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The law of identity: everything is identical with itself. The law of non-contradiction: there are no true contradictions, a claim and its negation cannot be true at the same time and in the same sense. The law of excluded middle: either a statement is true or its negation is true, there is no other option for a claim besides being true or false.

These apparently trivial observations form the foundation of our reasoning to this day. At any given time and place, it is either raining or not raining. If it is raining, then it cannot (in the same sense and at the same time and in the same place) be not raining. And that rain? It's rain! Seems clear, right? Well what Aristotle showed was that if you took these as axioms one could lay down a system of rules that codified all logical reasoning. All proofs, all chains of argumentation, could be rationalised by these axioms.





Take our simple debaters rule above - what explains why that works? Well, suppose we know that A is true or B is true, and in either case that C is true. Then if C were not true while A or B was true, we would have a contradiction - since we have just granted that it is also true in that case. But by Aristotle's second law, we cannot have a contradiction, so C must be true and not false. And by Aristotle's third law, there are no other cases to consider - so C is just true, as one's opponent was concerned to deny! The debater's trick now stands on a firm scientific basis, rationalised by Aristotle's laws.





Logic is under attack in the contemporary academy. By this point readers are no doubt aware of the repeated assaults on Reason as a patriarchal tool of Western domination, or however it is the Social Justice Activists (SJAs) express their grievances nowadays. So perhaps it was inevitable that logic itself would come under attack from those who seek to politicise every aspect of our lives. But it can still be instructive to see how an apparently objective and neutral, mathematical, field like logic can fall prey to the regressive leftism sweeping the academy. If you understand this, you'll understand how even the hard sciences won't remain safe from SJAs in their bitter struggle against the Enlightenment and our Western tradition.Like so much of our intellectual heritage, the story of logic begins in ancient Greece, especially Athens. Already it had been discovered that a culture of vigorous debate was essential for preparing people for life in a democracy. From this experience of debate people began to notice that there were certain rules which could guarantee victory. Suppose, for instance, your opponent granted that either A or B, but was concerned to deny that C. It turns out that if you could argue that if A was true then C must be true and also that if B was true then C must be true, then your opponent could be forced to admit that therefore C must be true! Things like this were useful to know, if you are a lawyer looking to make their name before the courts of the new democracy.But useful as such debaters tricks may be, and as with so many fields, the first leap into real science was made by Aristotle. He had the foresight to see that a few simple rules could underlie all of our reasoning. And while much of the specifics of what he said has since been updated, the core axioms he discovered still underlie rational thought. What are those axioms?Guided by these laws we have seen centuries of progress. Especially after the 19th century, when it was finally discovered how we might integrate classical logic with algebra and other branches of mathematics. Such intellectual giants as Frege and Gentzen built upon these foundations to create. This culminated in the invention of the computer ; that's right, dear reader, it was Aristotle's work that made it possible for you to read my words. An interested reader can check out the excellent Logicomix if they want to read about Bertrand Russell's contribution in particular. This is not the time to enter into these achievements, but suffice it to say that for all the advances made in logic, this tradition never abandoned the insights of Aristotle's three laws.That is, not until the SJAs turned their attention to logic. While there had been rumblings of discontent before, it was the work of Michael Dummett that launched one of the 20th century's most sustained attacks on Aristotle's laws. Dummett's target of ire was the third law. Why, he thought, should we believe that statements are always either true or false? What if a claim was such that we could neither prove nor disprove it - what grounds could we then have to call it true or false? Such were Dummett's questions, and they might seem reasonable, until one realises the incipient subjectivism that underlies them.Why should our capacities to prove or disprove things decide what is true? Aristotle had believed in objectivity, and so made a bold stand for reality over subjectivity when he said that claims are always either true or false - regardless of what we do or do not know. Aristotle was, one could say, the first to note that facts do not care about our feelings. Whereas Dummett, in line with what is typical of today's grievance studies "scholars", thought that it was our perspective on reality that decided what was true, and so called for yet more "constructivism" in logic. The result was a denial of Aristotle's third law. Rather than even countenance realism, Dummett the noted anti-racist activist tried to change logic itself to better suit his subjective sense of what is possible.Perhaps emboldened by this brazen attack on the foundations of Western thought, things have only got worse since then. It may seem obvious that one would not want to endorse a contradiction - and indeed it should be obvious! But, despite the repeated failures of communism, culminating in the on going tragedy in Venezuela we see today, a number of logicians decided to try and put a " human face " on the typically irrationalist idea from Marx that some contradictions are true. This kind of politicised logic is now typical, with recent work by these logicians embracing the feminist anti-logic agenda . Of course this open embrace of communist contradictions has only opened the flood gate to more irrationalism. Forwarding the diversity agenda, some contradiction mongers even ask us to take on board exotic metaphysical ideas drawn from Buddhism. One shudders to think of what the intersectionalists will do with the law of identity, once they get around to it.Rampant subjectivism, an obsession with multiculturalism and anti-racism, tacit sympathy for communism despite enjoying the privileges of capitalist wealth and freedom. These are the tools of the grievance studies "scholar", and now they're assaulting the foundations of logic.Besides demonstrating that even rigorous mathematical fields are not safe from SJAs, it's worth noting that these things have a wider corrupting effect. We start seeing academics write articles attempting to invoke guilt by association with the irrelevant politics of logical pioneers . When academics try and raise questions about the SJA role in logic that come from outside the grievance studies consensus they are attacked and mocked on prominent blogs. You would think that philosophers and logicians of all people would discuss their disagreements, but SJAs always prefer to use shame to silence dissent - perhaps all the more so when they are attacking the proper standards of logical discussion itself! And the corruption doesn't just stay in the academy, as they seek to push their anti-classical thinking on undergraduates, and there are popular articles denouncing Aristotle's laws as to blame for all our modern ills.One can see why the SJAs are so keen to dominate logic. For, logic is a tool that takes us from premises to conclusions. Already in the social sciences the SJAs have gained effective control over what premises we are allowed to take seriously. If only they controlled logic, then they would also control what inferences we can draw from their ideological premises. They would hence be able to choose our starting place and the destinations available to us. Their domination of intellectual life would thus be unassailable, and we could say goodbye to freedom of inquiry, and the practical benefits like computing which have arisen from it in the past.How did it come to this? How did we allow a logical tradition that has underpinned western science and given us the marvels of modern computing technology come to be spurned by these brazen irrationalists? It is because we in the West have lost confidence in our own reason. Rather than being willing to stand up for objective reality, like Aristotle once did, we now let the SJAs dictate to us their subjective absurdities. But there's nothing racist about standing up for objective truth, and there's nothing misogynistic about clear logical reasoning. The SJAs wish to unhinge us from reality, their ultimate goal is an anything goes logical anarchism - only in that way could they push their irrationalist agenda through. They're not yet at the point where they can openly proclaim this, but if we don't act to defend Reason now they might soon be. We should stop being ashamed of what is best in our tradition, we should stand up for logic.----------------------------------------------------------Not all of the above is wrong. Aristotle really did make huge advances in logic, amongst which was explicitly formulating his famous three laws. (Like... I think? Please don't hurt me, Aristotle scholars.) For obvious reasons, people who have liked paraconsistent logics have also tended to be more sympathetic to the idea from Marxist-Hegelianism that reality as it now stands is characterised by true contradictions. There's a real intellectual link there, and likewise between this and greater sympathy for Buddhist metaphysics. At one point I link to a Nye book, calling it part of the feminist anti-logic agenda: it really is feminist, it really is anti-logic, and it's really not very good. The popular article denouncing Aristotle's binary thinking is also (as far as I can tell) real, and also not very good. These latter two evince the more general point: there really does exist some hostility to formal logic in some parts of the broad-academic-left, and often this hostility is somewhat poorly informed by actual knowledge of logic.All the same, this was not a maximally sympathetic job, and nor was it intended to be. I didn't want to Steelman my opponents, but present them as they are, foibles and all. So the history isn't entirely wrong, but it's simplistic, over-claims on behalf of its heroes, and gets some of the details wrong. There's some innuendo - sure Dummett was an anti-racist campaigner and he did indeed attack the law of excluded middle, but there is no good grounds for suggesting that the one influenced the other! Restall's work is linked to the Nye in being part of the very broad cluster of feminist philosophy, but beyond that there's not much connecting them. It's not fair to say biographical interest in Frege is guilt by association, it's just true that some of the pioneers had noxious politics. At some point it lapses into vague praise and sacrifices a proper understanding of the topic matter for it. Identifying logic per se with the particular way of understanding things the author prefers is a cheap rhetorical trick, yet underlies the article's claim that logic is under attack. The enthusiasm for the idea of a continuous western tradition leads to very significant differences being papered over. In all these ways I think this is typical of the genre.And these (especially the errors in detail) make it tempting for scholars to reply in a certain way, typical of our training and temperament. The exposition of Aristotle's laws confused bivalence with excluded middle! Aristotle's opinion on the excluded middle is actually quite nuanced! Classical logic isn't a straightforward extension of syllogistic! Convenient that you skipped over all the Arabic contributions to the history of logic! Dummett's constructivism actually wasn't that subjectivist really though that depends on how one interprets... and so on. I am not above this. But it somewhat misses the point.For the more important point is surely that this is just a faintly absurd picture of what it is like to think or discuss logic in the contemporary academy. One is, of course, welcome to discuss the potential social impact of various ways of thinking, or its connections to broader metaphysical perspectives. As it should be! But one doesn't have to do this, and it'll go fine for you if you simply ignore all that and focus on one's favourite nerdy esoterica. This too is as it should be. Further, it would have been a huge hinderance to productive research if we were actually so deferential to the tradition and its greats as such articles typically are. As I noted in my anti-table screed , progress requires that we challenge traditions and explore counter-intuitive ideas. More broadly, the idea that the dominant way of doing things, still taught to undergrads by default, is under siege from a dedicated band of conspiratorial anti-logic SJs is just... ridiculous. It's silly.The real underlying problem here is one familiar to social epistemologists as the Novice/2 Expert Problem . The narrative I spun above contains enough truth, and its errors are sufficiently subtle, that I think if I were totally outside philosophical logic it would seem about as plausible to me as its denials. Of course a bunch of insiders would come along and angrily dispute it - but that would often seem like quibbling, and in any case didn't it tell me to expert that SJA orthodoxy tries to silence dissent? It would be a credulous and servile rule to say that all such critiques should be distrusted - institutional capture by bad actors is perfectly possible, and it may sometimes be that only outsider critique of this form can hold them to account. As I said, I don't think pieces in this genre are typically entirely devoid of truth, and some may contain more truth than falsehood. Ultimately in such cases, faced with pieces in this genre disputed by insiders, I am forced as a non-expert to do one of two things. I can embrace scepticism and say that I will refuse to either trust the logicians or the critics; and thus, in this case and some others, lower my trust in what is actually a fairly well functioning academic field. Or I can pick between experts in a fashion I am unqualified to do responsibly. Short of becoming an expert myself, there are no good options.