“What fundamental change did Galileo bring about in our understanding of the link that ties mathematics to the world? … Galileo… conceives of movement itself in mathematical terms, and particularly the movement which appears to be the most changeable of all: the terrestrial bodies. In doing so, he uncovered, beyond the variations of position and speed, the mathematical invariant of movement – that is to say, acceleration.”
– Quentin Meillassoux
(Note: this series of essays was written back in 2009-2010… and, do not reflect changes in science or philosophy since that time.)
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With Galileo’s discovery of mathematical laws that could describe the motion of heavenly bodies came a unique realization: that the world in which we live is autonomous, a world that is “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” (AF: 184-185).
Meillassoux reminds us that what is important is not so much the decentering of the earth from its theological framework within scientific knowledge that makes the Copernican revolution so interesting. Instead it is the disquieting paradox residing in this view, which is the “unveiling of thought’s capacity to think what there is whether thought exists or not” (AF: 186). And, this, and this alone brings us to that “sense of desolation” that Meillassoux speaks of saying: “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” (AF: 187).
The main point of this is that the laws that govern our understanding of the universe exist independent of our observation of them, and would remain scientific verities even if there had never been a human subject to conceive them. (AF: 188) The argument proceeds from the Cartesian thesis – that whatever is mathematically conceivable is absolutely possible. He tells us that this should not be conflated with a necessartarian idealism – “rather, the absoluteness at issue here expresses the following idea: it is meaningful to think … 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” (AF: 189). All this leads to Meillassoux’s formulation that “what is mathematizable cannot be reduced to a correlate of thought” (AF: 189).
He continues to show us that the ‘Copernican Revolution’ which is now associated with Kant is just the exact opposite of the one he just formulated. Instead of knowledge conforming to objects, objects now must conform to our knowledge: this is Kant’s revolution, no Copernicus-Galileo’s. With Kant the whole tradition of science that puts the observer at the center of the process of scientific endevour. This is the type of thinking that has led even such physicists as Stephen Hawking to surmise that “We create history by our observation, rather than history creating us” (GD: Loc 1,418).  Meillassoux states that the absurdity of this solution shows us that the very thought that allowed us to uncover knowledge of a world that is “indifferent to any relation to the world” also allowed for a transcendental philosophy – a counter-revolution against this very thought to revoke all non-correlational knowledge of this same world (AF: 191). He goes on to tells us that the astonishing thing is that it is this counter-revolution instigated by Kant himself that place the man of science over the metaphysician as the ‘piston of knowledge’ (AF: 193). From that point forward philosophy in the metaphysical mode was been constrained by empirical science in its descriptions of the real. He tells us that just at that point when philosophy took science to be the sole arbiter of knowledge into its domain that it lost its “speculative import” (AF: 193).
Meillassoux in repetition after repetition hones in on this absurdity of the Copernican counter-revolution and its correlationist gambit, then he asks us “Why did philosophy not take the course exactly opposite to the one followed by transcendental and phenomenological idealism…?” (AF: 195). Further, why didn’t it take “the course of a thought capable of accounting for the non-correlational scope of matematics, which is to say, for the very existence of science, the latter being properly understood as the power to decentre thought?” (AF: 195). In a disquisition of the failings of correlational philosophy in the post-Kantian variety, he returns to 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” (AF: 199).
Ultimately the question arises as to why Kant’s counter-revolution take hold instead of a non-correlational mode of thinking in the way science itself had done? As he states it: “Why did transcendentalism’s rejection of speculative thought exert such an undivided sway over the realm of philosophy at the very moment when science called … for the constitution of a form of speculation capable of identifying its conditions of possibility?” (AF: 200). Meillassoux discovers the ultimate culprit, the one that Kant himself pointed to, is none other than David Hume – “the problem of the causal connection” … “or to put it more generally, the destruction of the absolute validity of the principle of sufficient reason” (AF: 201). All this lead to philosophy renouncing every form of the absolute along with every variety of metaphysics. (AF: 203).
Instead of this Meillassoux tells us that philosophy’s new task “consists in re-absolutizing the scope of mathematics – thereby remaining, contrary to correlationism, faithful to thought’s Copernican de-centering – but without lapsing back into any sort of metaphysical necessity, which has indeed become obsolete. He continues, saying (and I quote at length):
“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” (AF: 204).
This leads him to a new question: how is a mathematized science of nature possible? He breaks this down into two further others of speculative import (and I quote at length):
“1. First, the speculative resolution of Kant’s problem presupposes the factial resolution of the problem of ancestrality (or of dia-chronicity), 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 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 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. (AF: 205)”
What will be required now is a twofold absolu-tization of mathematics. One that is ontical (i.e., “it pertains to entities that are possible or contingent, but whose existence can be thought as indifferent to thought” (AF: 206).); and, ontological, “rather than ontical, because it now states something about the structure of possible as such, rather than about this or that possible reality” (AF: 206). He continues, saying, “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” (AF: 206). This new speculative philosophy will need to resolve “both the problem of dia-chronicity (ancestrality) and that of Hume” (AF: 207). The condition for resolving is both a speculative and non-metaphysical resolution of the general problem: 1) a speculative resolution “without which science loses its intrinsically Copernican sense; and, second, non-metaphysical resolution “without which science loses itself in the mysteries of real necessity” (AF: 207). Ultimately each of these will require a “factial resolution of the problem, insofar as the factial is defined as the very arena for the speculation that excludes all metaphysics” (AF: 207).
In summing up he tells us that the resolution to these problems will need further clarification and work in the future, and that the “goal here was not to tackle this resolution as such. Our 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” (AF: 207). His final thoughts on the subject are that if “Hume’s problem woke Kant from his dogmatic slumber, we can only hope that the problem of ancestrality (dia-chronicism) succeeds in waking us from our correlationist slumber, by enjoining us to reconcile thought and absolute” (AF: 207).
With this I leave the reader to ponder how this will be done. I have only tried to relay a set of notes rather than commentary to understand the issues and concerns around which Meillassoux’s philosophy turns, and why it has had such an impact on our current speculative turn. The problems are left unresolved, yet the path to their resolution has been iterated and ultimately it will either lead toward a resolution or a dead end. Only time will tell which path, speculative or materialist, will win out in this new journey.
1. After Finitude: An Essay on the necessity of Contingency (AF) (2008)
2. The Grand Design by Stephen W. Hawking and Leonard Mlodinow ( 2010 Bantam Books)