In the old days, occultists with a high school education and a penchant for misunderstanding and misapplying science would wax lyrical about quantum mechanics. It offered – for those not willing or able to take the time to learn anything about it – an alluring prospect of “probability waves” which gave the occultist the delusion that by bellowing charges to Goetic demons, or concentrating hard on the end of his nose, he could somehow “nudge” those probability waves into making his own pretensions to miraculous magical power just that little bit more likely. What’s more, the Uncertainty Principle enabled the occultist to both believe that the universe possessed intelligence and volition on a sub-atomic level – because particles, on being observed, naturally “decide” to alter their velocities in an unpredictable way to vex and fox their natural enemy, the objective observer – and, conveniently, to believe in all manner of silly nonsense safe in the knowledge that “complete knowledge is impossible” and that his delusions can never be disproved.

Today’s crop of fools have a new tool with which to delude themselves – Godel’s incompleteness theorems. One occultist sorely in need of a clue recently uttered the following in a thread over at LAShTAL.com, after posting no less than eight paragraphs from the Wikipedia article on the subject:

See further on this as you will, [of course! We’d never expect you to be able to actually explain this sort of thing – EH] self-contradiction certainly seems the name of the game, but the bottom line is that Reason may always be, ultimately, governed by the law of bullshit …Reason is always, perhaps, ultimately bullshit.

Those following this blog will recognise this as part of a popular theme, here, that of the credulous occultist who desires – for reasons we will examine again later in this post – to discredit the role of reason insofar as it is applied in criticism of their delusions.

(In fairness, we should mention that the same poster wrote, shortly thereafter, “I do not mean to underestimate the value of Reason … I simply mean to caution against overestimating its value.” Somehow, I don’t think most sane and sensible people would interpret “Reason is always, perhaps, ultimately bullshit” in such a manner.)

The main objective of this post is not a large-scale examination of Godel’s theorems, but we must give them a cursory examination with which to both provide context for the discussion that will follow, and to relieve those capable of rational thought from the popular conclusion which this amateur clown mistakenly presents.

The theorems deal essentially with the limitations of systems of formal arithmetic. To simplify, it should be evident that in any formal system of logic – which includes axiomatic statements, which are declared to be a priori true, and deductive statements which are derived from those axioms using first-order logic – a limited amount of information can be contained in a set of axioms, and that therefore no statements deduced from those axioms can possess more information than was inherent in them. The axioms of certain systems – in particular, those rich enough to contain the whole of arithmetic – contain less information than some arithmetical statements do. Therefore, Godel’s first theorem states that such a logical system – if we assume it to be consistent – cannot by itself determine whether these more information-rich statements are true or false.

This is, in a nutshell, what the first incompleteness theorem implies. There is something very important to notice, here. The question of the “reliability of reason” is not addressed one tiny little bit by this theorem. On the contrary, the theorem itself is a very model of formal logical proof. As we have mentioned before, the irony of somebody claiming reason is “ultimately bullshit” by referring to a conclusion based in rigorous formal rational proof displays the very heights of cognitive dissonance. The theorem affirms the reliability of reason; if it did not, it would not be a “proof”. What the theorem actually does deal with is formal logical systems, not “reason”, not the rational process itself.

There are three very important things to understand about this theorem. The first is that it applies only to formal logical systems rich enough to contain the whole of arithmetic. Any formal logical system not so rich does not suffer from Godel incompleteness. For instance, “Presburger arithmetic” – which excludes the multiplication operator – was shown by Godel himself to be complete. Both Euclidian and non-Euclidian geometry are also complete systems.

The second important thing to understand is that the implication of “incompleteness” means that there are some statements that cannot be proven true or false by the system in question. It is eminently possible that those statements can be proven true or false with a different system.

The third – and most relevant for our purposes – important thing to understand is that incompleteness implies that there are some statements that cannot be proven true or false by the system in question; it does not in any shape or form imply that there are no statements that can be proven true or false by the system in question. In the context of the search for the fabled physical “theory of everything”, for instance, it is quite possible – indeed, some physicists consider it “very likely to be true” – that “the laws of nature use only the decidable part of mathematics.” Thus, the laws of nature may be decidable with reference only to those statements which can be proven true or false by the system in question. This is a very, very different idea to the one that “reason is … ultimately bullshit.”

It is this third observation that provides the launching point for the meat of this entry, and in simple terms, it is this: you don’t need to know everything in order to know something.

This is such an important observation that it’s worth pointing out again, and highlighting:

It is not necessary to know everything in order to know something.

The traditional misunderstanding of the occultist, which holds that because “reason is imperfect” that “nothing can be known”, or that “knowledge is impossible”, is instantly revealed to be nonsense. As a simple demonstration, ask yourself the following two questions:

1. Do you know, beyond any shadow of a doubt, the position and velocity of every particle in the universe at the current time, and the complete set of laws that govern them, such that you can deduce – with 100% accuracy – the precise positions and velocities of all the particles of the universe at any given time in the past or future that you choose? and
2. Do you know what 2 + 2 equals?

If you answered “no” to question 1, and “yes” to question 2, then you have demonstrated to yourself that it’s not necessary to know everything in order to know something, and you have demonstrated to yourself that the delusional occultist’s schoolboy appeal to Godel is misguided. If you answered either “yes” to question 1 or “no” to question 2 then please stop reading and go do something else.

So, having demonstrated that it is not necessary to know everything in order to know something, we can safely dispense with the “problem” that complete knowledge is impossible. Instead, we can turn to the question of whether or not we can know what we need to know for our current purposes.

Let’s be practical for a moment. It is very rare for someone to claim “I have discovered the ultimate meaning and knowledge of everything, and here it is in this nice little equation, enjoy,” and on the rare occasions they do, they are laughed out of town so quickly that it doesn’t warrant a mention. Therefore, nobody really ever appeals to the “imperfection of reason” in response to a claim of “complete knowledge”. So, when do they make such an appeal, and why do they do it?

The first common situation is easy to understand. There is a strain of idiot who appears to believe that, in questions that could even remotely be described as having a relevance to “religious” or “spiritual” matters, they have some sort of “right” to be correct. The theory appears to be that because such matters are so “personal”, then nobody else could possibly have anything sensible to say on the subject, and the individual can consider “truth” to reside in “what works for him”.

Here’s a good example from a recent discussion I had on another blog:

I don’t need to agree with anyone else, according to Uncle Al Crowley, provided I remain within my own true orbit. If I, and you, and everyone else, does that, then the universe works fine.

Here we have intellectual sophistry and dishonesty on an almost breathtaking scale, even for an occultist. We can translate it as “I don’t need to be correct, provided I remain with ‘my own true orbit'”. Any halfway alert reader will be able to instantly spot the flaw in this argument. In order to be able to disregard your own incorrectness, you’d have to satisfy yourself that you were, indeed, “in your own true orbit”. To do this, you’d have to know five things:

1. Know that there is a “true orbit” that someone can be in in the first place;
2. Know what the nature of this “true orbit” is;
3. Know what your particular “true orbit” is;
4. Know that you are in your particular “true orbit”; and
5. Know that if everyone “remains within their own true orbit…then the universe works fine.”

Thus, in order to be able to disregard your own incorrectness, you’d need to satisfy yourself that you were correct on each one of these five points. Of course, you can’t do this if you disregard your own correctness.

There is a tendency amongst self-professed Thelemites to reduce the concept of “will” to a statement of personal pride: “I’ll do what I want, because it’s my will!” or “I don’t care if I’m wrong, I’m doing my will!” If “will” is something we can do by simply declaring that we are doing it, then it is nothing at all. If someone declares “I am doing my will!” without knowing what will is, let alone what their will is, and without knowing whether or not they are doing it, then they are simply deluding themselves. And, if will is anything at all, then it is something, and if it is something, then it is something we can have knowledge of. Crucially, if it’s something we can have knowledge of, then it’s something we can be incorrect about.

And there’s the rub. Nobody wants to believe that they are incorrect about it. As opposed to bridge-building, or nuclear powerplant construction, people can quite safely believe themselves to be masters of their own being without any catastrophic side-effects, just by declaring themselves to be such. Moreover, if one persistently fails to understand what being the master of their own being actually implies, and accordingly fails to pay attention to the evidence that would suggest they are not, they can continue in this belief without fear of disillusionment for an indefinite period of time. The one thing that can threaten this delusion is the idea that it is possible to be incorrect in such matters, and that an extended study is required to decide the question, which – naturally – requires highly unpleasant qualities such as intelligence, discipline and courage. The occultist does have any easy way to avoid acquiring such qualities; he can simply declare the investigation into such matters to be invalid, and instead appeal to “experience”, or “intution”, or “feeling what’s right for you” to replace actual work.

So, is it possible to have the required knowledge? Is it possible to know what “will” is, and to know what one’s own “will” is? Well, you’d better hope so, because if it isn’t, then you’re all wasting your time with Thelema. The only alternative is to suppose that the requisite “knowledge” can be acquired by some other process than rational extrapolation from evidence, and the only other options are:

1. Irrational extrapolation from evidence;
2. Rational extrapolation from the imagination; or
3. Irrational extrapolation from the imagination.

Either way, none of these three alternatives arrive at anything worthy of the name “knowledge”, and it is simply contradictory to on the one hand claim to be a “student of the mysteries” or some such, and then on the other to claim that “knowledge of the mysteries” is impossible, and that a simple proud declaration of competence is all that is required.

However, consideration of this situation is of limited interest, since it is so self-evidently contradictory and nonsensical. The “objection to reason” arises not because of an actual philosophical issue with reason, but from simple idleness in some cases, downright incompetence and lack of qualification in others, and willful self-delusion in the worst cases.

The second situation arises in the case of people who like to describe themselves as “experiential occultists” (which, incidentally, is an odd phrase – what other type of occultism is there?). Most often, they claim to be seeking “truths” which are “supra-rational”, and that reason is just fundamentally incapable of apprehending such “truths.”

Now, there is a grain of validity in this type of approach. One cannot appreciate the taste of strawberries by reasoning about them. The enjoyment of the grass under one’s feet and the breeze on one’s skin is not a rational enjoyment; it is an experiential one. The problem with the “objection to reason” in this case is that nobody ever claims to the contrary. The so-often decried “rationalists” certainly don’t.

The objection to reason comes, in this case, from the fact that these “experiential occultists” are being slightly disingenuous in the categorisation of their activities. Experience is one thing, but these occultists don’t want to stop there; they want to take their subjective experiences, and use them to make factual claims. A common one might be “I know there are discarnate praeternatural intelligences out there, because I’ve communed with them; I’ve experienced it.” The moment you take an experience and attempt to build an actual factual “truth” out of it then you have wandered right out of the realms of “experiential occultism”, and right into the realms of reason. Once you start saying that “I have had experience X, therefore Y is true” you are engaging in rational knowledge-building. An “experience of communing with aliens” may be evidence for any number of possible conclusions, ranging from actual contact with aliens at one end of the scale through to abject hallucination at the other. The moment you start singling out those possibilities, and claiming “this is what is true”, then you are engaging with reason.

And, with that observation, the motive for the objection to reason is clear; a sober, objective application of reason to the conclusions these occultists draw will show those conclusion to be at best unreliable, and at worst downright false. The occultist wants to believe that his experiences represent something special, that he really is communing with aliens and talking to demons, and if a rigorous application of reason will show those beliefs as false, the only avenue open to the occultist is to criticise the application of reason, to argue that it is somehow “invalid” for solving such questions.

Naturally, the problem is that if one asserts a conclusion to be “true” despite the fact that rational investigation would imply the opposite, and one supports that assertion by claiming the rational investigation to be “invalid”, then the inevitable implication is that there is something else other than reason that is capable of supporting those assertions. And the simple fact is that there isn’t. As we have demonstrated, when a conclusion is drawn from evidence, it is a rational process. There is no way around this. The occultist who has an experience, and asserts something to be true as a result of it, is necessarily using reason to make that assertion. Naturally, he may be using it ineptly, but he is using it.

Is reason capable of answering these particular questions? Maybe, and maybe not. But we know perfectly well that nothing else is. Therefore, it doesn’t matter how imperfect reason is, one thing the occultist ought to is that there is nothing else to support his assertions, and if he is questioning the application of reason, then he needs to disbelieve those assertions to avoid deluding himself.

This is so important that it needs highlighting again. Whenever the occultist makes any assertions based on his “experience”, he is using reason to do so, and if he discards the use of reason in questioning those assertions then they will, naturally, remain unquestioned and unsubstantiated, and if he continues to believe them then he is merely arbitrarily choosing what he considers to be true. Either way, his belief that his assertions are “justified by experience” are woefully mistaken. By discrediting reason, he is discarding the only tool he has with which to verify the implications of his experience, buying himself a one-way ticket to delusion.

The third and final situation we shall discuss here is more straightforward, and relates to factual claims about the supernatural. Occultists – presumably from a desire to feel that the universe is mysterious and special, and cares about them – have a bizarre tendency to make all sorts of claims about reincarnation, or “karma”, or “praeternatural beings”, or questions of morality and “divine justice”, and goodness knows what else. This is where the objection to reason becomes really pernicious. In the previous case, we can at least be charitable enough to accept that the “experience” in question at least suggested something along the lines of the resulting unfounded assertion, but in this case we are dealing simply with random and arbitrary claims.

Reincarnation is a good example, and one which we have discussed recently. The pieces of evidence supporting a belief in reincarnation can be counted on the fingers of no hands. It is interesting that, amongst occultists, it is difficult to find anyone who will actually come out and say that they have any kind of reason to suppose that reincarnation actually is true. In some cases they will assert that they “believe” that it’s true, and in some particularly disingenuous and distasteful cases they will assert that whilst it cannot be demonstrated to be true, it nevertheless has been demonstrated to be true “for them”, as if adding those last two words relieves one of the requirement to base truth upon evidence. The most popular form of appeal to reason is to argue that it has not been proven either way, so it “might be true, it might not”, and that there is therefore no reason to prefer “reincarnation is true” to “reincarnation is false”, and they simply choose the former as being as good as anything else.

Here is a prime example of where it is not necessary to know everything in order to know something. Whilst we cannot “prove” that reincarnation either does or does not occur in any kind of absolute sense – in exactly the same way as we cannot “prove” anything to that degree of accuracy – it is categorically not the case that the evidence gives no reason to select either interpretation.

The particular root of this form of ignorance is the mistaken belief that if something cannot be “proven”, then there is an equal probability of it being true as there is of it being false. This can be easily demonstrated to be not the case.

Firstly, even if we accept that the fact we cannot “disprove” the theory of reincarnation means that it “might be true”, we are compelled to accept that this reasoning applies precisely as well to any and every other theory of the afterlife, including the Christian conception of heaven and hell, the Wiccan concept of the Summerlands, the Ancient Greek conception of the Underworld, and all the others. There is absolutely no reason to simply select reincarnation from amongst this huge list because “it might be true”; so might any of the others. There are a potentially infinite number of ways in which we can imagine an afterlife. Occultists often describe themselves as being “agnostic” when they say that “reincarnation may be true” or some such trite statement, but they actually aren’t. If they were being “agnostic” then they would give each possibility its proper weighting, which would result in the probability weighting of any one alternative being so fantastically low that it would be sheer folly to prefer any of them. The fact that someone does prefer reincarnation to the others puts a lie to the idea that they are being “agnostic” or “open-minded” – they are just selecting the alternative that they personally want to believe in, and then inventing a lot of bullshit about their “agnosticism” being the rational and proper response.

Secondly, occultists – either deliberately or unintelligently – give almost no thought to the question of “disproof” in the first place. They think in terms of actually observing the “transference of the soul” from one body to another, and that either observing this or “proving” that it does not occur is the only category of evidence that could possibly contribute to an understanding of the issue. This is simply woefully small-minded and ignorant.

We can demonstrate this simply with just a couple of examples. For reincarnation to be true, we are forced to assume a dualistic view of the universe, where there is some “soul” of a completely different order of existence to regular material stuff. It can be argued that the “soul” is material, but this would involve supposing that some actual material stuff floats away out of the brain when someone dies, hangs around somewhere indeterminate, and then at some point sneaks its way into the brain of another and starts getting to work replicating memories and influencing the personality, all without anybody ever being able to detect it; naturally, this is a strain on credulity too far. Furthermore, the theories of “karma” which often accompany a belief in reincarnation and rendered invalid by the presentation of the soul as being material.

The fact is that the evidence casts severe doubt on this dualistic worldview. If memories, for instance, were contained in this non-material soul, then we would not expect damage to the physical brain to affect them. Yet we do, predictably so. This suggests a material basis for memory, and not a non-material basis. Of course, it’s possible to suggest that whilst the memories are “blueprinted” on the non-material soul, they need to be physically represented in the brain if the conscious individual is to be aware of them and to have access to them, and that whilst the soul can influence the development of the infant brain to implant those memories in there, it can’t influence a damaged adult brain to recreate those memories. But isn’t this oh so very convenient? It’s always possible to invent an imaginary metaphysical basis for any phenomenon; we can’t “prove”, for instance, that gravity is not actually cause by billions of troupes of invisible unicorns flying round the sky and hauling objects towards the ground. It is simply inconsistent to claim that one is “agnostic” about a matter, and then to respond to any conceivable contrary evidence with a metaphysical assertion that “something else is driving it” which cannot possibly be demonstrated. To do so is to demonstrate that the “agnostic” is not an agnostic at all, but a “political agnostic”, but who retains an “open mind” purely in order to enable him to maintain a particular belief.

Further, the “karmic” theories that often accompany a belief in reincarnation require some kind of intelligent and interventionary “higher power”, and the inexorable order we observe in the world casts severe doubt on the possibility of such a power. Some people try to dishonestly reduce “karma” to “the law of cause and effect”, but this is simply playing with words; they describe it as “the law of cause and effect” in order to legitimise their usage of the word, but then they apply it as meaning something completely different, something involving some indeterminate form of “divine justice”, of which they believe themselves to have knowledge despite the fact that they cannot explain where they got it from.

Of course, none of this “disproves” reincarnation, and we have already accepted this as being impossible in theory. But, these observations do put a lie to the idea that there is no evidence at all that has any relevance on the question; there is plenty of evidence that does, and all of it points in a single direction. There is plenty of evidence that reincarnation is unlikely, but none at all that it is likely. This being the case, the rational person would side with “unlikely”, instantly revealing that being “agnostic” on the question is not a rational position at all, but an irrational one. Once again, and ignorance of – and a rejection of – the validity of reason leads the believers to be fooled by it. They have – ironically – reasoned that reason has no bearing on this question, when it palpably does.

So, our short analysis has led us to a patently reasonable (no pun intended) observation – all the common objections to reason are fundamentally flawed. Godel’s incompleteness theorems are no recourse at all for the believer, since it is not necessary to have complete knowledge in order to have some knowledge. The “imperfections” of reason do not preclude us from having reliable knowledge on all manner of subjects, and the transparent weaseling of the occultist who invokes such perfections – or who invokes Godel – in order to attempt to thwart any rational criticism of his position whatsoever is revealed as the lie that it is. We can see that the “experiential occultists” who make claims based on their “experiences” are in fact making rational claims – which are obviously subject to reason – and that if reason is not suited to verifying their claims, then nothing else is. Finally, we can see that the contortions believers in the supernatural put themselves through in order to convince themselves that “agnosticism” – read, “license to believe” – is itself a rational position in such cases is nonsensical.

In closing, I will hazard a prediction. The current zeitgeist appears to be turning against the believers; as we move into the twenty-first century we are seeing a surge in disbelief, as the ill-effects of belief and self-delusion have been painfully visible across the globe. The religious believer and the delusional occultist appear to be squarely on their back feet, as evidenced by the vociferousness with which they – unsuccessfully – try to “defend” their position, if we can even call it a position. I predict that this trend will continue, and that there is a light at the end of the tunnel for those people involved in this field of study but frustrated by all the bullshit that is continually being spouted by occultists. Further, I consider that this can only be a positive development for Thelema.