Essay Ten

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I am publishing here several of Guy Robinson's Essays. One or two of them had until recently been posted at Guy's site, which no longer exists. In my opinion, Guy is one of the few Marxist Philosophers whose work is genuinely worth reading. Indeed, I'd go much further: I cannot praise his book, Philosophy and Mystification (Fordham University Press, 2003), too highly; it seems to me that this is how Marxist Philosophy should be done.

I only encountered Guy's work in 2005, but I soon saw that he had anticipated several of my own ideas -- except he manages to express in two paragraphs what it takes me several pages to say! In this case, Guy anticipated some of what I have to say about 'the process of abstraction' in Essay Three Part One.

Unlike the vast bulk of material that claims to be Marxist (particularly that which has been produced by academics), Guy's work is a model of clarity. It is no accident, therefore, to see Guy writing in the Wittgensteinian tradition.

[Many on the left think Wittgenstein was a conservative mystic. I have comprehensively refuted that idea here. Moreover, Guy's work alone is testimony to the fact that Wittgenstein's work is in fact conducive to Historical Materialism.]

This material has been posted here with the permission of his son, but no one should assume that Guy would have agreed with any of the views expressed at this site -- other than those already contained in his essays. Nor should anyone assume that I agree with everything Guy says.

I have re-formatted these essays to agree with the conventions adopted at this site; spelling has been altered to conform to UK English. In addition, I have corrected a handful of minor typos and added several links. I have also highlighted any changes made to the original text by the use of curly brackets. [These are modifications that any sub-editor or proof-reader would have recommended.]

This essay comprises Chapter Seven of Guy's second book, Philosophy and Demystification, which has yet to find a publisher. Other chapters from this book can be accessed here.

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Naturally, the first question is how I propose to get three such unlikely bedfellows together into the one bed. The answer to that deliberately laid puzzle will come out as we give close attention to a passage in the Preface to Newton's Principia which sets out a view of the foundation of geometry which locates it in human practices. That view was so radical and so subversive of the world-picture which was being assembled in Newton's time and has prevailed subsequently, that the very passage became invisible to Newton's contemporaries and to his successors. They made no remark on it nor even any attempt to explain it away but simply averted their eyes in their eagerness to recruit his work to the mechanical world-picture that was being put together to reflect the new era emerging in Western Europe -- a picture intended to displace the scholastic world-view associated with the feudal social order that was itself being displaced.

The program of the 17^th century philosophers was to show that the features of the world confronting humans -- including human institutions -- were the work of Nature and not of God and were to be studied through science and secular philosophy, not theology. The philosophers working to that agenda, including some of our contemporaries -- such as the sociobiologists -- were incapable of making a serious assessment of that ambition to explain everything as ordained by Nature, and therefore failed to take in Newton's radical and subversive suggestion that geometry, which has served as a paradigm of knowledge at its most external, necessary and eternal, had its origin and foundation in human practices. And even if they had gone on to accept that human practices were the origin of any of those things, they would no doubt have tried to take the sting out of that suggestion by going on to present those practices themselves as the result of evolution or of that old favorite, 'human nature'. That is, they would have tried to drive the element of historical contingency out of the picture and to absorb humanity and human practices into what they saw as the realm of 'scientific and natural necessity'.

We will have to look not only at the question of how the philosophers and others managed to convince themselves of the externality of what in fact had its origins in human practices, but we need to go on to ask ourselves why it was that they seemed so determined to do so and why what has been called "the mechanical world-view" still has such a hold that it can motivate the attempt to explain those practices and that history as having been determined by biological necessity.

Though Newton's view of the origins and foundations of geometry in what he called "mechanical practice" (by which he meant the practice of mechanics) was clearly not the inspiration for the corresponding views of both Marx and Wittgenstein, it can be accommodated comfortably within the perspective put forward by Marx on the basis of a broad analysis of human historical development and the principles of understanding that development. It could even have served him as an excellent example of those human accomplishments and creations that humanity tends to see not as its own work but as externally imposed and eternally existing -- as geometry has traditionally been seen. That perspective of Marx's for which Newton could have provided an illustration is expressed most tersely and forthrightly in his 8th Thesis on Feuerbach:

"Social life is essentially practical. All mysteries which mislead theory into mysticism find their rational solution in human practice and in the comprehension of that practice."

He could equally have said that "Human life is essentially practical" and added that human life and practice are also essentially historical -- in that they develop out of the life and practice of the preceding generations. The practices which Newton, Marx and Wittgenstein are invoking are ones that grow out of the history of human social life and human struggle with the material world. In the course of that history there is a development of aims and aspirations which go on to generate new practices and new skills which make possible new aims -- in an endless cycle of development.

Wittgenstein came to an analogous view in relation to language, logic and mathematics generally, through his careful analysis of what one could call the "mysticism" one is driven to in trying to give an account of them on the assumption that they are externally existing entities, or that they reflected constraints or necessities that had their source outside of humanity and human life. Rejecting that picture he said in the Philosophical Investigations:

"What has to be accepted, the given, is -- so one could say -- forms of life." [1953 edition p.226. Italic emphasis in the original -- RL.]

And his constant emphasis on the practice of mathematicians as explaining the features of mathematics led to him being labeled "conventionalist" by Michael Dummett (though it has never been clear to me what that particular sin amounts to.) Of course one has to supplement Wittgenstein's formulation with the observation that the "forms of life" themselves are not given absolutely and externally, but are given historically to each generation by the preceding generations which have developed their life, language, institutions, skills and physical environment to that point.

None of those things are external, timeless givens but are the product of human activity, human practice and human history. A form of life has, of course, a source that is external to any given generation. The members of each generation will have, as children, been inducted into the community and its practices by the previous generation -- their parents, teachers, mentors and older contemporaries. Some of the things given by one generation to the next are embodied in practices, skills and institutions; others will have been externalized in the form of tools, houses, cleared fields, and so forth. Though we should remember that even those externalized products are what they are only in relation to existing or historical practices. A tool is not, in itself and abstractly a tool but is only a tool in relation to certain existing or historical practices. And the same goes for housing, clothing, fences, bridges, boats or whatever has been produced by human wit and skill. They are all only the specific kind of thing they are in the light of associated practices of use. Even a word or a symbol is what it is and gets what life it has from the set of practices in which it is embedded.

However, we are getting away from Newton here and his view of the origin and foundation of geometry in what he calls "mechanical practice". We need to look at the reasoning in that short passage of the Principia and we need also to look at the historical reasons why the philosophers of his time were unable to take in its message and had, in effect, to write the passage out of his famous work -- though the Principia was otherwise so influential. When we have looked at those historical reasons we can see that the whole inability of Newton's contemporaries and successors to take in his message will {suffice} as a paradigm example of what Wittgenstein called "being held captive by a picture".

When we have done all that, I want to add as a supplement supporting Newton's view of geometry, a discovery of my own about the meaning of Euclid's definition of a straight line -- a definition which seems to have baffled commentators for the best part of two millennia. Since I don't regard myself as more intelligent than all those commentators on Euclid and certainly not a better geometer, it is worth reflecting on the reasons why that definition of Euclid's was unintelligible to so many for so long and how it was that I was able to see not only the sense of it, but that it was the only definition which could have an actual function in geometry. Those reasons for its apparent unintelligibility for so long turn out also to be a captivity by that same picture which prevented the understanding and acceptance of Newton's reasoning. The reason why I was able to see the sense of Euclid's definition was that I was able to relate it to a practice and then to various other practices. And the reason for this is that I had a practical relation to geometry through having worked as a draftsman for a while.

We will look at that captivity by a picture and a program of explanation shortly but first we need to look at Newton's reasoning behind that subversive view of his about the foundations of geometry. There are rich pickings and much to be learned from a careful consideration of various parts of Newton's Principia, but here we are going to confine ourselves to that section of the Preface where, very correctly and properly, he begins with a discussion of the nature of the mathematics which is going to form the basis for a work which he called The Mathematical Principles of the Philosophy of Nature. He aims in that section to make the principles of that mathematics clear as a starting point, and he does so from a point of view which we should note is diametrically opposed to that of Bertrand Russell in his similarly named Principia Mathematica.

Herewith the long withheld section of the Preface, in which one needs to be aware that when Newton uses the words "description" and "describe" he is referring not (as we might) to words and definitions, but rather to the actions of drawing straight lines and circles.

"...the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn, for it requires the learner be first taught to describe (i.e. to draw) these accurately before he enters upon geometry, then it shows how by these operations problems may be solved. To describe right lines and circles are problems, but not geometrical problems. The solution to these problems is required from mechanics, and by geometry the use of them, when so solved, is shown; and it is the glory of geometry that from those few principles brought from without, (my italics -- GR) it is able to produce so many things. Therefore geometry is founded in mechanical practice and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring. But since the manual arts (again, my italics -- GR) are chiefly employed in the moving of bodies, it happens that geometry is commonly referred to their magnitude, and mechanics to their motion." [Preface to Principia -- RL]

Geometry is here presented as a practice and a technique for solving certain sorts of problems, one that grows out of reflection on an earlier practice and technique of fitting things and moving things and performing certain sorts of physical operations. To see the radical subversiveness of this perspective, we have to understand that geometry has been the paradigm for philosophers from Plato to the modern era, of knowledge of something that stood outside of humanity, and was objective and eternal, quasi-divine, you might say -- there, in some heaven to be contemplated by humans only from afar. There was, of course, a problem of where this something was supposed to reside and what sort of existence it was meant to have, as well as the problem of how we mere humans could come to have knowledge of it. That non-problem disappears as soon as we join Newton and root geometry in human practices instead of trying to derive it from some mythical source in the heavens.

All of the problems generated by trying to make the sources and foundations external and timeless turn out to be entirely intractable and the answers that were traditionally offered, entirely unconvincing. This should have suggested that there was something wrong with the assumption that generated the problems, but it didn't. Plato constructed the world of Forms as a locus to house this external something that geometry was supposed to study, but he then was stuck with the problem of how we were meant to have any knowledge of that construction of his that was itself located nowhere in the known world. His answer in the form of the theory of anamnesis -- the recovery of the memory of a pre-birth existence -- only added another layer of mystification and convinced nobody except those who were determined to be convinced. Kant tried to tackle the problem of how the certainty which attaches to geometrical discoveries combines with its application to the physical world about us, a world full of contingency and unpredictability. He hit on the happy solution of making it a condition of our seeing things as "external" that they conform to geometrical principles. However he never gave us an adequate account of how that particular condition came to be imposed on us humans.

My aim has been to undermine the perspective and the assumptions which generate those insoluble problems and in that way not to solve them but to dissolve them, to knock the props from under them. However I have still left two problems to be dealt with: one is to understand how generations have managed to convince themselves that the origins and foundation of geometry lay not in human practices but in some externality, located no one knows where and existing no one knows in what manner, and yet needing to be accessible, though no one knows how, to human knowledge. The other problem is to understand why those generations of philosophers were determined to drive themselves down that thorny cul-de-sac.

To see how those generations contrived to convince themselves that geometry studied something independent and external to humanity we need to look at the way that mathematicians and logicians as well as scientists and other theoreticians deal with their subject matter. They all abstract from the particular and deal only with the form of the relations between concrete things, whether particular physical things or particular beliefs and arguments. That act of abstracting produces something which appears to stand outside of and above the world of particulars from which it is drawn -- the form, the principle, the law -- something which seems entirely more noble and powerful than the grubby and chaotic world of particulars from which it is drawn. From there it is no great step to think of it as independent and prior and even determinative of those particular formations, behaviors, or beliefs of which it is the form, principle or law.

It is no great step, perhaps, but it is one that lands us immediately in mystification because there is no way to describe or understand how those would-be entities produced by abstraction are supposed to produce or determine the constitution and behavior of the concrete and particular things of this world. The relation between principle, form or law and the concrete and particular things of this world can no longer be understood because it has been inverted. In the act of abstracting it is the particular and the concrete that are determinative of and are prior to the form or the law that is drawn from them. We are then asked to invert this relation and see the form or law as determinative of the particulars from which we started. No wonder we can give no account of that relation. We need simply to turn things right side up and locate the source and basis of those abstractions in the concrete things, classifications and practices as do Newton, Marx and Wittgenstein.

Of course, we can learn logic and master its rules and laws, for example, and then use those abstract rules to guide and extend our concrete reasoning and argumentation. In that way the principles and laws would be determinative and prior to our particular reasonings. But if we ask which came first in human history, the laws of logic or human reasoning and argumentation, we know perfectly well that it is the latter and that logic arose out of the study of human reasoning and argumentation that was already taking place. As Locke himself put it (though rather tendentiously) "God was not so sparing of man as to make him barely two legged and leave it to Aristotle to make him rational." (Locke is here teetering on the edge of that Rationalism of which he is regarded as the first serious opponent.)

Logic, of course, we can learn and therefore can make it stand ahead of and be determinative of our particular reasonings. Physical and biological laws enjoy no such advantage. They can't be learned by the bodies and the species that are meant to be 'governed' by them, and that particular metaphor of 'law' is therefore hopelessly misleading. It is in fact impossible to understand what someone may mean by describing those 'laws' or principles as existing independently of and being prior to and determining the particular happenings which exemplify them. They arise only in the human act of abstracting and nowhere else. Determinism is a monster we have created out of our own misunderstandings.

"But mustn’t there be a pre-existing regularity for the theoreticians to discover?" you want to ask. However, my response is to say that that very question involves a return to that mystified notion of 'a regularity' as something existing on its own, standing 'over and above' (as Plato used to put it) in separation from the particular things and happenings from which we have abstracted, something whose existence and relation to those particular things becomes incomprehensible as soon as we separate it from them.

However, it is essential to supplement my claim that it is the acts of abstracting which bring into being the principles, laws, or 'natural kinds'. It is necessary to add that these are not unfettered and arbitrary acts of pure creativity. We humans are not creating the world out of nothing. There is a material world there with which we have to work in creating our laws, principles and typologies -- not to mention our physical artifacts -- and we can make of that world only what it will allow us to make with the skills and conceptual equipment we have at hand at any historical moment. We must not fall into the one-sidedness of the social constructivists or the post-structuralists who seem to attribute absolute and unfettered creativity to human societies. For them we are become as gods, so it seems. If there is no "outside of text" (as the pronouncement goes) it would seem that there would be nothing to shape, limit or veto that "text" and we could make it up arbitrarily according to whim in acts that were like acts of creation ex nihilo. But all that is a fanciful picture and hardly corresponds to the world we know -- a material world which, though it may not contain abstract laws, principles and systems of classification which predetermine our way of grasping it, will quickly distinguish those "texts" which enable us to manipulate and predict and advance our lives -- from those with which nothing useful can be done.

This analysis of the act of abstracting gives us the answer to one of our questions -- the question of how it was that the philosophers of the modern era managed to convince themselves of the 'external' origin and basis for geometry and the other laws, principles and typologies that were in fact generated by those very acts of abstracting. It also goes some way toward answering our second question: why, despite all the difficulties and incoherencies of that way of looking, they persisted in creating for themselves that shadow world of abstract entities that could not be located anywhere and whose nature and relation to the concrete world could not in any way be described. Even Plato gave up on that one and showed Socrates being driven to silence by Zeno in the Parmenides. This unprecedented event takes place as Socrates attempts to explicate the notion of participation (methexis in the Greek) -- a word which Plato has wrenched loose from is normal sense of "taking part" by humans or animals in some action or conspiracy, or even "catching on" to a joke. He then tried to give the word a new sense and a new job -- that of describing the relation between the concrete particular things of this world and the Forms which he placed in some other world. The Parmenides is a record of the failure to provide a new sense for the word and its consequent failure to describe the relation between his abstract world of Forms and the concrete things of the world we live in.

The ease with which the act of abstracting can present itself as the discovery of an abstract entity external to the concrete things from which the abstraction is made, can explain much of the reason why the philosophers persisted despite the horrible difficulties that those abstract entities presented to rational understanding. But there were other reasons for the philosophers' persistence in the face of the difficulties they generated for themselves. Those reasons were related to the way in which philosophy was embedded in the history of European development in that era which marked the transition between the feudal hereditary social order and the new social order based on the market and production for the market. One of the historical tasks of that time was not only the dismantling {of} the feudal hierarchy, a hierarchy which had been presented as divinely ordained in a world-view that they felt also had to be replaced. Beyond that there was the corresponding task of facilitating the new social order whose imperatives and whose rationality were determined by the secular forces of the market. The philosophers of that era took on the job of trying to make sense of and therefore justify that new social order, its dynamic and its canons of rationality in the same way that the scholastic philosophers had tried to make sense of and justify that feudal hierarchy of liege and vassal which stretched from the king to the lowest villein, together with the rights and duties pertaining to each, by describing them as 'ordained by God'.

The new philosophers had no other model to work from and in addition felt they had the need to compete with the scholastic philosophy on its own ground. They looked for something similarly external to, and imposed on humanity to explain and present as rational and necessary the new social relations. They sought to present them as 'natural' -- as arising from 'Nature' in some way. To function in that role, 'Nature' had to be externalized and given quasi-divine status -- to stand above and outside the concrete, material world to govern it and keep it in line. And this provided the core of the second line of motivation to conceive the products of the abstractions of theory as separate and independent entities despite the impossibility of giving any coherent account of the relation between those abstract 'entities' which their conception of explanation required and the concrete world they were meant to explain. In this case they proposed something called 'human nature' as the 'natural' source of the new social relations. This was seen as something timelessly imposed on humanity -- genetically, perhaps and with no historical dimension. This view was a reflection of the fact that in their time there was no sense of the sweep of human history and human development from pre-human forms of the genus homo. This allowed them to attribute totally unreal characteristics to this {...} unrealistically fixed 'human nature'. This whole picture needs to be inverted so that the concrete world and concrete human practices become the explanation of those laws and classifications which have been mystified by being projected outward and given an independent existence.

Explanation by appealing to abstractions conceived as external was the general framework of understanding for which the philosophers wanted to use geometry as a paradigm of certain knowledge with an external and objective source which was God-like in its eternity, authority and its separation from the world. Newton's account of geometry as arising out of human practices posed a subversive threat not only to this use of geometry but to the whole perspective, framework and style of understanding which underpinned their world-view. No wonder they averted their eyes.

I think I have now made good on most of my earlier promises or at least indicated the sort of answers they should get, and it only remains to add my account of the meaning of Euclid's definition of a straight line, an account which I suggest supports, and is supported by, Newton's description of the origins and foundations of geometry as "lying in mechanical practice".

Euclid's definition is at first sight extremely opaque and one has every sympathy for the bafflement of the commentators from ancient times down to the present. He described a straight line as "a line that lies evenly along the points of itself." The commentators from Proclus in the fifth century down to Sir Thomas Heath in the twentieth, were unable to make any serious sense out of that definition or find a place for it in the fabric of geometry. However, they made the job impossible for themselves by trying to tease the sense out of the words of the definition alone and by not looking for a practice to which the words could be related. In a way this is surprising because the only other two definitions of straight line in circulation both related to "mechanical practices". Socrates definition of straight line as one of which "the middle obscures the end" pretty obviously refers to the carpenter's practice of sighting along a plank to test its straightness. But this optical definition has no function within geometry itself where sighting would not be a permitted operation and could not enter into the reasoning by which theorems are established. But most importantly, it could not establish the essential geometrical properties of a straight line that enter into and establish the truth of those theorems.

In addition, it would be necessary first to establish that light travels in straight lines. The very legitimacy of this question implies that we already have a separate concept of straightness for which the sighting along is a test but not a definition. However we should note that the carpenter does not sight along the plank and plane it till "the middle obscures the end" for aesthetic reasons but because of the practical part the plank's straightness plays in his constructions. This is obviously not the "obscuring" of the ends by the middle. So the 'optical' definition fails on two counts -- it is a test and not a definition and it is geometrically useless. More importantly it has no relation to those practices that give geometry both its foundations and its function in human life.

Much the same has to be said about the famous definition: "A straight line is the shortest distance between two points" which has for too long defaced school textbooks. This definition clearly comes from the carpenter's chalk line method of generating straight lines. But the definition even more clearly has no function in geometry, where measurement could not be used to establish whether a line was the shortest and therefore straight. More importantly this putative definition cannot not serve to determine any geometrically relevant properties of straight lines and can therefore not enter into the theorems of geometry.

It is in fact a scandal that this definition has been taught to generations of students who were supposedly being introduced to the rigors of geometrical reasoning and proof, as well as to the idea of an axiomatic system. The "shortest distance" definition subverted the whole enterprise by inserting a lack of rigor right at the start. No theorems could be established on the basis of that definition of straight line, and its substitution for Euclid's own definition undermines his proofs of the most fundamental propositions -- as was pointed out not long after Euclid's time by Zeno of Sidon. But also, analogous to the fact that the sighting constitutes a test not a definition, the chalk line "shortest distance between two points" gives us a method of producing straight lines and not a definition. We have to have some other and separate conception that allows us to call the lines produced in that way 'straight'. To get at that conception -- which is Euclid's -- we have to ask what is the point of straight lines and why do we go to such trouble to make things straight?

Euclid's definition has sense when related to a simple operation and as well, to the point of making things straight. But, beyond this, it needs to be seen to be the only definition that has a function within geometry. It establishes a fundamental property of straight lines without which no theorems could be proved. Having worked briefly as a draughtsman I was able to recognize the meaning of Euclid's definition by reference to an operation that a draftsman would use to check the straightness of a straightedge. The draughtsman would draw a straight line and then rotate the straightedge through 180º and draw another line on top of the first. If and only if the points of the two lines coincide completely ("lie evenly along themselves" as Euclid has it) is the straightedge straight. Unlike the other two definitions, Euclid's has a function in geometry -- it establishes the fundamental property of straight lines that, as the geometricians put it: "Two points determine a straight line." This follows immediately from the definition because of the stipulation in the definition that if two points coincide, so will all of them. It also obviates the need (which Zeno of Sidon felt was necessary to Proposition 1) of Euclid's Elements to assume an axiom to the effect that two straight lines cannot have a common segment. This 'axiom' of Zeno's is also made redundant by Euclid's definition properly understood.

Euclid's definition also relates to and arises out of the function of straight lines in our practical life, and the property which makes them so important to carpenters, builders and others. Things which have been made straight will fit together without gaps. The function of straight lines is precisely to "coincide" -- to fit together without gaps. If we have made them straight, the floorboards fit together, the door fits the frame, the lid fits the box, and so forth. We can, of course, make curves fit together but that is generally a more difficult business and only undertaken for special purposes. It would also create great problems where hinges were involved.

Our concept of straightness does not come out of the air nor is it deposited in our minds by God or by Nature. It arises out of the practical activity of building in stone and wood. One of the objects of building in those materials is to keep out wind and rain. To fulfill that aim the builders would want the stones and the planks to fit snugly together and have the points on the edge of one plank or stone to "lie evenly with" the points on the edge of the other. Once we see that our concept of straightness has its base and origin in the requirements of those practical activities of building, fitting and measuring, the appearance of otherworldliness for geometry and consequent mystery fades and the only thing we are left to wonder at and be in awe of is our own human creativity and ingenuity.

Of course{,} right from the beginning there was a tendency not to recognize that creativity and a consequent tendency to project outward and deify those human creations which then became the objects of an awe of a different sort -- as something thought to be external to humanity and not its own creation. An ancient people in the Lebanon built perfect cubes all over the country that had no practical function because they were closed. Their function was clearly religious and they can be taken as an example of the deification of the things of geometry. And the Egyptians built pyramids. But we can advance beyond that era of idol worship to recognize geometry as a human creation which arises out of human practices and projects.

This analysis of the practical background to Euclid's definition serves to underwrite Newton's view of the origin and foundation of geometry as lying in concrete human practices. Still, we need to go back over the discussion to see what we have accomplished and what remains to be done.

The first thing we need to look at is Newton's equating of the foundation of geometry with its historical origin and pedagogical starting point in certain practical operations. It is hard to offer anything but negative arguments in support of this equation and to ask anyone who wants to separate foundations and starting points, what different sense they wanted to give that much misused and misleading metaphor of 'foundation' and in what do they propose to locate it and how establish its authority? Perhaps we need a word here about foundations and starting points.

Aristotle makes a distinction between what is a starting point (arche) for us in our investigations and what is a starting point 'in itself' and this looks as though this might offer us some way in which a 'foundation' might be distinguished from a "starting point". However, when we look more closely this turns out to involve no more than what the ancients called "analysis" (as opposed to "synthesis") and to consist in the result of successive acts of abstraction and analysis carried on till we can push them no further. A perfect example here would be the Euclidian definition of a straight line which arises out of an examination of the practice and aim of carpenters, masons, draughtsmen and others in checking for, or producing straightness. We can carry that analysis no further and so it becomes a starting point 'in itself' and, if you like, a 'foundation' of geometry. But the analysis we have made cannot be given a life and a being separate from and prior to the practice which is the end point of that analysis and the starting point of our understanding of geometry. In that way, practices can be seen as 'foundational’' starting points because analysis comes to an end there and can proceed no further. Practices become the basis for classification, language, knowledge and truth -- even though there is no sense in which they themselves are true or false -- nor are they fixed and unchanging in the way the traditional 'foundations' were required to be. The practices and the knowledge of different cultures clearly differ from one another but there is no sense in which we can say that one set is 'truer' than another.

I have elsewhere examined Aristotle's arguments for what he considers the deepest laws of being, namely, the Law of Contradiction and the Law of Excluded Middle.¹ The examination (of Metaphysics 1006 a10 et seq.) throws up something pretty interesting. In effect Aristotle's argument rests the authority of those laws on our inability in practice to deny them. That is, we can put together some words and even mouth them, but we can't make them stick because the supposition that the denial makes sense would itself undermine the conditions of any words at all making sense -- and so that assemblage of words purporting to deny the laws cannot themselves make sense. As Wittgenstein would put it: "They cannot be lived." From this we can see that those laws are themselves drawn out of, and founded on the human practices of making distinctions and making sense, of saying one thing and denying another -- and are implicated in our ability to do so.

Everywhere we turn, if we look carefully, we find we are returned to human practices and abilities as the foundation and starting point of things that had been presented to us as requiring foundations that stand outside humanity and human history. This is because we have been following Newton's lead in our questioning and seeing that clarity and understanding require us to reject a whole program and conception of explanation which has proved empty and barren. That program set itself the task of finding foundations which lay outside of human history, to explain and justify human practices and human abilities, skills, and systems of understanding that have in fact been developed in the course of human history. The barrenness and incoherence of that other program lies in its inability to do anything with the so-called 'explanations' that it comes up with. Since the would-be 'foundations' present themselves as 'ultimates' without further explanation, they cannot be the basis of any research program or further investigation. Their claimed function is in fact to bring investigation to a halt at some 'ultimate' explanation. But when we look at those purported explanations, we see that they are entirely without content or use and advance things not at all. This is because there is, and can be, no independent evidence to confirm the existence of those would-be 'ultimates' that are being offered as explanation. They turn out to be no more than a repackaging of the things they are supposed to explain.

I have joined Newton, Marx and Wittgenstein as proponents of a form and a program of explanation that refers back to historical human practices and have offered this as a form of explanation which has substance and can offer insights as well as pointing the way to further investigations. This I wanted to contrast and oppose to that program which almost defines that purported branch of philosophy, metaphysics, a program which seeks to explain the things of this world by deriving them from entities imagined as external to it and to human life, entities that are supposed to be fixed and unchanging. I have gone on to suggest that this purported form of explanation was no more than a sleight-of-hand in which the things to be explained are dressed up, tricked out and handed back to us as 'explanations' that simply cast a veil of mystery over the things to be explained.

That program and those simulated explanations it operates with can have no practical function in human life -- except perhaps the ideological one of convincing us that we are surrounded by fixed, unchangeable and inexplicable necessities and mysterious entities which determine our life and our understanding of the world in which we live and on which we operate. It is here that we can see the ideological function of this framework of thought which it is the aim of Historical Materialism to unmask and sweep away. We have been trying to show that in this enterprise Marx could call on both Wittgenstein and Newton as allies.

1. Chapter 3, 'Following and Formalization' in Philosophy and Mystification (London and New York, 1998, Routledge and in paperback by Fordham University Press, 2003.)

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