Simeon Scott
The formation of the cult
Coming from the Latin cultus, the word culthas several meanings. Originally used neutrally to describe a set of religious practices, it later took on negative connotations referring to unorthodox religious beliefs. More recently, and more relevant here, it can refer to obsessive secular beliefs. For instance, following the French Revolution, some members of the intelligentsia adopted the name Cult of Reason to indicate their opposition to the Catholic Church. After executing the king and members of the aristocracy, along with some uncooperative workers, the French Jacobins began to murder each other. Similar facts apply to the Bolsheviks, with their logical cult of dialectical materialism. Modelling themselves on the Jacobins, after murdering and starving workers and peasants after the civil war ended in1921, the Bolshevik leaders also began killing each other.
So, today what are the distinguishing features of a cult? How do they establish who is, and who is not, a member and how does a cult establish and retain power? Despite its seemingly terminal decline in the early 21st century, formal logic can be considered a cult. With its pantheon including Aristotle and Frege, in the 20th century its adepts tended to come from elite British and American universities. Within philosophy departments, cult members tend towards analytical or linguistic philosophy, but are opposed to the so-called continental philosophy of the European mainland. Outside of these departments, allies of the cult tend to be members of mathematics and computing departments. Financially secure, but not usually wealthy, cult members have a problem recruiting and retaining students; for the simple reason that the subject is difficult and, to be frank, boring. Therefore, adepts focus their dwindling power within philosophy departments by trying to force potential student victims to enrol on at least one logic course in order to obtain a degree. To this end, one of the cult’s claims is that some facility in formal logic is useful in both the law courts and computer programming; a claim which, as we will note, is difficult to sustain.
In his Preface, one adept, Tomassi (1999), admits that: “Formal logic is widely perceived to be a difficult subject”, referring to “the anxious moments which every student experiences”, also noting the number of students who “failed the course in earlier years”. Some students, he adds, were “so daunted by symbols” and therefore “missed classes”, with the result that they “frequently just failed to catch up”. Perhaps worried about losing his job, Mr Tomassi writes further: “fail rates in formal logic courses might ultimately contribute to a decline in the teaching of formal logic in the universities”. Finally, he admits that the subject can lead to “anxiety attacks”. Confirming this, one American former logic student, Amber Callahan of the University of Michigan, reporting on the Quora website, acknowledges: “The class had me in tears with a constant migraine. I paid hundreds of dollars to just drop it instead of dealing with it, and the price was more than worth it. There is obviously nothing logical about the class”. Perhaps learning from the methods of torture used by the Catholic Inquisition, adepts insist that their students learn an alien language, consisting of Latin and ancient Greek terms and letters, along with the symbols used in mathematical set theory.
Formal logic as autism
Judging by their biographies, it seems that the key players in the development of formal logic, i.e. Russell, Frege and Wittgenstein, suffered from an inability to engage in social communication; what today is referred to as autism. Each of them expressed their ideas on logic in the context of matching their thoughts to individual objects around them: tables, chairs or cats being oft-quoted examples. In their writings, rarely if ever, do these logicians refer to real human encounters, socio-economic contexts, facial expressions, body language, metaphors, sarcasm, humour or any of the other basics of human life. One reluctant cult member, Cheng (2019), admits adepts may, according to their formal rules, be logically precise but notoriously socially inept. A friend, Terry Dawson, told me that, seeking assistance from a cult member in the entrance to Bradford University, he asked a professor if the latter knew the way to a conference room; to which the only reply was “yes, I do”; whereupon the adept continued on his way. As student reports confirm, when the cult’s high priests revert to ordinary language, such as English, it is often of the most banal and socially stunted kind. So, effectively assuming that their students are 5 year olds, we find such gems as: the cat sat on the mat, are a commonplace. Indeed, two high priests, Beall and Logan (2017, 4), write: “Agnes is a cat…All cats are smart”. Reminding us of the esoteric thinking of the Grand Inquisitor Tomás de Torquemada, adepts are often unable to tolerate critical discussion of their subject, describing rival forms of logic as “deviant” (xv). When not referring to the above mentioned cat themes, such as: “My uncle’s cat is a cute, furry creature.” (6), Tomassi claims that his cult helps him argue logically about “religion, politics…or anything else” (2). Yet, he seems anxious to dispense with meaningful social communication, quickly reverting to such symbols as p and q, thereby squeezing the life out of his subject. Oh dear, like Ms Callahan, do you the reader feel an “anxiety attack” coming on?
Two-valued logic: the search for the holy grail of truth
Two-valued logic is a way of reasoning that declares that a statement, referred to as a proposition, is either wholly true or wholly false. Adepts typically take two propositions in order to see what conclusion follows from them; a way of reasoning which is called a syllogism. Thus on the cat theme, adepts might begin with the proposition: all cats are furry, followed by a second proposition: Molly is a cat. The syllogism is completed with the earth shattering conclusion: therefore Molly is furry. So, if you are thinking of enrolling on a logic course, beware, as the cult’s holy books are full of this sort of stuff. In Britain, as A-level mathematics students know, a theory is often ‘proved’ to be true because assuming it to be untrue leads to a contradiction; and contradictions, adepts routinely argue, indicate falsehood. In fact, as Hegel (1977) argued, most of these ‘proofs’ are tautologies, empty truths which merely assume what they claim to prove. At the core of the rules of logic is the law of non-contradiction; a thing or event is either A or not-A, it is either raining or not raining in the same place at a given point in time, being a common example. Amongst contemporary critics of the cult, Kosko (1994) challenges the exclusivity of A or not-A; in reply to the claim that it is either raining or not raining, he writes: “Rain can spit or drizzle or shower or drench…It’s a matter of degree” (159).
Revealing the most profound ignorance of thousands of years of logical reasoning, ignoring the challenges of Kosko and the otherinfidels, as non-believers were known in the middle ages, logicians press on, insisting that there can be no intermediate position, or middle, between A and not-A. Their faith in such reasoning, true or false, A or not-A, locks logicians into applying this rule to a range of everyday practical situations. Where appropriate, we all do this informally; indeed, human life is not be possible without distinguishing truth from falsehood. But, and it is a big but, there are limits to such reasoning. So, in any capitalist economy contradiction, i.e. both A and not-A, is the order of the day; for example, there is always an ongoing cycle of boom and slump and an antagonistic relationship between wages, profits and inflation. An obvious scientific example of contradictions is in sub-atomic physics, where a radically different mode of reasoning, known as quantum logic, is applied in this field of mechanics; much of this logic being expressed in terms of statistical likelihood. Simply put, rather than individual self-contained things, as asserted by cult members, the world is composed of relationships; things are what they are only by reference to their connections to other things. Indeed, some of the logic underpinning the simplest of syllogisms is reliant upon an appeal to the power of capitalist ideology. For instance, based on an example offered by the sceptical cult member Cheng, we can analyse the following syllogism:
A 10+1=11; B 1+10=11; therefore C 10+1= 1+10.
Adepts often argue that acceptance of axioms A and B makes acceptance of C inevitable, it would, they argue, be folly to do otherwise. This, they claim, demonstrates the inherent power of logical deduction since, as the faithful’s cliché goes; A and B would lead to C “in all possible worlds”. In point of fact, this type of logic, which underpins much of contemporary arithmetic, is not a universal truth at all. This is because the differences between A and B are irrelevant to the transactions we all engage in on a daily basis which are the mainstay of capitalist economic relations. From a contrasting perspective, however, things look rather different. A 10+1=11 is a simple example of the axiom of succession in positive integers, i.e. counting from 1, its successor is 2, then 3…up to 11. B is different in that, in both theory and practice, it is less clear how succession works here, as the difficulties faced by young children, for instance, clearly demonstrates. The point is that there exists no invisible logical power that forces us to accept C; rather it depends on our perspective. We take the symbols and logic of capitalist-orientated mathematics for granted, seemingly unaware that it is a relatively recent approach to numbers. Today’s arithmetic is radically different from the way numerical operations were performed prior to the industrial revolution, when populations were overwhelmingly both illiterate and innumerate. Calculations were largely the preserve of a fee-charging elite, many of whom drew links between numbers, religion and mysticism.
The green pastures of Cambridge University
I remember watching the Oxford-Cambridge boat race one year…I am privileged to have studied at Cambridge; Cheng(2019, 5 and 223). These comments, made by one of the cult’s adepts, remind me of a conversation with a retired maths teacher, who asked me: how do you know that a stranger you meet went to Cambridge or Oxford? He explained that they always tell you in the first few minutes.
Following in the footsteps of Russell and Wittgenstein, one Cambridge alma mater, Cheng, asks rhetorically: “Wouldn’t it be helpful if everyone were able to think more clearly?” (ix) especially, she adds, when the “world is a vast and complicated place” (3). However, from the comfort of her rooms, Cheng does not seem overly concerned with the world as experienced by billions of workers and landless peasants. She might well be surprised to learn that most of these people would challenge her priorities, finding it more “helpful” to know where their next meal is likely to come from. Cheng informs us: “Everyone is privileged relative to some contexts and underprivileged relative to some others” (113). It is difficult to see how the millions, yes millions, of children who die each year in India, for instance, are “privileged”, if only “relatively”. Cheng’s blasé attitude is similarly evident in the discussion of the logic underpinning pure mathematics presented in Hardy’s Apology (2019). Another Cambridge chap, Hardy took the view that the logic of proof in pure mathematics, as opposed to its applications in engineering, architecture and the like, was an intellectual exercise in deduction. He advocated a Platonic approach, which adepts often apply to logic: “mathematical reality lies outside us…our function is to discover or observe it” (123; emphasis in original). Comparing his reasoning to solving chess problems, a simile used by Wittgenstein, yet another Cambridge chap, Hardy argued: the “function of a mathematician is to do something” and that something is “to prove new theorems”; other aspects of maths, he argued rather snobbishly, “is work for second-rate minds” (61). Yet, Hardy was not averse to exploiting the mathematician Ramanujan, whose practical, rather than formal and ‘logical’, approach drew on ancient Indian reasoning. In the tradition of an ancient leisured slave-owner, Hardy was committed to what he referred to as the Greek method of proof, frequently citing Euclid and Pythagoras, claiming the method is “clear cut” and “unanimously accepted” (82). Regarding the logic of maths, he argues that “very little of mathematics is useful practically, and that that (sic) little is comparatively dull…I am interested in mathematics only as a creative art…I have never done anything ‘useful’” (89,115 and 150). In other words, for Hardy, his proofs were not relevant to the real world of qualitative processes, such as workers struggling to feed their kids. For the likes of Hardy, logical proofs are totems of their alleged intelligence, dare we say genius, which seemingly legitimises their relatively privileged lifestyle.
Frege and the new synthesis
As formal logic became established in elite British and American universities in the late 19th and early 20th century, cult leaders offered a synthesis of Aristotle’s writings on logic with the then new fashion in mathematics: class or set theory. As Nye (1990) points out, advocating the subjection of women and legitimising the institution of mass slavery, Aristotle’s texts were intended to be used by the leisured land- and slave-owning classes as a means of winning arguments in the law courts and debating chambers. Giving little thought to the plight of victims of the wage labour system who would clean their rooms, adepts such as Russell, and his disciple Wittgenstein, used set theory as a model for logical thinking. To this end, they turned to the German Frege, who had pioneered attempts to synthesize maths and logic. Frege soon achieved the status of godhead in the cult of formal logic, an exalted position that, despite an embarrassing discovery, he retains to this day. Tomassi, for instance, writes: Frege’s “text certainly heralds the dawn of the modern tradition of classical formal logic…an event whose significance…is inestimable” (22).
The discovery in question was contained in a 1924 diary found by cult member Dummett. In summary, despite adepts’ claims of value-neutrality, the diary revealed that Frege was an anti-Semite, with a dislike for democracy; in short, a proto-Nazi. This would suggest that a lifetime studying logic, as the alleged road to Truth, in no way prevents a person from supporting an ideology that, in this case, later lead to mass murder. Yet, the truth was that most European and American intellectuals, including those involved in mathematics and logic, in the late 19th to early 20th century were racists and sexists. Advocating the subjection of women along with the inferiority of people of colour and Jews; most supported Sir Francis Galton’s eugenics agenda, openly expressing varying degrees of contempt for working class people. Far from weakening the cult’s resolve, the views expressed in Frege’s diary were put to one side, having no effect on the view that, like mathematics, logic’s alleged search for “clear thinking” and truth should continue apace.
The truth and the cult
Despite the doubts expressed by Russell and Wittgenstein, following the horrors of world war, in public at least, adepts continued to claim to be offering a value-free mode of reasoning, divorced from potentially embarrassing political, social and economic considerations. To this allegedly value-free end, logic should be analysed by means of algebraic deduction, particularly by the use of Cantor’s set theory, and other branches of mathematics. By this time, as we have noted, quantification had long since divested itself of its earlier qualitative associations with religion and the occult. Capitalist social relations were driven by money transactions, numbers being the lingua franca; thus had quantity triumphed over quality. Taking the above mentioned form of the syllogism, only those propositions which could be verified as factually true by means of sense perception could be considered worthy of consideration for the basis for a sound argument. Therefore, amongst English speaking adepts the term “is the case” was used to verify that a particular proposition was factually correct, i.e corresponds with an individual’s sense perception, or what she or he sees, hears, tastes, smells or touches. From this process, the term truth-bearing proposition duly took its place amongst the cult’s holy commandments.
The swan sailing on the canal is white, is an example of a truth-bearing proposition, because it can be verified as either true or false by the senses. So, the faithful assume that an observer will compare the parts of the proposition, here the terms swan, canal and white, with what they see with their own eyes. The extent to which the proposition and what they observe coincide determines whether the proposition has been established as true or false. Thus, truth bearing propositions can be tested against the real world, our senses are thereby assumed to give us a mirror like reflection of this world; a process referred to as the correspondence theory of truth. It would seem that truth is, to quote Hegel, a “ready minted coin”and, in keeping with this doctrine, those adepts who were aware of alternative theories of truth rejected them as apostasy.
Clearly, the correspondence theory of truth, where what we say, write or think is compared with our sense perception, appeals strongly to what we might call common sense. Indeed, our day to day lives typically depend on using this theory both explicitly and implicitly; obvious examples being the routine decisions we make when driving a car or crossing a busy road. Returning to our white swan example, one famously used by Popper (1975), we can readily see that comparing the proposition with what is seen on the canal, there is a more or less perfect correspondence. Yet, as those studying psychology or optics know only too well, things are not quite so simple. It is the case, to use the logicians’ phrase, that the sense data that we receive is not simply a mirror like copy of objects around us. Our brains adjust, filter and mediate sense data in various ways. So, if we begin with the colour white, it is pretty obvious that the whiteness of the swan will vary according to the time of day or night. The biological make-up of the human eye’s cones will also mediate the whiteness we observe; we can identify various types of colour blindness, gender differences, ageing and various eye diseases as obvious examples of varying receptions to colours in general. In point of fact, our reception of colour is subjective, so that the sky is not really blue and indeed any colour is a synthesis of the colours of the spectrum. We may ask: is my reception of the colour I call white the same as that of other people? Researchers, it seems, continue to speculate on the answer to this question.
Turning to the swan part of the proposition, whilst noting the genus and its sub-species were repeated subjects of discussion for the cult’s demigod Aristotle, defining this waterfowl is not so simple as it at first seems. Therefore, we may note that swans on lakes, rivers or canals are not pure white due to the pollution of our waterways. The colour of various types of swan, including some flightless and large species, now thought to be extinct, are unknown. The white swan, typical of the northern hemisphere, was thought to be the only species by early European researchers, though the young were readily observed to have patches of brown and black. However, when Europeans became aware of a range of swans with other feather colours, the obvious question was: were these to be defined as swans at all? We may note, for example, that white pigeons are called doves. Whilst noting that investigating the range of colours of swans is progress of a one-sided kind, as Hegel (1977) argued with regard to the colour of roses, this abstracts from the living being that is the swan by focussing on its whiteness, or blackness in the antipodes; a case of the lifeless predicate distracting us from the living subject. Needless to say, such considerations call into question the ‘facts’ contributing to the correspondence theory offered by the orthodox of the cult.
Alternative approaches to truth
Ignoring the above considerations, or condemning them as “deviant”, adepts continue to present their, typically tedious, examples of propositions and applying the correspondence theory of truth. Citing Hegel again, this theory is a good starting point in any investigation into the journey that is the search for truth. So, given that I think that the sun will rise in the east and, if I get out of bed early enough and it is not too cloudy, sure enough I will see the sun rise in the east. Useful though this sequence is for most day to day activities, for hundred of years scientists have been telling us that the sun does not rise in the morning, or fall in the evening, our senses therefore do not tell us the truth. This would suggest that what we perceive via our senses, is not a pure mirror-like reflection, but rather is mediated by our understanding; as psychologists and others tell us, what we think and what our senses tell us are interconnected. This has lead some philosophers to propose a coherence theory of truth which, being heretical to their belief system, is rejected out of hand by formal logic’s faithful. Another, American grown, theory of truth is pragmatism, supporters of which, in simple terms, claim that if a theory works it’s true; which is again rejected by cult adepts. Returning to the sun rising and falling example, pragmatists argue that what we see works or has a “cash value”, to use a term from the American capitalist lexicon. Needless to say, pragmatists are aware that for astrophysicists, for example, the sun rising and falling over our horizon has no cash value; thereby acknowledging that truth varies according to context. This would suggest the coherence theory would have to be used to reconcile conflicting perspectives; which in turn suggests that the journey that is truth seeking has to accommodate all three of the above mentioned theories. Such polytheism would obviously be anathema to the cult.
Hegel’s thinking
Given that he has been referred to several times, we may note that in the Preface to his Phenomenology, Hegel (1977) rejects the “rigid” distinction between truth and falsehood, the positive and the negative, indicating this distinction is typical of “popular opinion”. He refers to one-sided truths, arguing for a process of “organic unity” (8) in which both the true and the false are part of a journey that leads to a higher truth. Referring to the logic of geometry, Hegel argues some truths are a “lifeless generality” a “corpse”, which must be understood as a “moment” in the process of “becoming” (10). So for Hegel: “The true is the whole. But the whole is only the essence perfecting itself through its development” (32); whereas logicians, he argues, distinguish between the true and the false like “oil and water” (60). Anticipating modern critics of the cult, Hegel argued logicians typically focus on “instantaneous” or lifeless events, thereby assuming the existence of a timeless motionless world, in keeping with Plato’s archetypes.
Being steeped in ‘Greek’ geometry as a student, Hegel argued that it, and most of mathematics, is based on dogma, i.e. commands which must be blindly obeyed, and is therefore “defective knowledge…Its purpose…is magnitude”. It proceeds, he adds, “on the surface”, it “does not touch the matter itself, not the essence…and is therefore not comprehension….its distinctions (are) an empty, dead element in which they are equally immobile and lifeless”. Human life or “the actual”, continues Hegel, “is not something spatial the way it is considered in mathematics”, which offers “only unactual truths”, its “knowledge proceeds along the line of equality…and therefore it also does not attain the transition from the opposed into the opposed, nor the qualitative, immanent movement, nor self-movement” (66). Anticipating the marriage of logic and mathematics, Hegel writes: “mathematics considers only magnitude which is the unessential difference”; it is time to “both cleanse mathematics of this false finery and show the limitations of mathematics and thus also the necessity of another kind of knowledge…concerning…this pure unrest of life” (68). Mathematics then “reduces that which moves itself to mere material in which it then has an indifferent, external, lifeless content” (66-68). With regard to proof by contradiction, as mentioned above, Hegel writes: “it is not difficult to see that positing a proposition, adducing reasons for it, and in the same way refuting the opposite by giving reasons, cannot be the form in which truth appears. Truth is its own self-movement” (72). More generally, Hegel notes the way in which the natural and social sciences study the life of the universe by parcelling it into categories and labelling them “like a skeleton with little pieces of paper stuck all over it” (78), rather than seeking to understand its “inner necessity”. Those readers wanting to learn more about Hegel and the history of dialectical thinking could do worse than refer to Scott (1999).
Fuzzy logic
As is made clear in Scott (1999), for hundreds, if not thousands, of years logicians in India, China and elsewhere formulated notions of truth that transcend the two-valued logic of A or not-A, with its excluded middle. In this tradition, Kosko (1994) argues the integers, 1, 2, 3, etc. are, when taken out of the Platonic fantasy land of pure maths, merely approximations of the processes that mark the genesis of real life. So, the number 1 can be used to describe a thing, such as a cup, but in terms of height or weight or whatever, particular cups vary greatly; yet each cup is given the number 1. Similarly, as farmers know when they go to market, despite the arithmetical claim that 1 + 1 = 2, each cow or sheep is different. In other words, assuming a minimum level of consumer expectation, the routine use of numbers in the capitalist mode of life indicates that the notion of quality has been banished by quantity. On the use of set theory, which is obligatory for cult members, one critic argues they have “very little relevance to the practice of mathematics in everyday life…Strange symbols were introduced for seemingly simple things…An idea that was meant to simplify in fact complicated matters”; Gullberg (1997, 232). Kosko agrees and has advocated the use of fuzzy sets which, he argues, “live outside of math” (127) in that they are not hidebound by the A or not-A of formal logic.
Yet, although aware that their cult is withering, pious logicians follow Hardy, producing texts on the logic of Bletchley Park, Soduko puzzles, games of chess and the like. In terms of the Star Trek logical dilemma, for example, between the Many and the Few, or the One, adepts claim that their articles of faith, based on autistic individualism, are applied in such areas as neo-liberal economics, decision making techniques such as the prisoner’s dilemma, the law courts and artificial intelligence (AI). Such radical individualism is promoted in the philosophy of Ayn Rand, and in economics by Milton Friedman, the latter’s texts remain on many university reading lists. Adepts will no doubt be troubled by the likelihood that fuzzy logic may well prove to be of far more relevance to developments in neural nets, AI and more; with formal logic orthodoxy pushed to the margins. As regards police interrogation of suspects, an example much cited by adepts, two-valued logic remains highly conservative in that it does not address such issues as why do we have crime, or who decides the answer to the key question: what is a crime? As regards logic in the law courts, it is clear that the best paid lawyers are those arguing their corporate clients’ cases in such areas as fraud or tax avoidance/evasion. Lawyers are not usually trained in formal logic but, in keeping the ancient Greeks and Romans, are no doubt aware of the rhetorical tricks of their trade. To close this section, on the topical subject of AI, I suspect that the leaders in this field are the American military, with Russia, China and India some way behind. With reference to the relevance of formal logic in AI algorithms, I would not presume to comment except to say that my limited reading on the subject suggests that formal logic is not the prime mover.
The death agony of the cult
Despite the cover up, the cult’s credibility was shaken when Frege’s political affiliations became public knowledge; but worse was to come. Russell more or less repudiated his early work on both maths and logic; informing his fellow logician Frege that there was a gaping hole in set theory, much to the latter’s discomfort. After leaving the cult and denouncing Bolshevism, following a visit to the USSR, Russell became an anarchist and, in contrast to fiddling around with symbols, a campaigner against nuclear weapons. Both Tomassi (1999) and Stoneham (2022) refer to Wittgenstein, but omit to mention that the latter, in effect, resigned his membership of the cult; thereby condemning himself to purgatory. It could be argued that, in his later texts, Wittgenstein’s notion of “language games” anticipated the post-modern idea of self-contained narratives. A fashionable term amongst journalists, narratives are self-contained in the sense that adherents of one narrative are seemingly unable to communicate with those affiliated to another. However, we may note that the ideology, being a better word than narrative, that underpins the wage labour system marginalises all other “language games”, since in order to obtain our subsistence we all need to play the game according to rules imposed by national power elites.
Suggesting a breakdown of Inquisition-style supervision, today cult members openly express dissident views; Cheng, for instance, is critical of the true/false split central to formal logic. Pointing out that such logic tolerates no ambiguity or socio-economic context; risking excommunication, she adds: “nothing in the real world actually behaves according to logic” (208). With their one to one, word to thing, correspondence view of the world, formal logicians continue to struggle with the simplest of ordinary language terms. For instance, such words as nothing or nobody present major difficulties, as do non-existent things such as, the oft cited, unicorns or kings of France. Given their commitment to a timeless lifeless world, logicians continue to agonise over such fundamental issues as movement and events in the future. Repeatedly referring to “paradoxes”, cult members jump from one unsatisfactory ‘solution’ to another in order to root out such heresies. They continue to claim that movement, such as arrows flying through the air, is to be understood as ever smaller discreet distances, so that arrows never actually reach their targets. Some developments in modern mathematics also present major doctrinal assaults on the faith. Andrea Nye’s (1990) excellent text, Words of Power, offers not only a sacrilegious critique of the history of formal logic, from the ancient Greeks to Frege and Russell, but also explains how each key development in this history was related to reinforcing the interests of ruling elites in successive socio-economic contexts. In the 20th century, she explains, following the views set out in Frege’s diary and the Vienna Circle’s logical positivism, it was vital that all political and socio-economic thought was, in theory, dismissed as “metaphysics” because, according to the correspondence theory of truth, it could not be verified, rendering it “meaningless”. Crucially, Nye writes: “If truth is more than a sterile formality, more than a mechanical semantic matching of formulae with other formulae, we must first know the meaning of the words that we are to judge true or false” (174).
Logic and Jacobinism
A bizarre convert to the cult is Burgis (2019) who, despite presenting himself as some sort of political revolutionary, is a convert to the cult of formal logic. For those of us wanting to rid the world of capitalism and create one in which everyone, at the very least, has sufficient food, clothing and shelter, it is not clear how using such symbols as p and q, along with the rest of the cult’s commandments, is of any use to us. In keeping with his excluded middle, either A or not-A, Burgis occupies much of his text with the familiar spatial political metaphor of left and right, taken from the seating arrangement of the post-1789 French debating chamber. If we take the term the left, which is even included in the subtitle of the book, we have to ask: to what does it actually refer? Putting to one side all the qualifications of the term, such as centre left, hard left and so on, it is clear that Burgis himself is, frankly, all over the place with regard to his political agenda. On page 1, Burgis writes of “a Jacobin-reading leftist who I agree with about most subjects”; the name of this American publication refers to those previously middle class French intellectuals who unleashed the terror following 1789. Throughout his book, Burgis swings between Leninist/Trotskyist vanguard-ism and democratic movements initiated by working class people themselves. Yet, in spite of their obvious inadequacy, but in keeping with his formal logic, the author sticks to the designations left wing and right wing with its excluded middle.
With regard to his presentation of formal logic, Burgis fails to point out that it is a dying cult abandoned by its originators Russell and Wittgenstein, not to mention the proto-Nazi tendencies of Frege. As a result, it was long ago taken off the list of subjects offered to students in all but those elite universities to which the wealthy send their sons and daughters. Given his apparent affiliation to Jacobinism and presumably Leninism, one would expect Burgis to refer to Hegel’s devastating critique of formal logic. Alas, Hegel gets barely a mention and instead Burgis gives us a number of extracts from Trotsky on the dialectics of nature. Such an approach to nature owes everything to Engels and very little, if anything, to Marx. Mr Burgis would benefit greatly from a study of the history of logic, such as the Jain reasoning of ancient India. It could also be mentioned that Burgis’ commitment to formal logic has not helped him, or more likely has hindered him, with regard to understanding the philosophical nature of time or indeed the ideological function of classical statistics, especially opinion polls, as set out in Scott (2022).
Conclusion
Confirming the troubled state of formal logic, we can end by citing an interview with Tom Stoneham (2022) Professor of Philosophy at the UK’s York University. He begins by referring to people “engaged in talking about what’s true and what’s false and have no other interests”. Typical of the asocial frozen thinking of formal logic, the idea that anyone in the world has no interests is a comment that is naive in the extreme. Obviously, the citizens of every nation have all manner of affiliations, class, race, ethnicity etc., along with a unique national history and all manner of cultural and political norms; consciously or not, we all tend to promote those interests which in turn profoundly affect the way we think, argue, speak and write. After declaring logic to be “a very general form of algebra”, Stoneham implies the pointlessness of the cult’s agenda: “I often say when I’m teaching logic, ‘Don’t use this at home or you’ll end up unhappily single’”. Similarly, suggesting that formal logicians should occupy their time more productively, he informs us that “People write books and papers about how you map the English word ‘or’ onto the logical symbol for disjunction; it turns out to be quite controversial, and there are heated disagreements”. He adds: “if you try to teach logic to a microbiologist, you’ll find they’re not interested. It doesn’t help them do their job. So its not clear that formal logic has a direct, practical application”. In answer to the obvious response: then what is the point, the best that Stoneham can come up is that it can “allow you to engage in certain philosophical questions”. Finally, suggesting that he retains some grasp on social reality, Stoneham discusses the issue which seemingly troubles cult members: when does adding grains of sand result in a heap, admitting that “no one’s going to care about that. If you go on about it at the beach, someone’s just going to come and kick the sand in your face”. To cult members: rest in peace.
Dedicated to the memory of Terry Dawson, a tireless seeker of social justice.
Bibliography
Beall, Jc. and Logan, S. A. (2017) Logic: The Basics; Routledge: London.
Burgis, B. (2019) Give Them an Argument: Logic for the Left; Zero books: London.
Cheng, E. (2019) The Art of Logic: How to Make Sense in a World that Doesn’t;
Profile Books: London.
Gullberg, J. (1997) Mathematics: From the Birth of Numbers; Norton: New York.
Hardy, G.H. (reprinted 2019) A Mathematician’s Apology; Cambridge University Press: Cambridge.
Hegel, G. W. F. (1977) Texts and Commentary: The Preface to the Phenomenology; Notre Dame Press: Indiana.
Kosko, B. (1994) Fuzzy Thinking: The New Science of Fuzzy Logic; Hyperion: New York.
Lee, S. F. (2017) Logic: A Complete Introduction; Hodder & Stoughton: London.
Nye, A. (1990) Words of Power; Routledge: New York.
Popper, K. (1959) The Logic of Scientific Discovery; Basic Books: New York.
Scott, S. (1999) Thought and Social Struggle: A History of Dialectics; available at:
https://bradscholars.brad.ac.uk/handle/10454/4205
Scott, S. (2022) Statistics and Capitalism: Number as Fetish; available at: https://1drv.ms/b/s!AuQwLizvJZqNgnZLgG5f95cSgDe8?e=jfpO69
Stoneham, T. (2022) The Best Books on Logic; available at
Tomassi, P. (1999) Logic; Routledge: London.
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