELECTIVE SENSATIONALISM-

Well, there’s perhaps another way to resolve this. I will call it “selective sensationalism”. In epistemology, sensationalism is the theory that our perceptual experience is constructed from our abstract concepts, wherein these abstract concepts arrange raw sensations into structures to form perceptual objects. Now, ordinarily I would reject sensationalism, for reasons I’m not currently able to recall. But I could remind myself by reading what David Kelley wrote about it. But right now I think a kind of selective sensationalism might apply. Right. So if infinity is a logically impossible imaginary concept that we can know the meaning of abstractly, perhaps this capacity to know its meaning abstractly imposes a structure on our raw sensations to construct a perceptual experience of infinity. But it stops there. Beyond this basic experience of infinity, abstractions do not structure our raw sensations.

This is Kantian. From what I’ve read about Kant, he had a similar idea about certain basic a-priori abstractions (categories) shaping raw sensations into perceptual experience. And Objectivists hate Kant. But maybe he was right about this one thing. My own epistemology in general seems a lot like Kant’s, while preserving realism, e.g. my “super deep relationalism”.

-I DON’T LIKE ANY OF THIS-

But in the end, I still dislike all these candidates for explaining how we can perceive logically impossible phenomena. I just don’t like them, I tell you. So for me, it remains an open question.

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