– It’s becoming more and more important in philosophy…That’s what makes Pascal so amazingly modern: mathematician and philosopher are one.
– Ah, good old Pascal. Funny you should mention him, I’m rereading him at the moment.
– I’m very disappointed … I feel I know him by heart, and yet it tells me nothing…it all seems so empty. I’m a Catholic, or at least I try to be…But if that’s what Christianity is about, I’m an atheist … Are you still a Marxist?
– Absolutely. For a Communist, Pascal’s wager is very relevant today. Personally, I doubt very much that history has any meaning. Yet I wager that it has – so I’m in a Pascalian situation … only that hypothesis allows me to go on living.
– Mathematical hope. Potential gain divided by probability.
– It was Gorky, Lenin or maybe Mayakovsky who said, about the seizure of power in the Russian Revolution, that they were forced to take a one in a thousand chance, because hope became infinitely greater if you took that chance in a thousand.
— Eric Rohmer, Ma Nuit Chez Maud (1969)
Jean-Réné Vernes, Le Principe de Pascal-Hume et le fondement des sciences physiques (The Pascal-Hume Principle and the Foundation of the Physical Sciences).
We could begin perhaps with what appears to be a commonly-agreed aspect of the critique of ‘correlationism’: that it singularly fails to account for the ‘resistance’ of things in the world, not only to each other, but to our thoughts [see below, ‘The Phantasm of the Object’]. On my reading, it is exactly this resistance that Vernes will identify as ‘matter’ per se, and his work details the consequences of Hume’s failure to make a proper place for it within rational philosophy. Vernes locates the genesis of the declination of modern philosophy from science in Hume’s solution to ‘his’ problem of causation. Apparently revealing the lack of any rational basis for the hypothesis of matter, his solution led to philosophy redefining its role as that of giving an account of the concatenation of sensations – whether under an ‘phenomenological’ or ‘empiricist’ rubric—and thus to its ineluctable divergence from the science of ‘real things’, indissociable from the ‘materialist hypothesis’. That this divergence is held as a constitutive triumph of modern philosophical reason represents a baffling problem for would-be opponents of correlationism—after all, must they not agree that Hume proved that there was no rational basis for causality? In which case, how to escape its fateful consequences? What is strongest in Vernes’ book is that he approaches this puzzle as one that cannot be solved through denying Hume his reasoning but only through a reconfiguration of our model of ‘reason’ itself.
The fundamental argument of Vernes’ book is not only that our ‘common-sense’ notion, shared with the working hypothesis of the physical sciences—namely that there is such a thing as matter, independent of our consciousness—is ultimately correct, but that it can be founded rationally. And what is so disconcerting about the survival, the dominance even, within philosophy of the conviction that matter does not or may not exist, suggests Vernes, is not so much its conflict with common sense but its incompatibility with the scientific conception of the world. Vernes shows how Hume and Kant, beginning with a quite justified and groundbreaking critique of common-sense realism and its unquestioned trust in the existence of matter, foundered on an important point and failed to establish what would properly be a ‘speculative realism’—one in which matter would become problematic but nonetheless unquestionably existent. Vernes sets out to furnish the missing, positive part of the argument. There is no question of refuting Hume’s argument, then, but rather of showing that Hume himself drew unwarrantedly prohibitive conclusions from it, which were then profoundly exacerbated by Kant.
Indeed Vernes claims that it is in Kant’s solution to Hume’s problem, ‘modern philosophy, characterised by its rejection of matter, was born very precisely in 1781, at the moment that Kant published his Critique of Pure Reason.’[p67] Before Copernicus, it was believed that the earth, and man, were at the centre of the universe. The greatness of the actual Copernican revolution was that he replaced this with an ‘objective conception’. But whereas we believed before Kant that it was the properties of material objects that determined the order of our perceptions, Kant adopted Hume’s own misconstrual of his critique of causality and ended up ‘transferr[ing] the necessity of laws from the object to the subject’[p67], with the result that we have lived through ‘two centuries of a strange philosophy, in formal opposition with science’[p67]
To replace both common-sense realism and philosophical scepticism with a rational materialism means reconfiguring rationality as such. To do this, we must pick apart the supposedly essential bonds between logic, causality, and necessity: ‘we must reject the rigid conception of reason forged by classical thought on the model of geometry, which leads us to an intransigent determinism, in favour of introducing in parallel to deductive reason an aleatory reason’. Vernes’ proposition is that ‘the existence of matter does not result from the principle of causality, as Hume very rightly showed, but it can be established, with the same certitude as that with which Hume ruined the belief in the principle of causality’ [p.66-7]
Imagine that you—a sharp-witted Scottish philosopher—have just arrived in 17th Century France, eager to immerse yourself in the shady demi-monde of Parisian gambling dens. Arriving at such an establishment, you loiter nearby whilst a game is played with small cuboid objects. Unaccustomed to such games, you take the opportunity, unnoticed, to secretly examine one of these ‘dice’; observing its six equally-spaced and equally-sized sides, and concluding that there is no reason to believe it will fall on one side rather than another, you decide as a rule of thumb that any of the six numbers are equally possible. Armed with this knowledge, you join the game confidently, but in the course of twenty rounds, and apparently to the amusement of the more seasoned players at the table, your die seems to turn up ‘1’ on every single throw. Do you (a) protest loudly that something untoward is at work here, and demand the die be cut open to establish whether it has been ‘loaded’; or (b) conclude that, since your hypothesis has proved useless, and one can evidently know nothing a priori about the outcome of such games, that your only remaining options are either to devote yourself to keeping a meticulous record of every dicethrow you see; or to just slink off with your purse a great deal lighter?
It is the fundamental thesis of Jean-René Vernes’ book that such a choice is at the root of a misprision of the nature of reason that has reigned for hundreds of years and that has bequeathed to us all the problems of post-Kantian doubt as to the existence of matter. In short: if Hume had played dice rather than billiards, he would have avoided drawing a conclusion in favour of empiricism from ‘his’ problem, which was an exemplarily rational one.
This problem, as is well known, is announced in the Enquiry into Human Understanding through the example of the billiard balls. There is no way to deduce a priori how one ball will react when impacted by another. Any number of different outcomes are equally conceivable, and since nothing rationally constrains possibility except for conceivability, no rational basis can be furnished for the principle of causality. Therefore, the principle of causality must be garnered from experience alone.
In demonstrating the rational illegitimacy of the principle of causality, observes Vernes, Hume not only breaks any a priori causal link underlying the constant conjunction of perceptions, but also any reference of those perceptions themselves to some supposedly underlying matter. Hume’s solution results in a reversal of the chain of deduction between an independent matter governed by causal laws – now considered illegitimate—and our perceptions. Now it is the concatenation of perceptions alone which, through experience, might give us the idea of an underlying, causally-linked matter, which idea, however, can never be rationally founded.
Vernes’ account of the results of Hume’s solution to his problem is dramatic, to say the least. Indeed it is depicted as ‘one of the most important revolutions in the history of philosophy’. Logically, if not historically, it leads immediately to the denunciation of science as ‘transcendent’ on the basis that it posits a material hypothesis which neither rationality nor phenomenology can support. Since philosophy thus comes to see the theoretical part of the physical sciences as illegitimate, then it can represent these sciences, if at all, only in a pragmatic, instrumental register: this is the root, then, of the Heideggerian ‘critique’ of the hegemony of technology and science, on the basis of philosophy’s deeper engagement with the world. However, as we well know, philosophy, being equally deprived of any means to explain ‘how’ things act, must retreat to a contemplation of the fact that they are at all, and their manifestation ‘for us’—the Heideggerian-Wittgensteinian meditation presiding over much of twentieth-century philosophy.
Vernes affirms that Hume’s verdict on causality, both impeccably rational and catastrophic, cannot be rescinded. Rather he seeks to return to its scene and, supplementing Hume’s reasoning with a principle drawn from probability theory, to suggest a widened conception of reason itself. Thereby, he suggests, we would not only resolve the vexed question concerning the relation between rationality and the physical world, but would simultaneously bring science—for which the materialist hypothesis is a sine qua non—and philosophy—with its distrust of anything beyond immediate appearance and/or the power of reason—back into accord.
Hume’s operation is firstly to reduce causality to its immediate evidence: certain perceptions follow others consistently, and the analysis of causality is therefore to start with these ‘givens of consciousness’. Concluding that there is no rational basis for our expectation that these constancies should continue into the future, and that all thinkable outcomes of the impact of the billiard balls are, according to reason, equally possible, Hume finishes by admitting an essential contradiction between reason and experience, and by ceding the domain of causality, and thus of matter, to experience: Nothing can be said a priori of the relations between what we had taken to be real material things, nor of their supposed relation to our perceptions.
Hence Hume’s peculiar position as both the author of a profound breakthrough in our rational understanding of the world and as the progenitor of empiricism and perhaps even phenomenology, with all its woes: he founds an impeccably rational deduction upon the givens of consciousness, in order to show that the principle most important to our rational explanation of the order of the world cannot be justified. What went wrong?
Vernes’ answer is that the first moment of the analysis—that all imaginable outcomes are equally possible—is understood by Hume as a negative conclusion, as the signal for a resignation to experience, whereas in fact it is a highly significant positive rational precept. Of course, for Hume too, everything hangs on this moment: if any one of the multiple possible outcomes attendant on the impact of the billiard balls were a priori more thinkable than the others, then the ‘problem’ would not exist at all: the physical order of things would be rationally cognisable. But having secured this important truth, Hume understands it negatively and thus fails to draw the correct consequences from his problem.
Kant exacerbated the problem by affirming Hume’s critique but finding nevertheless what seems a solid basis for causality. But the enthusiastic adoption by later philosophers of Kant’s solution failed to take account of the drastic trade-off it entailed: for here causality is saved only by seating it in the subject of cognition and thereby depriving material objects of any independent reality. In effect Kant—again, with impeccable rationality—generalises and infinitises Hume’s ‘negative’ observation: it is not only that we have no reason to think that one or another outcome will result from the impact of the billiard balls; equally, we have no reason to think that they will even remain billiard balls from one second to the next. This radicalisation is clear in the progression from Hume’s example to that of Kant: the latter invokes the famous cinnabar, ‘being sometimes black, sometimes red, sometimes light, sometimes heavy’, and men ‘transforming now into one animal, now into another’. He extends to infinity the realm of possible, thinkable outcomes for any physical situation, seeming to drive home with ever more force the need for a principle of causality to reconcile the gap between thinkability and reality, whilst never rescinding Hume’s demonstration of the impossibility of providing one on a purely logical basis.
Thus extending the changeability of things unto their very objectivity, Kant deduces the reciprocity of substance and causality: with no principle of causality, there would be no substance either, nothing whatsoever for experience to grasp. As is well known, Kant then uses what is essentially a transcendentally-inflected reductio ad absurdum to argue for the necessity of a causal principle, arguing that since coherent experience is demonstrably possible, the principle of causality be located factically rather than rationally, in the constitution of consiousness. It is a priori since it is necessary for any experience whatsoever.
Whereas Hume had turned away from his incipient rationalism in admitting that, reason being powerless to prescribe a priori the principle of causality, we must rely on experience alone—an estrangement of rationality and experience—for Kant, experience per se must conform to the thinkable, and so he refuses the fallback into ‘habit’, introducing instead an anthropological a priori, satisfying the demand for the principle of causality without betraying Hume’s argument.
Now, Vernes salutes Kant’s genius no less than Hume’s, and his appraisal of the contribution of the former brings us to the central argument of the book. It may be true, as was argued almost immediately after the publication of the Critique of Pure Reason, that Kant’s solution begged the question, or simply amounted to an inverse statement of the problem (a memorable moment sees Nietzsche lampooning Kantianism’s tendency to account for every capability of reason with the idiotic ejaculation ‘by means of a faculty!’). But what Kant had realised, argues Verne, and what takes his solution a decisive step beyond Hume’s, is that, whereas in asking the question why there is a contradiction between the thinkable—pure cogitation—and real experience—pure perception—Hume had resigned himself to a recourse to an empiricism of pure perception, Kant had discerned that there was no pure perception: experience, in so far as it is ordered at all, in so far as it diverges from the ‘rational chaos’ of pure thought, is always already adulterated by ‘something else’ that explains this divergence.
Now, rather than ratifying the commonsense belief that this ‘something else’ was, indeed, matter, Kant was obliged to relegate it to the understanding, since he was so much impressed by Hume’s apparent demolition of the hypothesis of independent matter. Kant thus manages to develop the question further, but his implanting of causality in the subject of cognition merely compounds and, for much of modern philosophy, sets in stone Hume’s failure.
Hume had had within his reach a ‘new rationality’ that could have founded the principle of causality without conceding the defeat of reason and collapsing into empiricism; likewise, a development of this ‘new rationality’ would have prevented Kant from internalising the principle of causality, thus negating the hypothesis of real independent material objects and cementing the disastrous path to correlationism and the divergence of science and philosophy. And here Vernes is I think as one with Meillassoux: Hume’s new rationalism is never realised – indeed what Vernes calls Hume’s ‘virtual rationalism’  only becomes what we know as ’empiricism’ through its very default. But what resounds throughout modern philosophy as what we might call the ‘founding defeat’ of speculative realism, has a purely contingent premise. According to Vernes, what prevented Hume from seeing this was, purely and simply, that he used the wrong example, and that he did not approach ‘his’ problem with the mind of a gambler.
The most banal physical experiments provide the first step towards Vernes’ conclusion: if, like Archimedes, we have two crowns identical in appearance, and we wish to find out which is solid gold, which lead plated with gold, we simply weigh them. Finding that they have different weights, we are faced with ‘something’ beyond our perception that demands to be explained. According to Vernes this alone serves to refute the Kantian explanation: the difference is not to be sought within our understanding, since the perceptions of each are identical, but belongs to a still-problematic ‘something else’. We can, if we wish, cut open both crowns, there revealing a manifest difference which could be said to ‘explain’ the difference in weight – but of course we can continue the process by asking why the two substances gold and lead are of different weights This seemingly banal process provides an archetypical example of the process of materialist inquiry for Vernes, and demonstrates the essential importance within it of an encounter with a problematic ‘something else’ unaccountable either by consecutions of perceptions or by reason alone, and of something like the Principle of Sufficient Reason, as demand for a reason for that ‘something’; their combination resulting in the speculative leap to matter.
But for a rigorous Humean, Vernes is suggesting, this experience of two perceptually identical objects that behaved differently would be enough to trigger an empiricist tantrum that would abort all physical science before it had even begun—the thinkable does not coincide with the real, and must therefore be abandoned as any guide to the latter. All we can do is to weigh the crowns interminably.
But, asks Vernes, what is ‘the crucial experiment that will obviate all possible doubt in such a proof’? – that is, which will convince us of the rational necessity for an hypothesisation of matter?
Vernes now turns to Pascal’s theory of probability, first developed in an experiment analogous to that of Archimedes’ crown, and which will finally reveal the positive import of the first moment of Hume’s solution.
Pascal, asked by a gambling friend to calculate the probability of his winning a game of dice, reasoned that a properly-made die had as much chance of falling with one face up as any other. This, argues Verne, represents an essentially a priori conviction owing nothing to experience (Pascal himself not being a player), which puts forward a positive statement as regards a non-manifest, material structure of the die. Pascal’s principle is that what is equally thinkable is equally possible. And, in throwing the die a large number of times, the hypothesis can be justfied by experience, since each face will indeed come up an equal number of times. If, on the other hand, we throw another die, apparently identical, the same number of times, and most often obtain a ‘1’ we come up against a disparity between what is thinkable and what is real, and hence are led to posit a ‘something’ beyond what we intuit in the die—the contradiction between the thinkable and the real leads us to suspect it is loaded.
For Vernes this experiment represents the true ‘foundation of physical theory’[p33] for in ‘showing a case where a law of experience comes out naturally from the nature of things, supposed known, it reinforces the belief that we can do the same when we do not know this nature’[ibid.], that is that what is met with in experience can be cognized a priori through a calculus of probabilities. In other words, although our prior belief in causality, and hence substance, and independent material objects per se may derive from experience, from habit or from evolutionary imperatives, with Pascal’s principle it can for the first time be rationally founded. What blinded Hume to this was that, rather than thinking like a gambler – in terms of what likelihood a given outcome had of obtaining, and thus in terms of a space of possibilities – he thought still in terms of classical reason, in supposing the only viable reason to be a necessitistic rather than probabilistic one.
It is owing to Pascal’s choice of example that, rather than a negative a priori statement (there is no way to choose any one outcome over another), he is able to draw a wholly positive one (all outcomes are equally thinkable, therefore equally possible). He thus confounds the fallback into empiricism or transcendentalism, and, with the principle of a priori probability instead founds the possibility of a rational physics.
Order is an obstacle to thinkability: Experience, in so far as it is ordered at all, can be said to be ‘loaded’ like a die: there is ‘something’ beyond what is thinkable, that makes the real diverge from the latter. Whereas with Hume this apparently inexplicable ‘loading’ of experience, as in the ‘loading’ of a die, was a signal to resign reason and correlate nature with experience alone; and whereas Kant, discerning that experience is never ‘alone’ but unable to reactivate the common-sense belief in matter, attributed the ‘loading’ to the subject of cognition, for Pascal undecidability becomes for the first time a positive rational proposition, the founding proposition of the calculus of probability, a proposition through which we first gain a priori some precious knowledge of that ‘matter’ that is obdurately independent of us.
And this principle is necessary for physical experiments: if we put the apparent ‘loading’ of the results of an experiment involving the freefall of a body down to the constitution of our understanding, this immediately forecloses the possibility of any physical theory. However, such a theory, greatly elaborated, enabled scientists to predict, for example, the rate of freefall of the same body on the moon, even before this was verifiable experientially. In short, if Vernes can convince us of its effectiveness, the founding of physical theory upon Pascal’s principle as rational speculative practice averts all the disastrous ‘correlationist’ consequences with which we are familiar. Otherwise, there is no way to understand the accuracy of scientific predictions concerning circumstances of which we have as yet no experience (and of course a fortiori of ‘ancestral phenomena’):
But if all this still seems in the realm of a demand (and thus of the Principle of Sufficient Reason), it is Vernes’ final aim to reconfigure the relation between causality, the Principle of Sufficient Reason, and a priori reasoning, in order to finally convince us of the efficacy of the Pascal-Hume principle.
In supposing causal reasoning to conform to the necessities of geometry, ‘classical reason’ had imputed to it the character of necessity. Thus we had the principle what is a priori unthinkable (for example, a triangle with four sides) is impossible. The necessity of geometry, transposed to the physical world as the principle of causality, first issues in Descartes rational mechanics, wherein an occult ‘quantity of movement’ must be posited. This occult quantity is, if we may say so, ‘sublimated’ in the Principle of Sufficient Reason as a demand of reason; and, still with geometry as the model, the only way this demand can be satisfied is apparently through a necessity. Therefore the positing of physical determinism results directly from the configuration of ‘classical reason’: PSR is uppermost; it is satisfied analogously in thought by the laws of geometry, in physical reality by the principle of causality. Hume throws this trinity into chaos in realising that the causal principle, far from being self-evident, or guaranteed by divine providence, is a mere hypothesis; and therefore does not satisfy the demand of PSR. Kant resolves this moment of crisis by reversing the terms, so that in effect PSR ends up justifying the principle of causality, situating the source of its necessity in the laws of the understanding.
What should have happened, according to Vernes, is that the principle of a priori probability—that what is equally thinkable is equally possible—ought to have replaced PSR, as highest principle of reason, applicable equally to thought and to physical reality. Seeing sufficient reason not in terms of necessity (which can, as we know after Hume, never be legitimately posited) but in terms of a priori probability, there is opened up the possibility of its rational justification.
But ‘[i]s the axiom that what is equally thinkable is equally possible legitimate? For a rationalist it is legitimate because it is the expression of an immediate evidence, as we saw with the game of dice. But a rational confirmation of this axiom can be found in the following observation: there is no other way in which we can explain aleatory facts’
That is, if several events are a priori equally thinkable, there can be no rational contesting of their equal possibility. It is possible that repeated experience shows us that in fact they are not equally possible; in this case we uncover ‘something’ beyond our perception of the events that must then be accounted for. (But experience cannot teach us this principle itself; it is truly an a priori principle of rational thought.)
Vernes’ more radical reconfiguration suggests that even the principles of geometry are subject to the principle of a priori probability: the reason we need proofs of geometry is because it seems unlikely to us that, for any right-angled triangle, a2=b2+c2 [p45-6]. We can think many other possibilities. PSR—which in classical reason, governs both logical and real reasons according to the model of necessity—in this new model of reason is shown to be derivative of the principle of a priori probability. Likewise, the postulate that underlies logical necessity, that the unthinkable is impossible is reduced to a particular formation of this more powerful principle.
A final, not at all negligible, result of Vernes’ analysis is that there is no paradox, no problem, in this reconfigured model of reason, in accounting for quantum indeterminability: it is an exception that makes manifest the rule. In fact, Vernes suggests that physics has conspired in maintaining its philosophically questionable status: the standard experiments which are held up as exemplary of the physical sciences, like Hume’s billiard balls, obscure rather than manifest the true nature of the principle of a priori probability, because they are non-aleatory cases: this is a block to the imagination in conceiving of the Pascalian principle. Thus, once more, if Hume had chosen crapshooting instead of billiards, the history of Western philosophy may have unfolded differently: Hume’s defeatism takes on the status of a failure of imagination: he could not think in terms of probability; he failed to find the ‘image of thought’ his problem demanded. Therefore he failed to realise the reconfiguration of reason that would replace the necessitarian demand of PSR with the probabilistic principle of a priori probability. Only the latter gives a rational basis for the discovery of matter, in enabling us, beyond the pure observation that ‘experience is loaded’, to discover the infinitely complex nature of this ‘loading’:
I believe there is also posited here a rationalist argument for the indissociabilty of the problematic-speculative and the materialist; moreover, Vernes argues that not only does such an approach mend the rift between philosophy and science, but affines particularly with contemporary—indeterministic—science.
All this, I think, puts into a new perspective Meillassoux’s argument in ‘Potentiality and Virtuality’ (and elsewhere), which is in fact an argument against Vernes. Vernes argues that the reduction of all physical reason to necessity cannot give any account of chance; the latter would necessitate an account of the causal independence of a series of ‘dice-throws’; something that only Pascal’s principle can satisfy: therefore the latter ‘completes reason’ by supplementing ‘necessitating reason’ with an ‘aleatory reason’ But for Meillassoux the Pascalian calculus itself amounts to a betrayal of the chaos Hume’s solution opens up to us. Meillassoux argues that whereas probabilistic reasoning can be applied in the world, the transfinite extent of possible outcomes of any real situation proscribes its use in the case of Hume’s problem. Simply, Meillassoux spoils the congruence of Hume’s and Pascal’s principle by arguing that the probability calculus proposed by the latter can only be applied to phenomena already totalised into a set of cases (the die) and not to the thinkable set of all possible universes (which is, precisely, unthinkable). Therefore Hume has not so much, according to Meillassoux, mistaken the import of his solution as fallen short of its most radical consequences: Meillassoux argues that from the solution that Hume understood as merely negative and limitative we can draw a positive rational conclusion which will allow us to make a supplement to reason very different to that proposed by Vernes: where the latter sees the reappropriation of Hume/Pascal as founding a new legitimacy for physical science and as mending of the divorce between science and philosophy, Meillassoux sees it as resolving a post-Galilean schism within philosophical materialism (viz. that between ‘hylozoism’ and ‘eliminativism’) by rationally legitimating ‘irruption ex nihilo’
There are two different questions to be asked here: not only must we examine Meillassoux’s reasoning (which I think we are in a much better position to do having also considered Vernes’ work) but its motivations, when probability is proposed as the basis for a rational foundation for the physical sciences, for insisting upon preserving a ‘supernatural’ role for ‘true chance’, for a chaos beyond probability?
I will end in suggesting that we must recognise therefore a fundamental difference between Vernes and Meillassoux: it lies in the fact that, however speculatively bold Meillassoux’s thesis, it appears not to be motivated by the promise of a grounding for physical science nor the prospect of a speculative realism but rather by presentiments of an ethical order. Suffice to say that in the sense that in its insubordination of ‘true hazard’ to any calculation, Meillasoux’s refusal of Pascal’s Wager is maybe of a piece with Badiousian Paulism. (Badiou as sublation of Rohmer’s two antagonists: the catholic-mathematician who finds Pascal’s probabilistic christianity ’empty’, the marxist-philosopher who finds the wager indispensable to revolutionary hope!)
Finally, if the whole episode of anti-realism in philosophy was the result of a fateful English disposition not to suspect the good sportsmanship of others, and if the only sure remedy is to bring more cardsharps into philosophy, then we should be doubly glad of Vernes’ presence: he is not only a philosopher but also a world-famous expert on bridge (known best for the Law of Total Tricks).