The Cartesian insistence on the power of logico-mathematical deduction and intuition as the cardinal methodical tools for the asseveration of Truth meet an insurmountable obstacle in their own formalism. The “truth” of logico-mathematics has no substantive content: it is “true” by definition – quod erat demonstrandum (as was to be demonstrated) – in that the conclusion (the demonstrandum) is already contained (erat, “was”!) in the premises (the demonstrans) and, worse still, the premises already contain the conclusion! But if the premises and the conclusion are so formally related that they are tautological, then no practical conclusion – no “demonstration”! - can ever be extracted from such formal reasoning! Only if the logico-mathematical calculation is “false”, in the sense that it is purely practico-conventional because it involves heterogeneous elements and therefore has substantive content, - only in that case can logico-mathematics be “useful”, not “true”, in a strictly conventional sense!
Here, Descartes’s reliance on the intellect or Reason as the foundation of human knowledge quite simply falls apart. Specifically, the twin foundations of the intellect – intuition and deduction – prove to be categorically antinomic because intuition has a substantive immanent materialist basis, whereas deduction is entirely formal and tautological. A life-world in which any reality could be deduced logico-mathematically from intuited premises simply begs the question of how this “original intuition” (the phrase is Leibniz’s, see the 24 Metaphysical Theses, discussed in M. Heidegger, The Metaphysical Foundations of Logic, and his dissection in the dimension of philosophical anthropology [Husserl’s plaint against Heidegger] of the Kantian intuitus in the Kantbuch) came about in the first place – of what its substantive content is. Similarly with cause and effect. If indeed the effect is in the cause and the cause is in the effect, then it is simply meaningless to connect the two separate events – cause and effect – in terms of causation because they are not in fact “separate” events! Far from being “laws of nature or of physics”, scientific findings are “conventions” in the sense that (a) they are based on induction, and, (b) they reflect a specific human practical orientation rather than any “universal laws”. Indeed, mathematical calculations and logical deductions – not to mention scientific “laws” based on causation – can be valid only if all their categories are formally equal. But this formal equality necessarily requires the substantive equality of the elements that these categories represent! Yet, this is logically impossible, given that substantive elements are categorically different (different toto caelo, toto genere) from the logico-mathematical categories that supposedly “stand for” them! This is the paradox: logico-mathematical categories cannot be “deductive” but merely practico-conventional or empirico-inductive because deductions must be based ultimately on intuition - and it is quite simply impossible to identify and isolate formally the “intuition” that is supposedly “behind” these entities, because intuition is a substantive, not a formal, entity! Given that the “truth” of logico-mathematical deductions is entirely formal, its demonstration must be based on a substantive content – it must be “shown” to be true. But such a “showing” (Latin, de-monstrare, to show) is necessarily a practical, physical, substantive and material task that contradicts the supposed “formality” and “logico-mathematical necessity” of every “deduction”!
Hume’s skepticism in the Treatise of Human Nature effectively demolishes Descartes’s analytic a priori precisely by dissecting every causal relation in terms of individual “images” that – as “images” – cannot have any con-nection in a pictographic sense or indeed in any other sense! It was in a colossal effort to rescue Reason from this nihilistic assault that Kant enucleated his critical idealism and synthetic a priori as an Ubergang to bridge its antinomic opposition to Nature. The Kantian attempt to define and refine the “aesthetic” basis of Pure Reason through the Schematismus fails miserably once the inescapably “conventional foundation” of every intuition and every “truth”, of every mathematical identity and every “law of nature” is laid bare. There is no “synthesis”, let alone any “a priori”, linking events in the universe! The “legality” of Kant’s theorization of Pure Reason is precisely what Schopenhauer and Nietzsche will be first to attack, and quite validly so.
Just like the Self or the Ego, the idea of God must take the mental form of some particular thought, of which actual physical ec-sistence (physical embodiment) cannot be predicated. For the Ego in the cogito, for the human intellect, the perception of the world is necessarily “false” because no sensual perception can ever match the formal “purity” of logico-mathematical deduction. In that case, it is not merely that the human senses err in their estimation of the world: it is rather that the intellect itself will never be able to comprehend the world, given that the world is inevitably made up of “appearances”! According to Descartes, the intellect’s comprehension of the world is imperfect and prone to error not because of any intrinsic flaws in the intellect – which shares its status as “substance” with the divine -, but because it is deluded by the will – which is the “mortal” facet of the intellect - into trusting the lure of “mere appearances” (Kant’s “bloss Erscheinungen”). But if the intellect’s “perception” of the world is false, for whatever reason, then for Descartes, vis-à-vis the intellect, the world has really and truly become a “fable”: what is more, a fable that, in his requirement of logico-mathematical determinism of the world – the vera mathesis – can also be nothing more than a lifeless, soul-less mechanism! (Again, see Nietzsche’s savage parody of Descartes’s reduction of the world to “a machine” in The Anti-Christ, par.14). Given that Descartes’s ontological proof is incapable of bridging the hiatus irrationalis (Fichte) between Subject and Object, between Reason and Nature, his rationalism, his “method” cannot but amount to a dogmatic moral imperative, an early version of the Kantian categorical imperative, the dictamen of the divine affinity of the intellect. Whence Nietzsche’s riposte in Twilight of the Idols, “Taken from the moral viewpoint, the world is false!” Not indeed because for Nietzsche the world is “false” (pace M. Cacciari in Krisis, ch. 2) – because that would entail the existence of a universal “truth” against which the world was “false” – but precisely because for Nietzsche no “universal truth” is even meaningful, let alone possible! (In this regard, the link established by Cacciari, loc. cit., between Nietzsche and Wittgenstein is quite valid and fertile: for Wittgenstein, the world cannot be com-prehended by language: the world can only be “shown”, but not by language – cf. Tractatus Logico-Philosophicus.)
But, leaving all this to one side, how can the human mind interact with the universe, then? More saliently, if science and technology are purely a means of knowing a strictly deterministic universe, of finding a unique “universal key” to the interpretation of “the great book of nature”, (a) how can humans then be aware of acquiring this “knowledge” given that any such knowledge would amount to a mechanical operari necessarily deprived of any “awareness” or “consciousness”? (This is a paradox that Spinoza tackled as well, unsuccessfully.) And, (b), how can humans interact with the world without transforming it? Furthermore, even assuming that such interaction with and trans-formation of the world by humans is possible and real, how can it be said to emanate causally from the world itself and, worse still, how can such trans-formation of the world by humans exclude any negative outcomes or degradation of nature and the world? The optimistic bias and aporetic nature of Cartesian rationalism is all here – specifically, Descartes’s well-nigh total neglect of any negative outcomes from scientific discovery or research is a sign of the bourgeois mission “to recover and discover” the world toward its own vision of perfection (per-ficere, to render flawless through work) – toward its own Utopia. Hence, the positive charge of Cartesian rationalism goes beyond a mere inert “mechanicism” – robotic, conflictual, and pessimistic, like Hobbes’s – in favour of a more Baconian eudaemonic slant. In the event, even as he sought to evade it, mechanicism was Descartes’s only way out of his helpless idealism: he remained so close to mechanicism – especially Hobbes’s in physics and politics (cf. C. Schmitt’s “The State as Mechanism in Hobbes and Descartes”, Appendix to Der Leviathan) – that whenever he sought to elucidate his “method” or “rules” he invariably resorted to the industrial artisanal reality around him.
Because of the impossibility of reconciling the (idealistic logico-mathematical) intellect with the (material scientific) world, Descartes was forced to point to a (scientific?) “method” that is purely “deductive” and therefore tautological! In attempting to reconcile the universal mathesis and its absolute determinism with the drive to reconstruct the truth and the world to a humanized environment, to an earthly paradise, Descartes is forced to resort to human “skills” in which he sees a “method” (non-existent in reality) that is literally pro-ductive and mechanical at one and the same time.
Our method…resembles the procedures in the mechanical crafts, which have no need of methods other than their own, and which supply their own instructions for making their own tools. If, for example, someone wanted to practise one of these crafts…but did not possess any of the tools, he would be forced at first to use a hard stone…as an anvil, to make a rock do as a hammer, to make a pair of tongs out of wood…Thus equipped, he would not immediately attempt to forge swords, helmets, or other iron implements for others to use; rather, he would first of all make hammers, an anvil, tongs and other tools for his own use (Rules).
In reality, what Descartes has done is to reduce his purported “scientific method” to the mere instinctive human practical – immanentist – invention of means to satisfy their needs! By conceding that his method “resembles the procedures in the mechanical crafts” (“mechanical”, not intellectual, crafts!), Descartes ends up proving the exact opposite of what he intended – that is to say, precisely that there is “no need of methods other than” the practices that humans end up adopting instinctively to satisfy their physio-logical (physical and mental) needs! But here it is no longer the mathesis universalis that determines work; rather, it is work that subsumes the mathesis, the physics, the science, the technology, to itself in order to satisfy existing human needs and to pro-duce new ones (cf. Negri, op.cit., p.299).
It is not “science” that dictates our technical productive activity, but rather it is our technical productive activity that we rationalize and institutionalise as “science”. The very fact that Descartes resorts to manufacturing skills to exemplify the substance of his “method” evinces, first, the inability to distill such a method from human technical activity, and, second, the impossibility of splitting human activity into the “scientific-theoretical” and the “technological-practical”! In reality, all human productive activity is technical-practical. Homo faber and homo sapiens are identical entities. Descartes intuits but does not see that his “rules” and “method” merely mimic the practical activity of homo faber – that, in other words, science is merely the abstraction of technological activity – or, put succinctly, that homo faber and homo sapiens form an indivisible whole.
Descartes could never bridge the gnawing gap that his rational idealism opened between the two antinomic approaches to the lifeworld; consequently, he cannot explain the world except as a mechanism because his logico-mathematical deductive reasoning is simply and wholly inapplicable to the empirico-inductive productive manufacturing practices humans adopt in reality – and in vastly growing numbers in his own time as capitalist manufacturing industry supplants the old and moribund feudal mode of production and its theocratic societies. Regardless, he could not ignore completely the epochal changes occurring all around him in his theoretical epistemological framework. Descartes himself highlights this “turn” in the Discourse on Method where his insistence on the bon sens (good sense or common sense) goes hand in hand with the adoption of French as the discursive language freed from the logico-deductive strictures and metaphysical and theological prejudices embedded in the Latin language – clearly heralding his adherence to the growing revulsion at the segregation of the logico-deductive reasoning of the Latin-speaking learned strata in favour of the empirico-inductive productive practices of artisans.
To summarise, then, the antinomies of Cartesian rational idealism encapsulate, on one side, the inability of the earliest bourgeois philosophical reflection to comprehend the profound transformation of European society from a theocratic absolutist feudal order to that of a rapidly expanding capitalist marketplace society founded on formally free labour and manufacturing industry; and, on the other side of this antinomic thought, they provide the theoretical impetus for a revaluation of technical-scientific and empirio-inductive industrial labour as against the millenary dominance of dogmatic Scholastic logico-mathematical deductive thought. The socio-political and economic significance of this “great transformation” (to borrow a phrase used in a different historical context by Karl Polanyi) is lucidly recapitulated by Paolo Rossi here:
Also within the ambit of philosophy there arose a valorization of the arts and crafts vastly different from the traditional: some of the procedures utilized by technicians and artisans to transform nature help in the understanding of natural reality….To introduce tools and instruments in science, to conceive them as a source of truth, was not an easy task. Truth, in the science of our time, refers, almost exclusively, to the interpretation of signs generated by instruments…The defence of mechanical arts from the charge of being undignified, the renewed emphasis on the coincidence of the horizons of culture and that of the liberal arts, on one side, and practical work and servile work , on the other, implied in reality the abandonment of a millenary image of science, they implied the end of an essential distinction between knowing and doing. (My translation and emphases.)
Tambien en el ambito de la filosofia surge lentamente una valoracion de las artes bastante diferente de la tradicional: algunos de los procedimientos que utilizan los tecnicos y artesanos para modificar la naturaleza ayudan al conocimiento de la realidad natural…Introducir los instrumentos en la ciencia, concebirlos como fuentes de verdad, no fue una impresa facil. Ver, en la ciencia de nuestro tiempo, quiere decir, quasi exclusivamente, interpretar signos generados por instrumentos….La defensa de las artes mecanicas de la acusacion de indignidad, el rechazo de la coincidencia entre el horizonte de la cultura y las artes liberales y entre las operaciones practicas y el trabajo servil implicaban en realidad el abandon de una imagen milenaria de la ciencia, implicaban el fin de una distincion esencial entre conocer y hacer. (P. Rossi, El Nacimiento de la Ciencia Moderna en Europa, p.27.)