The Sheer Stultifying Weight of Our Traditions, Composing, 09/04/2014

Most of my philosophical activity today was spent working on a review/reply for Social Epistemology’s dialogical website. So I don’t really want to discuss in detail that issue, because it’ll be up next week on a site that’s far more official and gets much more visibility. However, I do have some more thoughts on Graham Priest’s old book, Beyond the Limits of Thought, that I figured were worth throwing online.

I’m extremely happy that Dr Arthur examined this book in his graduate seminar this semester, because I wasn’t familiar with it, and I’m glad it’s given me the opportunity. Priest’s book examined various thinkers throughout the history of Western philosophy (and the afterword to the second edition even included an engagement with the Indian philosopher Nagarjuna’s conception of nothingness) in terms of how they conceived of the limits of thought. One issue that I had with Priest’s book was that he skipped over many philosophers too quickly, and as a result badly misrepresented their own thoughts. 

No, philosophy isn't that kind of blood
sport. But we'd probably make more
money if it were that entertaining for
spectators.

Now, Priest wasn’t going for complete or comprehensive pictures of these philosophers, only how a particular problem appeared in some of their key writings. But because he couldn’t fill out the full conceptual contexts of their work, it constitutes a vulnerability. Philosophy can become a bloodsport, especially when you express controversial ideas as bluntly as Priest does.* I discussed this winter how Priest’s account of Immanuel Kant includes fundamental mischaracterizations because it only refers to The Critique of Pure Reason and not the positive aspect of that broad argument in The Critique of Practical Reason. As well, his account of Georg Hegel refers only to the Logic, and not the Phenomenology of Spirit, which is the project that links the abstract conceptual framework of the Logic to a practical account of politics and history, the articulation of Hegel’s aufheben movement in real life. 

* Honestly, I kind of want to study the early history of Priest’s career just to figure out how he wasn’t completely marginalized out of the university system because of his radical and unintuitive innovations in logic.

However, here’s a list of the philosophers Priest covers in his exploration of the nature of the limits of thought and how the idea arises in various contexts and thinkers. In historically chronological order, including the afterword to the second edition:

Cratylus

Plato

Protagoras

Aristotle

Nagarjuna

Sextus Empiricus

Anselm of Canterbury

Thomas Aquinas

Nicholas of Cusa

Gottfried Leibniz

Bishop George Berkeley

Immanuel Kant

Georg Hegel

Georg Cantor

Gottlob Frege

Bertrand Russell

Frank Ramsey

Martin Heidegger

Ludwig Wittgenstein

Willard Quine

Jacques Derrida

Donald Davidson

That’s 22 of the most diverse and individually complicated philosophers who have ever lived. The most sustained treatment they ever get from Priest is when he gives two chapters over the Kant and a chapter and a half to Wittgenstein. And when each philosopher is treated separately, introduced with his own chapter and section headings, it looks as though you’ve mastered them, or that you’re at least giving what aims to be a definitive account. 

It doesn’t matter if you admit your partiality or the limits of your project; if you present “The philosophy of X with regard to A,” you’re expected to have the whole system entirely in the bag. You look as though you’re writing secondary material, even if, in Priest’s case, you’re writing primary material with a pile of historical references. You’ll be held to the standards of secondary material (which weirdly, are higher with regard to philological accuracy than primary material). So his incompleteness leaves him vulnerable.

The only way to engage this many ideas from this many philosophers constituting such a diverse set of perspectives is not even to mention the other philosophers, aside from footnotes. Don’t present your own work as giving an account of these other historical figures; just adapt the ideas into your argument, indicate their source, and concentrate on the ideas free from historical context. It will keep you out of the distracting argument about whether you got the figures “right,” and let you develop your new ideas in peace. That’s how you keep yourself rooted in the broad tradition without getting your progressive ideas bogged down in debates about historical accuracy.

The only philosophical writer I’ve seen do this successfully is Gilles Deleuze. Ironically, he’s one of the few figures who would have written a book with his historical influences as chapter headings and still gotten them right, so comprehensive and detailed was his knowledge of philosophy’s history. Read What Is Philosophy? if you want to see precisely what I mean.

All for the Sake of an Experiment, Research Time, 08/04/2014

I returned to my Facebook account last night to find a wonderful comment by my friend D: “If these were shorter, I’d read every one.” With this in mind, just a few short reflections. And they actually will be short this time.

I didn’t get many chances to visit Dr Arthur’s seminar on Graham Priest at McMaster this semester, even though I wanted to attend more often. But I got to the last session yesterday, and it was a wonderful class to take part in. If you remember my various discussions of Priest’s book, Beyond the Limits of Thought when I was reading it last semester, I have a very positive attitude toward his general philosophy, though I have some criticisms of his particular inquiries.

The fascinating and contrarian Graham Priest.

A quick refresher for those who don’t want to follow the links. Graham Priest is a logician who has developed dialetheic logic, a form of symbolic logic that allows for the truth of some contradictions. Beyond the Limits of Thought is a survey of huge swaths of the history of Western philosophy for examples of such true contradictions. Priest’s mission statement is that one kind of true contradiction is the attempt to think the limit of thought. It isn’t that tough to conceive: try to think what cannot be thought, or say what cannot be said. Every time we attempt to think through the limits of human language and thought, we always have to straddle this weird borderline position where we can actually articulate what kind of thing would lie outside the limit. So we delineate a limit of thought by being able to point just beyond it. And in pointing, we think what we’ve just declared unthinkable.

It’s a trippy concept, and I quite enjoy it. One point we discussed in the last class, however, was precisely what was the upshot of true contradictions existing other than simply marvelling or meditating upon them. After all, progress in thought often arises from thinking through contradictions that arise in thinking and trying to resolve them. But even if you accept a contradiction as true, its structure is usually remarkably complex. If the limits of thought are any indication, when a true contradiction arises, it already results from an amazingly complicated philosophical investigation. Discovering a true contradiction would, for me, add a further dynamic tension to an already-roiling conceptual mix. 

I’d be comfortable with that, but I fully understand that I’m not like most people. Whether or not you agree that true contradictions are possible, at the very least, Priest's work constitutes a complicated and remarkable philosophical experiment that can push the discipline into strange new directions. It's at least worth testing thought's limits in case it turns out we can step beyond them.

The Content of a True Contradiction, Research Time, 29/01/2014

Having finished Graham Priest’s Beyond the Limits of Thought, you might wonder what one of these true contradictions might be. I discussed the basic logical foundation of it a few posts ago, and one of the conversations I had with friends who read it revolved around what contradictions would actually be true. Because when you open the possibility of true contradictions, you also open yourself to straw man arguments from your enemies to make you look ridiculous.

After all, just because there can be true contradictions doesn’t mean that every contradictory sentence is true. There can be true propositions of regular sorts. That doesn’t mean that every proposition is true. The sentence “I am Adam Riggio and a root vegetable” is contradictory, but it isn’t true because I’m just Adam Riggio, no matter what dreams and aspirations I may have to become a turnip. The sentence “Adam Riggio was born in Jakarta” is a sentence with a non-contradictory form, but its form doesn’t make it true, because it’s empirically false. I don’t even think I want to go to Jakarta. The climate would kill me in the face.

The whole book is an exploration of one type of true contradictions, the contradictions which indicate a limit of thought. We reach a point in our conceptual exploration beyond which our powers to think don’t work. The tricky part of this idea, where contradictions appear, is that in order to identify a limit of thought, we have to transcend the limit. That’s why Priest identifies this contradiction in terms of transcendence and closure. A limit concept of thought generalizes over the totality of what can be thought or expressed or iterated, closing the set. But in order to generalize over that totality, we must refer to what can’t be generalized, transcending the set we just closed. In referring to what can’t be encompassed in the totality of what can be thought, we think it. So we both can think it and are unable to think it. 

Bertrand Russell's most fertile period in philosophy was
spent working to overcome what he held to be intolerable
contradictions in logic. Personally, he also reminds me of
an interesting take on Doctor Who.

In the history of philosophy, this was often conceived as the thought of the infinite. Finite creatures can’t conceive of the infinite, so goes the idea. Especially since in some periods of philosophy’s history, the infinite was conceived as the uncountable, and mathematical conception only included very simple counting methods. When set theory was developed, we now had a system of rules that could count infinite quantities, or at least quantify over them. Being able to do this helped clarify a confusion, or rather identify that our previous thought had been less transparent than we believed. Set theory was a new standard to think about infinity.

Priest’s book looked through the history of philosophy to find the common thread in all these limit concepts of thought: totalizing self-reference. The perfect example in logic is the set of all sets. Being itself a set, it would have to include itself in its own set. But that would make it subject to the classic Russell paradox, that a set being a member of itself implies that it is not a member of itself. Russell’s generation of logicians spent years obsessed with overcoming this contradiction because they took as an unquestionable premise that consistency was a necessary condition of the true, that a contradiction could never be true because reality was consistent. It’s been an obvious and clear truth since Aristotle declared it to be so in his writing.

Aristotle was also a teleological evolutionist and believed in a geocentric cosmology. Aristotle is no authority.

Self-reference is one species of true contradiction. There are probably others, but I don’t want to talk about them today. Except perhaps for one little moment of jamming, a speculation that I’ve wondered about for years, ever since I started studying the nature of human thought and mind. 

The limit of our thought lies in the contradictions of self-reference, reflexive and reflective thought, self-consciousness. We wouldn’t have the personalities we do without self-consciousness, the ability to think beyond immediate needs and immediate perceptions. Self-consciousness is the ability to imagine the future and the past, planning for uncertainties and conceiving of priorities and desires. Self-consciousness is the ability to critique and change ourselves and our behaviour. To do so, we must refer to ourselves, include ourselves in our statements about the world, even as referring to the world implies that we are somehow separate from the world. Sartre, for example, described human consciousness as beyond the world, but embedded in it. Self-conscious creatures like humans may very well be another species of true contradictions walking around all over this planet.

Strict Certainty Will Kill Your Thought, Research Time, 28/01/2014

To start, a note about Graham Priest himself, in addition to the praise I heaped on him yesterday: Having finished Beyond the Limits of Thought, I wish there was more of it. But his point in writing the book was to demonstrate that people have been writing about true contradictions for centuries, and that true contradictions occur when people try to think about the limits of human thought. Because when we conceive of those limits, we face the phenomenon of having to go beyond what we identify as a limit of thought in order to identify that limit.

The most obvious illustration of this idea is in the work of Ludwig Wittgenstein. All of his work has the common theme of identifying and proving that philosophy has limits. One of the reasons I was drawn to Wittgenstein more than anyone else in the Analytic tradition when I first began learning the history of philosophy. But I was also disturbed by his conclusions, and the conclusions of those like him in identifying the slipperiness of meaning, and therefore the slipperiness of truth.

Priest’s last chapters about Willard Quine and Donald Davidson also describe ideas that I found disturbing when I was young. The idea that the meanings of words couldn’t be fully determined, that there would always be uncertainty in communication and even uncertainty in the meanings of words themselves unsettled me. When I first learned about the inevitably shakiness of language, I thought this was a problem that needed to be solved.

Ludwig Wittgenstein, a very neurotic man
who was a great theorist of knocking
down the pretensions of certainty.

I smile a nostalgic smile when I think of my youthful naiveté. But it seems I’m not the only one who thought of the indeterminacy of language and meaning as a destructive conclusion. I’ve never read Saul Kripke’s book about Wittgenstein,* but Priest describes Kripke’s conclusion that Wittgenstein was a skeptic about meaning. An action can express any rule (linguistically, an utterance could express whatever meaning) that our ingenuity can formulate for it. And the same utterance can have a variety of justifications, some of which are mutually incompatible. Therefore, meaning is not a matter of conforming our utterance to the precise concept underlying it, and understanding is not a matter of knowing a precise meaning. Kripke calls is a “skeptical solution” to the problem of meaning’s indeterminacy, because Wittgenstein has the disappointing conclusion that language and meaning rest on customary practices.

* Here’s a key reason I never went into Wittgenstein studies as a specialty: the field was  so fucking immense with secondary material, it intimidated me away from it. I’m usually not one to become irritated. But when I send articles for review, I often get the response from some reviewer who’s a specialist in a writer I refer to, that I should read X’s book about this writer. I sometimes think they’re talking about their own book. But there was so much secondary material written about Wittgenstein that I didn’t think I’d be able to sort through it all without devoting myself entirely to the exegesis of Wittgenstein for my career. I wanted to do more than that. Sadly, I think the same phenomenon is happening now with Deleuze: so much secondary material is being written about him that its scale would frighten new students away from Deleuze and his ideas.

I now know this to be a better conclusion. If meaning were determinate in the sense of a strong determination of concept to word or proposition, then I can’t see how it would be possible for language to adapt or change. Hell, I can’t see how language would evolve at all. Certainty is the same as freezing, the super-stability that amounts to sterility, the stillness that amounts to being dead.

For Wittgenstein (and David Hume, and Hannah Arendt, and Gilles Deleuze), language is a matter of external action and relation. We know we understand what another person says because our response to their words elicits a happy response from the speaker, or at least the appropriate response. There is vagueness underlying all language, but this vagueness permits creativity in action, adaptability to new circumstances. Utterances and sentences aren’t disconnected from the messiness of worldly action. The drive for certainty always comes at the expense of flexibility. Just look at the certain beliefs of religious or ideological extremists: the American, Islamic, or Buddhist Taliban. Flexibility, adaptability, and change are necessary for the vitality of life, language, and meaning.

I don’t think I’m naive about this question anymore. I think Kripke might have been.

Accepting that Reality is Paradoxical, Research Time, 27/01/2014

Graham Priest is not only a logician and
professor, but an advanced martial artist.

Graham Priest is a logician. This is one important fact about him that you should know. Out of all the achievements of philosophers in the last few decades, I think I have the most respect for what Graham Priest managed in the field of logic. This regards the second fact everyone should know about Graham Priest. He’s probably done more than any other single philosopher to pioneer paraconsistent and dialetheic logical systems, systems of logic that can accept and understand inconsistencies and contradictions. Priest often says it himself: there are true contradictions.

Intuitively, I don’t think that makes sense to a lot of people. It just seems obvious without even having to think about it that one part of reality can’t contradict another part. ‘A and not-A’ is impossible. Today, someone working in logic can use a dialetheic system, a logical calculus in which true contradictions make sense, and if someone accuses them of peddling nonsense, they can simply refer to the precedent of Priest. I’ve done this in conversations with some very narrow-minded philosophers who accused me of being stupid when I just wanted to talk about dialetheic logic. 

This is why I’m so impressed with the success of his career. When Graham Priest was just a young researcher working on his first projects and some older, more established logician scoffed at his work as nonsensical, he couldn’t refer to Graham Priest to back himself up. He hadn’t even yet become The Graham Priest that everyone refers to when they want to get stodgy old traditional logicians off their backs. All he had was his own ingenuity.

The argument he gives in Beyond the Limits of Thought for why you can have true contradictions goes like this. Consider two possible states of affairs, that A is true, and that A is false.

He writes, “Given two states of affairs, there are, in general, four possibilities: one but not the other holds, vice versa, both, or neither.”

1. “A is true” is true, and “A is false” is false. One but not the other.
2. “A is true” is false, and “A is false” is true. The other but not the first.
3. “A is true” is false, and “A is false” is false. Neither.
4. “A is true” is true, and “A is false” is true. Both.

Most commonly, we only believe that (1) and (2) are sensible statements. But the common belief is only one way among many that you can define a negation operator.

The third part of Priest’s Beyond the Limits of Thought engages with the work of Georg Cantor, Frank Ramsay, and Bertrand Russell to remove the paradoxes of self-reference from set theory. These paradoxes all have the basic logical form: a chain of reasoning involving a statement that refers to itself or a set that includes itself will lead to inevitable contradiction. Since there’s nothing in set theory’s basic rules that prevent such self-referring sets from existing, the logical operations of this kind of mathematics are always open to contradiction.

My former colleague in McMaster’s doctoral program, J, returned this semester from her post-doc to take the department’s rotating post as the visiting Bertrand Russell scholar. She gave a talk at the department’s visiting speakers’ series where she discussed some of Russell’s historical work on Leibniz. One of the priorities Russell explicitly had was examining the disparate, uncollected writings of Leibniz’s corpus looking for the principles and interpretations that would make them all internally consistent. He wrote that consistency is the best guide to truth.

A central premise of Russell’s thought (along with Ramsey’s, Cantor’s, Gottlob Frege’s, and just about everyone in the Western philosophical tradition up to Graham Priest) was that a contradiction could not exist, because the truth must be internally consistent. The entire revolutionary period in the creation of contemporary logic from the 1890s to 1910s was defined by the drive to remove the contradictions from self-referring propositions, or at least modify logic and set theory so those self-referring propositions can’t exist. Logic, set theory, and mathematics must be made consistent.

But Priest’s point (and Kurt Gödel’s, if you go back in the history) is that self-referring propositions are inevitable, and can’t be gotten rid of. You need a dialetheic understanding of truth because the ability to form a proposition that refers to itself will always result in contradictions. Any discussion of a totality (such as the set of all sets) refers to itself, because quantifying over all propositions will include the proposition that quantifies over all propositions; otherwise, you’ll fail to quantify over all propositions. When a set includes itself as a member, it simultaneously belongs and does not belong to itself. To a logical perspective that considers contradictions to be nonsense, this would make set theory (and therefore pretty much all the logic developed in the Frege-Russell-Ramsey revolutionary period) nonsense.

Only a dialetheic perspective, that is the perspective Priest developed and endorses, can understand self-referring sets, propositions, statements, and sentences. Only a dialetheic perspective is not offended by the conclusion that the set of all sets both belongs and does not belong to itself. The contradictions of self-reference that arise from set theory do not render set theory nonsensical, but dialetheic. The true heir of the revolution in logic isn’t whoever manages to make the contradictions of self-reference disappear (since no one can do that anyway), but whoever manages to make sense of the contradictions of self-reference. To the best of my knowledge, that person is Graham Priest.

Understanding How to Think the Unthinkable, Research Time, 24/01/2014

Climbing at last into contemporary thought about the nature of the infinite, Graham Priest’s book is finally losing that weird feeling of frustration. When he was examining the Ancient, Medieval, and Enlightenment periods of philosophy, the tension was difficult between his own mission of exploring the inherent contradictions of infinity and the utterly different philosophical priorities of his analytical subjects. In the context of Ancient Greek ontology, Medieval speculation about the nature of God, and the onto-moral twists and turns of German Idealism, Priest’s concerns jarred a little too much.

I'm also interested in Cantor's approach to
paradoxes. Priest, dialetheic logician that he
is, has no problem with set theoretical
mathematics implying inevitable paradoxes.
Cantor and other set theory mathematicians
desperately wanted to erase or nullify the
paradoxes that arose because they took
contradictions to be impossible, invalidating
an entire mathematical approach. Priest
doesn't care, and I think philosophy is better
for escaping its fear of paradoxical reasoning.

You can’t say the same when he starts in on Georg Cantor. I’m still not entirely sure where he’s going (as I’m working on editing a paper, working at my other editing job, and preparing to move apartments at the end of the winter, so I’m not reading the book quite as fast as when I started), but one idea in his first chapter on modern set theory is fascinating to me. This is the switch in status of potential and actual infinity.

For pretty much the entire history of Western philosophy until Cantor et al’s set theory was developed, actual infinity was conceived as a weird, strange, impossible thing. It was spoken of in the hushed and information-free tones of negative theology. We are finite creatures living in a finite world, so we can’t conceive of an actual infinity as anything other than the negation of the finite. As Hegel said, this isn’t even really an infinity, just putting a ‘not’ in front of the word ‘finite.’ The concept doesn’t even have any content.*

* Priest discusses Hegel’s conception of the infinite in terms of the absolute briefly, but the Hegelian metaphysics of thought as dialectical progression is rather outside his philosophical wheelhouse. I myself find the idea that there is a single concept, arrived at through a single determined progression of dialectical logic, which encompasses all that can be, rather repugnant.

But transfinite numbers, which are defined as sets with an infinite number of members, are now pretty easy to do mathematics with, once you conceive of w as an operation performed at the end of enumerating an infinite series. You can conceive of w + 1, 2w, w², or whatever. Once you can increase an infinite set, things can get crazy. But the upshot of this regarding how philosophers have traditionally conceived infinity is that set theory mathematics clearly define an actual infinite, define multiple such infinities, and you can increase or decrease them.

The reversal appears when you think of the potential infinite, an infinity that isn’t complete, but is growing serially over time. In other words, it’s a process that’s finite now, but will continue to grow indefinitely into an infinite span of future time. It used to be that this was the sensible infinity, because it was the only infinity that a finite human mind could conceive of with any content: an ongoing series that isn’t done yet. Actual infinities were conceived as some body so big that it literally was infinite, and it was thought that understanding such a body meant comprehensively conceiving or experiencing all its parts. 

But set theory mathematics gives us a shorthand for conceiving of actual infinities and comparing them. On paper, they look like ordinary bits of algebra that obey idiosyncratic rules of arithmetic, like these operations of belonging, inclusion, and diagonalization. Yet these mathematical operations define the nature of actual infinite quantities. They can be clearly defined and compared.

Potential infinities can’t work in quite the same way. The mathematics of limits come close, but a limit is a point that is infinitely deferred in a mathematical progression. A limit makes what would be a potential infinite a clearly defined quantity: an asymptotic approach to a given point.

Potential infinities are continuing movements, developments, or becomings. Only the philosophies of Henri Bergson (and to my mind, Gilles Deleuze, when he’s thinking in a Bergsonian direction) can manage this. Even then, these durational infinities, movements of infinite growth if you will, aren’t expressible in mathematics. Bergson himself defined it that way, describing mathematics as limited to abstract generalities. Only experience, he says, can give you the potential infinite: a power of development that need never stop. Yet this is exactly the impasse with which Priest ends his chapter on Cantor’s set theory.

Stumbling Through the History of Philosophy, Research Time, 22/01/2014

You see, the reason I’m reading Graham Priest’s book right now is that it’s the central figure of Dr Arthur’s graduate course at McMaster this semester, even though I haven’t been able to show up yet (the first week, I was in Newfoundland; the second week, I had only just gotten back from St Catharine’s). What I found fascinating about the book, why I wanted to take part in the seminar, was that Priest was exploring the nature of the limits of thought (hence the book’s name) using the framework of the dialetheic logic he developed in which there can be logically coherent and true contradictions. 

But the historical explorations of the first half of the book are starting to grow stale. I’m not sure what their purposes are. He states at the beginning of Beyond The Limits of Thought that the historical explorations are very partisan and skip over most of the contextual issues. His goal is to identify a point where the totality of what can be coherently thought is defined, and a particular concept, according to that definition, lies simultaneously within and without the limits of that totality.

The first step to understanding Kant is accepting that Kant's
philosophy is an enormous, complicated edifice that's very
difficult to understand.

So his exploration of Immanuel Kant as one of the philosophers who at least could conceptualize this limit both intrigues and frustrates me. Priest discusses Kant’s antinomies* as identifying how the limitations of thought involve contradiction. The antinomies are laid out in a section of the Critique of Pure Reason where arguments for and against four ideas that are beyond the human ability to prove their truth one way of another: 1) whether the universe had a beginning or was eternal, 2) whether matter has simple parts or is indivisible, 3) whether there is or is not an active causality, freedom, and 4) whether there is or isn’t a necessary being. But Priest spends so much time disproving the arguments of the antinomies that he misses the entire point of their construction, which builds its own twisted logic of true contradiction.

* There’s another chapter where he discusses the categories of the understanding, but that involves too much technical Kant for this post.

The most egregious example of Priest misunderstanding Kant’s purpose is clear in the antinomy of the universe’s origin. He dismisses both of Kant’s arguments, for and against, on the cosmological grounds that we’ve since discovered through empirical observation that (at least the observable) universe had a beginning, the Big Bang. What’s more, he analyses the logic of Kant’s arguments to show that he can't prove either side of the antinomy.

But the point of the antinomies is that they’re unprovable, and it was never the point to prove them in the first place. These arguments were laid out in a two column text, where the thesis and contra were adjacent to each other. The typography itself implies their parallel unprovability. The antinomies are rhetorical: a demonstration of the futility of reasoning about the traditional ontological roles of God and freedom. Reason and understanding can’t solve these arguments on one side or another. That’s why Kant puts the arguments next to each other, and never tries to resolve them. 

The proper resolution of the roles of God, the immortality of the soul and the universe, and human freedom in the world is a moral one. The existence of God, God’s role in creating and developing the universe, the immortality of the soul, and human freedom to act beyond the necessity of causation are all postulates we have to make in order for morality to be valid in our everyday lives. This is the central argument of the Critique of Practical Reason.** The contradictions of the subjects of the antinomies remain in cognition, but must be accepted as part of the universe if we want to maintain the consistency of our morality.

** I don’t actually believe in this moral philosophy at all, but I respect it as a brilliant philosophical creation.

Priest doesn’t seem to understand that at all. The bibliography of Beyond The Limits of Thought doesn’t even include the Critique of Practical Reason. He writes as if he were completely ignorant of the moral dimensions of Kant’s thought, even though the Critique of Pure Reason acts, in many ways, as a prologue to the moral philosophy. Its negative arguments set the conditions for the positive arguments of the later book.

If anything, the logic Kant uses to maintain the contradictory
nature of our knowledge of properly moral concepts is
stranger than Priest's relatively simple account of how
'A and not-A' can be true.

Even in Priest’s long quotations from The Critique of Pure Reason regarding the possibility of there being a necessary cause, he makes a show of cutting the parts of those quotations that identify such a cause as God. He considers that immaterial to the logic of Kant’s argument for there being a necessary cause. But that’s only because Priest is oblivious to the longer game Kant is playing: removing the subjects of God and freedom from cognitive or scientific domains to solidify their place in the moral domain. Instead of incorporating a historical example into his exploration of how to articulate true contradictions in philosophy, Priest only looks like a fool to anyone more familiar with Kant’s corpus.

• • •

All this sounds like it could make a really interesting article exploring several different ways to discuss figures in the history of philosophy, what the purposes of historical research can be, and an interesting way to teach some of the stranger details of Kant’s ideas. But there are too many mitigating factors against publishing this in a journal. These ideas are disconnected from the major issues of Kant scholarship at the moment, and it’s in reference to a 20 year old book that isn’t even centrally focussed on Kant or the history of philosophy. And Priest’s book itself is too old to be considered worth talking about in journals anymore. Even though this idea would make for a great article, a blog post is all it can get.

The Study and Use of History, Research Time, 21/01/2014

For some years now, I’ve thought of two different, broadly defined, relationships that contemporary folks can have to the history of philosophy. One is the historical study of philosophy: becoming a specialist in the philosophy and ideas of a particular era, group, or single notable figure. This is the route that leads academics to call themselves Russellians, Kantians, Hegelians, Spinozists, and other various adjectivized names. 

Another, which I prefer myself and think is, on the whole, more philosophically productive, is to use the history of philosophy. This is similar to what Gilles Deleuze did in many of his historical works, and in his creative philosophical projects, filled with references and call-backs as they were. Using the history of philosophy takes a figure or work that was developed in a particular past time and place, and adapting those ideas into new problems. 

It’s very difficult to do this well. Here are some ways I’ve seen the use of philosophy’s history go wrong. One is where you simply don’t distinguish your mutative plundering of philosophy’s history strongly enough from straight scholarship. So readers will fault you for historical mistakes, when you’re not actually interpreting and explaining an idea in its original context, but instead adapting an idea to a new context. Another problem is where you mutate your source philosopher too much, or have a skewed version of them that doesn’t even capture their initial concept. 

An intriguing way to use the history of philosophy is as a foil for a broader investigation that you want to put in dialogue with a contemporary issue. I’ve been reading Graham Priest’s book, Beyond the Limits of Thought, over the last few days. And his early chapters explore a variety of philosophers from the tradition’s history, looking for a particular kind of contradiction, identifying a contradiction which indicates a limit to what can be conceived. He gets intriguing results regarding this problem from the historical figures from which he draws, but some other historical engagements can get in the way of his larger goals.

Medieval philosophers (especially those with
freakishly long fingers) are frequently forgotten
or marginalized in contemporary practice.

In particular, I find that his explorations of historical figures sometimes get bogged down in disproving the truth of these figures’ arguments. I noticed this especially with his treatment of some Medieval philosophers. For example, he discusses an intriguing idea in the work of Nicolas of Cusa: that the nature of God is inexpressible because human language is of a kind of being that is so different from God, it’s inadequate to God’s existence. So an apparent contradiction would appear at the limit of expression: we discuss and think about God, but God’s nature is itself inexpressible. 

Priest takes too fast a swipe at Nicolas’ argument, essentially missing the most interesting concept that he developed: the equivocity of being. Priest very summarily dismisses the idea that the means of understanding a body must be of the same kind of being as that body: length doesn’t have to be long. But the ontological concept underlying Nicolas’ vision of a negative theology doesn’t reduce to such a simple idea as this, which is just an analogy in the original text. Nicolas’ idea is that God subsists in an entirely different manner of being than humans. We’re material, spatial, temporal in nature. God would be none of these things, but subsist in a mode of existence that’s entirely foreign to possible human experience and thought. Following this concept through leads one to conceive of a genuinely alien existence, and opens an intriguing path in philosophical thinking. It’s not really the path I’m working on myself, but Nicolas deserves credit. 

Priest doesn’t give him that credit when he blasts through this argument. I have no problem with Priest’s mining Nicolas for an example of a contradiction manifesting a limit point of human thought, and analyzing Nicolas to uncover the logical structure of that contradiction.* But the use of the history of philosophy must have some fidelity and respect to the thinker and the context of his time. We must not mutate a concept too much, or ride over it too haphazardly. Otherwise, instead of updating and revitalizing the thought of a philosopher, we trample over them in the service of our own purpose.

* Because Priest developed dialetheic logic, he can analyze the logical structure of a contradiction as a truth. Such logic accepts that there can be logically consistent true contradictions. The idea is very controversial, and counter-intuitive to many. But logic is a tool for systematizing and regulating thought. We can make whatever rules for a symbolic logic as we wish, as long as we’re careful enough to make a properly functional logic, able to build formulae and arguments. 

Creep on Creeping On: The Challenge of Daily Life, Research Time, 27/07/2013

One of the late chapters of Jean-Louis Dessalles’ Why We Talk discusses how language works in argumentation, and what we can learn about language’s origins from its argumentative function. This section should be gold mine for philosophical applications, because so much of philosophy of language over the last hundred years has been based on analyzing propositions as the building blocks of arguments.

And I was sadly disappointed for traditional philosophy once again. The problem is a matter of logical rigidity, or rather the rigidity of philosophical logic. Dessalles considers, as an example of the worldly phenomenon of arguing, a conflict over whether some proposition is true. That is, one person is arguing for proposition F, the other for proposition Not-F. A fairly simple matter of marshalling evidence of one over the other. Then he introduces a very strange (for philosophy) idea. If the question of F or Not-F isn’t actually interesting to the people having an argument, the truth of F becomes irrelevant. And as far as understanding that worldly situation, F and not-F wouldn’t have a truth value. They’d be neither true nor false nor meaningless. Just indifferent.

This way of thinking doesn’t quite jive with the logic we learn in introductory philosophy classes. When we learn logic, we’re taught clearly that every statement is either true or false or nonsense, and that logic is, in its practical application, about analyzing statements about the world to understand their precise truth value: the conditions by which the statement can be true. 

Graham Priest has become something of a philosophical hero
to me, because his inventions of multiple logical systems that
put aside typically intuitive logical rules made mathematical
logic more creative than it's ever been since Russell and
Whitehead. He should be remembered with Aristotle, Russell,
and Kripke as humanity's greatest logicians.

Alternatives to this black-and-white logical system were first seriously developed only in the late 20th century by Graham Priest. Of all the philosophers who practiced in the last hundred years, and who are still alive today, I probably stand most in awe of Priest. Priest first gained notoriety (some more philosophically conservative would say he became notorious) for developing what is called a paraconsistent logic. A symbolic logic whose rules allowed contradictory propositions (A and Not-A) to be true. It blatantly flies in the face of everything that was taken for granted, to be so obviously true that only a fool would question it. Logicians and mathematicians have worked on paraconsistent logics over the years, but Priest put the most effort into them. By demonstrating that you can build a logical system that was valid, workable, and practically valuable, that also stripped away all the intuitively basic rules of logic traditionally conceived, he opened up new possibilities for creativity in mathematical logic. These possibilities were not even considered before Priest’s popularization, were not even really thinkable by most people.

Symbolic logic isn’t my strong suit. I can teach it at the introductory level in a philosophy department if I have to, but the student evaluations won’t be the best, and all the computer science students taking the course for an easy mark will make fun of me the entire time. That’s why I stand in awe of Priest’s achievement. He introduced and popularized new directions in a field of philosophy where only one direction was ever conceived as even making sense at all.

These days, if a philosopher wants to do something absolutely weird with logic, he can just refer to Graham Priest as a precedent. Any peer reviewer who would otherwise stand up for the traditional logic of the law of non-contradiction, reductio ad absurdum, the law of the excluded middle, and modus ponens just has to drop his rage. ‘Well, if he’s appealing to Priest as a precedent, then I guess I can grant his dropping all these basic rules and inventing a bunch of different ones.’ That makes his achievement all the more impressive. Before Graham Priest became The Graham Priest, there was no Graham Priest to refer to!