Hegel Boot Camp and grappling with Reason

On Mike Roberts's blog The Next Recession (arguing that the most important factor driving the current crisis in capitalism is the tendential fall in the rate of profit/LTRFP), there is a lively discussion in progress taking its starting point in the misrepresentations of Marx and his ideas perpetrated by Marxists without Marx such as Michael Heinrich and his sponsors the Monthly Review group. The discussion has ranged well beyond Heinrich and his shallow work and moved on to important differences between serious Marxist economists. These differences include the approach to fundamentals of scientific inquiry, which induced me to make the following proposal for a Hegel Boot Camp to bring all would-be Marxists up to speed on the Hegelian foundations of Marx's work:

Well, I’d like to send everybody here on a summer boot camp to work through Hegel’s Logic together.

Programme:
Prepare by reading the lot — Part One, Objective Logic, Book One: Being, Book Two: Essence; Part Two, Subjective Logic: The Concept.

Daily routine: participants take turns presenting papers in plenum, followed by group sessions. Morning and afternoon same story. Evening free form social hive buzzing over day’s harvest.

Expected course of events:
First week, “Being”: leads up to dissolution of Kant’s mind-forged manacles and Saturday night dance and barbecue round the bonfire of the Antinomies.
Second week, “Essence”: leads up to acknowledgment of contradiction as fundamental and inescapable ground of knowledge, thought and being. Dissolution of “induction” as a possible source of knowledge ;-)
Third week, “The Concept”: leads up to acknowledgment that Kant’s a priori insight was a damn sight more powerful than he ever imagined ;-) , and that Hegel didn’t exactly stand him on his feet regarding this but rather blew open the gates of concrete and steel that he misused the antinomies to construct in the path of scientific and philosophical inquiry.
Fourth week, Science and Philosophy: papers and discussion on Anti-Dühring, Dialectics of Nature, Empirio-Criticism, and free choice topics. Purpose: to digest general methodological consequences of weeks one to three.
Fifth and final week, Economics and Politics: “Capital” and Marx’s and Engels’s trajectory from the 1840s using the methodological foundations and consequences thrashed out previously.

After such a learning experience our present discussion would be much less of a mess. Fewer misunderstandings and grabbing the wrong end of sticks. Because everyone would have a much better grasp of criteria for scientific validity in general, and of Marx’s understanding of scientific procedure in particular.

For instance, we wouldn’t be sloshing around in the dark in an Arctic quagmire trying to wallop each other with cudgels labelled “induction” or “inevitability”. We’d have a much better idea of what Marx considered his categories of the theory of capitalism to be, as he presented their unfolding and development from the simplest “cell” of economics, the commodity, into the most advanced organism the capitalist mode of production could generate – the credit system.

There’s a technology of thought as well as machines, and except for a very few exceptions (Boolean logic, for instance) it’s been stagnating since 1848. The suppression of Hegel’s revolutionary advances on Kant, and Marx’s revolutionary advances on Hegel has been much more effective in crushing progress in thought than even the institutional and legal instruments of patents and copyright have been in crushing progress in material technology and culture.

As I’ve written earlier, there’s a difference between the collapse of capital as a mechanism of production and circulation (the immanent, ideal, “mathematical”, pure, deductive, theoretical, whatever aspect) and the collapse of capitalism as a social formation, a mode of production. Capital is a process involving dead elements of completed labour. Capitalism is a social formation composed of living human producers caught up in the capital process. Living labour trying to orient itself and navigate a violent ocean using alien instruments in a ship it has been forced to build to an alien design.

The better we understand the design of this ship Capital, and the currents swirling under it, and the strengths and weaknesses of its boiler and hull, and the way it is being sailed, the easier it is for us to mutiny, seize it and expel the capitalists from the bridge, sail it into calmer waters, and carry out a complete refit to our own design for our own ends.

This discussion is not just about Economics, it’s not even just about Political Economy. It’s about understanding political economy in the context of human society and history in general. And while digging into what Marx actually wrote is a sine qua non for being able to do this, and consequently a huge benefit emerging from this discussion of Heinrich and his distortions of what Marx actually wrote, we mustn’t stop there or we’ll just end up being so many clever dick Jack Horners admiring the plums our thumbs have pulled out of the pudding and pie. We have to understand why he wrote it, and how he was able to write it, and in what circumstances, both material and immaterial.

This is the challenge of social-historical practice, of thinking politics, and it is the challenge that would make our Hegel boot camp into a more exciting intellectual experience than most of us might imagine. Hegel is no agnostic, unlike Kant. He is after the Truth and won’t rest till he can grasp it, judging the correlation between ideas, reality and experience. And once you are in the hunt for the truth, you’re hooked: “das einzig konsequente Mittel gegen die Vernunft ist, sich mit ihr gar nicht einzulassen” (“the only consistent way to fight reason is not to engage with her at all”).

Andrew Kliman was good enough to comment on this:

I don’t think Morph’s comments sufficiently appreciate the differences between (a) philosophical knowledge of the kind that Hegel sought, (b) the kind of knowledge that Marx understood the LTFRP as providing, and (c) what people are engaged in when they make inductive inferences, which is not knowledge-acquisition. AFAICS, Hegel was saying that philosophy needed its own methods, not that other methods are incorrect in their own spheres.

and I responded:

Thanks for “engaging with reason” ;-)  We shouldn’t forget that our Reason is not just thundering in revolt, but is also Red in tooth and claw!
Hegel was concerned with the processes of thought and logic in relation to the truth. The energy with which he explored the foundations of every element involved in this is unexampled – his intensity is on a par with Marx’s and I’m not exaggerating. But it was a different field and more in thought than reality – although once he came to a conclusion he applied what he had learned in more applied fields of knowledge. So I think Andrew K needs to be more specific about “philosophical knowledge” before we can start comparing. But let’s say that Hegel sought the ultimate foundations of knowledge, continuing and developing Kant’s almost equally ferocious and dedicated drive in the same direction.
We can’t single out Marx’s view of the place of the LTFRP and compare it to this. We have to see it in its place in the totality of Marx’s public work, both intellectual and political to make a fair comparison. Marx tackled the whole of Western Philosophy head on as a student, as we know from his doctoral thesis among other things, and came to the conclusion that Hegel, using the whole of this tradition, had found the ultimate foundations of knowledge as far as they could be discovered using an idealist perspective. From then on Marx applied himself to continuing and developing Hegel’s revolutionary work on a materialist basis – the dialectical aspect of Marx’s work coming in from Hegel’s fundamental solutions of the problems of thought, which Marx had no reason to reject or modify, except as regards their roots in the spirit. We know this from his comments in the correspondence with Engels regarding the use he made of Hegel’s logic. (And as we also know, Marx never regarded anything as correct unless it arose from first principles, and he applied first principles everywhere and always, with a speed and sure-handedness that comes from long practice that makes it hard to spot sometimes).
So Andrew’s distinction between Marx/LTFRP and Hegel’s search for philosophical knowledge doesn’t really hold water. Marx was criticizing a whole mode of production, a whole civilization, and this is a very general agenda that has clear parallels with Hegel’s criticism of all hitherto practised philosophy, especially given Hegel’s extremely broad and inclusive view of philosophy as including thought and human practice – maybe I should have mentioned the Phenomenology or brought it in as part of the preparatory reading for my boot camp to make this clear.
As for inductive inferences not being knowledge acquisition this is nothing but verbal wand-play. I brought in induction in a slighting (not sleighting ;-) ) way because all induction is based on principles and axioms that can only be teased out deductively. This is the inescapable a priori of thought so to say, the revolutionary insight Hegel acknowledged in Kant, and an insight that freed up Marx to pursue such a ferociously (again) deductive method in his study of capital.
We could compare it to the gravitational power of a black hole – the deductive theoretical black hole of Capital centred on the commodity and the value theory sucking astronomical quantities of inductive empirical material into its orbit (eg the material on the 10-hours day, primitive capitalist accumulation and all the parliamentary Blue Books). Only I won’t, because we’d have to invert the whole metaphor and turn a black abysmal Inferno of a black hole into a Paradiso of clarity and light.

"Embodied Cognition" -- empirio-criticism rides again

An article in Scientific American on "Embodied Cognition" prompted a commenter to declare: "The phrase "embodied simulation" is confusing." I agreed and added the following comment as a rider to a previous comment I made referring to Lenin's book on empirio-criticism:

jayjacobus is right about the confusion. There's an interplay between reality and perception of it, and perception itself is a reality, so we have perceptions of perception. It's like consciousness and self-consciousness, and this relationship has been a central problem for philosophy. One of the most primitive responses has been to invent a previous cause, and stop the infinite regression by calling some given cause final or ultimate or prime or whatever. This "embodied simulation" nonsense is the same kind of thing - what it doesn't do is answer the question of reality, ie what is being simulated.
This is a philosophical perpetuum mobile that pretends it isn't. 
Now Kant was smart, so he stopped his infinite regression pain by claiming that the ultimate ground for everything was ultimately unknowable, which was the agnostic thing to do. Hegel was smarter but far less diplomatic, and said "look, reality and our perception of it is full of contradictions, live with it", and moved beyond Kant, opening the way for Marx to move beyond the whole supernatural 'perception/consciousness/thought first' approach. 
For empirical beings, we are very attached to abstract ideas. The reason is simple - we process continuous empirical reality including ourselves using discrete abstract reflections of it in thought. So if you want to call this processing 'simulation', be my guest. Ditto if you want to be empirical by calling it 'embodied'. Well done. Which leaves us as bodies that think. Square one.
Moving in a world of discrete, abstract reflection our mirror minds naturally assume everything is discrete and abstract as soon as it thinks about it, except that the basic presupposition for our survival in reality is concrete continuity. And since survival is opportunistic and iconoclastic, we survive in reality at the expense of broken intellectual dogma, icons and fetishes. 
This drama is entertainingly embodied for me in Lucretius's great Latin poem On the Nature of Things (De rerum natura), and in Hegel's two great works The Phenomenology of the Spirit and The Science of Logic. These are guaranteed pre-Marxist so clear of any ideological tarring and feathering that anything written after 1848 might risk. For a scientific mind they are immensely rewarding, and even a short dip is very invigorating!

Science, reason and bad philosophy

Aimee Whitcroft blogs about rational discussion, aka science, at  http://sciblogs.co.nz/misc-ience/2012/10/09/no-actually-everyone-is-not-entitled-to-their-opinion/  (includes a link to the original blog location) and argues that some opinions are better than others. She doesn't go too deeply into how better opinions are validated, however, so I added the following comment, which gave me the opportunity to quote an astonishingly refreshing passage from an article on quantum physics in last month's Scientific American on why quantum obscurantism is an ideological artefact of bad (bourgeois) philosophy:

The problem is that all formally incontrovertible proofs are based on axioms that can’t be formally proven. So you can argue till you’re blue in the face and never satisfy the ideological sceptic who demands absolute proof.

What it comes down to is a combination of material empirical demonstrations and serious debate of a principled kind. And more often than not debate will equal struggle or even war.

So all truth is fundamentally institutional, rooted in people organized in society.

Which means it has to be fought for and defended in institutional ways, ie using social pressures such as armed force (the queasy might prefer the euphemistic terms 'laws' or 'government').

The litmus test here is the understanding of 'serious'. A frivolous or deliberately obscurantist opponent can’t be talked out of a mistaken position. Rationality won’t bite. Jews, gypsies and socialists will be incinerated if the fascists aren’t removed from power by force.

So I hope Patrick Stokes adds a few words about institutional clout to his riff on "you’re entitled to what you can argue for".

Hegel was well aware of all this as he watched the French Revolution changing the institutional foundations of truth, and he grasped the nettle and accounted for this in his philosophy. The World Spirit and the Spirit of the Age went on to don new socialist personas soon afterwards, however, so 'serious' bourgeois philosophy stopped dead with Kant, ie turned into its opposite and became frivolous and obscurantist.

Which left serious (no quotes) science in bourgeois society groping around in Plato’s cave so to speak.

An article in Scientific American special issue September 2012 by David Deutsch and Artur Ekert (“Beyond the quantum horizon”) lays the blame for the fumbling confusion entangling the quantum field squarely on "bad philosophy".

I’ll leave you with the relevant chunk of the section "Beyond Bad Philosophy":

"Erwin Schrödinger, who discovered quantum theory’s defining equation, once warned a lecture audience that what he was about to say might be considered insane. He went on to explain that when his famous equation describes different histories of a particle, those are "not alternatives but all really happen simultaneously." Eminent scientists going off the rails is not unknown, but this 1933 Nobelist was merely making what should have been a modest claim: that the equation for which he had been awarded the prize was a true description of the facts. Schrödinger felt the need to be defensive not because he had interpreted his equation irrationally but precisely because he had not.

"How could such an apparently innocuous claim ever have been considered outlandish? It was because the majority of physicists had succumbed to bad philosophy: philosophical doctrines that actively hindered the acquisition of other knowledge. Philosophy and fundamental physics are so closely connected—despite numerous claims to the contrary from both fields—that when the philosophical mainstream took a steep nosedive during the first decades of the 20th century, it dragged parts of physics down with it.

"The culprits were doctrines such as logical positivism ('If it’s not verifiable by experiment, it’s meaningless'), instrumentalism ('If the predictions work, why worry about what brings them about?') and philosophical relativism ('Statements can’t be objectively true or false, only legitimized or delegitimized by a particular culture'). The damage was done by what they had in common: denial of realism, the commonsense philosophical position that the physical world exists and that the methods of science can glean knowledge about it.

"It was in that philosophical atmosphere that physicist Niels Bohr developed an influential interpretation of quantum theory that denied the possibility of speaking of phenomena as existing objectively. One was not permitted to ask what values physical variables had while not being observed (such as halfway through a quantum computation). Physicists who, by the nature of their calling, could not help wanting to ask, tried not to. Most of them went on to train their students not to. The most advanced theory in the most fundamental of the sciences was deemed to be stridently contradicting the very existence of truth, explanation and physical reality."

A short reading list

On a discussion list DO wrote the following:

"The sapient brain continues to evolve, and teaching methods continue
to improve, but the underlying hypothesis of traditional liberalism
(John Locke & Voltaire), and of Marxism, that the human brain is a
blank slate or general-purpose computer waiting to be programmed or re-
programmed, is biologically preposterous."

And  I replied:

Locke and Voltaire might be liberals (traditional??) but they're not so much philosophers as popularizers. The blank slate thing is the hallmark of mechanical  materialists - empiricists like Hume and a lot of the enlightenment encyclopedians. It has NOTHING WHATEVER to do with Marx's ideas. Stalin's social-darwinism is related to it, of course, but that has NOTHING WHATEVER to do with Marx's ideas, either. D, I think you should take time off from reading folks like Lakoff and dig into the mother lode of modern ideas. For me this means the following short reading list.

Kant:                 Critique of Pure Reason

Hegel:                Phenomenology of the Spirit

                           Science of Logic

Marx:                The German Ideology - part 1, Feuerbach (including the Hegel section)

                           The Grundrisse 

Too skeletal? ;-)

Add before:   

Machiavelli:     The Prince

Hobbes:            Leviathan

Rousseau:        The Social Contract

Include:

Kant:                  Critiques of Practical Reason, and of Judgment

Marx/Engels:   The Communist Manifesto

Engels:               Anti-Dühring

Marx:                 Capital I-III and Theories of Surplus Value

Add afterwards:

Freud:             The Interpretation of Dreams

Lenin:              The State and Revolution

Trotsky:          The Permanent Revolution, and The Revolution Betrayed

Chomsky:       Cartesian Linguistics        

All of them (and the idea of  evolution which I haven't "crystallized" in a single book recommendation cos that shouldn't be necessary) are concerned with ripping away illusion, false appearances, and exposing the real elements and forces at work in our lives and our world. With the possible semi-empiricist exceptions of Hobbes, Rousseau and Kant. Kant in fact going too far the other way and declaring impossible the unveiling of the hidden depths of the Thing-in-Itself. The least empirical hard-nosed empiricist you can imagine :-)

For a light-hearted frame to all this, I'd recommend Lucretius On the Nature of Things 

"Sed tua me virtus tamen et sperata voluptas
Suavis amicitiae quemvis efferre laborem
Suadet et inducit noctes vigilare serenas
Quaerentem dictis quibus et quo carmine demum
Clara tuae possim praepandere lumina menti
Res quibus occultas penitus convisere possis.
Hunc igitur terrorem animi tenebrasque necessest
Non radii solis neque lucida tela diei
Discutiant, sed naturae species ratioque." 

rounded off by Sartre's Critique de la Raison Dialectique.

The alternative? Being consigned in perpetuity to Intellectual Hell - a dim, draughty, library with hard, splintery, rickety chairs, flickering lamps, traffic noise, machines throbbing and whining at unpredictable frequencies and volumes, musty air, moaning twitching whimpering snivelling readers radiating chill not warmth, with inaccessible and scrapy loudspeakers pouring out Stephen Hawkings reading the collected works of Jacques Lacan. For ever.

Cheers

Chops

On change, growth, Swiss rolls, men and feet

Response to Kenodoxia, who writes:

Friday, March 16, 2007

Dion's foot, again

Nick (see comments to the last post [Dion's foot, Thurs March 15]) is surely right that something important is being done in this example by the usual conception we have of the relationship between a person and his foot. Is this a problem for the Stoics? It may increase the plausibility of their analysis of this example, but does it thereby make it less likely that we will draw a general metaphysical lesson on the basis of a particular case of a man and his foot?

Consider an alternative version of Chrysippus’ story. Imagine Dion as before, but rather than imagining Theon to be that part of Dion which omits only Dion's foot, now assume Theon to be only Dion's foot. Again, Theon is a part of Dion. (True, Theon cannot – in this example – be easily thought of a potential persisting individual in his own right, but this is itself an interesting point to bear in mind for later.) Now, rather than considering what will happen if the foot is removed, we might ask what would remain if everything other than the foot is removed. That is to say, let us remove all that constitutes Dion but which is not also part of Theon. Is what is left Dion or Theon? (It cannot be both.) Now, if we have any intuitive response to this admittedly peculiar position, I think that the more likely answer is that the single disembodied foot before us is more likely to be considered to be Theon than Dion. Now this thought experiment was just like that provided by Chrysippus, but it produces quite the opposite result. In both cases the part discarded is the 'overlap', the portions of Dion which are not shared by Theon, and in both cases what is left was at one time both part of Dion and part of Theon. Indeed, in both cases what is left was once part of Dion and is the whole of Theon.

So if these two examples are relevantly similar, how can we explain the different reactions to them? Chrysippus' original example offers us a picture of two conceivable and viable individuals and focuses on one small part which one has and the other has not: a part which is, we would agree, inessential to the larger individual. (But: Polly Low once pointed out to me that for some people it may be the case that their feet are so essential to their persona (if not their identity as a persisting individual) that for them the removal of a foot may be a more telling loss. What if David Beckham’s right foot were removed?)

It may be suggested that Chrysippus' example is not unfair, indeed that it is perfectly suited to his purposes, since – remember – it appears in the context of a counter to the 'Growing argument'. This argument proceeds precisely by asking if small and apparently minor alterations in material constitution, namely the gradual process of growth or diminution, should in truth be thought to be cases of coming to be or passing away of whole individuals. Chrysippus counters this by generating the conclusion that Dion persists throughout the process of losing a foot, even though there is another candidate for what remains once the foot has been removed – namely Theon. On this account, there is no need for Chrysippus to consider such radical cases as that of my alternative formulation of the story of Dion and Theon. He is not concerned with such radical cases as this, and might well agree that is all that is left at the end of the process is a single foot, then it is in fact reasonable to conclude that Dion has passed away! All that remains is a foot, strangely designated by the name Theon.

But if Chrysippus were to agree to this account, and were therefore to accept that this particular radical case of diminution will count as the passing away of Dion, then a further obvious question arises. Just how much of Dion can we take away without concluding that what is left is not Dion? It may be easy to think that a foot is a non-essential part of a person, but how much could we shave off and still have Dion at the end? If the Academics were to press this point then it is a perfect context for the application of a sorites argument. Now it is possible to ask whether the answer to this question is a matter of specifying in quantitative terms how much could be lost (49%?), or is it better to think about the particular parts which can be lost? (For example: perhaps feet, hands, even limbs are eliminable, but what about heads, hearts, brains and so on?)

Indeed, the Stoics themselves may have produced difficulties for Chrysippus' favoured account. In Sextus Empiricus' discussion of the theories offered by dogmatic philosophers about parts and wholes, he gives us this piece of Stoic theory:

But the Stoics assert that the part is neither other than (ἕτερον) the whole nor the same; for the hand is neither the same as the man (for it is not a man) nor other than the man for it is included in the conception of the man as man (σὺν αὐτῇ γὰρ ὁ ἄνθρωπος νοεῖται ἄνθρωπος).

SE M 9.336, trans. R.G. Bury

The first part of this is straightforward. A hand is not the same as a man (presumably the man whose hand it is) since one is a hand and the other is a man. But there is of course a link between hands and men, and this is what the Stoics try to characterise in the second half of this text. A hand is not 'different from' a man, since when you think of a man you think of a man with hands. Hands are not, in other words, merely optional accessories for humans.

But the Stoics do not make so clear exactly what this last claim amounts to. Does it, for example, make 'handed-ness' an essential property of a human, so that anything which does not have hands cannot be a human? I assume that the Stoics would have known of cases of people losing their hands in accidents or in battle, and if so then they would have to give an account which allows these too to count as humans. Perhaps 'having at some point had hands' is an essential characteristic of a human.

In any case, what does this mean for Dion and his foot? It might explain why it is a foot which is removed rather than a hand, since the footless Dion is not on anyone's account in danger of failing to be a human. And a foot on its own is on no-one’s account likely to be thought of as an individual. Having feet, after all, is not a peculiar characteristic of humans as having hands might perhaps be thought to be; lots of creatures have feet, but not many have hands.

***************************

Choppa's response:

First, a thank you for getting me to look up "sorites" in "sorites argument", which led me to the wonderful entry on teuэ- at Bartleby:

http://www.bartleby.com/61/roots/IE531.html

relating thigh, thousand, thumb, butter, tumescent, quark, and creosote.

So, when is pile not a pile, a beard not a beard, a man not a man?

It's interesting to me that the practical engineer and mathematician Archimedes had a description of this kind of movement - growth and negative growth - in his pre-calculus. "The greatest mathematician of antiquity, Archimedes of Syracuse, displayed two natures, for he tempered the strong transcendental imagination of Plato with the meticulously correct procedure of Euclid." (C.Boyer, History of the Calculus, Dover 1959:48) Further: "In the seventeenth century, however, the infinitesimal and kinetic methods of Archimedes were made the basis of the differential and fluxionary forms of the calculus." (ibid:59) To calculate changing surfaces and volumes he imagined them as made up of "mathematical atoms" or thin sheets and pursued their interaction to exhaustion, so to say. BUT Boyer explains, in relation to A's work on the parabolic segment that: "In order to define 4/3 A as the sum of the infinite series, it would have been necessary to develop the general concept of real number. Greek mathematicians did not possess this, so that for them there was always a gap between the real (finite) and the ideal (infinite).
"It is not strictly correct therefore to speak of Archimedes' geometrical procedure as a passage to the limit, for the essential part of the definition of the limit is the infinite sequence." (ibid:53)
So not even Archimedes was able to give a clear and explicit answer to the problems raised by Zeno's paradoxes.
"The notion of the limit of an infinite series is essential for the clarification of the paradoxes; but Greek mathematicians (including Archimedes) excluded the infinite from their reasoning. The reasons for this ban are obvious: intuition could at the time afford no clear picture of it, and it had as yet no logical basis. The latter difficulty having been removed in the nineteenth century and the former now being considered irrelevant, the concept of infinity has been admitted freely into mathematics." (ibid)

Boyer emphasizes that in his "Method" Archimedes "realized that it is advantageous to have a preliminary notion of the result before carrying through a deductive geometrical demonstration..." (ibid:49)

And this is where Hegel's disembowelling of Kant's antinomical dragons starts. A notion of the Whole, that works (eppur si muove), of movement, change, growth, in a word of the interaction of Being and Nothing generating Becoming, the full understanding of which is an understanding of the Whole and all its parts.

If we take a subsidiary Whole (one considered as such just for the illustration) and instead of calling it Dion or Swiss Roll or Capital we call it A, then we should perhaps not exclude from our intuitive consideration of it the existence of other similar As, as this helps us get a "preliminary notion of the result" before our analysis.

Then we add or subtract a bit to A, leading to positive or negative growth of some kind. So we can call the result A', with the addition of an absolute bit (plus or minus) to the original entity.

Boyer mentions Democritus and the Platonic school "groping" towards "infinitesimal considerations", and this is what happens here - a series of A', A'', A'' etc arises, and regardless of the size of the [increment] sooner or later the quantitative change turns qualitative, and A becomes different from the other As not merely in degree but in kind.

And here the collective judgment of those considering the matter comes in. Consensus in human communities rules, and is codified sooner or later into habits, concepts, laws, and given linguistic expression, and proceeds dialectically in conflict or harmony with the consensus results of other communities to generalize itself or shrivel.

The Greeks reached no consensus about the growth problem, and the gap between the real and the ideal remained unbridgeable. The potential solution of fusing "Archimedes" with "Democritus" never happened. Even Descartes insisted on having an unbridgeable. And Kant.

And even today most maths teachers go by rote and flog the algorithm rather than visualize the result and give the maths its head.

Perhaps our philosophical unbridgeable today has moved on to the gap between our behaviour as humanity and our behaviour as human individuals or limited collectives (states, say).

The foot of a man is a more drastic example than a slice of Swiss Roll. Perhaps the more drastic the better and we should present Dion with his balls chopped off. Popular culture grapples with these problems asking when is a man not a man in terms of man-like creatures - replicants, zombies, vampires, aliens... Political culture grapples with them by adding or subtracting various defining bits (veils, hair, sex organs, skin colour, ethnic or geographical origin, missing or damaged chromosomes or genes) and sanctioning perceived non-As. History grapples with them by making certain As work side-by-side with "their" non-As for common goals and discover their original definitions were wrong.

For me now, the question of What bit of Which (Foot of Dion, Slice of Swiss Roll, Surplus Value of Capital) takes on a new relevance. Because what's at issue is understanding ourselves and what we become and how.