Belief and Logic

Hive Groin CardToday’s entry is a bit of a cheat because it’s something that I actually wrote in September last year. However, it deals with an idea that is still a very important part of my thought so, for the sake of completeness, I want to include it in this blog as well. This is it:

I was talking to the proprietress of the Atlantis Bookshop at a book signing recently and she recounted an amusing story. A man had once poked his head inside the door and asked if they had any books on logic. “Sorry,” she replied, “we don’t believe in that.” Much mirth ensued. Anyone who has visited the Atlantis Bookshop or spoken to its regular customers will recognise that attitude. However, it is not clear exactly what is being stated. Logic appears to have been identified as a belief system akin to more obvious religions. “Logician” seems to play the same rôle in speech as “Christian” or “Muslim”. This is wrong. Logic is a tool and nothing more. It makes no more sense to claim to believe in logic than it does to claim to believe in a hammer. One can believe that a hammer exists and one can believe that a hammer is useful but most people would not say that they believe in a hammer. To say that one does not believe in logic implies a fundamental misunderstanding of what logic actually is.

For a start, there is no single thing that could be called “logic”. There are all sorts of different types of logic depending on what you want to do. Aristotle is generally considered to be the father of formal logic, although logical systems certainly existed before him. His goal was to create a formal system that could model the way humans thought. If he could enumerate a set of rules that determined whether or not a statement was true then, by applying those rules, he could conclusively state whether or not a person’s argument was correct. For example, one of Aristotle’s basic axioms has come to be known as the Law of Contradiction. This states that if a thing is A then it cannot also be not-A at the same time. So if I now give an argument in which I claim that “this box is red and it is also not red” then Aristotle could apply his axiom and declare that my statement is wrong because it violates the Law of Contradiction. Aristotle listed a number of other simple axioms and they formed the basis of logical argument – that is, argument tested against a set of formal rules – for hundreds of years. Now, one may think that one or more of his axioms are incorrect. Certainly, Thelemites would recognise the duality inherent in the Law of Contradiction and claim that such a law cannot hold above the Abyss. However, that has absolutely nothing to do with belief in Aristotle’s logical system. His logic is designed to model human thought in a formal manner so that it can be studied and refined. If you think that the model is incomplete, incorrect or in any other way not up to the job then that just means that the model is broken. It is much the same as thinking that a rubber hammer would not be very good at hammering nails. Such a thought would not provoke one to claim that one does not believe in hammers: it is only that this particular hammer is no good for this particular job so a different design is needed. Indeed, this is exactly what has happened in the field of logic. In the 19th century, Gottlob Frege recognised that Aristotle’s logic could not express current mathematical ideas so he expanded it into what is known as “predicate logic”. There are now many other logical systems that have been designed for different tasks. Computer programs designed to exhibit “artificially intelligent” behaviour often make use of “fuzzy logic”, which denies the Law of Contradiction. Some modern logicians would like logic to return to its roots as an attempt to model human thought, but the very fact that this is a controversial issue shows logic for what it is: a tool.

So, why do many people – particularly those attracted to “New Age” ideas – reject logic so vehemently? Why are they willing to make use of all sorts of other symbol systems, such as the Kabbalistic Tree of Life, the Tarot, Astrology, Norse Runes and many more, but not logic? I’m sure that if I claimed that tarot was nonsense because it’s just a stack of pieces of cardboard then they would dismiss my claim as naïve and ignorant. Tarot is a symbol system and a deck of cards has no more to do with tarot than an abacus has to do with arithmetic. There may be other arguments against tarot but that is certainly not one. I find it irritating when people ask me whether or not I “believe in tarot”. If I say `yes’ then I imply that I am a gullible fool – probably the sort of person who studiously reads his horoscope in some magazine every week. So I usually say `no’. However, by saying `no’ I am acknowledging that the question is a valid one. It is not. One does not believe in tarot. One can believe in its efficacy, or not, but it does not make sense to ask whether or not someone believes in tarot itself. Such a question could only be asked by someone with a very superficial acquaintance with tarot and thus no real understanding of what it actually is. I have a similar problem if I am asked whether or not I believe in logic. Again, I would rather not answer the question at all because it does not make sense, but neither can I be bothered to explain all this in casual conversation. By answering `yes’ or `no’ I am lumped into one or the other religious camp – the camp of the Believers in Logic or the camp of the Heretical Unbelievers. But logic, like any symbol system, has nothing to do with such belief. How has this divide into religious camps come about?

The first people to treat logic as a belief system were not New Age hippies rejecting logic but rather avid proponents of logic. They believed that if a statement could not be incorporated into a coherent formal logic system then that statement must be false. One could decide between contradictory logic systems by testing them against empirical evidence. Metaphysics is a famously wishy-washy and vague discipline so certain prominent philosophers seem to have decided that philosophy would be better off without it. This movement culminated in the Logical Positivists of the 1920s and 30s. They planned to do away with metaphysics by insisting on the “verifiability criterion”. This said that the meaning of a statement is conveyed completely by the means by which it is verified. So if I say, “When I let go of this apple it will fall to the ground,” then the meaning of that statement is conveyed by testing it empirically, i.e. watching me let go of the apple and seeing whether or not it actually does fall to the ground. If a statement cannot be tested in that way then, according to the verifiability criterion, it is meaningless. Since metaphysical statements cannot be tested in such a rigorous empirical manner they cannot be verified, thus the verifiability criterion says they are meaningless. In this way, the Logical Positivists declared that the natural sciences were the only way to seek knowledge and that metaphysics and anything else that did not fit into their logical system was completely meaningless. But there was a flaw in their plan: the verifiability criterion is itself unverifiable. There is no empirical experiment that can be performed to verify that it is true. So, according to itself, the criterion is meaningless. This mistake came about because they failed to recognise that logic is a tool for making models. They accorded logic a greater status than it deserves: in effect they accorded logic a metaphysical status. They believed in logic. However, Logical Positivism is exactly the right attitude to take in the natural sciences. This is hardly surprising because the goal of natural science is to create a model of the physical world in order to predict physical events. Prediction requires determinism – or at least fixed probabilities – so the model must be internally consistent. In other words, Logical Positivism is just sensible scientific method applied to inappropriate topics. It is good and appropriate in the natural sciences but as soon as one forgets that science is about models of reality and not about the entirety of reality itself, then logic becomes a Golden Calf and the scientists become priests. Although Logical Positivism has deservedly died out among academic philosophers, it is still popular among some “pop philosophers” and some sections of general society.

The New Age disdain for logic and science is a backlash against Logical Positivism. They have rightly perceived that Logical Positivism is in error but have failed to accurately discern the cause of its error. As a result, they have copied the Positivists by considering logic to be a matter of belief but have chosen to avoid its taint altogether by not believing in it. This is just as absurd as the Positivist approach and even more damaging. While the Positivists have taken up their hammer and decided that everything is a nail, the New Age has decided that hammers do not exist.

Clearly, the best approach is to possess a good hammer but to make sure that something really is a nail before you hit it. So what is logic good for? Logic is the tool of the rational. It is common to divide ideas into the rational and the irrational. If we do so, it does not take great insight to see that rational humans succeed where the completely irrational fail. A man can successfully feed himself by employing rational agricultural techniques but a man who tries to feed himself solely by waiting for manna to fall from the sky will starve. Rational natural science affords modern humans a mastery of the physical world that provides great opportunities for survival and luxury. It is no wonder that the Logical Positivists wanted to elevate science: clearly rationality is far preferable to irrationality in such areas. Yet logic does not apply to every area. Logically it cannot: not only does the verifiability criterion fail but Kurt Gödel proved that no axiom that does the job that the Positivists wanted the verifiability criterion to do could possibly exist. Any rule designed to delimit the rational must itself be irrational. To mix my metaphors and flog the dead horse of the hammer analogy: not everything is a nail.

The problem arises from this simplistic division between the rational and the irrational. It is far more useful to divide the irrational further into what some have called the “pre-rational” and the “trans-rational”. Plato knew this but somewhere along the line it has been forgotten. The mistake of both the Logical Positivists and the New Age is, by failing to further divide the irrational, confusion between the pre-rational and the trans-rational. The New Age thus considers anything irrational as equally valid. Incidentally, this behaviour is by no means limited to the New Age, I only pick on them for convenience (and the term itself is suitably nebulous.) Tertullian’s famous remark – “I believe because it is absurd” – also falls into this category, as does Theo Hobson’s “average Christian” who “tries to believe things his clever friends mock.” All of them recognise the limitations of logic but throw the baby out with the bath water and leave themselves with no way to distinguish between different categories of the irrational. In the backlash against Logical Positivists, anything irrational is considered good and anything rational must be avoided, which just leaves them in an undifferentiable morass of incoherence with no way out. On the other hand, the Logical Positivists, by paradoxically according rationality the highest metaphysical status, are forced to consider all irrationality as equally invalid. They do not make the mistake of elevating the pre-rational above the rational but they make the similar mistake of forcing the trans-rational beneath the rational. A more productive hierarchy would place the pre-rational firmly at the bottom, the rational above that and the trans-rational above that.

Note that the term is trans-rational – i.e. it transcends the rational, it does not replace or discard it but rather includes it and then goes further. Therefore no-one can possibly approach the trans-rational without first mastering the rational. Although the terms do not correlate exactly, the same idea can be found in the Platonic hierarchy of eikasia, pistis, dianoia and noesis. The path to noesis is through dianoia. Logic is indispensable to the development of a human. It has a limit, beyond which other tools must be employed, but without skill in logic one cannot get anywhere. Crucially, if one ever has cause to use the phrase “believe in” then one is on the wrong track.

“Roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing.”
— Ludwig Wittgenstein

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Published in: on April 13, 2006 at 12:00 am  Leave a Comment  

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