The problem of ancestrality, or of the arche-fossil, such as we described it in Chapter 1, bears upon the following general question: how are we to understand the meaning of scientific statements about a manifestation of the world which is supposed to be anterior to any human form of the relation to the world? Or again: how are we to conceive of the meaning of a discourse which construes the relation to the world, whether living and/ or thinking, as a fact inscribed within a temporality in which this relation is merely one event among others – a fact situated in a sequence of which it is merely a stage, and not the origin? How is science even capable of conceiving such statements, and in what regard are we to attribute an eventual truth to them?
We must now try to render the formulation of this question more precise. Closer inspection reveals that the problem of the arche-fossil is not confined to ancestral statements. For it concerns every discourse whose meaning includes a temporal discrepancy between thinking and being – thus, not only statements about events occurring prior to the emergence of humans, but also statements about possible events that are ulterior to the extinction of the human species. For the same problem arises when we try to determine the conditions of meaning for hypotheses about the climactic and geological consequences of a meteor impact extinguishing all life on earth. We will use the term ‘ diachronicity’ to provide a general characterization of all such statements about events that are anterior or ulterior to every terrestrial-relation-to-the-world – the former expressing the temporal hiatus between world and relation-to-the-world that is inherent in the very meaning of such discourse. Accordingly,
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it is the conditions of meaning for diachronic statements in general that concern us.
But the latter does not only pertain to certain types of scientific statement, or only to a specific type of scientific research, such as could be restricted to the science of dating, for instance. For what is at stake in diachronicity is indeed the nature of empirical science in general. The problem of diachronicity is not just a function of the fact that science has actually established a temporal hiatus between being and terrestrial thought; it concerns the fact that this is a possibility that was rendered meaningful by the very inception of modern science. It is not the question of fact that we are concerned with – i.e. the fact that diachronic statements are verified or falsified – but rather the question of right or principle; that is to say, the question of the status of the discourse which renders the verification or falsification of such statements meaningful. Science could in principle have discovered a synchronicity between humanity and world, since there is nothing to rule out a priori the compatibility between mathematical physics and such a hypothesis (i.e. the hypothesis of a human species as old as the cosmos) – yet this would not have prevented us from raising the problem of diachronicity in spite of it. For the fundamental point is this: even if science had discovered this synchronicity, this would still have been a discovery – which is to say that it is precisely insofar as modern science is mathematized that it is capable of raising the question of a possible temporal hiatus between thinking and being – of construing the latter as a meaningful hypothesis, of giving it meaning, of rendering it tractable – whether in order to refute it or confirm it. It is precisely this capacity of scientific discourse which concerns us – its ability to give meaning to the possibility of the diachronic – not whether this possibility is confirmed or rejected. Ancestrality has allowed us to highlight the difficulty which modern philosophy has when it comes to thinking a certain type of contemporary scientific discourse – but what we are ultimately concerned with pertains to what seems to us to be the fundamental property or trait of Galileism, which is to say, of the mathematization of nature.
In order to properly grasp the nature of this property, it is necessary to understand in what regard Galileism endowed diachronic discourse with a hitherto unprecedented scope. Certainly, humans did not have to wait for the advent of empirical science in order to produce accounts of what had preceded human existence – whether in the shape of Cyclopes, Titans, or Gods. But the fundamental dimension presented by modern science from
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the moment of its inception was the fact that its assertions could become part of a cognitive process. They were no longer of the order of myths, theogonies, or fabulations, and instead became hypotheses susceptible to corroboration or refutation by actual experiments. The term ‘hypothesis’ here is not intended to suggest a kind of unverifiability that would be peculiar to such statements. We do not mean to imply the idea that no ‘direct’ verification of diachronic statements is possible by definition, since the occurrences to which they refer are posited as anterior or ulterior to the existence of human experience. For as a matter of fact, this absence of ‘direct verification’ holds for a great many scientific statements, if not for all of them, given that very few truths can be attained through immediate experience and that generally speaking, science is not based upon simple observations, but rather upon data that have already been processed and quantified by ever more elaborate measuring instruments. Thus, in qualifying the statements of empirical science as ‘hypotheses’, we do not seek to undermine their cognitive value but rather to confer upon them their full value as instances of knowledge. It is the discourse of empirical science which, for the first time, gives meaning to the idea of a rational debate about what did or did not exist prior to the emergence of humankind, as well as about what might eventually succeed humanity. Theories can always be improved and amended, but the very fact that there can be such diachronic theories is the remarkable feature made possible by modern knowledge. It was science that made it meaningful to disagree about what there might have been when we did not exist, and what there might be when we no longer exist – just as it is science that provides us with the means to rationally favour one hypothesis over another concerning the nature of a world without us.
But if science thereby renders diachronic knowledge possible, this is because it allows us to consider all of its statements – or at least all its statements about the inorganic – from a diachronic point of view. For the truth or falsity of a physical law is not established with regard to our own existence – whether we exist or do not exist has no bearing upon its truth. Certainly, the presence of an observer may eventually affect the effectuation of a physical law, as is the case for some of the laws of quantum physics – but the very fact that an observer can influence the law is itself a property of the law which is not supposed to depend upon the existence of an observer. Once again, the fundamental point at issue is not the fact that science is spontaneously realist, since the same could be said of every discourse, but rather the fact that science deploys a process whereby we
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are able to know what may be while we are not, and that this process is linked to what sets science apart: the mathematization of nature. Let us try to be more precise about this. What fundamental change did Galileo bring about in our understanding of the link that ties mathematics to the world? There was nothing new about the geometrical description of phenomena, since Greek astronomy had already described stellar trajectories in geometrical terms. But these descriptions pertained to the ‘immediately geometric’ aspect of the phenomenon – what was subjected to mathematics was the unalterable form of a trajectory or a determinate surface area – in other words, a motionless expanse. Galileo, by way of contrast, conceives of movement itself in mathematical terms, and particularly the movement which appears to be the most changeable of all: the falling of terrestrial bodies. In doing so, he uncovered, beyond the variations of position and speed, the mathematical invariant of movement – that is to say, acceleration. From that point on, the world becomes exhaustively mathematizable – the mathematizable no longer designates an aspect of the world that is essentially immerged within the non-mathematizable (i.e. a surface or trajectory, which is merely the surface or trajectory of a moving body), it now indicates a world capable of autonomy – a world wherein bodies as well as their movements can be described independently of their sensible qualities, such as flavour, smell, heat, etc. The world of Cartesian extension is a world that acquires the independence of substance, a world that we can henceforth conceive of as indifferent to everything in it that corresponds to the concrete, organic connection that we forge with it – it is this glacial world that is revealed to the moderns, a world in which there is no longer any up or down, centre or periphery, nor anything else that might make of it a world designed for humans. For the first time, the world manifests itself as capable of subsisting without any of those aspects that constitute its concreteness for us.
It is this capacity whereby mathematized science is able to deploy a world that is separable from man – a capacity that Descartes theorized in all its power – that rendered possible the essential alliance between the Galilean and Copernican revolutions. In speaking of ‘the Copernican revolution’, what we have in mind is not so much the astronomical discovery of the decentring of the terrestrial observer within the solar system, but rather the much more fundamental decentring which presided over the mathematization of nature, viz., the decentring of thought relative to the world within the process of knowledge. The Galilean-Copernican
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revolution effectively consisted in the fact that both these events – astronomical decentring and mathematization of nature – were seized upon by their contemporaries as intimately corrected. And this correction in turn consisted in the fact that the mathematized world harboured within it what Pascal, on behalf of the libertine, had diagnosed as the eternal and frightening silence of infinite spaces – that is to say, the discovery that the world possesses a power of persistence and permanence that is completely unaffected by our existence or inexistence. From its inception, the mathematization of the world bore within it the possibility of uncovering knowledge of a world more indifferent than ever to human existence, and hence indifferent to whatever knowledge humanity might have of it. In this way, science carried within it the possibility of transforming every datum of our experience into a diachronic object – into a component of a world that gives itself to us as indifferent, in being what it is, to whether it is given or not. Thus, the Galilean-Copernican revolution has no other meaning than that of the paradoxical unveiling of thought’s capacity to think what there is whether thought exists or not. The sense of desolation and abandonment which modern science instils in humanity’s conception of itself and of the cosmos has no more fundamental cause than this: it consists in the thought of thought’s contingency for the world, and the recognition that thought has become able to think a world that can dispense with thought, a world that is essentially unaffected by
whether or not anyone thinks it.1 Let’s clarify the sense of this latter assertion. We claimed that the diachronic statement expressed the very essence of modern science, insofar as the latter made it possible to integrate such statements into the realm of knowledge, as opposed to that of myth or fabulation. Such statements certainly do not claim that there could be no relation to the world other than the human relation to the world – we cannot prove that diachronic events could not have been the correlates of a non-human relation to their occurrence (i.e. we cannot prove that they were not witnessed by a god or by a living creature). But science’s diachronic statements assume that the ‘question of the witness’ has become irrelevant to knowledge of the event. In other words, the decay of the radioactive material, or the nature of the stellar emission, are described in such a way that they must be assumed to be adequate to what we manage to think about them, while the question as to whether or not they were witnessed becomes irrelevant to the adequacy of this description. Or again: both this decay and this emission are conceived in such a way that they would
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have been identical to what we think about them even if human thought had never existed to think them. This is in any case a feasible hypothesis, which science renders meaningful, and which expresses the latter’s general capacity to be able to formulate laws irrespective of the question of the existence of a knowing subject. Thus, the decentring inherent in the Copernican-Galilean revolution proceeds by way of a Cartesian thesis, viz., that whatever is mathematically conceivable is absolutely possible. But it is important to note that the absolute here is not understood in terms of the capacity of mathematics to designate a referent that is assumed to be necessary or intrinsically ideal – rather, the absoluteness at issue here expresses the following idea: it is meaningful to think (even if only in a hypothetical register) that all those aspects of the given that are mathematically describable can continue to exist regardless of whether or not we are there to convert the latter into something that is given-to or manifested-for. Consequently, this diachronic referent may be considered to be contingent while simultaneously being considered to be absolute: it can be construed as an event, an object, or a processual stability, that need not be shown to be unconditionally necessary, since this would be contrary to our ontology. On the other hand, however, the meaning of the diachronic statement about a radioactive decay older than all terrestrial life is only conceivable if it is construed as absolutely indifferent to the thought that envisages it. Accordingly, the absoluteness of that which is mathematizable means: the possibility of factial existence outside thought – and not: the necessity of existence outside thought. Whatever is mathematizable can be posited hypothetically as an ontologically perishable fact existing independently of us. In other words, modern science uncovers the speculative but hypothetical import of every mathematical reformulation of our world. Consequently, the Galilean-Copernican decentring wrought by science can be stated as follows: what is mathematizable cannot be reduced to a correlate of thought.
Yet this is where we encounter a rather disconcerting paradox. This paradox is the following: when philosophers refer to the revolution in thought instituted by Kant as ‘the Copernican revolution’, they refer to a revolution whose meaning is the exact opposite of the one we have just identified. For as everyone knows, in the Preface to the second edition of the Critique of Pure Reason, Kant presents his own revolution in thought
under the banner of the revolution wrought by Copernicus2 – instead of
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knowledge conforming to the object, the Critical revolution makes the object conform to our knowledge. Yet it has become abundantly clear that a more fitting comparison for the Kantian revolution in thought would be to a ‘Ptolemaic counter-revolution’, given that what the former asserts is not that the observer whom we thought was motionless is in fact orbiting around the observed sun, but on the contrary, that the subject is central
to the process of knowledge.3 But what was the goal of this Ptolemaic revolution in philosophy, and what did it hope to achieve? What was the fundamental question on the basis of which the 1st Critique reconfigured the whole of philosophy? It was the question about the conditions under which modern science is thinkable – that is to say, the conditions of the Copernican revolution in the literal and genuine sense of the term. In other words, the philosopher who placed the task of understanding the conditions of possibility for modern science at the heart of his project is also the philosopher who responded to this exigency by abolishing its initial condition – thus, the Copernico-Galilean decentring carried out by modern science gave rise to a Ptolemaic counter-revolution in philosophy. Even as thought realized for the first time that it possessed in modern science the capacity to actually uncover knowledge of a world that is indifferent to any relation to the world, transcendental philosophy insisted that the condition for the conceivability of physical science consisted in revoking all non-correlational knowledge of this same world.
It is important to underline the ‘violence’ of this contradiction, the extraordinary nexus that it seems to constitute: ever since the Kantian revolution, it has been incumbent upon ‘serious’ philosophers to think that the condition for the conceivability of the Copernican decentring wrought by modern science is actually provided by a Ptolemaic re-centring of thought. While modern science discovered for the first time thought’s capacity to accede to knowledge of a world indifferent to thought’s relation to the world, philosophy reacted to this discovery by discovering the naïvety of its own previous ‘dogmatism’, seeing in the ‘realism’ of pre-Critical metaphysics the paradigm of a decidedly outmoded conceptual naïvety. The philosophical era of correlation corresponds to the scientific era of decentring, and corresponds to it as its very solution. For it was in response to the very fact of science that philosophy embraced the various modes of correlation – science’s decentring of thought relative to the world led philosophy to conceive of this decentring in terms of thought’s unprecedented centrality relative to this same world. Since 1781 (the date of the 1st edition of the Critique of Pure Reason), to think science philosophically
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has been to maintain that philosophical Ptolemaism harbours the deeper meaning of scientific Copernicanism. Ultimately, philosophy maintains that the patently realist meaning of the claims of modern science is merely apparent, secondary, and derivative; the symptom of an attitude that is ‘naïve’ or ‘natural’ – admittedly, the latter is not merely the result of a simple ‘error’, since it belongs to the essence of science to adopt such an attitude – but once again, it is a derivative attitude, a mere offshoot of that primordial relation to the world which it falls to the philosopher to uncover.
Ever since Kant, to think science as a philosopher has been to claim that science harbours a meaning other than the one delivered by science itself – a meaning that is deeper, more originary, and that furnishes us with the truth of the latter. And this more originary meaning is correlational: it construes those elements that seem to be indifferent to our relation to the world in terms of that relation itself. It collapses the decentring wrought by science onto a centring which delivers its veritable meaning. The philosopher thereby claims to have also carried out what he calls, following Kant, his own ‘Copernican revolution’ – a claim which cannot but strike us as a fantastic obfuscation. In philosophical jargon, ‘Copernican revolution’ means that the deeper meaning of science’s Copernican revolution is provided by philosophy’s Ptolemaic counter-revolution. We will henceforth refer to this ‘reversal of the reversal’ as the ‘schism’ of modern philosophy, which expresses the following paradox: it is only since philosophy has attempted to think rigorously the revolution in the realm of knowledge brought about by the advent of modern science that philosophy has renounced the very thing that constituted the essence of this revolution; that is to say, science’s non-correlational mode of knowing, in other words, its eminently speculative character. It is worth lingering a little longer over the astonishing singularity of the Kantian revolution, whose repercussions continue to be felt among the philosophical community. This revolution consisted, first of all, in providing a decisive ratification of science’s primacy over metaphysics in the realm of knowledge. It was Kant who succeeded in thinking – with a degree of radicality unmatched by any of his predecessors – science’s promotion over metaphysics as privileged guarantor of knowledge. Henceforth, it is the man of science, rather than the metaphysician, who becomes, by Kant’s own admission, the ‘piston of knowledge’. Since Kant, metaphysics has been forced to revise its claim to be in possession of a theoretical knowledge of realities that are equal or even superior to those
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known by the sciences. And since Kant, philosophers in general have become willing to admit that science and science alone provides us with theoretical knowledge of nature, and that speculative metaphysics can no longer present itself as harbouring knowledge of a supposedly higher reality (i.e. cosmos, soul, or God) than the reality accessible to us by means of empirical science.
But science’s promotion over philosophy as guarantor of knowledge has become the locus of a misunderstanding, not to say wrong-footing, that appears to be without precedent in the annals of thought – for it is at the very moment when philosophy attempted for the first time to think rigorously the primacy of scientific knowledge that it decided to abjure precisely that aspect of thought which constituted the revolutionary character of scientific knowledge: its speculative import. It is at the very moment when philosophy claimed to be acknowledging its own supersession by science in the realm of knowledge that it renounced as ‘moth-eaten dogmatism’ its own capacity to think the object ‘in-itself’ – precisely the mode of thinking that, for the first time, was concurrently being promoted to the status of potential knowledge in the context of this very science. Even as science, by virtue of its power of decentring, revealed to thought the latter’s own speculative power, philosophy, at the very moment when it was ratifying this takeover, did so by abjuring all speculation, which is to say, by renouncing any possibility of thinking the nature of this revolution. Something akin to a ‘catastrophe’ occurred in this changeover from metaphysics to science as guarantor of knowledge – Copernican science provided the impetus for philosophy’s abandonment of speculative metaphysics, but this abandonment was reflected back onto Copernican science as philosophy’s Ptolemaic interpretation of the latter. Thus, philosophy’s message to science was: ‘it is you (and not speculative metaphysics) that holds the reins of knowledge, but the underlying nature of this knowledge is the very opposite of what it seems to you.’ In other words, in providing the impetus for philosophy’s destruction of speculative metaphysics, science also destroyed any possibility of a philosophical understanding of its own essence.
Moreover, far from being mitigated, this ‘schism’ has only been further ‘aggravated’ since Kant. For the more science has exhibited thought’s actual capacity to probe ever more deeply into a world anterior to all humanity, the more ‘serious’ philosophy has exacerbated the correlational Ptolemaism inaugurated by Kant, continually tightening the ambit of the correlation while ascribing to this increasingly constrictive realm
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the true meaning of the ever expanding domain of scientific knowledge. While ‘the man of science’ has intensified the decentring due to scientific knowledge by uncovering diachronic occurrences of increasingly ancient provenance, ‘the man of philosophy’ has been narrowing the ambit of the correlation towards an originally finite ‘being-in-the-world’, or an epoch of Being, or a linguistic community; which is to say, an ever narrower ‘zone’, terrain, or habitat, but one of which the philosopher remains lord and master by virtue of the alleged singularity of her specific brand of knowledge. While the Copernican revolution has revealed its full extent, philosophers have accentuated their own pseudo-Copernican counter-revolution, remorselessly exposing the metaphysical naïvety of their predecessors by contracting the bounds of knowledge ever more stringently within the limits of humanity’s present situation. And so it is that philosophers today vie with one another in terms of Ptolemaic narrowness while hoping to unveil the genuine meaning of a Copernican decentring whose scope has never seemed so vast or blindingly evident as it is now.
How did we arrive at this state of affairs? What happened in philosophy after Kant to render philosophers – and only them, it seems – incapable of understanding science’s Copernican revolution as a genuine Copernican revolution? Why did philosophy not take the course exactly opposite to the one followed by transcendental or phenomenological idealism, viz., the course of a thought capable of accounting for the non-correlational scope of mathematics, which is to say, for the very existence of science, the latter being properly understood as the power to decentre thought? Why did philosophy, in attempting to think science, err towards transcendental idealism instead of resolutely orienting itself, as it should have, towards a speculative materialism? How is it that the most urgent question which science poses to philosophy has become, as far as philosophy itself is concerned, the pointless question par excellence, viz. how is thought able to think what there can be when there is no thought? We should not be deceived: no correlationism, however insistent its anti-subjectivist rhetoric, is capable of thinking a diachronic statement without destroying its veritable meaning, and this at the very moment when it claims to have excavated its supposedly deeper meaning. The veritable meaning of the diachronic statement is indeed, as we have seen, its literal meaning, which must concurrently be thought as its deepest meaning. The meaning of the diachronic statement is: ‘event X occurred
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at such and such time prior to the existence of thought’ – and not, let us emphasize it: ‘event X occurred prior to the existence of thought for thought’. The first statement does not claim that event X occurred prior to thought for thought – what it says is that thought can think that event X can actually have occurred prior to all thought, and indifferently to it. But no variety of correlationism, no matter how vehemently it insists that it should not be confused with subjective idealism à la Berkeley, can admit that this statement’s literal meaning is also its deepest meaning. And as a matter of fact, once one has conceded that it makes no sense to claim that what is can be thought independently of the forms through which it is given to a thinking being, then it is no longer possible to accord to science that what it says is indeed the last word about what it says. It becomes impossible to assign to philosophy the task of grasping the ultimate meaning of science in science’s diachronic statement, or of understanding how such a statement is possible as its ultimate meaning. Thus, correlationism will have no option but to try to recapture this diachronicity of scientific discourse in terms of the alternative we examined earlier:
- Either, this anteriority is only actually anterior to humanity insofar as
it is the correlate of a thought that cannot be reduced to our empirical
existence; in which case we proceed to eternalize the correlation in a
manner comparable to Husserl’s eternalization of the transcendental
ego, which supposedly survives the death of every empirical ego.4 2. Or, the genuine meaning of this anteriority consists in its being no
more than present thought’s retrojection of a past that gives itself to
thought as anterior to thought.
Since the first option (the eternalization of the correlation) would be tantamount to a return to metaphysics (the absolutization of the supposedly primordial determinations of subjectivity), correlationism in the strict sense will always opt for the second option, and hence for the retrojection of the diachronic past on the basis of the living present in which it is given. In this way, the schism of modernity – according to which the Ptolemaism of thought harbours the deeper meaning of the Copernicanism of science – reaches its apogee in this ‘topsy-turvy’ past, which has been trotted out and re-utilized in many different forms by thought. This is the ultimate expression of the schism: the deep meaning of the pre-human past consists in its being retrojected on
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the basis of a human present that is itself historically situated. While science, through its rigorous mathematization of nature, uncovered a time wherein humanity could come into existence or be abolished while that time remained unaffected, philosophical time has sought to demote the time of science to the level of a ‘vulgar’, ‘derivative’, or ‘standardized’ form of originary correlational temporality, being-in-the-world, or the
relation to a supposedly primordial historicality.5 And this transmutation of the diachronic past into a retrojective correlation exerts such a sway over thought today that it sometimes seems as though it encapsulated the modicum of knowledge philosophers can still lay claim to. You thought that what came before came before? Not at all: for there is a deeper level of temporality, within which what came before the relation-to-the-world is itself but a modality of that relation-to-the-world. It is this countersensical temporality that provides the originary sense for the naïve natural attitude espoused by non-philosophers, including those who are most knowl-edgeable. And the most marvellous thing of all about this whole business is that this becoming – in which what came before no longer comes before, and what comes after no longer comes after – allows whomever grasps its truth to propagate its counter-sense in such a way as to undermine every received idea. You think that a precursor is someone who comes before those who follow after? Well, you’re wrong: the precursor is not the one who comes before, but rather the one whom the successors subsequently claim came before. Thus, the precursor qua precursor comes after her successors . . . This is the peculiar knowledge to which philosophers lay claim, a knowledge that sometimes seems to amount to little more than these rigmaroles wherein time is turned upside down, the better to contrive a countersensical redoubling of the time of science. A peculiar knowledge indeed, which renders us incapable of grasping precisely that which is actually most gripping about the temporality of science – the fact that science does indeed think that what comes before comes before, and that what came before us came before us. For it is precisely this power of thought and none other that constitutes the formidable paradox of manifestation uncovered by science, which philosophy should have been endeavouring to think during these past two centuries: how is empirical knowledge of a
world anterior to all experience possible?6
Let us return to our original question: what is it that has kept this alternative course of thought blocked ever since Kant? Why did transcendentalism’s rejection of speculative thought exert such an undivided sway
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over the realm of philosophy at the very moment when science called – as it had never done before – for the constitution of a form of speculation capable of identifying its conditions of possibility? What is the meaning of this ‘Kantian catastrophe’, of which contemporary correlationism is
merely an exacerbated consequence?7 Why have philosophers accom-modated themselves for so long to this correlationist deception, which was supposed to provide them with the key to a scientific revolution that has continually contradicted their claims? We only have to listen to Kant for the answer: who was it that, by his own admission, ‘woke’ him from
his ‘dogmatic slumbers’?8 Who encouraged him – and every subsequent correlationist – to relinquish every form of absolute in thought? Kant tells us explicitly: it was David Hume – that is to say, the problem of the causal connection as raised by Hume – or to put it more generally, the destruction
of the absolute validity of the principle of sufficient reason.9 It now becomes possible to identify the three fundamental stages of the Kantian ‘catastrophe’, as well as the nature of the deception which lies at its source: 1. The Copernico-Galilean event institutes the idea of a mathematical knowledge of nature – a nature that is henceforth stripped of its sensible qualities. It is Descartes who provides the initial philosophical ratification for the Galilean event. An initial equilibrium between physics and metaphysics is established through Descartes’ rigorous distinction between the mathematical knowledge of nature and the knowledge of those qualia that are considered to be attributes of thinking alone. In short, it is Descartes who ratifies the idea that nature is devoid of thought (which is also to say that it is devoid of life, since the two are equivalent for him), and that thought is able to think this de-subjectivated nature through mathematics. But the absolute scope of mathematics is founded upon the metaphysical demonstration of a sovereign, perfect and supposedly veracious God who alone is able to guarantee the new science’s capacity to know the truth.
- However, as the Galileo-event unfolds, revealing the fallaciousness of all previous varieties of metaphysical knowledge, it also exposes the vanity of every attempt to provide a metaphysical foundation for physics. For the Galilean event does not only consist in the mathematical de-subjectivation of the world, but also in the destruction of every form of a priori knowledge of why the world is as it is. The idea that we could acquire definitive and necessary knowledge about what exists in this world – rather than having to be satisfied with reconstructing it as a fact – is gradually eroded as science exhibits its ability to destroy all previous
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forms of knowledge – including those that had been proposed under the aegis of the new science, as was the case with Cartesian vortices. Thus, the Hume-event constitutes the second philosophical ratification of the Galileo-event by demonstrating the fallaciousness of all metaphysical forms of rationality, which is to say, by demonstrating the fallaciousness of the absoluteness of the principle of sufficient reason – thought must renounce every form of demonstration intended to establish a priori that whatever gives itself as being thus and so must unconditionally be thus and so. The world’s being-thus-and-so can only be discovered by way of experience, it cannot be demonstrated to be absolutely necessary. 3. The Kant-event then exposes this collapse of metaphysics in its definitive and enduringly stable form by turning correlational knowledge into the only philosophically legitimate form of knowledge. Correlationism becomes the only licit form of philosophy as the henceforth conditional knowledge of our relation-to-the-world, which alone is capable of thinking science insofar as the latter has deposed speculative metaphysics, even though science itself has not renounced every form of universality. Since we can no longer accede to an unconditionally necessary truth of the kind sought for by Leibniz (whether in the form of an infinitely perfect God or the best of all possible worlds), we must renounce every variety of theoretical absolute, and content ourselves with uncovering the general conditions for the givenness of phenomena. In other words, in order to salvage the possibility of producing a priori statements, philosophy must dissociate the a priori from absolute truths, and construe it instead as the determination of the universal conditions of representation. Accordingly, the deception that presides over this catastrophe is revealed to be what we earlier referred to as the ‘de-absolutizing implication’, that is to say, the idea that there is an irrefutable inference from the end of metaphysics to the end of absolutes. Since science has convinced us that all metaphysics is illusory, and since every absolute is metaphysical, then it follows that, in order to think science, we must renounce every form of absolute. But by the same token, we must also renounce the belief in the absolute scope of mathematics – the absolute scope that actually constitutes the very essence of the revolution in thought engendered by modern science. Thus, the Kantian catastrophe within whose parameters we continue to operate does indeed consist in renouncing every kind of absolute along with every variety of metaphysics.
Yet this was not what modern science actually required. Certainly, the latter’s capacity to undermine all previous forms of knowledge enjoined
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us to stop believing that knowledge could demonstrate that a determinate reality must, absolutely and necessarily, be the way it is rather than some other way; but it also enjoined us to think that other mode of absoluteness that it had introduced for the first time into thought, in the form of the latter’s Copernican decentring. And this is why, if we are to think the Galilean-Copernican fact of science without denaturing it further, we must think, as Descartes did, the speculative import of mathematics, but this time without relying, as he did, upon the metaphysical pretension to be able to prove the existence of a perfect being, which alone is supposedly capable of guaranteeing mathematics’ own intrinsic mode of truth. Philosophy’s task consists in re-absolutizing the scope of mathematics – thereby remaining, contrary to correlationism, faithful to thought’s Copernican decentring – but without lapsing back into any sort of metaphysical necessity, which has indeed become obsolete. It is a matter of holding fast to the Cartesian thesis – according to which whatever can be mathematized can be rendered absolute – without reactivating the principle of reason. And this seems to us to be the task of the principle of factiality, a task that is not only possible but also urgent: to derive, as a Figure of factiality, the capacity, proper to every mathematical statement, through which the latter is capable of formulating a possibility that can be absolutized, even if only hypothetically. It is a question of absolutizing ‘the’ mathematical just as we absolutized ‘the’ logical by grasping in the fundamental criterion for every mathematical statement a necessary condition for the contingency of every entity.
Clearly, then, our speculative reformulation of what we must now call ‘Kant’s problem’ can be stated as follows: how is a mathematized science of nature possible? This problem can be broken down into two others, each of which concerns the speculative import of mathematics, but in a different way.
- First, the speculative resolution of Kant’s problem presupposes the factial resolution of the problem of ancestrality (or of diachronicity), which is to say, a demonstration to the effect that every mathematical statement – precisely insofar as it is mathematical – is not necessarily true, but absolutely possible. Thus, we must establish the following thesis, which we have already stated, by deriving it from the principle of factiality: what is mathematically conceivable is absolutely possible. 2. Moreover – and here we come back to our earlier discussion of the problem of the causal connection – the resolution of Kant’s
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problem presupposes that we have achieved a speculative rather than merely hypothetical resolution of Hume’s problem. For it is also necessary to establish the legitimacy of the assumption that the stability of natural laws, which is the condition for every science of nature, can be absolutized. If empirical science is actually possible, we said, this is on account of the actual stability of the laws of nature. But it is now clear that this stability must be established as a mind-independent fact if we want to achieve a decisive break with contemporary Ptolemaism. Thus, it is a question of establishing that the laws of nature derive their factual stability from a property of temporality that is itself absolute, which is to say, from a property of time that is indifferent to our existence, viz., that of the non-totalizability of its possibilities. This is just to reiterate once more the need to establish the speculative scope of mathematics, but with one significant difference – it would no longer be a matter, here, of deriving the absolute though hypothetical scope of any mathematical statement whatsoever, but rather of deriving the absolute and now unconditionally necessary scope of a particular theorem, viz., the theorem that allows us to maintain the non-totalizability of the transfinite.
Consequently, we are faced with the requirement of a twofold absolutization of mathematics. The absolutization inherent in the problem of diachronicity basically asserts that every mathematical statement describes an entity which is essentially contingent, yet capable of existing in a world devoid of humanity – regardless of whether this entity is a world, a law, or an object. Accordingly, this is an absolutization that could be called ontical: it pertains to entities that are possible or contingent, but whose existence can be thought as indifferent to thought. By way of contrast, the absolutization of the Cantorian non-All requires an absolutization that is ontological, rather than ontical, because it now states something about the structure of the possible as such, rather than about this or that possible reality. It is a matter of asserting that the possible as such, rather than this or that possible entity, must necessarily be untotalizable. Consequently, we are obliged to produce a factial derivation capable of establishing that, even if there are conceivable mathematical axiomatics that rule out the transfinite or disqualify the impossibility of a set of all sets, this does not imply that the non-All is merely one possibility among others. It must not imply that there are certain worlds whose possibilities are totalizable, while there are others whose possibilities are not. What must be demonstrated at this juncture is that only those theories that ratify the non-All harbour an ontological scope, while those others, which
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allow for some sort of conceivability of the All, would be merely ontical in scope, since the totality which they invoke, or the non-totality which they refuse to ratify, betray the fact that they are describing a totalizable entity, or a totalizable world, as opposed to the untotalizable being of worlds.
It is clear then that the speculative resolution of Kant’s problem will have to proceed by way of a derivation of the absolutizing scope of mathematics capable of resolving both the problem of diachronicity and that of Hume. The condition for the resolution of the first problem is a speculative resolution of the general problem – without which science loses its intrinsically Copernican sense; while the resolution of the second problem requires a non-metaphysical resolution of the general problem – without which science loses itself in the mysteries of real necessity. But both require a factial resolution of the problem, insofar as the factial is defined as the very arena for a speculation that excludes all metaphysics.
No doubt the question remains obscure in this formulation. But our goal here was not to tackle this resolution as such. Our only aim has been to try to convince the reader not only that it is possible to rediscover thought’s absolutizing scope, but that it is urgent that we do so, given the extent to which the divorce between science’s Copernicanism and philosophy’s Ptolemaism has become abyssal, regardless of all those denials that serve only to perpetuate this schism. If Hume’s problem woke Kant from his dogmatic slumber, we can only hope that the problem of ancestrality succeeds in waking us from our correlationist slumber, by enjoining us to reconcile thought and absolute.
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