It was Descartes’ most fervent desire to lay the ground work for a science in which certainty was not merely a distant hope, but a reality. The historical failure of philosophy to obtain such a firm grasp on the world, as well as the apparent shortcomings of the empirical sciences with respect to the certainty of their predictions, might have driven him, as it did others, to abandon the goal of certainty, and to retire to the realm of probability. Instead, he sought to bring such clarity to philosophy as to strike upon a new path, where certainty marked each progressive judgement, and the slow but steady journey toward understanding all that could be understood would ultimately reveal the total intelligibility of this world, for all humanity to behold. Descartes felt the fulfillment of this endeavour would likely not come in his lifetime, and the task was of such proportions as to exceed the lifetime of any single individual. Rather, he limited his task to the grounding of such certainty, and the explication of that method by which any person might build upon recognized certainties ever larger truths as they are successively revealed to the unfettered (and learned) intellect.

It therefore seemed surprising, especially to his contemporary commentators, that Descartes should refuse to find the truths of mathematics and geometry among the most certain available for contemplation. Indeed, it is quite clear that, while allowing that such truths are immutable and eternal, their certainty is nevertheless contingent to the existence of God. And this, most notably expressed in Descartes’ thinking in the Meditations, is to say that God (who’s existence is contained in, and the cause of, the idea of God) is the cause of the immutable and eternal truths. It is one of Descartes’ most subtle and important puzzles. How can a truth be both immutable (and eternal) and dependent upon something that so exceeds our comprehension as God? Indeed, how can a fact be dependent upon an idea? It appears to be the most profound crossing of necessity with contingency. Given his goal of obtaining a clear vision of certainty in all that can be known, it seems counterproductive to cast the certainty of such fundamental truths into question.

It should be noted in fairness that this tension is never expressed as paradoxically as I have chosen to do here. Descartes, when he does discuss such tensions, largely avoids mention of necessity or contingency, and instead looks directly to the causal order contained in the very fabric of intelligibility. Nevertheless, the tension is a real one, both for Descartes and for those around him. It is a difficulty whose resolution lay not merely in understanding the place immutable truths held in the Cartesian universe, but also, and more importantly, in understanding the interdependent nature of his notions of God, truth, and judgment. Ultimately, it is Descartes’ quest for certainty which demands the realm of judgment maintain a rule of causality, and so abandons the privileged status of eternal truths as needless of metaphysical justification (Eternal they may be; but without a cause they would be nothing). It is that endeavor which requires that such truths have foundations.

Although this tension first receives a public voice in the publication of his Meditations, Descartes had expressed it earlier in a number of letters to Marin Mersenne, as early as the Spring of 1630. At the time, he was working on his text of The World. He wrote Mersenne, “... I have found how to prove metaphysical truths in a manner which is more evident than the proofs of geometry ...”^[1] Where this might seem a boast of relative certainty only with respect to the firm grounding he had found for metaphysics, it soon becomes clear that it is also a challenge to the certainty attributed to the mathematical truths.

The mathematical truths which you call eternal have been laid down by God and depend on him entirely no less than the rest of his creatures. Indeed to say that these truths are independent of God is to talk of him as if he were Jupiter or Saturn and to subject him to the Styx and the Fates.^[2]

At first it might seem that the attribution of ‘eternal’ to the mathematical truths here is something Descartes wishes to distance from himself. The attribution seems to be one he considers blasphemous. Indeed, it would be rather easy to diffuse some of the tension by simply denying the status of such truths as being eternal. Later use of the expression might then be understood a grudging acknowledgment that his contemporaries held such truths in high regard, and would be too distracted by such a radical and explicit departure from precedent, to give proper attention to his examination of the ‘metaphysical’ truths. Unfortunately, such a direct alleviation of the tension is not accurate to Descartes’ thinking in the Meditations^[3], and neither is it accurate to his thinking at the time he wrote this to Mersenne. Assuming his work on the early portions of The World can be taken as an indication of his thoughts at that time concerning the eternal nature of such truths, he considered them central to the truths necessary for the generation of a world such as ours.

In the grand thought experiment, which is The World, Descartes embarks upon the task of generating a world capable of ideally replicating all “real” world phenomenon, in an attempt to isolate those relationships sufficient for its constitution. He identifies three primary physical laws: conservation of “state” (a law of material inertia); conservation of motion as distributed among many bodies (conservation of momentum, but without a clear recognition of, or role for, entropy); and, a clear distinction between the tendency toward movement and the motion of an object (now understood as the distinction between force and velocity). Then he adds:

... I shall be content with telling you that apart from the three laws I have expounded, I do not wish to suppose any others but those which follow inevitably from the eternal truths on which mathematicians have usually based their most certain and most evident demonstrations — the truths, I say, according to which God himself has taught us that he has arranged all things in number, weight, and measure. The knowledge of these truths is so natural to our souls that we cannot but judge them infallible when we conceive them distinctly, nor doubt that if God had created many worlds, they would be as true in each of them as in this one.^[4]

It would be an unfortunate irony if one were to conclude from this passage that Descartes still understood the mathematical truths as something God has followed in the creation of the world. Such an error can soon be corrected with a look back to the letters sent to Mersenne, but the point of this passage should be kept in mind. The mathematical truths, whatever their metaphysical status with respect to God, are eternal (even necessary) for Descartes. Indeed, in his Discourse on Method, he clearly places great metaphysical value on the truths of the mathematical sciences:

... I have noticed certain laws which God has so established in nature, and of which he has implanted such notions in our minds, that after adequate reflection we cannot doubt that they are exactly observed in everything which exists or occurs in the world.^[5]

However, here as elsewhere, he is cautious to warn against an inference often drawn from the startling power of the maths to capture reality. Responding to the possibility that men might think such truths are on that account independent of God’s will, he writes:

As for the eternal truths, I say once more that ‘they are true or possible only because God knows them as true or possible. They are not known as true by God in any way which would imply that they are true independently of him’. If men really understood the sense of their words they could never say without blasphemy that the truth of anything is prior to the knowledge which God has of it. In God willing and knowing are a single thing in such a way that ‘by the very fact of willing something he knows it and it is only for this reason that such a thing is true’.^[6]

It is from a comment of this sort that the sources of the tension, as well as its ultimate resolution, can be seen. Built into the Cartesian models of truth and understanding is a perspective rarely taken in the pursuit of reality. Ultimately, this perspective can only be adequately revealed in the relationship between the notion of truth and the role the idea of God plays in the Cartesian metaphysical reality of The Meditations.

Metaphysics, for Descartes, is not simply an endeavor into that which is, but more importantly remains an endeavor into that which can be known. It is a metaphysics which maintains an essentially epistemic flavour. It is the human understanding, and not the postulated behavior of physical entities, that forms the fundamental realm of reality. The mathematical truths, as relationships discerned among the entities of the extended realm, come to us, not as bodies, but as objects to the understanding. And their status before the understanding remains uncertain until their relationship to God, as God stands before the understanding, is revealed to the intellect. This is not to say that Descartes considered the mathematical truths incidental to the constitution of reality. Indeed, they remain central to the constitution of reality because they are so related to our understanding. Such truths, including all eternal truths, are the language by which the world is revealed to us.

There is no single [law in nature] that we cannot grasp if our mind turns to consider it. They are all ‘inborn in our minds’ just as a king would imprint his laws on the hearts of all his subjects if he had the power to do so. The greatness of God, on the other hand, is something we cannot grasp even though we know it.^[7]

Although elsewhere he is quick to assert “... the existence of God is the first and the most eternal of all possible truths and the one from which alone all others proceed,”^[8] God’s incomprehensibility remains, throughout Descartes’ thought, an important aspect of distinction between the truth of God’s existence and all other eternal truths. But before this distinction is faced directly, it would be imprudent not to clarify the realm in which the human intellect exists. It is only in this realm, radically divided from the realm of the corporeal early in the Meditations (represented by the categorical division between mind and body), that truth has any sense.

The activity of the intellect, by which Descartes finds such certainty in the proposition ‘I exist’, is the native ground of truth. That which is, and the relationships that exist, may be discerned with greater or lesser degrees of clarity only within the context of judgment and the ‘natural light’. In cases concerning the connections between ideas and truths, and the drawing of inferences from what is revealed by the ‘natural light’, judgement is the mind’s movement toward affirmation or denial. In cases concerning those ideas and truths themselves, refined to their pure being, it is the ‘natural light’ alone by which we know them.

Whatever is revealed to me by the natural light — for example that from the fact that I am doubting it follows that I exist, and so on — cannot in any way be open to doubt. This is because there cannot be another faculty both as trustworthy as the natural light and also capable of showing me that such things are not true.^[9]

The ‘natural light’ cannot fail to reveal truth. Just as the eyes do not lie, and the ears cannot deceive, but by the activity of our intellect in moving from sensory reports to judgment, so too, in a manner of speaking, the ‘natural light’ only reports the being of the intelligible world. It is only a manner of speaking, because it is only the ‘natural light’ which reveals to us the core components of thought, and reports the substance of intelligibility. Making sense of corporeal data can only take place in terms of what is reported by the ‘natural light’. Indeed, the reality of the corporeal is itself a postulation of the intellect, insofar as the attribution of existence to such a realm is an act of judgement which, as such, involves only the bare intelligibles objected to the mind by such a faculty (if it is to obtain the status of truth).^[10] It is this faculty then, above the corporeal senses, which has the most direct and certain contact with being.

Paradoxically, a result of such reasoning seems to be the attribution of being to those phantoms of thought, and flights of fancy, which seem to most often be the source of error concerning the constitution of the world. This is clearly avoided in the case of the imaginative fictions (such as the unicorn) by Descartes’ placement of the imagination along side the other corporeal senses (although distinguished by its being an active faculty), thereby removing the generation of corporeal fictions from the proper activity of the intellect. However, in the case of mathematical ‘fictions’ (in the sense that no one has ever experienced a perfect square in the corporeal world), and many other abstract entities, he does insist on their positive reality.

... I find within me countless ideas of things which even though they may not exist anywhere outside me still cannot be called nothing; for although in a sense they can be thought of at will, they are not my invention but have their own true and immutable natures. When, for example, I imagine a triangle, even if perhaps no such figure exists, or has ever existed, anywhere outside my thought, there is still a determinate nature, or essence, or form of the triangle which is immutable and eternal, and not invented by me or dependent on my mind.^[11]

The ‘natural light’ reveals the being of things other than (and independent of) the self. Truth is, in this sense, thoroughly substantial for Descartes. But it should not on this account be considered a perfectly uniform realm of being. A further distinction, within the substance so revealed to the intellect, is central to the conclusion that all truths, no matter how ‘necessary’, are contingent to God’s existence.

The mind’s acquaintance with the being of truths can be of two sorts for Descartes. The distinction is drawn between the finitude of our own thought and the infinity (i.e. God) necessary for the sustenance of such being as the mind experiences. The experience of God might be thought to entirely evade apprehension, as such being necessarily exceeds the mind’s capacity to ‘know it at a glance’. But Descartes responds:

... it is possible to know that God is infinite and all powerful although our soul, being finite, cannot grasp or conceive him. In the same way we can touch a mountain with our hands but we cannot put our arms around it as we could put them around a tree or something else not too large for them. To grasp something is to embrace it in one’s thought; to know something, it is sufficient to touch it with one’s thought.^[12]

Illuminated by the ‘natural light’, truth can confront the intellect in two forms. In those cases where we are said to grasp a thing, it is entirely revealed in uncontrovertible simplicity. However, where a thing so overwhelms our capacity for direct and utter illumination, we may still touch upon it with the intellect, such that its nature where we touch, as well as its total transcendence of our grasp, are equally (and completely^[13]) revealed.

... if I can comprehend something, it would be a total contradiction for that which I comprehend to be infinite. For the idea of the infinite, in order to be a true idea, cannot be grasped at all, since the impossibility of being grasped is contained in the formal definition of the infinite. Nonetheless, it is evident that the idea which we have of the infinite does not merely represent one part of it, but really does represent the infinite in its entirety.^[14]

Infinity here is not the common twentieth century mathematical notion, where various magnitudes of infinity have been discerned (eg. by which we now accept the notion that there are infinitely more irrational numbers than rational numbers, even though both number sets are ‘infinite’). Rather, the Cartesian notion of the infinite precisely means that which exceeds human understanding. The nature of our understanding concerning God, then, cannot occur by direct illumination, but only by the certainty of those conditions under which God’s nature would be contradicted.

... from the fact that I cannot think of God except as existing, it follows that existence is inseparable from God, and hence that he really exists. It is not that my thought makes it so, or imposes any necessity on any thing; on the contrary, it is necessity of the thing itself, namely the existence of God, which determines my thinking in this respect. For I am not free to think of God without existence [...] as I am free to imagine a horse with or without wings.^[15]

This kind of epistemic confrontation is no less a source of certainty than the direct intellection of simple truths. Indeed, because of the nature of the truth of God’s existence, it is entirely more certain than any other truths. Structurally, the inferential significance of such knowledge is not unlike that surrounding the more complex mathematical relationships.

... it is not necessary that I ever light upon any thought of God; but whenever I do choose to think of the first and supreme being, and bring forth the idea of God from the treasure house of my mind as it were, it is necessary that I attribute all perfections to him, even if I do not at that time enumerate them or attend to them individually. [...] In the same way, it is not necessary for me ever to imagine a triangle; but whenever I do wish to consider a rectilinear figure having just three angles, it is necessary that I attribute to it the properties which license the inference that its three angles equal no more than two rights angles, even if I do not notice this at the time.^[16]

Notice, however, that existence does not belong to the essence of a triangle. The status of truth corresponding to the various propositions properly said of a triangle are therefore only true, (i.e. something), insofar as they rest upon (are contingent to) the idea of God as a supremely perfect being. They are contingent to God, because their existence (or their somethingness — which is their truth) as eternal things is derivable only from an eternal being for which existence is a part of its essence. God is all that qualifies:

There are many ways in which I understand that this idea is not something fictitious which is dependent on my thought, but is an image of a true and immutable nature. First of all, there is the fact that, apart from God, there is nothing else of which I am capable of thinking such that existence belongs to its essence. Second, I cannot understand how there could be two or more Gods of this kind; and supposing that one God exists, I plainly see that it is necessary that he has existed from eternity and will abide for eternity. And finally, I perceive many other attributes of God, none of which I can remove or alter.^[17]

These attributes are not limited, either in number or inferential capacity, to those distinctly known by the intellect. Given the relationship of finite intellect to this infinite truth, it is hardly surprising that Descartes would assure Mersenne: “In general we can assert that God can do everything that is within our grasp but not that he cannot do what is beyond our grasp.”^[18] And here the notions of existence and causal activity come together. While God is the only being (native to the realm of intelligibility) which exceeds the comprehension of the mind, the transparency of all other truths itself demands a causal origin only God can satisfy. God’s existence is his causal necessity. The power of God, representing nothing other than his existence before the intellect, demands recognition of a hierarchy of being within the realm of truth.

... since God is a cause whose power surpasses the bounds of human understanding, and since the necessity of these truths does not exceed our knowledge, these truths are therefore something less than, and subject to, the incomprehensible power of God.^[19]

Still, it might seem puzzling, that such a truth (as that which necessarily exceeds human comprehension) can be known with sufficient clarity to ground the certainty of any other truths. Indeed, most of God’s attributes are determined by a sort of negative knowledge, where it is shown that God cannot be the sort of being without such properties. But Descartes provides a subtle and important observation concerning the sort of knowledge involved, when citing support from the words of St. Paul (and even echoing Plato’s work in the Symposium) he says:

... those who do not have love, and hence do not have sufficient knowledge of God, do not know things as they ought to know them, even though they may think they have some knowledge in other matters; for we must begin with knowledge of God, and our knowledge of all other things must then be subordinated to this single initial piece of knowledge, ...^[20]

It would be a grave disservice to Descartes if one were to dismiss such language as somehow tangential, or a mere salutation to the power of religion. Love and knowledge are essentially connected, and it is precisely the mind’s capacity to be ‘lost in the face of God’ that attests to the foundational character of God’s existence. This truth is not simply a matter of deferential inference, where “... it is just as much a contradiction to think of God (that is, a supremely perfect being) lacking existence (that is, lacking a perfection), as it is to think of a mountain without a valley,”^[21] but is a positive confrontation of the intellect to a thing eminently larger, and truer, than itself.

The exact inferential role God plays before the mind is more conventionally clear. It depends upon the implications drawn directly from the unity of God’s existence and God’s causal activity.

If anyone attends to the immeasurable greatness of God he will find it manifestly clear that there can be nothing whatsoever which does not depend on him. This applies not just to everything the subsists, but to all order, every law, and every reason for anything’s being true or good. If this were not so, then, ..., God would not have been completely indifferent with respect to the creation of what he did in fact create. If some reason for something’s being good had existed prior to his preordination, this would have determined God to prefer those things which it was best to do. But on the contrary, just because he resolved to prefer those things which are not to be done, for this very reason, ..., ‘they are very good’; in other words, the reason for their goodness depends on the fact that he exercised his will to make them so.^[22]

The causal hierarchy is critical. And symptomatic of the transcendent primacy of God’s existence over all other truths is the freedom of his will. But one should be careful here not to take such a faculty (or attribute) as univocal to both God and human mind. For Descartes, “In God, willing, understanding and creating are all the same thing without one being prior to the other ‘even conceptually’.”^[23] This, along with the recognition of God’s primacy among truths, requires a fundamentally existential God.

It is self-contradictory to suppose that the will of God was not indifferent from eternity with respect to everything which has happened or will ever happen; for it is impossible to imagine that anything is thought of in the divine intellect as good or true, or worthy of belief or action or omission, prior to the decision of the divine will to make it so. I am not speaking here of temporal priority: I mean that there is not even any priority of order, or nature, or of ‘rationally determined reason’ as they call it, such that God’s idea of the good impelled him to choose one thing rather than another.^[24]

Descartes is aware that such a metaphysical landscape gives rise to a number of conceptual difficulties, primarily when directing attention to the status of the eternal truths as being the sort of truths which are immutable and eternal. He responds:

... there is no need to ask how God could have brought it about from eternity that it was not true that twice four makes eight, and so on; for I admit this is unintelligible to us. Yet on the other hand I do understand, quite correctly, that there cannot be any class of entity that does not depend upon God; ... [and, therefore] it would be irrational for us to doubt what we do understand correctly just because there is something which we do not understand and which, so far as we can see, there is no reason why we should understand. Hence we should not suppose that eternal truths ‘depend on the human intellect or on other existing things’; they depend on God alone, who, as the supreme legislator, has ordained them from eternity.^[25]

It should be sufficiently clear at this point that, for Descartes, the truth of God’s existence obtains such a status among the truths available to the intellect that he can insist that, “... it is certain that [God] is the author of the essence of created things no less than of their existence; and this essence is nothing other than the eternal truths.”^[26] However, the exact causal mechanism by which God can properly be said to create (even sustain) essences might remain confused. Descartes, clearly not terribly concerned with such an issue, offers this alternative:

There is no need to ask what category of causality is applicable to the dependence of this goodness upon God, or to the dependence on him of other truths, both mathematical and metaphysical. [... Nevertheless,] it can be called efficient causality, in the sense that a king may be called the efficient cause of a law, although the law itself is not a thing which has physical existence, but is merely what they call a ‘moral entity’.^[27]

However, the Cartesian proof of the causal relationship between God and the eternal truths is based upon the necessities generated by the being of truth itself, and not upon the clarity with which we might understand the ‘category of causality’. As in the case where Descartes observes that the unintelligibility of the possibility that God not have made the eternal truths as they are^[28], it is also the case that the casuistry wherein God creates the substance of judgment need not be intelligible for its reality to be certain.

At the risk of oversimplification, Descartes’ path might be rendered in very simple terms. Truth is only meaningful in terms of judgment. The constituents of judgment are the discerned essences of that which is objected to the mind. Such essences are not subject to the human will. Two such essential truths emerge of critical importance: First, being must have a cause; Second, there is being which exceeds comprehension, i.e. God. Because being, or existence, is fundamentally an issue of mind, the intelligibility of God’s existence is not threatened by the incomprehensibility of his nature. Furthermore, no other object illuminated by the ‘natural light’ contains explicitly the necessity of its own existence. Therefore, whatever being there is, as it is objected to the intellect, must be caused by God. Whatever truth there is, as the successful discernment of being by the intellect in its movement toward judgment, must thereby also rest on the power of God: both in terms of the constituents of intellection, as well as the capacity of the mind to see those constituents (by the ‘natural light’).

Moving past the dangers of such a simplification, and acknowledging the complexities of God’s nature, beyond his incomprehensibility, which are necessary for the inferences to hold, attention can once more be drawn to Descartes’ quest for certainty. It is only when the metaphysical status of truth is resolved, that certainty can flow from the judgments of the mind. That the metaphysical standing of the eternal truths suffer somewhat in the process (by loosing their distinction of absolute self sufficiency), is not entirely surprising, or undesirable. Descartes raises serious questions concerning their standing as sovereign entities. It is for the preservation of the possibility of certainty that the Cartesian God must exist. For Descartes, rejection of this foundation, opens the gates of doubt not only in terms of confused fictions, but also in terms of those truths we find most clearly presented to the mind’s eye.

... the less power the atheist attributes to the author of his being, the more reason he will have to suspect that his nature may be so imperfect as to allow him to be deceived even in matters which seem utterly evident to him.^[29]