Is Logic Contingent?

Read my theory: http://www.mm-theory.com/

Although the human mind is capable of thinking along consistently logical lines, we more often than we like to admit stray from this line. We commonly commit logical errors. Logicians have therefore provided us a thoroughgoing list of logical fallacies so that we might be wary of them (for example, see http://en.wikipedia.org/wiki/Logical_fallacies). There is, for example, the fallacy they call "affirming the consequent" whereby the consequent of a conditional proposition is assumed to imply the antecedent. If I were to say "All criminals were breast fed as babies. Bob was breast fed as a baby. Therefore, Bob is a criminal."* I would be affirming the consequent. Yet when one hears this, there is at first a brief impression of soundness in the reasoning. Only the skilled logical thinker is able to suppress this impression and recognize the fault that lies therein. But so many are not so skilled, and the fallacy of affirming the consequent is readily made and passed over.

This is no doubt a consequence of neural wiring in the cognitive centers of our brains. But then it also follows that this wiring isn't uniform across individuals, for it is obvious that some are rigorous adherents to consistent logical thought whereas others are hopelessly poor at it. Furthermore, it is equally obvious that no one begins life as a logic expert. The kinds of fallacies known to logicians are most frequently succumbed to by young children. Logical thinking is a skill we acquire as we mature. Even then, however, not all people acquire the skill as easily, or at all, for there are many adults, even ones in prominent and highly valued positions in society, who are demonstrably lacking in the department of logical thoroughness. By no means does this mean that such adults can't acquire the skill with enough practice and attention paid to their thinking, and indeed it has been shown that such acquisition is possible even for those getting on in age. Therefore, it seems reasonable to suppose that logical thinking is not something innate, not something that can be simply passed off as the "nature of thought", but something learnt.

But then who is the teacher? Are we taught solely through our schools? Is logic just an arbitrary idea - like a particular religion, like a particular philosophy, like a particular political ideology - that we learn only because the older generation wishes to preserve it by passing it on through our educational institutions? Some may say so, but not I. I say we learn logic from the world itself. We learn by making mistakes. We learn after being shown, by the world itself, time and time again, the fallacies we inadvertently stumble over. Logic is where we come to rest when we've finally trained our minds to make predictions about real-world outcomes that consistently come true (notwithstanding predictions based on inductive reasoning and random guessing, of course). So logic is a style of thinking used by those who have acquired a deep understanding of the inherent pattern by which the world operates.

I say this understanding is "deep" because it touches on something more profound than what science teaches. Science can tell us about particulars and contingencies - for example, that Kepler's laws guide the manner in which the planets orbit the Sun, or that life is intricately determined by DNA, or that all matter is reducible to particles such as electrons, protons, and neutrons - but that Bob isn't necessarily a criminal if he was breast fed is something supported not so much by scientific evidence, but by the fact that the world is such that Bob couldn't be a criminal solely on the basis that he, along with all criminals, were breast fed. To understand this is to understand something so "deeply" fundamental to the nature of reality that the discoveries of science become irrelevant. Science could have taught us things radically different from what we know, and logic would still have to hold. Reality simply could not cohere otherwise. (I believe this is the distinction between David K. Lewis's possible worlds and impossible worlds - regardless of what world Bob lived in - whether it was one in which he was a criminal or another in which he wasn't - the erroneous syllogism given above could not be the basis for this in either world).

So then to the central question on which we will, from here on in, focus: if we indeed learn logic through real-world encounters, does that make logic contingent? And if so, what does this say about the seeming necessity of logic? Would the contingency of logic serve as license to generalize the necessary character of our thought (at least, how it feels) beyond strict logic? Beyond thought? After all, one who commits a logical fallacy does so because he/she is totally oblivious to the fact - he/she believes with all honesty that his/her fallacious conclusions are supported necessarily by the reasoning. Shouldn't we say, therefore, that necessity - at least, the veneer of necessity - is apparent in any style of thought insofar as it is taken to support one's belief?

Let's be sure the question is understood: we are not asking whether logical rules - such as modus ponens, modus tollens, D'Morgan's Law, etc. - are necessary - they surely are - rather, we are asking whether it can be taken as contingent that the world turns out to conform to those rules - and if so, whether this implies that a different logic would be equally necessary should the world have turned out differently (assuming that's even conceivable :)). In such an exotic logic, the fallacies mentioned above - such as affirming the consequent, illicit major, illicit minor, etc. - may turn out to be the rules. A further point to keep in mind is that contingency does not necessarily exclude necessity - so we are not asking whether it is either/or - for sometimes it's both. For example, it used to be believed, and still is by many, that the laws of nature were unyieldingly necessary - that they could never be broken under any circumstance - but even today we are hard pressed to understand why the world should adhere to the laws of nature (even if it is only an extremely high statistical probability). Therefore, from the standpoint of the human perspective, the laws of nature, despite whether they are necessary in themselves, are contingent to us. In the same vein, the fact that nature works according to logical principles, as well as logic itself, as well as the fact that the world teaches us to think logically, is not devoid of necessary underpinnings, but because these necessary cases are, from the standpoint of the human perspective, contingent, they may be both necessary and contingent at the same time. Even more interesting is the notion that this may imply that a completely different and contradictory logic may very well be just as necessary. Let's see how far we can go towards this notion.

First, let's talk neurology. It is no mystery that real-world experiences are one of the major contributors, if not the major contributor, to our neural programming - that is, to what determines which neurons are connected to which others and in what ways. To show how this might unfold, let's consider a purely hypothetical scenario - one in which, I must disclaim, I really have no idea as to its accuracy in reflecting the way our brains actually work, but works nonetheless in principle as a hypothetical model. I will assume - as a hypothetical model - that the fallacy of affirming the consequent can be modeled neurologically as follows.

Let's denote the antecedent of a conditional (i.e. "If one is a criminal...") as A and the consequent (i.e. "...then he was breast fed as an infant") as B. Then, I will propose that the statement "If A then B" primes two MODs or two neural firing patterns in the brain to be sensitive to one another. That is to say, if A corresponds to the thought "one is a criminal" then A represents the experience associated with one of the two MODs or neural firing patterns in the brain, and B, which would correspond to the thought "one was breast fed as an infant", represents the experience associated with the other of the two MODs or neural firing patterns. The statement "If A then B" would prime these two MODs or neural firing patterns to be sensitive to each other - meaning that if one is activated by the utterance of either A or B (which ever it corresponds to) then it stimulates the other into activation as well. The utterance "If A then B" doesn't actually trigger the activation of either - it only primes them for sensitivity to activation. What actually triggers the activation is the utterance of either A or B. That is to say, the major premise (if A then B) only prepares both to become activated in response to the other being triggered into activation, and the minor premise does the activation.

This is, of course, the neural configuration of a brain that has yet to learn the fallaciousness of such information processing. Using this configuration to predict the truth of A when B is shown to be true is sure to fail at least part of the time. These failures, if the brain properly adapts to them, should result in a re-wiring such that the configuration as it is changes to one in which the utterance "If A then B" only primes the MOD or neural firing pattern B into sensitivity to the activation of A, and not visa-versa.

Yet, there is still a difference between such a re-wiring as it takes place within the specific MODs or neural firing patterns corresponding to the thought "If one is a criminal then one was breast fed as a baby," and that corresponding to the more general understanding of the logical principle of modus ponens. That is to say, the former sort of re-wiring is only done to one's understanding of the relation between criminal status and having been breast fed, whereas the latter is done to one's understanding of the actual logical principles at work here. In the former case, one may learn from real-world experiences that one ought not to assume that if one was breast fed as a child, one is a criminal - and one may keep this lesson at the forefront of his mind for the rest of his days - but nevertheless fail to apply this lesson of logic to all such cases of affirming the consequent. In other words, one may still fall into the same trap, affirming the consequent to a whole array of situation, always being careful not to do so over the question of the criminality of those who were breast fed as infants.

So how should we model the neural process by which one learns the logical principle, as opposed to contingent states of affairs such as the fact that not all who were breast fed as children turn out to be criminals? How does one learn to apply proper logic to all situations one encounters or contemplates? Well, for one thing, we can expect that a MOD would exist or a specific pattern of neural firing would be frequent that represents the understanding of the logical principle in question. Let's call this MOD or neural firing pattern C. C might have effects on those corresponding to the more specific instances of modus ponens or affirming the consequent. That is to say, concerning A and B above, the MODs or neural firing patterns corresponding to them would react differently when C is present compared to when C is absent. C would have the effect of preventing the MOD or neural firing pattern corresponding to A from activating when the MOD or neural firing pattern corresponding to B is active, but it would allow B to activate when A becomes active. C would have to have the same effect on all instances of this sort - that is, all MODs or neural firing patterns corresponding to thought processes which adhere to modus ponens when C is present, and could potentially lead to affirming the consequence when absent.

Now, these neural changes are examples of changes in one's expectations over particular events, or changes in how poorly thought out logic is implemented. The individual who makes mistakes in his expectation due to poorly thought out logic will go on to make more mistakes, being corrected by the world each time, until he is corrected on a higher, or more abstract, level - that is, on the level where he grasps the basic principles of logic. On this level, he not only takes account of how he was wrong on any one particular occasion, but on the whole series of such occasions (insofar as he can remember them), and then - only then - realizes there is a principle of logic to be learnt from this. This lesson is encoded in his brain as the MOD or neural firing pattern we have denoted C and it oversee most, if not all, future applications of this logical principle on real-world situations.

So it would seem that the principles of logic are lessons learnt from our experiences with the real world. If it were possible to experience the world differently, we might learn a whole other set of logical principles. Far from being a fallacy, affirming the consequent may be one of these rules. So we are confronted with a world that just so happens to play by the rules of logic as we know them. We don't know why it does - it just does. Does this give us the right to say that logic is contingent?

The answer is yes and no. It is no in the following ways. First, logic in itself is necessary. We will not go so far as to say that if all men are mortal, and Socrates is a man, then Socrates may somehow be immortal. The conclusion is still bound by the premises. Second, the nature of the world itself may be necessary. We have been speaking as though the world could have been different - as though Socrates could have been immortal in another world even though he is a man and all men are mortal. But it may be that such a world is necessarily impossible. When we talk of possible worlds, we usually entertain different possible contingencies - such as the possibility of the dinosaurs having survived for much longer should there never have been an asteroid that hit the Earth, or the possibility of JFK serving his full term in office should he never have been assassinated - but when it comes to necessities - such as the rules of math and logic - these could not be different in any possible world. So the fact that the rules of logic hold in our world may be necessary. Third, it may even be necessary that we learn logic after so many experiences with the world. That's not to say that everyone, by necessity, must learn logic at some point, but that when it happens, it happens according to certain necessary principles. If we were to put this in term of physics, we'd say that the events in the world that teach us logic do so by way of their physical effects on our brains. We first experience these events through our senses, then our brains are programmed with the right neural circuitry to grasp the principles of logic. All of this can happen according to a complex system of physical laws that operate on our senses and our brains, thereby rendering the final effect - namely, our being programmed to think logically - an inevitability in such specific cases. We can also put this in term of MM-Theory - that is, in terms of experiences. We would say that the flow of experiences prior to our having sensations - which entail by necessity - necessarily entail our sensations, which in turn necessarily entail our cognitive experiences about them, which in turn necessarily entail the grasping of an insight - the principles of logic.

Of course, it is true that quantum mechanics has other lessons in store for us - namely, that the world does not operate right down to the bare bones by necessary processes. But this is simply the going consensus among the majority of scientists who make quantum mechanics their expertise. No one can be absolutely certain about whether the world is inherently probabilistic or necessary through-and-through. So we hold out for the possibility that the world is exhaustively ruled by deterministic - that is, necessary - forces after all, and that these necessary forces are there in the very processes by which we learn logic.

The way in which logic is contingent is in how we learn it, how we are confronted with it. If it's true that we don't begin life thinking perfect logic at all times, and that we make logical mistakes without realizing it, then it can't be said that we expect to learn it, that we can predict a future point at which we will stop making mistakes and start thinking more logically. In other words, that we should eventually learn logic is not something we can figure out a priori, for that term - a priori - presupposes a grasping of logical principles to begin with. Therefore, the real-world lessons that teach us the errors of our cognitive ways strike us as a matter of contingency. That is, after all, what it means for a thing to be contingent - that is, it can't be deduced as matter of logical necessity. From the point of view of the subject, the world just so happens to turn out that way.

That's not to say that one can't reflect on his/her own thought processes and figure out that one is making logical mistakes, but this doesn't count as a deductive prediction that one will eventually learn to think logically; rather, it is the very act of learning it. It requires logical thinking in order to occur. It's true that this wouldn't involve learning from real-world experiences, but it would be the equivalent as it takes place in a thought experiment built to simulate the real world. To put this another way, learning to think logically by reflecting on one's own thoughts and noticing the mistakes is the equivalent of using logical thought to deduce that a contingent fact is necessarily the case on account of seeing that it is the case. That is to say, it is like saying that if X is the case, then necessarily it is the case. It's a simple tautology. It's only true in virtue of Aristotle's first principle of logic: the law of identity. It doesn't make X any less contingent, for the type of circular reasoning that the law of identity leads to is no defeater of the contingency of anything. Just the same, learning to think logically by reflecting on one's own thoughts is no defeater of the contingency of the lesson learnt. To predict logical principles using logical itself is the equivalent of seeing that those logical principles hold - just like seeing that it so happens to be a rainy day - and this sort of 'seeing', whether of the real world or our thought experiments, comes upon us contingently.

Could the world have turned out differently? I highly doubt it. And by that, I mean I don't think so at all. Some contingencies may have turned out differently - for example, our solar system may not have been right for sustaining life, the dinosaurs may not have been wiped out, president Kennedy might not have been assassinated, etc. - but I can't imagine a world in which Socrates is immortal even though he's a man and all men are mortal. I can, however, imagine a world in which I have not learnt the basic rules of logic, and might expect Socrates to be immortal. I may not be using logic proper to back this expectation, but I can see how I might mistake myself for using it. The fact of the matter is, after all, people don't always think logically, even though they sometimes think they do. If they really believe they're thinking logically, it must be because they feel their thoughts flowing in a necessary manner.

What this means, then, is that the necessity we feel in the logic of our thoughts is there regardless of whether that logic is proper and formal or sloppy and flawed. So the question becomes this: on what grounds can professional logicians hold true to the claim that formal logic, as conventionally understood in the discipline, is the "right" logic and all other so-called "logics" are inauthentic and flawed? They can say this on the grounds that it is this formal logic that seems to be the destination, the final resting point so to speak, at which the cognitive programming stops. That is, it is the state the human mind tends towards as it gets programmed by real-world experiences. That is to say that although one person's brand of logic may feel absolutely necessary despite the many flaws a professional logician would point out therein, it is still subject to correction insofar as this person has the opportunity to experience his expectations and predictions, derived from his logic, being thwarted, and thereby coming a step closer to formal logic by learning from those mistakes and making the appropriate modifications to his thought. This process - the mistakes, the thwarted predictions, the learning, the adjustments - can go a long way, but it does reach a point of perfection, of completion. There seems to be a point at which one has learnt all that one can from the world about the proper way to think - and this we call formal logic. Once one has learnt the full set of basic logical principles, and has trained himself to heed them in his thinking, we can take his mindset, call it "formal logic", and hand it over to the logician as his field of expertise.

Note the implication: that formal logic doesn't so much stand out from other kinds of logic (informal logic, folk logic, flawed logic, etc.) in that it is necessary whereas the others are not, but in that the tendency is for those other kinds of logic to evolve towards the formal kind and not visa-versa (at least, it seems pretty darn unlikely that one's mind can be programmed from formal logic to another informal kind). To put this another way, formal logic seems to have the power to correct and assimilate other brands of logic (by example, by demonstration, by evidence, etc.), effectively converting or annihilating them, whereas the latter don't have the same power over the former. But insofar as the latter are left to their own devices, they will feel just as necessary to the beholder as the former.

This can be understood by considering what makes the flow of electric information through our neural circuits necessary. It doesn't matter how they're configured, the way they process information will be governed by the laws of chemistry, neurology, and electrodynamics. Therefore, whatever the thought process - whether ruled by a learnt set of formal logical principles, or as yet unrefined by these principles - it will feel necessary. The only reason logical fallacies seem necessarily impossible to the seasoned logical thinker is because the corresponding physics in his brain makes it impossible. His brain is physically wired to process information in a specific way, and any alternative is physically impossible. And because the lessons that teach us to use the rules of logic are contingent, the necessity of logic is also learnt contingently. One might very well learn as necessary something other than logic.

But now there arises certain paradoxical implications. How can Socrates be necessarily mortal for one person, while at the same time not necessarily mortal for another? How can the same conclusion follow from a set of premises both necessarily and not necessarily at the same time? To answer this, we need to look at the roll the UOS (Universal Operating System) plays in all this.

Should the reader recall from the Advanced Theory what we mean by the UOS, he will recall that we mean those experiences corresponding to atomic structures and process of all things in the universe. The importance of the UOS for our current purposes is to recall that it continues to run while no activity can be discerned on the more macroscopic level. That is to say, for example, that although no experience may correspond to an inanimate macroscopic structure like a rock or a table just sitting there doing nothing, there are indeed experiences corresponding to the more lively actions of the atomic structures composing the rock and the table, actions such as electrons orbiting nuclei, atoms vibrating, positive and negative charges attracting and repelling each other, etc. This flurry of activity can be seen not only in rocks and tables, but in the neural networks in our brains - that is, even when they are not actively processing signals.

Therefore, the way to show how the necessity of seemingly contradictory systems of logic holds is, first, to more precisely point out the sort of effect the real world has on the neural circuitry of logical thinking - the circuitry, that is, even in its latent state during which no signals are processed. We said it was to program those neural circuits such that logical thought becomes more standardized throughout the whole of our cognitive and neural networks. But programming neural circuits is not the same as activating or stimulating them - it is simply to fortify the neural connections, pathways, and overall configurations. What this entails is that the arrangement of atomic and molecular scaffolding making up the neurons and their overall circuitry is being reconfigured. What this entails in turn is that the UOS, at least that part of it corresponding to said atomic and molecular scaffolding, undergoes certain permanent changes. These changes introduce a set of experiences, still part of the UOS, that play a significant roll in the flow of the logical thinking corresponding to the circuitry. These experiences, corresponding as they would to activity that constantly reinforces itself, reacquiring its prior states, are more or less stable and endure even throughout long moments of silence on a more macroscopic level. In other words, syllogisms like the one about Socrates don't flow necessarily only because of the meaning in the premises, but because of the meaning in the experiences of the UOS that the structure of the circuitry is based on. In other words still, Socrates is not mortal only because he is a man and all men are mortal, but also for some additional reason that can only be expressed in the experiences of the UOS. Take away those reasons, and it doesn't follow from the explicit premises that Socrates is mortal - at least, not necessarily.

It's almost as though a third term is added to "All men are mortal" and "Socrates is a man" - namely, "the world works according to the rule of modus ponens". This third term is not part of the argument, of course, not part of the logic, not an explicit premise, but it's what makes the logic necessary. It's like saying the form of logic, as opposed to its contents, is the third term, and that it is learnt just as contingently as "All men are mortal" and "Socrates is a man". If we do not learn this third contingent term, as in the case of children and some adults, the UOS will be different amidst our cognitive networks, and so will be the third term.

So the reason why Socrates can be both necessarily mortal and not necessarily so is because in the one case, there is a third term that makes it necessary and in the other, that term is lacking (or there is a different term that makes it unnecessary).

The real world is partially responsible for this. It is responsible for laying down that particular form of the UOS in the vicinity of our cognitive neural networks. In terms of experience, it lays down the "third term" that defines the rule of modus ponen (and, more generally, all other rules of formal logic), and in terms of neurology, it lays down the specific neural circuitry that makes logical thinking necessary with the use of that circuitry.

Now I want to bring this discussion to a close by following it through to its logical conclusion - namely, that the scope of necessity spans far beyond formal logic. Patterns of thought which would be ordinarily deemed illogical and plagued with fallacies of every sort would be deemed necessary by the one who believes them. The necessity he feels is not to be found in logic, but in the narrow range of possible streams down which his thought can flow. This range is narrow because the neural wiring in his brain is configured in such a way to allow only for that particular flow of thought during that particular instance. In other words, the necessity is to be found in the rigidity of the physics of his brain. Whether he is extremely practiced in the science of logical thinking or hasn't got a clue, his brain and the neural circuitry within it are configured in a particular way. Given that configuration, the particular style of thought it makes possible - logical or fallacious - is necessarily the style of thought he employs. He can't help it. The laws of physics hold even in his logic depleted brain.

Now if this is the basis for the feel of necessity in our thoughts, then it must be the basis for the feel of necessity in any experience - cognitive or otherwise. All our experiences correspond to neural and chemical activity in the brain. This activity is likewise governed by physical laws. These laws regulate what goes on therein in quite a determined manner. Hence, what happens therein happens necessarily, and we feel that necessity in the very experience that corresponds to it.

Thus, I hope this lends some support to the argument made in the Advanced Theory, the argument whereby I tried to show how the necessity of the flow of our experiences spans far beyond the scope of logical thought. Although logical thinking is perhaps the best example of the necessity of this flow (because most reasonable thinkers will agree that logic is indeed necessary and that it describes the pattern according to which we think - some of the time anyway), it is only one very specific instance, and necessity can be generalized far beyond that. It can be generalized to all experiences as all experiences correspond to the operations of physical systems - operations that are characterized by necessity in virtue of their conforming to the necessary laws of nature. That, I say, is where we find necessity.


* My thanks to my grade 10 math teacher who provided this syllogism as a means of demonstrating the fallacy of affirming the consequent.

Read my theory: http://www.mm-theory.com/