Monday, 25 May 2015

The De-struction of Game Theory: Nash Equilibrium and Nietzsche's Invariance

In my Weber-buch I applied to Max Weber's concept of "ideal types" the devastating refutation implicit in Nietzsche's critique of "scientific and logico-mathematical laws". In light of the unfortunate demise of John Nash just days ago, I am proposing to our friends possibly the most difficult piece ever published on this blog presenting what I have styled "Nietzsche's Invariance". My aim here is to expose the colossal stupidity of those economists who have turned Nash equilibrium, and thence game theory, into what they bathetically claim to be an important tool of economic analysis: and I achieve this by destroying - more than simply de-structing - the very rationale behind game theory - by proving that it can be applied only to mathematical "problems" and that it is utterly inapplicable to "practical" problems such as those tackled in economic analysis. If, after reading this, all those economist charlatans who waste their time on game theory do not hang their collective dunder-heads in shame - then they ought to have their heads "hanged" in the other sense! Cheers.
In game-theoretic situations or “problems", “means” and “ends” (or goals) are “mathematically linked” in axiomatic fashion. Yet, as Wittgenstein has established conclusively following Nietzsche’s own critique of logico-mathematics, such game-theoretic problematics categorically subvert the whole “nature and character” of the "game", of the “situation” or “problem”, that they intend to define or “resolve”! That is because the “solutions” (the “equilibria”, like “Nash equilibrium”) to the “game” are apodictically deducible from the “premises” and “axioms” in which the “game” is couched. But in that case, the “game” can no longer be defined as a “problem”! Because its apodictic formulation has turned it into an “inexorable fate”! And the “solution” is not a “solution” because there was never a “problem” in any meaningful sense! If we say, with Don Patinkin, that the “solution” to mathematical problems consists in “shortening the time of calculation [for finding the solution to the problem]”, then we would have to argue that the “truth” of a mathematical equation or “argument” depended on the “speed” of its computation or “application” to practical problems. But that is clear and sheer non-sense! Because the very definition of “truth” is “logical” and therefore not subject to temporal or practical considerations!  One of two things: either a mathematical equation, argument or axiom is an ab-solute identity, in which case it is a tautology (it says absolutely nothing: it is meaningless and “purposeless” and per-fectly useless); or else it is not an identity, in which case it may be “useful” but can never be “true” because “usefulness” and “truth” are categorically different things and the very “usefulness” of a mathematical identity or axiomatic discipline becomes a “value judgement”, contrary to the economist’s attempt to preserve the “logical objectivity” and “technical rationality” of such “axiomatic disciplines”!      
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            But In the construction of all “ideal types”, as in all mathematical operations, it is precisely “the logical per-fection”, the numerical “id-entities” involved in their equations, that deprive these operations of any possible content because either the identities are entirely “formal” and therefore “self-dissolving”, or else they have real contents, in which case the “entities” involved are not “identical”! Similarly, in “game theory” the “rational choices” are nothing more than “mathematical tautologies” in that the “axiomatic” rules of the game are de-fined tautologically from the outset. But such sets of rules vitiate the entire ontological “reality” of the situation of “choice” in that they transform their defined “problems” into “destinies”.

Wittgenstein's devastating illustration of this point is insuperable for its shattering simplicity: he takes the instance of the law and analyses the following statement: – “the law always catches the criminal”. Hence, this definition of “law” excludes the possibility of “evading the law” which is implicit as “transgression” in the very concept of “law”. Similarly, in physics, he looks at the notion of traction and concludes that – “we cannot walk on a perfectly smooth surface” – despite the fact that “walking” and “traction” are implicit in the concept of “perfectly smooth surface”: a "surface" is a space on which motion can take place, but a "perfectly smooth" surface can have no traction by definition, so that the phrase "perfectly smooth surface" is a contradictio in adjecto. In such cases it is no longer “meaningful” to speak of "game" or of “freedom”  or of “evaluations” or indeed of “science and rationality” in any sense at all – given that the “problem” is actually a “destiny” similar to that of Joseph K in Franz Kafka’s novels! 

Just as a logical “truth” cannot be “self-evident”, so a “law” –  juridical or scientific - has meaning only if those who are subject to it have the theoretical ability to evade it or to confute it successfully – otherwise it is no longer an observable and detectable entity “separate” from transgressive behaviour or from the “reality” it supposedly en-compasses. This is the kernel of Nietzsche’s invariance whereby “truth” cannot exist if it is postulated to be the real correspondence of “concept” and “reality” – and it cannot be “truth” if it is not so postulated. For “the Law” to be “a law” rather than a “fate”, it must admit or allow implicitly at least the possibility of successful transgression or evasion or  “grace”; for a “game” to be a “game” in game theory, it cannot postulate “common knowledge” or “flawless execution” or “perfect calculation” or “symmetric information” (unaffected by “adverse selection”, see axiom 5 in the insert below) – eventualities that game theory axiomatically excludes because these are “possibilities” that prevent its “games” from having “equilibrium solutions”! Similarly, a “surface” must allow implicitly of the possibility of “traction” or movement on it; but then it ceases to be “smooth”, defeating the original axiomatic definition. In all cases the axiomatic framework must either lose its “formal validity” as soon as it is “applied” to reality, or else it must be inapplicable to any reality and become a sterile tautology if it is to preserve its postulated “formal axiomatic validity”!
A good illustration of the tautological nature of axiomatic models is given by the “conditions” or axiomatic assumptions that underlie Nash Equilibrium in game theory. If a game has a unique Nash equilibrium and is played among players under these conditions, then the NE strategy set will be adopted. Sufficient conditions to guarantee that the Nash equilibrium is played are:
 1.The players all will do their utmost to maximize their expected payoff as described by the game.
 2.The players are flawless in execution.
 3.The players have sufficient intelligence to deduce the solution.
 4.The players know the planned equilibrium strategy of all of the other players.
 5.The players believe that a deviation in their own strategy will not cause deviations by any other players.
 6.There is common knowledge that all players meet these conditions, including this one. So, not only must each player know the other players meet the conditions, but also they must know that they all know that they meet them, and know that they know that they know that they meet them, and so on.    ************    
Philosophically, these axiomatic conditions (note especially the regressio ad infinitum in 6) turn the “game” into a “fate” or a “destiny”, depriving it thereby of the very essence of what constitutes a “game” or a "problem" - the problematic unpredictability of its outcome! The game then becomes meaningless and purposeless – and so does any “analysis” based on it! – except to the extent that it is used as a semeiotic device to regulate human behaviour, as in the process of Rationalisierung that we are enucleating here.


The notion of axiomatic mathematical truth as “despotic” was not lost on the earliest theoreticians of the doctrine of the Ab-solutist State – the “statolatrists” – in Renaissance Europe. Yet again, it was Hannah Arendt who came closest to intuiting the complex problematic of logico-mathematical id-entities or “laws” and the theorization of ab-solute power in On Revolution:

There is perhaps nothing surprising in that the Age of Enlightenment should have become aware of the compelling nature of axiomatic or self-evident truth, whose paradigmatic example, since Plato, has been the kind of statements with which we are confronted in mathematics. Le Mercier de la Riviere was perfectly right when he wrote: 'Euclide est un veritable despote et les verites geometriques qu'il nous a transmises sont des lois veritablement despotiques. Leur despotisme legal et le despotisme personnel de ce Legislateur n'en font qu'un, celui de la force irresistible de l'evidence';26 and Grotius, more than a hundred years earlier, had already insisted that 'even God cannot cause that two times two should not make four'. (Whatever the theological and philosophic implications of Grotius's for-mula might be, its political intention was clearly to bind and
Foundation II:Novus Ordo Saeclorum 193
limit the sovereign will of an absolute prince who claimed to incarnate divine omnipotence on earth, by declaring that even God's power was not without limitations. This must have appeared of great theoretical and practical relevance to the political thinkers of the seventeenth century for the simple rea-son that divine power, being by definition the power of One, could appear on earth only as superhuman strength, that is, strength multiplied and made irresistible by the means of violence. In our context,contex~, it is important to note that only mathematical laws were thought to be sufficiently irresistible to check the power of despots.) The fallacy of this position was not only to equate this compelling evidence with right reason –the dictamen rationis or a veritable dictate of reason - but to believe that these mathematical 'laws' were of the same nature as the laws of a community, or that the former could somehow inspire the latter. Jefferson must have been dimly aware of this, for otherwise he would not have indulged in the somewhat incongruous phrase, 'We hold these truths to be self-evident', but would have said: These truths are self-evident, namely, they possess a power to compel which is as irresistible as despotic power, they are not held by us but we are held by them; they stand in no need of agreement. He knew very well that the statement 'All men are created equal' could not possibly possess the same power to compel as the statement that two times two make four, for the former is indeed a statement of reason and even a reasoned statement which stands in need of agreement, unless one assumes that human reason is divinely informed to recognize certain truths as self-evident; the latter, on the contrary, is rooted in the physical structure of the human brain, and therefore is 'irresistible'. (pp.192-3)

Arendt observes that “divine laws” and the “laws” of ethics and of States – in short, “all values” – differ from those of mathematics because the latter describe the constitution of the mind and therefore “cannot be resisted”, whereas the former, however “reasonable” they might seem, require “agreement” unless one appeals to a mystical “intuitus originarius”. Arendt, however, fails to comprehend the enormity of the problem she has dimly perceived, which is the reason why she is unable to enucleate it with the ruthless clairvoyance that Nietzsche applied to it. When Mercier calls Euclid a “despot” he is equiparating the “legislative” power of his geometrical axioms to the “ab-solute” power of despots in that both kinds of “power” effectually do not admit of “questioning” or “agreement”! Grotius, by contrast, is placing mathematical axioms above the power of Sovereigns and of God himself (!) – but in so doing he too is equi-parating the two powers in the sense that mathematical axioms in their “universality” offer a “guarantee” of “truth” and validity that even the power of Sovereigns and of God, in its “ab-soluteness”, cannot proffer. 

The significant feature that escapes Arendt is that both Mercier and Grotius interpret the “truth” of mathematical axioms as a “Value” – as an “ab-solute truth”, one that requires no de-monstration – that can stand as the ultimate, ab-solute guarantee of all human universal values, of that inter esse that is threatened by the arbitrariness implicit in the “ab-soluteness” (the “unanswerability”, the “unaccountability”, the “irresponsibility”) of any and all “political” or “divine” power! And because Arendt does not grasp the profound significance of this “equi-paration”, she is then unable to penetrate the next, the ultimate and most devastating conclusion – one that she eludes, or that eludes her, when she attributes the “self-evidence” of mathematical “truths” to “the physical structure of the human brain” (a “psychologism” already refuted by Wittgenstein and Husserl before him). 

Arendt seeks to keep separate and distinguish the “logical necessity” or “irresistibility” or “irrefutability” of logico-mathematics (as a “power of the human brain”) from the “political necessity” of human coercion. Yet, the devastating conclusion that Nietzsche was first to outline as the “con-clusion” or “com-pletion” or “ful-filment” (in the sense of “ex-haustion”, of “fully-ending”, Heidegger’s Voll-endung) of the Western metaphysical Ratio-Ordo is that it is precisely because human beings can conceive of logico-mathematical id-entities that we have ultimate proof of the complete value-lessness of life and the world! It is the very arbitrariness and con-ventionality of logico-mathematical id-entities that con-firms ineluctably the futility of all “Truths and Values”! 

Far from being “the ultimate and ab-solute guarantee” of the presence and reality of Reason and Order, of universality, in the human world logico-mathematical identities constitute the evidence of the ultimate instrumentality of human action, of its ultimate value-lessness, of the ultimate un-reality of “all values”, of all “Truth”! This is what Nietzsche meant by “the trans-valuation of all values”! 

Arendt completely fails to see that both logico-mathematical and juridical-ethical or practical “laws” are conventional (Nietzsche and Wittgenstein); that juridical-ethical and behavioural laws can also be given ab-solute logico-mathematical axiomatic form, as in game theory, and then they become a “fate” (in Wittgensteinian language games), which is the opposite of what “truth” is supposed to be! So, in fact, “self-evident truths” (Jefferson), whether logico-mathematical or practical, are not “truths” at all (thus, the Jeffersonian “we hold” can be applied to the former as well as the latter): – indeed, the required “ab-soluteness” of all ultimate values and truths demonstrates that there can be no such value or truth except for “truth as a value”.

Far from being the ultimate protection against political arbitrariness, it is the very human ability to erect con-ventionally the axiomatic rules of mathematics and logic to the status of ab-solute ultimate truth and value that reveals the utter “value-lessness” of life and the world and the im-possibility of “truth”!  It is for this precise and quite understandable reason that Mercier and Grotius both feel “tempted” to equiparate logico-mathematical necessity and political coercion – because “logico-mathematical necessity” is the ultimate instance of the ability of human beings to transmute a symbolic “con-vention” into “political coercion” and vice versa. This is the “secret” of the Rationalisierung!

(It will be recalled that in George Orwell’s 1984 the main character Winston Smith seeks refuge from the pervasiveness of Big Brother’s totalitarian power in the “truth” of the statement “two plus two makes four no matter what Big Brother says”. What Smith fails to perceive is that it is precisely the ability of human beings to devise logico-mathematical identities that exhibits the ultimate futility of “truth” as a “value” and that demonstrates instead its utter instrumentality, and therefore the possibility of Big Brother’s “ab-solute power”.)
Differently put, mathematical id-entities and logical axioms are borderline concepts (Schmitt, Politische Theologie); they de-monstrate (in the Wittgensteinian sense of “showing”, “pointing to” but never explaining meaningfully!) both the ultimate attempt and the ultimate inability of the human mind to con-ceive of “truth and value” as objective entities: they represent therefore not only the ultimate de-monstration of the “un-reality” of “truth and values” but also and most terrifying of all the possibility of turning human arbitrariness into a “science” and a “logic”. This is “the Will to Truth”. Arendt came frighteningly close to this terrifying conclusion when she wrote in On Revolution (already quoted above): -  

Whatever the theological and philosophic implications of Grotius's formula might be, its political intention was clearly to bind and
Foundation II:Novus Ordo Saeclorum 193
limit the sovereign will of an absolute prince who claimed to incarnate divine omnipotence on earth, by declaring that even God's power was not without limitations. This must have appeared of great theoretical and practical relevance to the political thinkers of the seventeenth century for the simple reason that divine power, being by definition the power of One, could appear on earth only as superhuman strength, that is, strength multiplied and made irresistible by the means of violence. In our context,contex~, it is important to note that only mathematical laws were thought to be sufficiently irresistible to check the power of despots.) The fallacy of this position was not only to equate this compelling evidence with right reason –the dictamen rationis or a veritable dictate of reason - but to believe that these mathematical 'laws' were of the same nature as the laws of a community, or that the former could somehow inspire the latter.

To echo Arendt by way of confutation, the fallacy of her position is failing to equate mathematical ‘laws’ with right reason and to believe that these mathematical ‘laws’ are not of the same nature as the laws of a community, or that the former cannot somehow inspire the enforcement of the latter! Even the most “irresistible laws” (Arendt), the “laws” of logico-mathematics, are just as “con-ventional” as “the laws of a community”: indeed, it is the ultimate “con-ventionality” of even logico-mathematical “laws” that demonstrates how all laws, including moral and juridical ones, are ultimately “con-ventional” and therefore political. This is what Mercier, more explicitly, and Grotius, implicitly, meant to say in the quotations that Arendt selected (which she reproposes in The Life of the Mind). It is the fact (understood in the Vichian and Nietzschean sense of verum ipsum factum, meaning that “the truth” is what human beings actually do, from the Latin facere, to do) that human beings can mis-take logico-mathematical con-ventions (agreements) for “irresistible truths” that evinces definitively the “con-ventionality” of all “truths” and all “laws” – their “legal” character, and therefore their lack of “legitimacy”, their dependency on some “authority” that is not and cannot be “ab-solute” (not requiring “further proof”). (On the antinomy of “legality and legitimacy” the reference is to Carl Schmitt’s homonymous work. We will examine the homology of Nietzsche’s Invariance and Schmitt’s notion of “decision auf Nichts gestellt” [made out of nothing] later.)
Here again what “betrays” Weber is his impossible aim to reconcile “freedom” and “rationality” (one could not imagine two greater “idols”, next to “the State” and “God”, for Nietzsche to desecrate and vilify [cf. his Twilight of the Idols]) – in circum-stances, in con-ditions – those of a “controlled experiment” - that make those very concepts utterly irrelevant to assessing – precisely! – the “political freedom” or less enjoyed by human beings in the “practical reality” that is under “scientific observation”. Not “scientific activity” per se is “ideological” (pace Heidegger and Marcuse and all other “late-romantics”) – because that would imply that human activities can be classified as either “ideological” or “non-ideological” (recall Nietzsche: “the real world has disappeared – and the apparent world…has disappeared with it!”) -, but rather its “abstract extension” as “empirical research” under the “real subsumption” of the capitalist wage relation to all spheres of human interest without regard to “consequences”. Because Weber (and Marcuse and Habermas even less) does not understand – nor does he ask – why and how human activity can be reduced effectually to instrumental action (the essence of the Rationalisierung), he gives proof of his failure to understand the “significance” of his own intellectual and political activity which in fact is often quite advanced in the direction of answering the “enigma” (see Freund discussed below) of the Rationalisierung. Weber looks for the “rationality” of “necessity” and forgets that he can find only the “in-variance”, either the ultima ratio of “dire necessity” or “the endless multiplicity of possible evaluations… [that] can be reduced to manageability only by reducing them to their ultimate axioms”. Finally, the “utopia” of the “ideal type” has degenerated into the logical purity, theaxiomatic tyranny of the Rationalisierung.

Thursday, 21 May 2015

The Bounds of Freedom - Part 2

The liberal bourgeois State – the State of capital – is founded upon the neat dichotomy between the sphere of necessity – that is, the economy whose “laws” are set by “the dismal science” of economics – and the sphere of freedom or public opinion. But how can these seemingly incompatible spheres – one deterministic and the other seemingly not - co-exist in a society and in a State? How can the sphere of necessity or economics be separated from that of freedom or politics when the economic behaviour of individuals is clearly influenced by their political choices and, in turn, their political choices are conditioned by their economic constraints? In other words, how can the liberal State claim legitimately to be able to reconcile these seemingly incompatible social spheres? It is obvious that the answer to this question, and ultimately the entire rationale of capitalism – its metaphysics, though its apologists and propagandists would never concede the necessarily metaphysical nature of their ideology – rests on the definitions of freedom and necessity. What we are exploring here is the thinking process – the development of the theory – that has led to the powerful ideology of capitalism as “the marketplace society” founded on the osmotic relation between market economics and liberal State. And we have started with the founders of what we call negatives Denken in Germany – Schelling and Schopenhauer.


Despite his express distaste for the German Idealists, Schopenhauer’s critique of Kant presents obvious and striking similarities with Schelling’s; but he goes much further in stripping off more layers of the Cartesian cogito. Just like Schelling’s, Schopenhauer’s critique of Kant challenges two tenets of Cartesian rationalism derived from the cogito: the first, which Kant’s critical idealism clearly confuted, is that there is a Subject, an Ego, whose existence is proven not by the content of thought but from the very act of thinking. If there are thoughts, Descartes reasoned, then there must be an id-entity, an Ego-ity (Ich-heit) that thinks (cogito as co-agitare). Kant showed, however, that the mere act of thinking does not and cannot prove the existence of an active thinker or Ego – which must therefore remain a transcendental Subject. But the second notion that Schelling and Schopenhauer disputed and dispelled was one in which Kant himself was implicated – and that is that the very content of thought, its logical consistency – its reasoning – showed the existence of a faculty of Pure Reason that required as a necessary premise of this existence the dialectical pre-supposition (the intelligible character, as against the Cartesian syllogistic deduction) of a thinking Subject that is autonomous and therefore “free” from the heteronomy of the causal chain that links the phenomena induced by the Object (the Thing in itself) and perceived by the Subject.


This “practical” inference from the very faculty of Pure Reason led Kant to postulate the existence of a Practical Reason that could found at least transcendentally an entire formal ethics. Like Schelling, Schopenhauer also strenuously denies the validity of such an inference first and foremost because it is based on the Cartesian unbridgeable “gap” between the Subject and its Object, the res cogitans – the Soul - that perceives the world, and the res extensa – matter - that is the material world itself made up, in Kant’s words, of the Thing-in-itself and the phenomena it produces.


If we wish to reach the real origin of this hypothesis
of Practical Reason, we must trace its descent a
little further back. We shall find that it is derived
from a doctrine, which Kant totally confuted, but
which nevertheless, in this connection, lies secretly
(indeed he himself is not aware of it) at the root
of his assumption of a Practical Reason with its
Imperatives and its Autonomy—a reminiscence of
a former mode of thought. I mean the so-called
Rational Psychology, according to which man is
composed of two entirely heterogeneous substances
—the material body, and the immaterial soul. Plato
was the first to formulate this dogma, and he endeavoured
to prove it as an objective truth. But it
was Descartes who, by working it out with scientific
exactness, perfectly developed and completed it.
And this is just what brought its fallacy to light, as
demonstrated by Spinoza, Locke, and Kant successively.
It was demonstrated by Spinoza ; because his
philosophy consists chiefly in the refutation of his
master's twofold dualism, and because he entirely and
expressly denied the two Substances of Descartes,
and took as his main principle the following proposition
: " Substantia cogitans et substantia extensa
una eademque est substantia, quae jam sub hoc, jam
sub illo attributo comprehenditur.''^* The thinking substance, and substance in extension are
one and the self-same substance, which is contained now
under the latter attribute {i.e., extension), now under the
former {i.e., the attribute of thinking).
—Ethica, Part II.,Prop. 7. Corollary.

^ It was demonstrated
by Locke ; for he combated the theory of
innate ideas, derived all knowledge from the sensuous,
and taught that it is not impossible that Matter
should think. And lastly, it was demonstrated by
Kant, in his Kritik der Rationalen Psychologies as
given in the first edition. Leibnitz and Wolff were
the champions on the bad side ; and this brought
Leibnitz the undeserved honour of being compared
to the great Plato, who was really so unlike him.


For Schelling and Schopenhauer, the only inference that can be drawn from the Cartesian cogito is not the existence of Reason as the logical content of thought, as Kant desumed, but rather the very materiality of the act of thinking, not in the sense of the existence of a thinking Subject or Ego but rather the mere, sheer, brute fact of existence. The act of thinking, like that of perceiving – and the two cannot be separated at this intuitive level (cf. Hegel’s hic et nunc) -, demonstrates that existence is a fact whose proof is the very act of thinking: – yet, the act of thinking does not in the least prove the existence of Reason or of the Ego! Schelling and Schopenhauer agree therefore with Kant that it is impossible to derive the existence of an Ego from the act of thinking, but they go farther in denying also, contra Kant, that the act of thinking shows the existence of Reason: Reason as a thinking faculty is incapable of demonstrating both the existence of a Subject that originates phenomena and of itself as the ability of the Subject to com-prehend – that is, understand and encompass - these phenomena!


It is this brute fact of existence, this contingency of thought and perception and intuition, that engenders the “freedom” of being human, - but only as a beginning, that is, only as a meta-physical state that lies beyond (jenseits) all human comprehension or consciousness.

Furthermore, the only “reason” possible within the phenomenic world is not the Reason (Vernunft) of Western rationalism from Plato through the Schoolmen and the Renaissance to German Classical Idealism, but only the heteronomous instrumental reason of the intellect (Verstand) that is unable to comprehend itself and yet, because of this, is subject to the strictest necessity and the most inescapable determinism.


Schelling and Schopenhauer accept with Kant and the entirety of post-Renaissance rationalism the “necessity” of science: once we lower ourselves into the phenomenic world, the laws of causality are universally valid and binding. But this necessity is only an experimental one that changes with the changing phenomena that we experience: it is not a necessity that reveals a universal or even divine – absolute – set of “laws of nature” or a rational order that can be comprehended as a totality by human beings. Such comprehension would necessarily entail the Freedom of the Subject that is capable of it. Yet this is precisely the Totality that Schopenhauer says is impossible to reach. Thus, no Freedom as a universal human ideal is possible. In Kelly’s summation of this crucial point:


Schopenhauer criticises Kant's conception of the thing-in-itself in the same manner in which he had criticised his theory of the a priori character of the causal law.
“Both doctrines are true, but their proof is false. "^ Kant argues that "the phenomenon, thus the visible world, must have a reason, an intelligible cause, which is not a phenomenon, and therefore belongs to no possible experience."^ But this is perverting entirely the meaning of the law of causality, which applies exclusively to relations between phenomenal changes, and can therefore in no way account for the phenomenal world as a hypostatized entity.



The “necessity” of the physical world cannot be proved absolutely. It can be only demonstrated empirically through the principle of sufficient reason – in the sense that whatever exists has greater reason to be than what does not exist. It is pointless, therefore, to seek to establish, as Kant did, the “necessity” of physical laws – because such necessity can never be established epistemologically; it is simply an empirical reality based on the fact that it is always possible to establish empirically predictable connections between phenomena. Only outside the world as we know it - the world of phenomena - is freedom possible; and then not objectively, cognitively or consciously, but rather in a pre-conscious state. Freedom and Reason are thus irreconcilably divorced: freedom is inconsistent with reason unless it is placed beyond the conscious world of human perception – in which, of course, reason as the necessity of the causal chain (the laws of nature) reigns supreme. Freedom can exist only with-out the World as we perceive it – only beyond the world of phenomena as they appear to us. But within the World, freedom is impossible because the world of phenomena is ruled by the laws of nature as established by reason. In this sense, once it is divorced from Reason, Freedom becomes mere contingency or chance, mere Da-sein, and Reason is reduced to instrumental reason, to mere intellect.

For Schelling as for Schopenhauer, to put it in the words of Malebranche whose epigram the latter used in his essay On the Freedom of the Will, “la liberte’ est un mystere” – freedom is a mystery. But even in its mysterious shroud, what kind of “freedom” does Schopenhauer intend? To find out, we need to understand how Schopenhauer absorbs and subverts – though he claims simply to invert – Kantian metaphysics and ethics. The answer will also reveal the theoretical philosophical underpinnings of neoclassical economic theory and of its political counterpart, liberalism.

The strict and absolute necessity of the acts of
Will, determined by motives as they arise, was first
shown by Hobbes, then by Spinoza, and Hume, and
also by Dietrich von Holbach in his Systeme de la
Nature ; and lastly by Priestley it was most completely
and precisely demonstrated. This point,
indeed, has been so clearly proved, and placed beyond
all doubt, that it must be reckoned among the
number of perfectly established truths, and only crass
ignorance could continue to speak of a freedom,
of a liberum arbitrium indifferentiae (a free and
indifferent choice) in the individual acts of men. Nor
did Kant, owing to the irrefutable reasoning of his
predecessors, hesitate to consider the Will as fast
bound in the chains of Necessity, the matter admitting,
as he thought, of no further dispute or doubt. This
is proved by all the passages in which he speaks of
freedom only from the theoretical standpoint. Nevertheless,
it is true that our actions are attended with
a consciousness of independence and original initiative,
which makes us recognise them as our own
work, and every one with ineradicable certainty
feels that he is the real author of his conduct, and
morally responsible for it. But since responsibility
implies the possibility of having acted otherwise,
which possibility means freedom in some sort or
manner; therefore in the consciousness of responsibility
is indirectly involved also the consciousness
of freedom. The key to resolve the contradiction,
that thus arises out of the nature of the case, was
at last found by Kant through the distinction he
drew with profound acumen, between phaenomena
and the Thing in itself (das Ding an sich). This
distinction is the very core of his whole philosophy,
and its greatest merit.

The paramount inference to be drawn from this passage is that Schopenhauer carefully and steadfastly situates the Will at the metaphysical interface between pre-conscious freedom and conscious necessity. In other words, the Will serves the role of a metaphysical osmotic membrane, so to speak, that allows for the philosophical reconciliation of the unknowable Thing-in-itself, which opens up the sphere of freedom as a qualitas occulta, as a “mystery”, on one side, with the knowable phenomena that belong to the sphere of Necessity, on the other. For Schopenhauer, “the greatest merit of his [Kant’s] entire philosophy [consists in drawing] the distinction… between phaenomena and the Ding an sich” (Appendix to WWR) as two entirely heterogeneous and categorically different entities. But Kant’s greatest demerit was his vain attempt “to bridge the Gap” between the Thing-in-itself and appearances, first, by understanding the Thing-in-itself as an actual “thing”, as a material Object, and then by positing – indeed requiring quite arbitrarily! - a Sub-ject or an entity such as Reason separate from its Ob-ject and therefore opposed to it (Object in  German is Gegen-stand, standing against) that is yet able both to perceive or re-present this Ob-ject through phenomena, and then in insisting that despite this antinomic opposition, despite this chorismos, it is possible to identify a Pure Reason (reine Vernunft) by means of which this Subject or Ego-ity (Ich-heit) can com-prehend, give sense to (Sinn-gebende), that is, be both ground and sum of the phenomena produced by the Ob-ject and therefore provide the indispensable adaequatio rei et intellectus in the guise of an ordo et connexio rerum et idearum. (On this Kantian “Gap”, cf. Fichte’s hiatus irrationalis and Lukacs’s “antinomies of bourgeois thought” – and see E. Forster’s account, Kant’s Final Synthesis.)


So when Schopenhauer claims that “it is through Kant’s doctrine” that we reach this inversion, he is really saying that “Kant’s doctrine” - the distinction between Ding an sich and phenomenon -has allowed him to reach this inversion, but only by radically re-directing Kant’s distinction “inwards” toward “the sentient organs”, past pure intuition and into “the Will”!

Del resto in tutta
la tradizione filosofica è spesso presente l’idea della metafisica intesa
come un sapere filosofico che integra il sapere scientifico, come
un ampliamento necessario del campo del sapere. Nel caso di
Schopenhauer le cose non stanno in questo modo. Certamente, nel
paragrafo di apertura del secondo libro del Mondo (§ 17), le considerazioni
sulle scienze in genere e in particolare sulle scienze della
natura sembrano a tutta prima rammentare il vecchio discorso sulle
insufficienze del sapere scientifico e sulla necessità di una sua integrazione.
Ma si avverte ben presto che l’accento del problema è
nettamente spostato dal terreno propriamente conoscitivo ad un
terreno essenzialmente diverso, che mette in questione piuttosto il
nostro modo di essere nel mondo, di riferirci alle cose ed agli eventi
che accadono in esso – il nostro modo di vivere questo rapporto, o
meglio ancora: di sentirlo. Naturalmente è possibile anche nella
metafisica della tradizione cogliere questo aspetto come sfondo del
problema metafisico, ma ora esso è nettamente in primo piano.
Potremmo forse dire addirittura che in Schopenhauer l’accento si
sposta esplicitamente sul versante esistenziale, mentre si attenua
l’aspetto della metafisica come integrazione del sapere, come una
questione filosofica astratta. (G. Piana, Commentari su Schopenhauer, 3, p.7)

(After all, philosophy has often espoused the idea that metaphysics is a mode of knowing that simply integrates scientific knowledge [as epistemology], as a simple broadening of the field of knowledge. In Schopenhauer's case things are different. Certainly, in the opening paragraph of The World [17], his considerations on science in general and natural sciences particularly seem to harp back to the inadequacy of scientific knowledge and the necessity of its integration. But one can sense immediately that the stress here is now shifted from the cognitive ground to one decisively different, one that lays the emphasis on our manner of being in the world, on the way we relate to things and events that happen in it - on the way we live this relationship, or even better on how we sense it. Naturally, it is possible to detect this aspect even in traditional philosophy, but now it is placed decisively in the foreground. We could even say that in Schopenhauer the focus of philosophy has been shifted explicitly to the existential aspect, whilst instead the aspect of scientific integration [epistemology], as an abstract philosophical question, has been neatly attenuated.)

It is here that Schopenhauer, just like Schelling before, effects his own inversion (Um-kehrung) of Kant’s transcendental idealism – but now no longer within the confines of Schelling’s existentialism. In line with the critique of Kant propounded by Schelling, Schopenhauer contends that the “sphere toto genere different from the idea (from knowing and being known, from Reason)” is a sphere that lies “beyond” (jenseits, not just “behind”) the sphere of representations or appearances, of the known-Object and the knowing-Subject.

"Upon the path of the idea one can never get beyond the idea; it is
a rounded-off whole, and has in its own resources no clue leading
to the nature of the thing in itself, which is toto genere different
from it. If we were merely perceiving beings, the way to the
thing in itself would be absolutely cut off from us. Only the
other side of our own being can disclose to us the other side of
the inner being of things. This path I have followed."^ Kant
is correct in holding that we are unable to arrive at the ultimate
reality of things by the road of knowledge; but he then proceeds
to deny the possibility of all metaphysics, thus ignoring,
in his Critique of Pure Reason, the paramount ontological significance
of non-cognitive experience.

Schopenhauer agrees with Kant that the representations or phenomena that we experience as “reality” cannot possibly themselves stand for reality – that there must be a Thing-in-itself that stands for these phenomena, that constitutes their being, their sub-stance or esse-nce. This is because, first, no amount of scientific learning will ever be able to account for the totality of phenomena, for our experience of the world; and second, more important, it is because phenomena themselves, even when connected by scientific regularities or “laws”, cannot go beyond their status as mere phenomena or appearances (Kant’s blosse Erscheinungen) or representations (Vorstellungen), even when we can connect them causally with one another.

The task of meta-physics, therefore, cannot be limited or confined to the cognition of mere representations and their inter-connection (epistemology) – because all this can ever tell us is that phenomena are linked together, and even how they are so linked. But this epistemology or science will never answer the question as to what these phenomena – however “connected” – really are, what their substance is, unless we postulate like Kant the existence of an inscrutable Object (the thing in itself) that stands “behind” or “beneath” them, as their sub-stance. But such a positing of an inscrutable and unknowable Object will inevitably render it a qualitas occulta about whose nature we can never know anything because by definition we are unable to experience or intuit it directly! A metaphysics of knowledge (epistemology) is impossible; only a metaphysics of experience, the intuition of the Will, as against its cognitive consciousness, is open to the intellect (again, this is a clear echo of Cusanus’s docta ignorantia).

It is the purely ideal nature of this Reason and then the formal nature of Practical Reason and “consciousness”, of the “self” or Subject that can com-prehend the inscrutable Ob-ject – it is this “transcendental Subject” that Schopenhauer denies, because of the very irreconcilability of the Kantian phenomenon and noumenon, because of their very anti-nomy. Kant has gone too far by postulating these entities as the formal requirements of Reason, and then has not gone far enough by failing to see that the thing in itself is not an entity from which the phenomena themselves can be derived, which he agrees is impossible – but rather a faculty that is intuitively reachable, though not knowable, by us from the very nature of these phenomena, not from their cognitive content – from the information they convey – but from our very experience of them!

La nostra domanda è ora: “Che cosa è questo mondo oltre il
fatto che esso è una nostra rappresentazione? Che cosa resta se si
prescinde dal divenire rappresentazione, ovvero dall’essere rappresentazione?
Che cosa significa l’intero mondo della rappresentazione?
Che cosa è l’essenza di questo fenomeno, che cosa si manifesta
in esso, che cosa è la cosa in sé? Questa domanda è il problema fondamentale
della filosofia” (Lez., II, p. 61). – p.8. Berlin lectures.

(Our question now is: "What is this world beyond the fact that it is our perception? What is left of it if we prescind from this representation, from its being merely a representation? What is the essence of this phenomenon, what is manifested in it, what is the thing-in-itself? This question is the fundamental problem of philosophy",)

To posit the Object independently of the Subject, as a “thing”, as Kant did with his transcendental idealism, is to objectify the Subject (this is also the crux of Adorno’s critique of Hegel’s Objective Spirit – in Lectures on Negative Dialectics). Conversely put, with Schopenhauer, “to know [the subject] objectively is to desire something contradictory”. As argued by Cusanus, empirical knowledge can never surge to a totality – the absolute – because its character remains “partial” or “heteronomous”. Similarly, this totality cannot be a causa causans because by definition all causes must be the effect of a prior cause and therefore remain heteronomous. True autonomy or freedom must belong to a sphere toto genere different from that of causality – which in turn cannot be absolute but merely instrumental, and is therefore incapable of “com-prehension” given its heteronomous instrumentality. It is a sphere that “generates” the entire “possibility” of experience as its innermost “being”. It is the Lichtung, the “self-understanding of being”, it is the very “being that interrogates being”, the “being in the world”, which at once unifies “known” and “knowing”, subject and object in an “identical subject-object” (Lukacs) – because

"the thing in itself can, as such, only come into consciousness quite directly, in this way, that it is itself conscious of itself; to wish to know it objectively is to desire something contradictory."*

It follows that there is no hiatus or chasm or lacuna between Subject and Object and that therefore “Phenomena” or “Representations” are not “images” or “aspects” of the Object as perceived passively by the Subject but are instead “objectifications” of the body – not of the Subject! - as a sentient entity itself – they are a subject-object unity – an “identical subject-object”. 

(It is now pellucid, therefore, that the true source of Lukacs’s identification of the working class as “the identical subject-object of history” in History and Class Consciousness is the direct result of Schopenhauer’s critique of Kant’s idealism elaborated in a Hegelian dialectical-historical dimension in which Schopenhauer’s Wirk-lichkeit [work-likeness] is transmuted into the centrality of Labour [of work] in human history – whereas, as we are about to see, for Schopenhauer this “reality” or “work-likeness” is the Veil of Maya that uncovers the futility of Labour, of the Arbeit, of its Strife and Pain [Leid] – precisely the dis-utility of labour theorized in Neoclassical Economics. See on all this our “Capitalist Metaphysics”.) 

No “Object” or “Reality” stands “behind” the phenomena: no Subject can either initiate or fully com-prehend (understand and encompass) them as a totality. Instead, the phenomena are the “actu-ality” (Wirklichkeit), the mani-festation or re-presentation (Vor-stellung) of the Will intended not as an Ego but as a life-force, as the Welt-prinzip.

"He does not say, as truth required, simply and absolutely that the object is conditioned by the subject, and conversely, but only that the manner of appearance of the object is conditioned by the forms of knowledge of the subject, which therefore, come a priori to consciousness. But that now which in opposition to this is only known a posteriori is for him the immediate effect of the thing in itself, which becomes phenom-
enon only in its passage through these forms which are given a priori/'^
And Kant fails to realize that "objectivity in general belongs to the forms of the phenomenon, and is just as much conditioned by subjectivity in general as the mode of appearing of the object is conditioned by the forms of knowledge of the subject; that thus if a thing in itself must be assumed, it absolutely cannot be an object, which however he always assumes it to be, but such a thing in itself must necessarily lie in a sphere toto genere different from the idea (from knowing and being known). "2
CHAPTER IV. from Tsanoff.
Experience and Reality: The Will as the Thing-in-Itself.
A change of philosophical method is to be observed at this stage of Kant's exposition, which Schopenhauer interprets as follows. Kant does not affirm, clearly and distinctly, the absolute mutual dependence of subject and object in all possible experience.

Reality (ontology) cannot be found in an Object or a “thing”: it cannot be “re-ality” (Latin, res, thing) as a sum or totality of “things”. Instead, quite to the contrary, the ultimate reality, the one accessible to us, is the very experience of phenomena through our physiological faculties, both mental and physical – through the body. The phenomena and the Thing are irreconcilable, but the path to the Thing lies through the intuition or experience of the phenomena themselves; not through their cognitive or epistemological content but through their experiential content! Rather than as an array of “things” (Re-ality), Schopenhauer understands “reality”, the world, from an active standpoint – not merely an existential one as did Schelling before him. What we are aware of through the body and its perception or intuition of the world, well beyond its cognition as consciousness, is the fact of Volition, that is, not merely of our ec-sistence, or even of our passive perception – of our being before thinking -, but above all of our active willing!

Here, the conatus or appetitus is much more in evidence than the perception, even than in Schelling. Again, this critique is entirely similar to Schelling’s existential critique of Kant’s transcendentalism; but it goes further in that it does not stop at the mere fact of existence or contingency but penetrates the active character of human perception and intuition – its purpose, its being volition! Schelling saw only the materiality of thought, its being as ec-sistence: Schopenhauer instead sees not just thought, but the entirety of human sensation, as the actual inter-action of the body and the object in the representation – as sensu-ality, as actu-ality (Wirklichkeit).

We say “of the body” and not “of the Subject” or of the Ego, because, as we have demonstrated, for Schopenhauer the Will must not and cannot be mistaken for a Subject or an I that wills! Even one of the most perspicacious commentators on Schopenhauer falls into this understandable but crucial error, as this quotation shows:

Così si fa notare che potremmo sentire una forte resistenza
interna ad ammettere la concezione del corpo come pura rappresentazione,
una resistenza che il riconoscimento del corpo come
oggetto immediato non è in grado di far venire meno. Questa resistenza
si spiega ora con il fatto che, facendo del corpo una rappresentazione
come tutte le altre si espone il corpo stesso, il mio corpo,
e dunque io stesso, alla possibilità che esso sia ridotto a pura parvenza.
Ma una simile riduzione entra in conflitto con l’esperienza
che io ho di me stesso ed in particolare in quanto io costituisco me
stesso come un io che vuole. Dobbiamo ora osservare che l’esperienza
dell’io come un io che vuole è anche esperienza del reale al suo massimo
grado – ecco come si ripresenta in rapporto alle considerazioni
metafisiche il tema della realtà! Ciò che per me è soprattutto reale
sono io stesso, quell’io stesso che si percepisce in una inscindibile
unità con il corpo stesso – si sarebbe tentati di pensare di essere qui
in presenza di una singolarissima e svisata ripresa, in un contesto e
con esiti tanto diversi, del tema cartesiano dell’ego cogito.
La “massima realtà da noi concepibile” è il nostro corpo. “Il
proprio corpo è per ciascuno la cosa più reale” (M., p. 143, Lez. II,
p. 81). La metafisica di Schopenhauer inizia proprio da questa affermazione
tanto notevole. In essa è contenuta una conseguenza
molto forte: se non vogliamo che il mondo intero che ci appare,
con tutte le cose di cui esso è costituito, animali, vegetali, e le stesse
altre persone da cui siamo circondati sia ridotto a pura parvenza fenomenica,
dobbiamo essere disposti ad attribuire ad ogni cosa
quella stessa realtà che noi attribuiamo al nostro corpo. Ma ciò significa
null’altro che fare di ogni cosa un fenomeno della volontà. O
sostenere, detto in altri modi equivalenti, che la volontà è l’essenza
dei fenomeni, che essa è la cosa in sé di cui parlava Kant. – (G. Piana, op.cit., 3, p.21)

([Schopenhauer's thesis] focuses on our resistance to the conception of our body as pure representation, a resistance that our perception of our body as an immediate object can only strengthen. This resistance is explained by the fact that the idea of the body, of my body, and therefore of myself, as a representation like any other, opens it to the possibility of being seen as a mere appearance. But such a reduction comes into conflict with the experience that I have of myself and particularly to the degree that that I constitute myself as an I that wills. We must observe now that the experience of the I as an I that wills is also the experience of reality in its highest degree - that is how we represent the notion of reality in metaphysical terms! What is real above all for me is myself, that myself that is perceived as an inseparable part of my body - one is tempted here to see in this thesis a singular and misconceived reprise, in a context and with outcomes that are so much different, of the Cartesian theme of the ego cogito [ergo sum]. "The highest reality conceivable by us" [says Schopenhauer] is our body. "One's body is for each of us the most real thing" [World]. Schopenhauer's metaphysics starts from this affirmation so notable. In it is contained a very strong consequence: if we do not wish that the entire world appears to us, with all the things that constitute it, animals, vegetables, and the same persons who surround us, be reduced to a mere phenomenal appearance, then we must be prepared to attribute to everything the same reality that we attribute to our body. But this means no more than to make of every thing a phenomenon of the Will. Or to assert, put in other words, that the Will is the essence of phenomena, that it is the thing in itself that Kant to which Kant referred.) 

There are two possible confusions in Piana’s otherwise accurate summary of Schopenhauer’s radical inversion of Western rationalist metaphysics that need clarification: the first is that Schopenhauer’s emphasis on the Will as a primal experience – as an intuition conscious of its being pure intuition – is meant precisely at de-structing the concept of an “I that wills”. Indeed, the whole point to the Will as a Welt-prinzip, a world-principle, as a universal “Will-to-Life” (Wille zum Leben, which he therefore admits is “ein Pleonasmus” [World, II, par.54]) is to deny that a Cartesian ego exists as an entity because for him the Ego is only a faculty – a force that wills and that is present universally. The second confusion is that the Will is a faculty or property that belongs to individuals – because, as we have just explained, Schopenhauer sees it instead as a universal force that is individualised in every aspect of existence, in every “being” (Fr. etant, Ger. Seiende) as distinguished from Being (Etre, Sein) – and this occurs through what Schopenhauer calls “the principium individuationis”, by which he means that there would simply not be a “World” if the Will could not assume a different ex-pression in each single “being”, so far as “beings” can be isolated from “Being”.


In this regard, one may think that Schopenhauer has escaped what is our greatest criticism of most philosophical and social theory – that human beings can be understood ontogenetically rather than phylogenetically. But in fact, because the Will is – just like Nietzsche’s, albeit very different, notion of Wille zur Macht – a universal force that must be individualised, then clearly it cannot serve as a phylogenetic approach to human species-conscious being (Gattungswesen).


It is to this ethico-political aspect of Schopenhauer’s metaphysics that we will turn in our next section.