– Aleister Crowley, Liber Aleph
Those sentences above are descriptions of the foundational laws of thought (or the “laws of logic”). The first thing that you’ll notice about them is that they are tautologies. They’re circular statements that are necessarily true because the contrary in each case is impossible. While it may not be possible to demonstrate in any absolute way that they are true (I’ll get to this in a moment), it would appear that these laws are true and applicable to everything (or, more accurately, to our conceptualization of everything).Without these laws, thought itself would be impossible because each thought is what it is and is not what it’s not. Ditto with language: every word is what it is. That is to say, each word encompasses a range of meanings and uses, and these meanings and uses all together comprise what that linguistic building block is. Each one has to be what it is – and not what it’s not – in order for there to be language at all. The same holds true with logic: logic is built on the foundation of these laws, which establish that true, mutually-exclusive dichotomies are possible. Without dichotomies, it would be impossible to construct and validate syllogisms.
There seems to be a great deal of confusion about these laws, on the side of believers and nonbelievers alike. These laws are not contradicted by quantum mechanics, they are not contradicted by the fact that people can develop logical systems with different categories for ranking truth value (“Multi-valued logic”), and they cannot be argued against (because to argue is to invoke these laws).Their place in Thelema is also frequently misunderstood. As Crowley clearly states, logic is the code of the laws of thought, which cannot be abrogated. Though he acknowledges that these laws are “Limitation,” they are also “the rules of thy Game which thou dost play." To use the analogy he invokes often in Liber Aleph, the laws of logic are like the rules of chess. So long as we’re playing chess, it’s absolutely true that bishops can only move diagonally. It is senseless to object to this statement on the grounds that it’s possible to pick up a bishop and put the piece in your pocket. Whether or not this “law” applies in contexts outside of playing the game is irrelevant. It’s one of the rules of the game, and within the bounds of the game it’s absolutely true. By agreeing to play the game we bind ourselves to it.
The laws of thought are very much like this. So long as we play the “game” of thinking and logical argumentation, we are bound by them, and there is no way to escape them. Whether or not they are “really” absolute is irrelevant because within the game they are as absolute as the rules of chess are in that game.This remains the case even when thinking and reasoning about subjects that are irrational, counter-intuitive, and paradoxical. A photon of light may behave like a wave and a particle, but it’s something that behaves like a wave and a particle and it’s not not-something-that-behaves-like-a-wave-and-a-particle. An abstract painting may exist to defy our conventional notions of what art is, but it’s still an abstract painting and it’s not not-an-abstract painting. We may have a conflicted desire that partially wants to commit to a sexual partner and partially wants to remain single, but it’s a desire that partially wants to commit to a sexual partner and partially wants to remain single, and it’s not not-a-desire-that-partially-wants-to-commit-to-a-sexual-partner-and-partially-wants-to-remain-single.
So long as we’re playing the game of thinking and talking about stuff, you have no choice but to play by its rules. You cannot abrogate these rules, as Crowley tells us.Read on for way too much more on this subject. Toward the end of the post, I start talking about the more direct relevance of all these ideas to Thelema.
The first thing to note is that these laws, as the foundation of thinking, obviously cannot be proven or demonstrated to be true. This is necessarily so because any attempt to demonstrate these laws has to begin with them as a foundation already. This renders any attempt to argue for them or demonstrate them circular.Essentially, it appears impossible to use reason to confirm that reason is totally accurate. Read here for my full thoughts on this subject.
But luckily, this turns out to be entirely irrelevant in any practical context. The fact that we cannot confirm that reason is absolutely accurate matters as little as the fact that we cannot confirm that reality is “really real” in any ultimate sense.
The simple fact of the matter is that absolute claims are absolutely useless. I’m not making an absolute claim when I call the world I experience “reality,” and I’m not making an absolute claim when I correctly observe that the process of reason produces results that are consistent and useful within the world I call “reality.” Whether or not any of this corresponds to some “absolute truth” is seemingly impossible to determine and totally irrelevant. This being the case, we can set aside the question of “absolute truth” as an absolute waste of time. The only thing that need concern us is whether the process of reason produces consistent and useful results in the world that we experience, whatever its ultimate ontological status (which it appears cannot be determined).It’s sometimes claimed that the laws of logic are “presuppositions” or “axioms,” ideas that cannot be absolutely proven as true but are accepted nonetheless, without evidence, as the starting points of thought. I’ve addressed in another post (the one I linked to above) how I think that the term “presupposition” is misleading when it comes to these laws because the word implies a deliberate act. There are many religious believers who disingenuously conflate holding these presuppositions with “faith” in the religious sense. “Law” is similarly a misleading term because it implies to some people a conscious law-giver (“law” is meant in the sense of a descriptive law, a statement of what is probably the case, based on observation). Even “axiom” is somewhat misleading because – as a term of formal logic – it suggests a deliberate choice.
I didn’t wake up one fine day and decide to myself, “Gee, I think I’ll presuppose that objects are what they are and are not what they are not.” I also didn’t think to myself, “You know what? I’ll just decide that the world my senses reveal to me is really real. Yeah, I choose to believe that on faith.”
No, none of that happened. What happened is that, since my birth, my senses have revealed to me a relatively consistent world. As part of interacting with that world, I have come to use the word “reality” to refer to that world (which is what every other person I know does). As part of interacting with this reality on its own terms, the consistency of this reality has shaped the way I think. At no point was there a conscious act of faith on my part, and this is the reason that religious buffoons are being dishonest when they try to conflate reasonable thought with faith.When I use the word “reality,” I am in no way making a metaphysical claim about the ultimate nature of the world revealed to me by my senses. I am simply labeling that world. Similarly, when I use the laws of logic in coming up with logical arguments, I am not making a metaphysical claim about the ultimate truth of these laws. I am simply applying a mode of thought that my mind has been guided to employ by the brute facts of reality and that has demonstrated itself as effective in arriving at conclusions that are consistent with the world revealed to me by my senses.
It is thus deeply disingenuous to describe the use of logic as “faith,” since it is nothing like what is typically meant by the word “faith.” We might go back to Crowley’s chess analogy here. It’s not “faith” for me to accept that bishops can only move diagonally in a chess game: it’s just a rule of the game that I’ve chosen to accept for the purpose of playing it. The difference between the rules of chess and the foundations of logic is that there is reason to conclude that thinking agents developed the rules of chess but there is no reason to conclude that thinking agents developed the foundations of logic. Since the rules of chess were the products of thought, I need to be taught the rules before I can begin using them, but since the “rules” of logic are really grounded in the brute facts of reality, I was thinking in ways governed by the foundations of logic without having to be explicitly taught them.So what are the laws of logic?
One misconception about the laws of logic is that they are conceptual by nature. There’s a certain dishonest religious argument involving the laws of logic that runs like this: the laws of logic are concepts, but they are not dependent on any human mind. Humans didn’t invent these laws; they discovered them. If all human minds vanished tomorrow, the laws would still apply. Since they are concepts, they must depend on a mind, and we just established that they don’t depend on any human mind. Therefore, they must depend on a transcendent mind, and that mind is the mind of God.What a load of horseshit.
The fact is that the laws of logic are not concepts. The mere fact that we can conceive of these laws doesn’t mean that the laws themselves are concepts, any more than the fact that we can conceive of a rock means that a rock is just a concept.Concepts point to things. The concept of a rock points to a physical rock. The concept of the laws of logic points to the foundational facts of reality.
So what *are* these laws? I heard it expressed once rather nicely: these laws aren’t things that have a nature. They are our expression of the nature of things. That is to say, they appear to be brute facts of reality. They are the essence of what is, what is not, what could be, and what could not be.In other words, they (the stuff pointed to by the concepts) are not conceptual but essential.
This point is important because it will readily grasped that these laws are also not contingent on humans minds or on anything at all, it would seem. The conceptual statements of these laws are indeed contingent on the existence of a mind to conceive of them, but the essence to which the statements point (that is, the foundational facts of reality) are seemingly not contingent on minds or on anything at all.As a thought experiment, imagine a universe identical to this one except for one difference: there are no humans or human minds or even any minds of any kind at all in it. In such a universe, a rock still would be a rock and not not-a-rock. Granted, nobody would be around in that universe to make or evaluate that statement, so the statement would have no meaning in that universe, but here in this universe (where I’m making the statement about this hypothetical other universe) it does have meaning. And a rock would still be a rock even without someone around to notice that it’s a rock.
Let’s push the thought experiment further: let’s say that nothing exists at all. The laws of logic still apply because nothing would have to be nothing and not not-nothing.All of this is to say that the laws of logic aren’t “things” that “exist” within the universe. They operate on a meta-level: the universe is subject to them.
Everything is subject to them, it would seem, even things that don’t exist or can’t exist. If we can conceive of it, it’s subject to the laws of logic. Even the laws of logic are subject to the laws of logic: the law of identity is the law of identity and it’s not not-the-law-of-identity, etc.This is just the way things are. They are brute facts, and so long as you’re thinking, there is no escape from them, even by means of word games.
The Folly of Word GamesOf course, none of the above stops people – theists and atheists both – from trying to use word games to try to “abrogate” these laws.
But what these people do not realize is that the laws of logic are the grounds for playing word games. They couldn’t even play their little word games without the laws of logic. When they bring up quantum mechanics as an example of why the laws of logic are invalid, they can’t make an argument without first presupposing the laws of logic because argumentation is predicated on those laws.But further, if we sit down and examine what’s actually happening in the examples that these people invoke, we’ll observe that no laws of logic are being violated.
Take perhaps the most famous example, Schrödinger's Cat. In this classic thought experiment, a cat is said to be in a state of superposition and can be described as simultaneously alive and dead.The laws of logic still apply: the cat is in a state of superposition and it’s not not-in-a-state-of-superposition. Or, alternatively, we could say that it’s both alive and dead, and it’s not not-both-alive-and-dead. When we make a statement about what it is – even if that statement is that it’s this-thing-that-cannot-be-precisely-determined-and-possibly-can-only-be-described-in-seemingly-contradictory-terms, then we’re saying that it is this-thing-that-cannot-be-precisely-determined-and-possibly-can-only-be-described-in-seemingly-contradictory-terms and it’s not not-this-thing-that-cannot-be-precisely-determined-and-possibly-can-only-be-described-in-contradictory-terms.
I recently had someone on Lashtal object that Schrödinger's Cat demonstrates that the laws of logic (along with “two value logic”) are “empirically false” because it is an example of “mutually exclusive states” existing at once.But it’s not.
The law of non-contradiction (A cannot be equal to not-A) simply tells us that true dichotomies can be formed, and in this case there is a true dichotomy: Alive vs. Not Alive. Using that distinction – and carefully defining what we mean by “alive” – we can categorize everything in a mutually exclusive way. Notice, however, that the dichotomy is not between Alive and Dead. While Dead is one kind of “Not Alive,” there are other conditions that we can describe as “Not Alive.” For example, being both-alive-and-dead in a state of quantum superposition would qualify as a kind of “Not Alive” (assuming that we define “alive” as meaning only being alive and nothing more). Other potential entries in the “Not Alive” category might include Undead, Reanimated, Undergoing a Near Death Experience, etc.It works the same for all the other examples. If we discover an alternate dimension in which the cat is dead, then the cat is alive in this dimension (and not not-alive in this dimension), and it’s dead in the other dimension (and not not-dead in the other dimension). Or, alternatively, we could phrase it that the cat is alive in dimension A and dead in dimension B and it’s not not-alive-in-dimension-A-and-dead-in-dimension-B.
The laws of logic are also not violated by looking at the same phenomena on different levels. For example, I could perceive the chair I’m sitting on as a single thing, as a collection of several pieces put together, or imagine it as a collection of billions of atoms arranged in a certain pattern. The fact that I could choose to see it as any of those things does not violate the laws of logic because within each frame of reference, it is what it is and it’s not what it’s not.It’s further irrelevant that the chair, like all things, is in a constant state of flux. When I say that it’s a chair and it’s not not-a-chair, I’m speaking about the thing I’m defining as a chair, which includes all of the billions of atomic changes happening within the parameters of that definition. Furthermore, the fact that it will one day fall apart and no longer be identifiable as a chair doesn’t change the fact that right now it is the thing I’m defining as a chair and it’s not not-that-definition.
The essential point is that when I say A is A, I mean that we can conceive of A as having all of the A-properties and that it cannot, by definition, not have A-properties (otherwise, it would not be A). You can substitute anything for A. I’m not sure how much clearer I can make it than that, and I’m not sure that it’s possible for a word game to undermine what is, at its core, the fundamental tautology on which all thought and logic is built.One last point: the laws of logic are in no way undermined by “multi-value logic.” The term “mutli-value logic” refers to any system of logic that has more than two categories for ranking truth statements. In other words, rather than just “True” and “False,” a multi-value logic might consider a statement to be True, False, or Indeterminate. There are lots of situations in which three categories would be very useful. For example, there are some philosophers who are considered “presentists,” and they consider the present to be all that exists. To some such philosophers, the statement “I will go to the park tomorrow” can’t be considered true or false because it’s a statement about a world that doesn’t exist yet. So it can be classified as “Indeterminate” (meanwhile, a statement like “I intend to go to the park tomorrow” can be true since it’s a statement about the present).
That’s very good and all, and I’m all for using whatever categories you like to rank truth statements according to whatever’s most useful for your purposes, but such a logical system in no way undermines the laws of logic. Saying that a statement is neither true nor false is not a violation of the law of non-contradiction because “True and False” isn’t a true dichotomy.The law of non-contradiction allows us to set up true dichotomies that are direct negations. In the same way that “Alive or Dead” is not a direct negation (and therefore not a true dichotomy), so too is “True or False” not a direct negation (and therefore not a true dichotomy). The true dichotomy is “True or Not-True.” A statement must fall into one of those two categories and cannot fall into both at the same time and in the same way. “False” is one kind of “Not-True,” but there are many other kinds of “Not True” statements: internal contradiction, paradox, deliberate nonsense, etc.
And whatever the statement is – and whatever category someone puts it in – that’s what the statement is, and it’s not not-that (within that particular system and in that particular way in those defined parameters).It also doesn’t matter that different people can come up with different classification systems for the same thing. I might come across a statement and classify it as “Not-enough-evidence-to-accept-it-as-true.” You might classify it as “False.” Our usage of different systems in no way changes the fact that the statement is what it is (and is not what it’s not) and that in the context of each of our classification systems the statement falls in the category or categories that it falls into and it does not not-fall-into-that-category-or-categories.
Try all you want to abrogate the laws of thought. Word games cannot do it.
Reason is a Lie: The Laws of Logic in ThelemaMany self-styled Thelemites are under the mistaken impression that Thelema teaches that reason is not a reliable tool for evaluating some factual claims. In this post, among other places, I take an extended look at this issue.
In short, Thelema affirms that reason is absolute in the realm of the mind, and the foundations of reason – those laws of thought – necessarily hold true within that realm. Outside the realm of the mind – outside of conceptualization – reason and its foundations are not useful.As far as the foundations/laws of logic are concerned, Crowley was clear that these are true within the realm of thought. However, Crowley was clear also that at the highest levels of initiation, the individual comes to stand “outside” of thought and thus “outside” of those laws, which are then perceived as a “limitation.”
Crowley states this directly in a brief line in Magick Without Tears:
In the Ruach all the laws of logic apply: they don't in Neschamah.
The “Ruach” is the rational part of the individual, attributed to the central six sephiroth on the Tree of Life; Neschamah refers to the “higher” part of the individual, attributed to Binah on the Tree of Life (Neschamah is the direct experience that selfhood is an illusion – more specifically it’s the direct perception that selfhood is produced when thoughts apprehend other thoughts and manufacture the idea of a “thinker” [an idea that doesn’t actually correspond to anything]).In the context of the letter in which this line appears, Crowley is talking about AL I:22 ("Bind nothing! Let there be no difference made among you between any one thing & any other thing; for thereby there cometh hurt. But whoso availeth in this, let him be the chief of all!") which deals primarily with attainment to Binah (and thus to Neschamah).
Before interpreting this extract, it’s worth noting that variations of this idea crop up throughout Crowley’s work. Take Eight Lectures on Yoga, for example:
The first law of normal thought is A is A: the law of identity, it is called. So we can divide the universe into A and not-A; there is no third thing possible.
Now, quite early in the meditation practices, the Yogi is likely to get as a direct experience the consciousness that these laws are not true in any ultimate way. He has reached a world where intellectual conceptions are no longer valid; they remain true for the ordinary affairs of life, but the normal laws of thought are seen to be no more than a mere mechanism. A code of conventions.
Crowley thus claims that “above the Abyss,” the laws of logic are “no longer valid” and do not “apply.” Given what I said earlier in this essay, what precisely does it mean for the laws to be “no longer valid” and to not “apply”? We come a little closer to an answer when we examine Crowley’s use of very similar language in this extract from the Amalantrah Working:
These thoughts . . . . . . are ablaze in consciousness owing to the inhibition of the moral faculty as above stated. But in samadhi the higher faculties are ablaze too, so that one gets the details and the sum of them all aflame at once in a super consciousness fitted to comprehend them in this way, which transcends the laws of logic, because in this consciousness one does see each and all at once.
When Crowley says that the laws of logic are “transcended” by a certain state of mind – thereby making them “invalid” – he is talking about a state of mind in which one “does see each and all [thoughts and faculties] at once.”This curious phrasing needs to be considered side-by-side with the attainment ascribed to the Neschamah (where the laws of logic are “not valid”): the crossing of the Abyss and the attainment of the 8=3 grade.
Crowley writes in One Star in Sight that one attains this grade by “putting each idea against its opposite, and refusing to prefer either,” thereby achieving “emancipation from thought.”
We said earlier in this essay that the “laws of logic” apply to thought. By “putting each idea against its opposite and refusing to prefer either,” an individual comes to transcend thought and thus the laws of logic.
But what exactly does that mean? Consider the law of identity: A is A. Consider the law of non-contradiction: A is not not-A. But above the Abyss, one begins to see that any given thought (which we can designate A) necessarily implies the existence of not-A. In order to have the thought of a cat, one must necessarily be able to distinguish this thought from everything that is not-a-cat.Not only does A imply not-A, but A relies on the existence of not-A. It would be impossible to think of a cat if one’s mind had not separated out “cat” from “not-cat.”
It’s in this sense that every thought not only implies its opposite: every thought necessarily contains its negation. If it were not for not-A, then A would be impossible to think. Not-A is, we might say, the very A-ness of A.This is starting to sound a lot like some schools of Buddhism here, which assert that the interconnectedness of everything means that each thing basically is what it is not. A flower can’t exist by itself: it needs the soil, the rain, the sun, the air, animals to provide carbon dioxide or help them reproduce, etc. If we keep going, we can find a way to show how the flower depends on everything else in the universe, stretching all the way back to the Big Bang. What we regard as a flower is ultimately the entire universe because it depends on the rest of the universe and couldn’t exist without it. In much the way that a red object isn’t actually red – it absorbs all colors *but* red and reflects red back into our eyes – we might say that a flower is the one thing that a flower is not.
To be super-accurate, what we’re talking about here are thoughts, not things per se. The thought “flower” or “cat” has at its center the thought “not-flower” and “not-cat.” We’re not asserting that the thought is identical to its negation or is impossible to distinguish from its negation: rather, we’re pointing out that each thought necessarily contains its negation.We’re now in a position to figure out what it means to say that one can “transcend” thought – and the attending laws of thought – and what it means to say that one can “see each and all [thoughts] at once.”
When one puts “each idea against its opposite, and [refuses] to prefer either,” one necessarily stands “outside” of thought and “outside” the laws of thought – in the sense that one begins to see the *mechanism* of thought (which is also the mechanism by which the illusion of a “thinker” is produced).Normally, one is not aware of this mechanism. One has thoughts, including the thought that there is a source of these thoughts (a thinker). This remains true even in the 5=6 attainment. At this level, one has merely learned to distinguish between *kinds* of thoughts (the distorting lenses of the mind vs. the true preferences). 8=3 is a different kettle of fish entirely because one starts to see the *process* of thinking itself, the process by which a thinker/self is produced in the first place.
All of this is difficult to put into words, and I’m afraid I’m making it sound more active than it actually is. It’s easy to try to make oneself feel this: but the phrase “putting each idea against its opposite, and refusing to prefer either" does not mean to consciously and deliberately summon up the negation of each thought and think about how one does not prefer either. Doing this just increases mental noise, just multiplies the number of thoughts. Rather, the process is much more passive: gradually, one comes to pay attention to each thought and just naturally “see” the other side of each thought, almost by default. This is the thought that was thought, not any other thought. When this happens, the idea of “preferring” one side to the other just won’t happen. How could it? When you see a coin or a twig, you can’t help but notice that it has two sides, but does it ever occur to you to prefer one side over the other? It likely never occurs to our average coin-viewer, and to suggest to someone that one side could be “better” than the other would sound absurd.From this vantage point, one “sees” how thought is constructed, that thoughts are accompanied by the additional thought that there is a “thinker” (a fictitious entity bound up in the additional thought we might call “preference in thinking”). When this is seen clearly, it becomes obvious that there isn’t ultimately a “thinker” at all. It is in this way that one “transcends” thought and the laws that govern those thoughts.
But meanwhile, when thinking about and discussing things, the laws of logic continue to apply, in the same way that realizing that the rules of chess are arbitrary doesn’t mean that one can move the pieces anywhere during a game.