“When we look about us towards external objects, and consider the operation of causes, we are never able, in a single instance, to discover any power or necessary connexion; any quality, which binds the effect to the cause, and renders the one an infallible consequence of the other. There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument.”
– David Hume, 1737
“…the fact of the stability of the laws of nature seems sufficient to refute the very idea of their possible contingency… But it is precisely this claim about the real contingency of physical laws that we propose to defend in all seriousness.”
– Quentin Meillassoux
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Quentin Meillassoux proposes Hume’s problem as follows: is it possible to demonstrate that the same effects will always follow from the same causes ceteris paribus, i.e. all other things being equal? In other words, can one establish that in identical circumstances, future successions of phenomena will always be identical to previous successions? The question raised by Hume concerns our capacity to demonstrate the necessity of the causal connection. (AF: 137) He goes on to up the ante by rooting out the difference between Hume’s deterministic physics and our own conception based as it is on quantum mechanics and the Special Relativity theory of an indeterministic science of probabilities saying that we should not conflate Hume’s problem with his deterministic framework, but define it as a more “general problem concerning all laws of nature, irrespective of their eventual specificity” (AF: 140). Which leads to the problem of whether we can have “any guarantee that physics as such … will continue to be possible in the future” (AF: 140). Instead he reformulates Hume’s question saying: “can we demonstrate that the experimental science which is possible today will still still be possible tomorrow?” (AF: 140).
He tells us that up till now three types of responses to the Humean problem have been offered: the metaphysical, sceptical (Hume), and the transcendental (Kant). He briefly details out these responses to Humen’s problem as follows:
1) the metaphysical response defends its position by positing the existence of supreme principle governing the world;
2) Hume’s own sceptical solution is twofold: a) he subscribes to the position that it is impossible to establish the future stability of natural laws by any sort of a priori reasoning (i.e., no metaphysical solution is possible), and, b) he offers instead that since no metaphysical solution to the problem exists, then “we should stop asking ourselves why the laws are necessary and ask instead about the origin of our belief in their necessity” (AF: 143). Instead of a question about the nature of things, we are offered a question about the relation to things – “one no longer asks why the laws are necessary, but why we are convinced that they are” (AF: 143);
3) finally, in Kant’s transcendental response offers his own solution to the problem based on the elaboration of “the objective deduction of the categories as elaborated in the Critique of Pure Reason’s ‘Analytic of Concepts'” (AF: 143). Meillassoux elaborates it as follows:
“…the transcendental enquiry produces an indirect proof of causal necessity, which is to say, a proof by reductio ad absurdum. It proceeds as follows: we begin by assuming that there is no causal necessity, and then we examine what ensues. But what ensues, according to Kant, is the complete destruction of every form of representation, for the resulting disorder among phenomena would be such as to preclude the lasting subsistence of any sort of objectivity and even of any sort of consciousness. Consequently, Kant considers the hypothesis of the contingency of the laws of nature to be refuted by the mere fact of representation. This is the regard in which Kant’s response is conditional – he does not say that it is absolutely impossible that causality could cease to govern the world in the future; he merely says that it would be impossible for such an occurrence to manifest itself to consciousness – and this because if causality ceased to govern the world, everything would become devoid of consistency, and hence nothing would be representable. …[then Kant argues] causal necessity is a necessary condition for the existence of consciousness and the world it experiences. In other words, it is not absolutely necessary that causality governs all things, but if consciousness exists, then this can only be because there is a causality that necessarily governs phenomena.” (AF: 144).
What is common to all three solutions, Meillassoux informs us, is “the fact that none of them ever calls into question the truth of the causal necessity” (AF: 145). He continues says, “In all three cases, the question is never whether causal necessity actually exists or not but rather whether or not it is possible to furnish a reason for its necessity. The self-evidence of this necessity is never called into question” (AF: 145). Then Meillassoux asserts that this is exactly what his speculative philosophy refuses (i.e., the assumption of a causal necessity to begin with). He asks us how “could reason, for which the obvious falsity of causal necessity is blindingly evident, work against itself by demonstrating the truth of such a necessity?” (AF: 147). He tells us a more “judicious approach to the problem of causal connection would begin on the basis of the evident falsity of this connection, rather than on the basis of its supposed truth” (AF: 147). He is astonished by the whole gamut of the philosophical community from Hume’s time till ours saying “philosophers, who are generally the partisans of thought rather than of the senses, have opted overwhelmingly to trust their habitual perceptions, rather than the luminous clarity of intellection” (AF: 147).
Meillassoux suggests that we now must reformulate Hume’s problem as follows: “instead of asking how we might demonstrate the supposedly genuine necessity of physical laws, we must ask how we are to explain the manifest stability of physical laws given that we take these to be contingent” (AF: 148). This implies a further set of questions: “if laws are contingent, and not necessary, then how is it that their contingency does not manifest itself in sudden and continual transformations? How could laws for which there is no permanent foundation give rise to a stable world?” (AF: 148).
Without explicating each and every argument for or against the questions provided we will focus in on Meillassoux’s main thesis based as it is on Cantor’s theorem (transfinite), which provides Meillassoux a mathematical way of “rigorously distinguishing contingency from chance” (AF: 167). After explicating a gloss on Cantor’s theorem he offers a translation of Cantor’s transfinite: the (quantifiable totality of the thinkable is unthinkable (AF: 169). This brings us back his conceptual use of the terms chance and contingency. He describes his use of chance:
“We know that the terms ‘chance’ (from the Vulgar Latin: cadentia) and ‘aleatory’ (from the Latin: alea) both refer back to related etymologies: ‘to fall’, and ‘falling’ in the case of the former; ‘dice’, ‘dice-throw’, or ‘game of dice’ in the case of the latter. Thus, these terms bring together notions that, far from being opposed to one another, are actually inseparable -the notions of play and of calculation, and of the calculation of chance which is inherent in every game of dice. Every thinking in which the identification of being with chance is dominant foregrounds the theme of the dice-totality (which is to say, of the unalterable enclosure of the number of the possible), of the apparent gratuity of the game (the play of life and of a world whose superior artificiality is acknowledged), but also that of the cool calculation of frequencies (the world of life insurance and evaluable risks). The ontology of the enclosure of possibilities inevitably situates us within a world whose aversion to gravity is but the obverse of the fact that it only takes counting techniques seriously” (AF: 174-175).
The influence of Alain Badiou on the thought and practice of Meillassoux’s approach would take us too far afield from our current preoccupations; so I will refrain from explicating the impact of Being and Event on his thought and mathematical conceptual rigours.
On contingency he says,
“…the term ‘contingency’ refers back to the Latin contingere, meaning ‘to touch, to befall’, which is to say, that which happens, but which happens enough to happen to us. The contingent, in a word, is something that finally happens – something other, something which, in its irreducibility to all preregistered possibilities, puts an end to the vanity of a game wherein everything, even the improbable, is predictable. When something happens to us, when novelty grabs us by the throat, then no more calculation and no more play – it is time to be serious. But what is most fundamental in all this – and this was already one of the guiding intuitions of Being and Event – is the idea that the most powerful conception of the incalculable and unpredictable event is provided by a thinking that continues to be mathematical – rather than one which is artistic, poetic, or religious. It is by way of mathematics that we will finally succeed in thinking that which, through its power and beauty, vanquishes quantities and sounds the end of play” (AF: 175).
Now he enters the heart of his own speculative philosophy and the factual approach it offers, saying, “our aim is to supplant the contemporary dissolution of metaphysical problems by a non-metaphysical precipitation of these same problems” (AF: 176). Against this he tells us most modern philosophers will dismiss this issue as non-issue, for the simple reason that, they will tell you, that they find it strange that you are “perplexed by such ‘pseudo-problems'” (AF: 176). He goes on to say this is all part of a larger issue on the part of contemporary philosophy, which is “merely the consequence of the continuing belief in the principle of reason” (AF: 176). These philosophers have accepted, erroneously, that there are limits to thought, which “we now know to be a consequence of the perpetuating denial of metaphysics” (AF: 177). Ultimately it is by abandoning the principle of reason, he argues, that we will begin to make sense of these problems within metaphysics, which leads to a factial approach that abandons the “dissolvent approach to metaphysics as a procedure that has itself become obsolete” (AF: 177). In this type of approach he says that instead of “laughing or smiling at questions like ‘Where do we come from?’, ‘Why do we exist?’, we should ponder instead the remarkable fact that the replies ‘From nothing. For nothing’ really are answers, thereby realizing that these really were questions – and excellent ones at that. There is no longer a mystery, not because there is no longer a problem, but because there is no longer a reason” (AF: 177).
Returning to the factial resolution of Hume’s problem will “require that we derive the non-totalization of the possible from the principle of factiality itself” (AF: 178). In an elaboration of this solution he states it as follows (and I offer it in length):
“…entail absolutizing the transfinite in the same way in which we absolutized consistency – which is to say that we would have to think the former as an explicit condition of contingent-being, rather than merely construing it as a mathematically formulated hypothesis that can be advantageously supported by the speculative. But it is clear that such resolution of the problem would require that we be in a position to do for mathematical necessity what we tried to do for logical necessity. We would have to be able to rediscover an in-itself that is Cartesian, and no longer just Kantian – in other words, we would have to be able to legitimate the absolute bearing of the mathematical – rather than merely logical – restitution of a reality that is construed as independent of the existence of thought. It would be a question of establishing that the possibilities of which chaos – which is the only in-itself – is actually capable cannot be measured by any number, whether finite or infinite, and that it is precisely this super-immensity of the chaotic virtual that allows the impeccable stability of the visible world” (AF: 178-179).
His formulation is an oversimplification of the issue, and he tells us it would need a far more stringent analysis, a “far more complex, but also more adventurous than that of consistency, since it would have to demonstrate how a specific mathematical theorem, and not just a general rule of the logos, is one of the absolute conditions of contingency” (AF: 179). In summing up he tells us that we are now presented with two problems to overcome: the problem of the arche-fossil (i.e., the problem that demanded an unequivocal demonstration of the absoluteness of mathematical discourse), and the problem of Hume (AF: 180).
How he prosposes to do this we will take up in the next essay, for as he says we will need to connect these problems in such a way as “to provide a precise formulation of the task of non-metaphysical speculation” (AF: 180).
For those interested I just discovered Daniel Sacilotto’s blog Being’s Poem, which has an excellent essay on Meillassoux: Answer to Hume’s Problem: click here. Although I found it after writing my own commentary I find that it has some interesting and valid points to make.
1. After Finitude: An Essay on the necessity of Contingency (AF) (2008)