(Re)Search

I’ve been thinking about the relation, or possible identity, between paradox, contradiction, and duality. As such, I’ve been doing some research into a few concepts from logic. ^1.

I came across this take on the rule that anything follows from a contradiction. While the student’s exposition doesn’t explain it formally like on the wikipedia page, it’s nice to see someone who gets a sense of what follows from this principle: literaly anything is possible. And that’s what has always intrigued me since the first time this rule was shown to me, back in Logic I, some nine years ago. Perhaps others in my class were puzzled and incredulous like the author mentions in her piece, but me, hell, I was smiling because this explains everything.

Well, I bet I didn’t quite think exactly that at the time—I do know that in my head it entirely justified why magick works, and was directly linked to a cornerstone principle of occult thought: nothing is true, everything is possible—it took me a little longer to recognize the importance of this principle.

Another facet of logic I’ve been reacquainting with is proof by reductio ad absurdum. It’s apparent that there is a relationship between the structure of the reductio and the Principle of Explosion mentioned above: they both rely on contradiction, the structure of which can be expressed as A & ~A.

Of course, this brings in my old friend and sparring partner, the law of the excluded middle, which states that for anything, x, x either has the property P or it does not. In predicate logic, this is written Px v ~Px, which in the more basic symbolic logic is P v ~P, and we can simply substitute A for P and get A v ~A.

So we’ve got A & ~A, and A v ~A: like complements of One & Other, like a duality.

But then here’s a bit of self-referencing of sorts because I feel the structure of an understanding of duality goes something like ((A & ~A) & (A v ~A) ) & ((A & ~A) v (A v ~A) ). Or perhaps an even longer sentence, but adding more conjuncts and disjuncts simply seems to expand the point that, somehow, this ties together to create an infinitely rich tapestry.

Anyway, a paradox is basically the same thing as the case when the conjunction of A with its negation is true, so we could say that anything follows from a paradox. On the other hand, a reductio derives a truth so long as it discovers a contradiction in some set of premises: it proves the truth of the negation of some assumption which was used to derive the absurdity. So in both cases, we see how contradiction gives rise to some thing.

I guess where I’m trying to go with this, in part, is the idea that paradox and contradiction have an identical logical structure, and it is from this that everything else is created (derived). If anything follows from paradox, this includes self-consistent systems, i.e., an internally consistent set of sentences—a ‘true’ thing, say—can come from contradiction.



1. For potential readers, the symbols used in this entry are parsed as follows: & is ‘and’, v is ‘or’, and ~ is ‘not’. Hrmm, I ought to make something in the side bar about these things!

In the Beginning

In the beginning there was paradox: there was nothing and there was everything. In the end there was paradox: there was nothing and there was everything. In other words, the beginning is identical to the end, and in this identity there is nothing and everything.

This is how things got started, and this is why there is something instead of nothing. Our particular universe is a manifestation of some unfathomable number of possible universes. Each possible universe also exists, although we may be forever forbidden access to anything other than our own universe.

Time is a function of any specific universe; this is to say, without a universe there can be no time as time is what is formed when there are relations amongst parts. Space is also a function of relations amongst parts. Ergo, no relations means no spacetime.

Thus, we cannot get back to the singularity of the big bang because this is the initial point before time and space came into existence. Spacetime was created when the singularity became fragmented: its fragments formed the relations that both require and create spacetime.

Every universe begins the same; i.e., every universe starts from the same singularity. This is because the singularity transcends any specific spacetime matrix; thus, while any given universe blossoms forth from the singularity creating its own specific manifestations and its own unique spacetime structure, the singularity remains intact as the central force driving all possible manifestations. It is, in a sense, the Unmoved Mover of Aristotle.

The singularity is the ultimate paradox: it exists, and yet does not exist as existence is a function of some spacetime; it is nothing as something can only exist inside a spacetime matrix, yet it is everything as any instance of things is manifest only because of its fragmentation.

In the beginning there was I am & I am not.

Time and Energy

I was chatting earlier and got into a discussion about physics, the description of reality, and energy. The person I was chatting with appeared to take the position that physics can account for everything—all phenomena can be described in terms of energy. I mentioned that we’re not even sure what energy is, but he claimed that energy is a signal is information. But, I protested, this is mere tautology: it tells us nothing more about what energy is than the fact that maybe we have more than one word for it.

So I look up energy, and the Wikipedia entry has a great quote of Richard Feynman:

“There is a fact, or if you wish, a law, governing natural phenomena that are known to date. There is no known exception to this law; it is exact, so far we know. The law is called conservation of energy; it states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity, which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number, and when we finish watching nature go through her tricks and calculate the number again, it is the same.”

So, energy, as understood by physics, is ultimately without any properties other than a corresponding number. However, it also has many different appearances, and it is transition from one form to another that appears as motion or activity, and has more to do with the word’s etymology as “active,” “operation,” and “working.” Thus, there is a seeming paradox when it comes to energy: relative to a defined frame of reference, the activity of energy in a given space over time creates the phenomena that manifests within that space; however, the energy of the system remains identical to itself—it does not change. So what we find about energy appears to be that it changes in space over time, but it doesn’t change at all.

I also chatted with this person about how we don’t really understand what time is. Hir position was that we did, and that it could be understood as steps of progress in mutations, which seems to have intuitive merit; however, this merit, it seems to me, is based upon our perceptions of experiences as embedded within time, and not an understanding of time itself. Given that ‘space-time’ has no properties, but instead defines the dimensions of the system or structure in which energy exists, and that energy is merely some unchanging number, I’m not sure how we come to an understanding of what time is beyond a product of our own perceptions of something that, ultimately, does not change.

In other words, time makes no damn sense at all. And yet, this absurdity seems to be our reality.

A Fragment on Singularity

Here’s a funny thing, I have tried several times to write for this blog, and got bogged down in getting it perfect—like I had to say everything all at once, and in a way that was entirely correct. What ends up happening is I either save, or more often, delete the entry, and don’t really return to it—although I may return to the ideas several times while not writing about them.

This is contrary and counter-productive to an aspect of what I am trying to accomplish here, which is, namely, to start writing philosophy again, to pick up the ideas I was working on in times past.

Now, part of this hesitation to post incomplete or partially formed positions and thoughts is because one day I want to make this blog more public, and I want it to be functionally fabulous in relating the ideas it sets out to explore. So I’ve set myself up with a paradox: write freely about these ideas as if no one else is reading, but restrict the writing to only polished and perfected pieces that will be suitable for public consumption.

Heh, figures I’d create a strange loop for myself over this endeavour: after all, the strange loop is what this is all about!

Lol, in reading over the wikipedia article I find myself laughing at how I could attempt to explain the “…hierarchy of levels…[where e]ach level is linked to at least one other by some type of relationship, [so that the] strange loop hierarchy…is "tangled" …[such]…that there is no well defined highest or lowest level [resulting in a structure where t]he levels are organized such that moving through them eventually returns one to one's starting point” which makes me choose this term to describe my ambitions, but then I’d have to start and finish a blog that was identical to this one: yet another strange loop.

Anyway, I’d like to get on with an aspect of what I spend time thinking about, the singularity.

So let’s take a moment to consider one thing all on its own—let’s call it A. Further, if we think about what we mean by “one thing all on its own,” then we find that what we mean—literally—is a singular thing: a thing with no parts, no properties, but a unit in and of itself.

“A unit of what?” we might ask.

Well, we cannot answer this question because we are considering A as existing in relation to nothing else, and this means there is no possible observation of A because A is the only thing that exists.

“But aren’t we observing it now, as we consider it?” we might ask.

No we are not. What we are observing in our mind’s eye is, perhaps, a picture of some object that looks like the capital letter A surrounded by empty space. In other words, we are observing a representation of the circumstance described, but we are not observing A itself, because as we have said, we are attempting—and failing, apparently—to examine a thing as it exists as a singularity.

Kant also thought along these lines, I mentioned this before—this time I did look it up though—noumena is what he called a singular thing in itself. As Kant also reasoned, a noumena is “specified negatively as unknown and beyond our experience, or positively as knowable in some absolute non-sensible way.” ^1.

So the singularity, the noumena, remains unknown to us because it relates to nothing else. If we were to come to know it, then we would have to become it, but if we become it we lose ourselves which would necessarily include all our thoughts, ideas, modes of interpretation—since the noumena is not that—and all we are left with is being without any relations; being without anything at all.

Put differently, if A exists, then it exists as nothing, and the only way to understand “exists as nothing” is with the notion of ‘nonexistence.’ In other words A exists if and only if A does not exist.



1. Cambridge Dictionary of Philosophy, Cambridge University Press, 1995, pg. 400.

From Elsewhere Again

A basic problem when trying to come to terms with duality and dichotomy is pointed at in the following statement:

There are two kinds of people in the world: those who can be divided into two kinds of people and those who can't.

A specific dichotomy can be collapsed, reconciled, or understood as a unity, but only from the perspective of some other duality.

Even talk about "nonduality" is talk about negating something, and negation is merely one side of a duality captured in, for examples, 'yes or no' or 'on or off'. Put differently, "nonduality" can only make sense if there is "duality" for it to be contrasted to, and so, we see two polarities manifest a paradox.

Paradox is the generator of experience.