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Innate Ideas and the Infinite:
The Case of Locke and Descartes

G. A. J. Rogers

Pierre Gassendi, who did not like nonsense, said of the idea of infinity: ‘if someone calls something "infinite" he attributes to a thing which he does not grasp a label which he does not understand’. 1  Gassendi’s is a harsh judgement for, surely, we all do quite cheerfully and successfully use the concept of infinity, and in a variety of contexts. Yet if Gassendi’s judgement is too hard it is easy enough to have sympathy with his claim. For it is a perennial fact that we never, in Descartes’s phrase, seem to have an ‘adequate idea’ of infinity. Nor is this just because it is an abstract noun like friendship or strength, for it retains this familiar lack of adequacy when it appears in its adjectival or adverbial forms: infinite space, infinite power, infinitely large, infinitely good. It is not my intention in this paper to offer a philosophical account of this familiar state of affairs, though perhaps what I shall have to say will throw some little light on the matter. It is rather to explore how discussions of such questions take us into issues at the heart of the foundations of modern philosophy, and specifically, into the great debate which I will refer to by the usual title as that between the Rationalists and the Empiricists, of whom the protagonists are traditionally identified as Descartes on the one side and Locke on the other.
    It would not be out of place for somebody to say in response to that famous contrast that either it is hackneyed or else it is mistaken. It is hackneyed because we all know that Descartes and Locke represent contrasting traditions in modern philosophy and [49] there is nothing new to be said about it. It is mistaken because, as a matter of fact, it is simplistic to set them up as dogmatic exponents of their respective schools. There are rationalist elements in Locke’s Essay, especially in Book IV, and there is a strong empiricist element in Descartes, especially in his science. Those emphasizing the former, Webb for example in the last century and Aaron in this, 2  have underlined the place of intuition and demonstration in Locke’s account of knowledge. Descartes’s empirical leanings have been noted in his account of the role of experiment in the natural sciences. 3 
    There is of course no denying these aspects of their philosophies. But my path will be more revisionist than supportive of such readings of their work. I shall argue that the dominant (though not the only) strain in Descartes is a rationalist one and that Locke was keenly aware of this and strongly hostile to it. On the other side, whilst Locke was impressed by much of Descartes’s presentation of knowledge, and borrowed heavily from it, he never looks tike subscribing at all to the central rationalist doctrines, and indeed saw his work as a major refutation of them. In all of this his account of our idea of infinity plays an exemplary role. But before we reach Locke we should go back to Descartes. [50]

Descartes and the doctrine of innate ideas

We begin with key passages in Descartes’s third Meditation in which, after the doubts of Meditation 1 and the first truth of Meditation 2 we are offered proof of the existence of God. Inter alia he identifies a tripartite division of ideas into innate, adventitious, and the product of the imagination. 4  This in itself did not, as Descartes well realized, supply the basis for an epistemology. Nor was knowledge to be equated merely with what it was natural to suppose or judge, for example that the causes of my ideas resemble their effects, as is usually assumed in the case of ordinary perceptions. 5  But when some ‘natural light’ informs me of a truth, for example that from the fact that I am doubting it follows that I exist, then what I then accept cannot be open to doubt, because, Descartes says, such truths cannot rationally be brought within the sphere of the doubtful. 6 
    Famously, another such idea is that of God’s existence. As Descartes explains it, ‘the idea that gives me my understanding of a supreme God, eternal, infinite, {immutable,} omniscient, omnipotent and the creator of all things that exist apart from him, certainly has in it more objective reality than the ideas that represent finite substances’. 7  The natural light tells us that there must be as much reality in the cause as in the effect, and the more perfect could not come from the less perfect. So, roughly, the cause of the idea of God must be something itself perfect: the idea of ‘a substance that is infinite, {eternal,immutable,} [51] independent, supremely intelligent, supremely powerful, and which created both myself and everything else . . . that exists’. 8  It is the idea of an infinite substance which can be explained only by an infinite cause, for the idea of substance as such, Descartes says, we could have obtained from the idea of ourself. So the idea of God is both innate within me and explicable only on the assumption of there being an infinite perfect being as its cause.
    There are many facets to Descartes’s ‘proof’ of God’s existence in the third Meditation. But one that I wish to stress is its dependency on two claims: (i) that nothing could explain our idea of infinity except that there be something itself infinite to be its cause; and (ii) that the idea of God is innate. As Descartes says: ‘. . . there is within me the idea of a supremely perfect being. The whole force of my proof depends on this one fact’. 9 
    It follows from the first of these that if an alternative (non-infinite) source for that idea of infinity could be established then the argument for the existence of God would collapse. It is worth underlining this point. It is not simply that we have an innate idea of God as a supremely perfect being that is crucial, for we might have an innate idea that corresponded to nothing, as we might if we had an innate idea of, say, a dragon. The fundamental point is that our having the idea of God as a supremely perfect being, whether innate or not, fails to establish God’s existence unless our having that idea cannot be explained except by postulating the existence of an (infinite) deity to cause that idea.
    The issue of innateness is in itself another matter. It is Descartes’s programme that requires that the idea of God be innate, or at least so he believed. My idea of God as infinite being is one that does not logically depend on or assume the truth of any independent contingent truth external to me. This is important, for at that stage of the Meditations where the proof is introduced he [52] has not yet established the existence of anything other than the self. But if the finite self (because it is finite) cannot be the cause of the idea of something infinite, then something infinite must indeed be that cause, which is, of course, exactly what Descartes wishes to prove.
    Another way to see the point is to notice that it does not matter to Descartes’s argument as to when we acquire the idea of God with his infinite attributes. We might acquire it at conception, in the womb, at birth, or even when we reach some later stage of development. All that has to be conceded is that the cause of the idea could not be some finite thing, whether substance, idea or sense-experience.10 It must be, we might say, a priori or non-existent.
    Fully to appreciate Descartes’s position we must take notice of a very important quality of the Cartesian concept of infinity, namely, that it is a positive concept. To see what he meant by this we need to look deeper into Descartes’s account, and we can begin with a remark about what is involved in his claim that some ideas are innate. The text is a letter to Mersenne in which he reiterates the three-fold classification of ideas we have already noted and says of the third, innate, category that it includes ‘the idea of God, mind, body, triangle, and in general all those which represent true, immutable and eternal essences’.11 He continues: ‘. . . I can draw out from the idea of a triangle that its three angles equal two right angles, and from the idea of God that he exists, etc. . . .’.
    Taken seriously, and I can see no reason why it should not be, this one remark would supply strong reason to suppose that Descartes at least accepted that, say, some part of natural science, [53] certain truths about body, for example, might be known a priori. For a central feature, perhaps the central feature, about innate ideas is that they ground knowledge in a form of intellectual introspection. This position is amply confirmed when we turn to other parts of his writings, and in particular to the most comprehensive account of his metaphysics and natural philosophy, the Principia philosophiæ (the Principles). There he tells us that we can establish a priori not only that matter exists, but also what its essence is. The argument exactly parallels the earlier proof of the self and of God. Just as we can establish the existence and essence of a finite and imperfect mind (ourself) and an infinite and perfect mind (God) so we can also know that matter exists and that its essence consists ‘not in weight, hardness, colour, or the like, but simply in extension’.12 This provides, amongst other things, a simple and conclusive proof of the impossibility of a vacuum and, together with the known immutability of God, a basis for reaching later the fundamental laws of nature, the Cartesian laws of motion, and thus on to the vortex theory of planetary motion and the whole Cartesian cosmology.
    A crucial passage about his philosophical method and its connections with the infinite occurs comparatively early in the Principles. It comes in two parts. First it is an outline of his method and, second, a warning about the natural limitations of the human intellect.
    The method is this: Descartes tells us that since God alone is the true cause of everything, the best path to follow will be to start from knowledge of God himself and therefrom to deduce explanations of things created by him. We shall thus acquire ‘the most perfect scientific knowledge, that is, knowledge of effects through their causes’.13 So far we have the high priori road identified. But then comes the warning: if we are not to go badly [54] wrong, Descartes cautions us, we must always bear in mind that God is infinite and we are ‘altogether finite’. We should never enter into arguments about the infinite and other matters that are beyond our comprehension—for example, the mystery of the Incarnation or of the Trinity.
    It is well known that these passages in Descartes owe much to his very reasonable desire not to follow in the footsteps of Bruno and Galileo. But in the justification which he offers for his position he draws a distinction between the infinite and the indefinite which is of some philosophical interest to us. Our own minds, Descartes says, can discover no limit to, say, extension, or division, or the number of stars God created. But, so as to reserve the word ‘infinite’ for God alone, Descartes decides that these other cases will be called ‘indefinite’ rather than infinite. The implication is that the word ‘infinite’ is to be reserved for a positive feature of only one entity, God. That it is a positive feature of God follows from the fact that God can have no negative features. He is the ‘unity of all perfections’.14 Descartes put the point even more forcefully and without any ambiguity in a letter to Clerselier in 1649:

By ‘infinite substance’ I mean a substance which has actually infinite and immense, true and real perfections. This not an accident added to the action of substance, but the very essence of substance taken absolutely and bounded by no defects; these defects, in respect of substance, are accidents; but infinity or infinitude is not. It should be observed that I never use the word ‘infinite’ to signify the mere lack of limits (which is something negative, for which I have used the term ‘indefinite’) but to signify a real thing, which is incomparably greater than all those which are in some way limited.

He goes on: [55]

I say that the notion I have of the infinite is in me before that of the finite because, by the more fact that I conceive being, or that which is, without thinking whether it is finite or infinite, what I conceive is infinite being; but in order to conceive a finite being, I have to take away something from this general notion of being, which must accordingly be there first.15

Of course it does not follow from the supposed fact that God has the positive property of infinity that we ourselves can have a positive idea of that property, for our understanding of God, our idea of God, is necessarily an inadequate one. But, we are entitled to ask Descartes, if the actual idea we have of the infinite is necessarily inadequate, why to explain its existence is it necessary to invoke a cause for that idea which is much in excess of the effect? As Hume was to underline, an inadequate effect requires only an inadequate cause. But to pursue that line of thought now would be to lead us away from our story.
    Descartes’s claim for the positive nature of infinity as applied to God may be original with him. Certainly in the form in which we have it in the Clerselier letter it is not to be found in the scholastic tradition, even though it could be argued that it is related to a distinction made by Aquinas between the potential limitlessness (infinitum) of, say, matter, and the actual unlimitedness of God, which is an unlimitedness or infinity of being and is perfection itself.16 Aquinas does not, however, underline the distinction between positive and negative infinity in quite the way that is to be found in Descartes. For Aquinas, as for Aristotle, the weight is on the contrast between the potential and the actual, where the potential infinite, just because it is only potential, is thereby not the full infinite to be found only in God. Thus matter [56] is potentially infinite, in the sense that there is no contradiction in supposing it to go on endlessly, but is actually limited. There is something of the positive/negative contrast here but Aquinas never requires it to do the work that Descartes allots to it in the third Meditation. Certainly Descartes, if not original in his distinction, is departing from the standard scholastic account in a way which makes it reasonable to call it the Cartesian account of God’s positive infinity.17

The Cartesian inheritance

So far I have attempted to show that the idea of infinity occupies a central role in Descartes’s philosophy in two related ways. First, in the third Meditation’s proof of the existence of God. And, second, in justifying his commitment to innate ideas. We might ask what influence Descartes’s account had on his contemporaries and successors. Few thinkers of any note remained untouched by his arguments. But in England at least, few became disciples.18 Amongst his most sympathetic readers were the Cambridge Platonists, though none of them could be described as a Cartesian, and the most enthusiastic advocate of the study of Descartes in Cambridge, Henry More, was one of their number though he was never a wholehearted admirer of all Descartes’s views.19 It is to some of his claims that we shall now briefly turn. [57] More was a very different man from Descartes. His earliest works of poetry link him with a mystical Platonism that contrasts sharply with the clear crisp prose of the French philosopher. One of these, Democritus Platonissans; or an essay upon the infinity of worlds out of Platonick principles (1647), supplies part of the justification for Marjorie Hope Nicolson’s judgement on him that ‘[p]erhaps the most important service of Henry More to human thought was his making at home on English soil the idea of infinity’.20 It is doubtful if we should endorse that claim, even if it is true that his connected commitment to absolute space and time was to influence the young Newton. But More’s writings, especially the Antidote against atheisme, Or an appeal to the natural faculties of the minde of man, whether there be not a God (1653), provide something of a stepping-stone from Cartesian philosophy to that of Locke.
    More begins his case for a deity from a definition of God as ‘an essence or being fully and absolutely perfect’.21 Our ability to have this idea (More, like Descartes, very much employs the terminology of ideas in his philosophy) is compared by him, in ways familiar from Plato and Descartes, to that of our ability to have an idea of ideal mathematical, and specifically geometrical, concepts such as the five regular solids. Expanding on the idea of an absolutely perfect being, More comes to this: ‘a Spirit, Eternal, Infinite in Essence and Goodness, Omniscient, Omnipotent, and it [58] self necessarily Existent’.22 And if the terms eternal and infinite are troublesome, More says, ‘let him consider that he shall, whether he will or not, be forced to acknowledge something Eternal, either God or the World, and the Intricacy is alike in either’.23 And, he adds, he ‘will never extricate himself out of the Intanglements of an Infinite Space’. More’s argument here as elsewhere is not particularly subtle, but its direction is clear enough.
    Like Descartes, More argues that the mind, or, as he prefers, the soul, is no ‘Abrasa Tabula’. There is, he claims, knowledge in a dispositional sense—though he does not use that term—such that it can be drawn out by familiar intellectual processes. He illustrates this with the well-worn examples of geometrical knowledge and our immediate recognition of logical truths, such as that the whole is bigger than the part. And like Descartes he accepts a version of the Ontological Argument for the existence of God: that the very idea of God implies his necessary existence.24
    More’s argument lacks the sophistication and rigour of Descartes’s. There is, for example, no sign of an appreciation of Descartes’s distinction between a positive and a negative sense of infinity.25 But More’s works were, for a while at least, widely read in England, and they encouraged acceptance of several key Cartesian concepts in the intellectual community and strengthened a commitment to a philosophical position which on the rationalist/empiricist divide would certainly have to be counted as supporting the former, even if the general tone of English thought was moving in the other direction under the influence of Bacon [59] and the new science associated with the Royal Society. Indeed, More was himself associated with that development, keen to advance the new learning whilst utilizing it to support his own strongly theistic account of the world.

Locke and our idea of the infinite

From his earliest recorded thoughts on epistemological matters, Locke was committed to the empiricist principle. In his usual somewhat diffident way he begins the first draft of what was to become the Essay concerning human understanding with the words: ‘I imagin that all knowledg is founded on and ultimately derives its self from sense’.26 He goes on in that long opening paragraph to espouse what were to become, eighteen years later, several of the central themes of the published work: the distinction between simple and complex ideas; the thesis that words stand for ideas, the supposition of substance as a supposed unknown support of qualities, and so on.
    By the time that Locke wrote that draft in 1671 he was already familiar with the alternatives to his position. In his student days he had been required to master the central claims of scholastic philosophy. In the 1660s he made a careful study of Descartes’s major works, with special attention given to the Principia philosophiæ.27 From Boyle he had absorbed a keen commitment [60] to detailed and tmdogmatic empirical enquiry-the natural histories of the Baconian school of natural philosophy. And it was from this latter school, often in conscious and strong opposition to both Scholastic and Cartesian claims, that Locke took his lead, indeed much of the intellectual stance that so distinctively marks his epistemology. His objective was, as he was to tell us in the published work, to utilize a ‘Historical, plain Method’28 in his account of the nature and limits of human understanding. Whether, ultimately, his philosophy can be seen as quite living up to that characterization is one of the issues we shall in part explore.
    Locke’s relationship to Descartes is a complex and intriguing matter. It surfaces at almost every point that we might expect to find it if it was, as Damaris Masham tells us, first reading Descartes that ‘gave him a relish of Philosophical Studys’ even though ‘he very often differ’d in Opinion from this writer’.29 Further evidence for Locke’s close intellectual relationship with Descartes is that Descartes is the only philosopher mentioned by name in either early Draft of the Essay. Aristotle, by contrast, is mentioned in neither. Granted the early commitment to the empiricist principle, and granted, as we have already seen, that Descartes rejected it, Locke clearly has to demonstrate that the obvious putative counter-instances do not in fact falsify the principle. A central case was that of the source of our idea of infinity. Here the two early drafts are instructive, for both devote space to the issue. It is soon obvious that it is a position identical [61] with that of Descartes that Locke is attacking, even though Descartes himself is not named.
    In the closing sections of the first Draft, Draft A, Locke tells us of the two objections that he has met with against his empiricist epistemology. The first of these is the claim that there are innate ideas, which are required to account for our knowledge of certain truths which cannot be confirmed by experience, such as that all numbers are either odd or even. Locke of course does not deny that we know such truths. But he says he can account for them on his principles, and the details of his argument need not delay us.
    He then turns, in the penultimate section of the Draft, to what he sees as the second main objection to the empiricist principle, the fact that we have an idea of infinity. So it is clear that from his early epistemological engagement the issue of infinity was seen by him as a test case for his programme. That in the final printed version it does not appear to loom so large is misleading as to its original importance in his mind. In Draft A he introduces it thus:

The 2d Objection is of those men who say they have a positive Idea of Infinite, which Idea cannot possibly be had from our senses & therefor that we have Ideas not at all derived from our senses.30

We will have immediately noticed that the notion on which Locke immediately fastens is to us the familiar one: the positive idea of infinity. It is this that he sets out uncompromisingly to challenge.
    But do we know that it is Descartes he specifically has in his sights? The evidence at this stage of Locke’s development is perhaps not absolutely conclusive but points very strongly in that direction. First, as we have already seen, Descartes is perhaps the first exponent of this positive account of infinity, and he was the only person to put forward such an account that we know that Locke had read. It is a central feature of his proof of the existence [62] of God in the third Meditation and Locke could hardly have overlooked it. He would immediately have recognized its incompatibility with the empiricist principle. Finally, Locke’s discussion of the positive concept of infinity invokes the Cartesian concept of clear and distinct ideas as itself providing grounds for rejecting the positive account. He writes:

.  .  . it is not soe easy to have a cleare positive Idea of Infinite as anyone may imagin, & that we have reason to suspect those Ideas not to be cleare & distinct which when we suppose to be positive we cannot explain nor reconcile to those other positive Ideas which are very cleare in our understandings without a contradiction.31

It would be, if nothing else, good rhetoric to employ a Cartesian concept—clear and distinct ideas—a concept that Locke is happy to accept, to attack another Cartesian concept—the positive idea of infinity.
    These reasons seem to supply a basis for holding that it was Descartes’s rationalism in particular that Locke wished to repudiate in his account of the origin of our idea of infinity. This strongly suggests that from its inception the Essay was something more than merely the application of the plain historical method of the Royal Society to problems of the mind in the way that Locke claimed. It also, in all likelihood, had a polemical purpose.
    There can be no doubting Locke’s target seven years later. In a journal entry for 16 July 1678 he wrote the following:

The Cartesians say that conceptus infiniti est conceptus positivus quia finis at quid negativum ergo illius ablatio est positio rei positiva, To which I say that Infinitum is never the lesser negative for by it we take away and remove that negative End of which we have a cleare and destinct Idea, which is indeed the utmost point or surface of any body, and in the place of it by infinite put a confused Idea which is negative of [63] that clear Idea which we have of end and negative also in respect of our understanding for when we speake of infinite we speake of something which at the same time we confesse we cannot comprehend and soe it seems to be conceptus negativus.32

Locke was in Orléans at the time, on one of his prolonged visits to France, and often in those years amongst many other subjects he entered into reading and discussion of Cartesian philosophy with his French friends.33
    Locke’s argument against the Cartesian positive concept was in essence very simple. In the second of the early drafts he had explained how we come by our idea of infinity as the product of addition. Just as we can add one foot to another as many times as we please—indeed ad infinitum, because there is no incoherence in any such continued addition. But this idea of infinity is essentially negative: ‘when we speake of Infinite either duration or Extension it seemes not to me that we have the positive Idea or actuall conception of any such thing but barely the power of addeing still any assigneable or conceivable length of duration or extension whereof we have the actuall positive Idea to any number of the same lengths’.34
    Nor could we ever have any positive idea of infinity, he goes on to argue, because it would lead to a contradiction: ‘.  .  . if I could have an actuall positive Idea of an infinite length I could repeat it in my minde & adde these two infinites togeather nay I could adde as many of them togeather as I could of days or years, yards or miles, which are lengths of which I have actuall positive [64] Ideas, & soe make one Infinite Infinitely biger then an other, which is an absurdity soe grosse that noebody can admit’.35 Rather, Locke goes on to argue, we must see that we can account for our idea of infinity as itself derived from simple ideas of length or duration plus that of repetition, something that we see may be done endlessly because there is no logically compelling terminus.
    In the third draft of the Essay, Draft C, Locke includes a whole chapter in Book II on the topic and he draws on the earlier drafts in setting out his position.36 A similar, if different, version appears as chapter 17 of Book II in the published work. Constantly Locke argues that our concept of infinity is never a positive one. Finite and infinite, he says, are modes of quantity and apply in the first instance only to those things that have parts and which are capable of increase or diminution. Of course Locke admits that we do apply the concept to God. But we do it ‘primarily in respect of his Duration and Ubiquity’, he says. It is ‘more figuratively’ applied to his power, wisdom, goodness and other attributes. What is crucial is that when we do so we do it in exactly the same way as we apply it to the primary ones of duration, etc. Our idea of infinity (in contrast, perhaps, with any idea that God himself may have of it) is necessarily like this.37
    Locke brings home the connection between the idea of infinity and that of parts of extension or duration by an interesting argument. To the largest idea I have of extension or duration, he says, any addition makes an increase. ‘But to the perfectest Idea I [65] have of the whitest Whiteness, if I add another of a less or equal whiteness . . . it makes no increase.’38 You cannot sensibly talk of adding degrees of whiteness to obtain or approach some ideal infinite whiteness, because whiteness does not, in the same sense as extension does, consist of parts.
    Much of the remainder of Locke’s chapter on infinity is a series of arguments against the Cartesian position that infinity can be a positive idea. Much of it is ingenious and often it is compelling. Thus, to take one example, Locke believes one reason why people are inclined to think the idea of infinity to be positive is that it involves the notion of the negation of an end, which is itself taken to be a negative. But this turns on an equivocation in the word. When something comes to an end, is finished, we think of this as a negation. And we therefore think of its continuance as something positive. But the end of a pen, say, the nib perhaps, is a real physical thing, a part of the pen, and not a negative at all. Furthermore to say that something is eternal is to say it is without end, which is a negative, not a positive idea.
    Locke does allow that there is a sense in which there is a positive content to the idea of infinity. We think of a thing’s doubling in length as a positive attribute and we conclude that if something became indefinitely or infinitely long this would also be positive. But, he says, there is an important difference between our idea of say, one mile, two miles and an infinite number of miles. For whereas the second is greater than the first and in some sense more positive, there is no idea at all that corresponds to the notion of infinite length. It is just length which has no end, a negative concept. Finally, Locke appeals to the argument that we have already seen him use in the Drafts, that if infinity could be a positive idea then we could add two infinities together and get something which is greater than infinity, which is an absurdity.39 [66]
    Locke’s strategy, then, is to argue that the concept of infinity is no threat to the empiricist principle. We can account for the idea quite satisfactorily by appeal to simple ideas of extension and duration combined with the idea of repetition. There is no such thing as the positive idea of infinity that the Cartesians required. Whether Locke is in all respects successful in that endeavour is another matter.
    Discussion of infinity did not, of course, stop with Locke. But he did present a strong case against the claim that its explication requires the notion of an innate idea which itself required as its cause something that was itself infinite. As such it was vital to his programme that he could offer a plausible alternative for its origin. What I have tried to do in this paper is to show how this was a central issue in his argument with the rationalist position, primarily represented to him by Descartes’s philosophy. The thought would be that Locke saw himself as engaged in a debate of some consequence with a rationalist opponent who occupied the intellectual field before him. To see Locke as positively engaged in such a struggle, if it has any merit as an interpretation of his thought, will perhaps help us to escape from the picture of his activity which he himself did something to encourage, later supported by Voltaire, as merely a recorder of the facts of human consciousness—writing a natural history of the soul. Such recognition will, I hope, also help us to see further into his philosophy on other issues. [67]


The editor wishes to thank the author for agreeing to have this article appear on this site. It should be noted that some of the original formatting features have been lost to the present HTML format. Note also that the original page endings are indicated by lightly printed numerals in square brackets, and also that these endnotes were originally footnotes.

‘Fifth Set of Objections’, in The philosophical writings of Descartes, tr. J. Cottingham, R. Stoothoff and D. Murdoch, 3 vols (Cambridge 1985-91), vol. 2, p. 200. Hereafter cited as PW.

Thomas E. Webb, The intellectualism of Locke: An essay (Dublin & London 1857, reprinted with an Introduction by J. Yolton, Thoemmes Antiqarian Books 1990); R. I. Aaron, John Locke, 3rd edn (Oxford 1971).

For recent examples see D. M. Clarke, Descartes’s philosophy of science (Manchester 1982) and John Cottingham’s Presidential Address to the Aristotelian Society and Mind Association, Aristotelian Society proceedings, supplementary volume, 1992.

The distinction is made in the Third Meditation, PW, vol. 2, p. 26.

ibid., p. 27.

His actual words are ‘. . . there cannot be another faculty [or power for distinguishing truth from falsehood] both as trustworthy as the natural light and also capable of showing me that such things are not true’ (brackets indicate additions in French version), PW, vol. 2, p. 27.

ibid., p. 28.

ibid., p. 31.

‘First Set of Replies’, PW, vol. 2, p. 78.

10  Presumably there could not be an experience of the infinite as such. All experience must of necessity be either of something finite or some finite aspect of something that is itself infinite.

11  PW, vol. 3, p. 183.

12  Principles of philosophy, Part II. 4, PW, vol. 1, p. 224.

13  ibid., Part I. 24-5, PW, vol. 1, p. 201.

14  ‘Second Set of Replies’, PW, vol. 2, p. 100.

15  PW vol. 3, p. 377.

16  See especially Summa theologiae, II, Question 7 (London 1964), vol. 2, Existence and Nature of God, esp. pp. 95-109.

17  There is surprisingly little discussion of Descartes’s theory of infinity in the literature. But see R. Ariew, ‘The infinite in Descartes’s conversation with Burman’, Archiv, für Geschichte der Philosophie 69 (1987), pp. 140-63. See also A. W. Moore, The infinite (London, 1990), esp. p. 76.

18  For a survey of Descartes’s impact in England see G. A. J. Rogers, ‘Descartes and the English’, in The light of nature: Essays in the history and philosophy of science presented to A. C. Crombie, ed. J. D. North and J. J. Roche (Dordrecht 1985).

19  For More’s relationship with Descartes see A. Gabbey, ‘Philosophia Cartesiana triumphata: Henry More (1646-1671)’ in Problems of Cartesianism, ed. T. M. Lennon, J. M. Nicholas, and J. W. Davis (Kingston & Montreal 1982), pp. 171-250, and A. R. Hall, Henry More: Magic, religion and experiment (Oxford 1990), esp. ch. 8.

20  The Conway letters, ed. M. H. Nicolson, revised edn, with an introduction and new material, ed. S. Hutton (Oxford 1992), p. 43.

21  Quotations from the Antidote against atheism, abbreviated as AA, are taken from what is effectively the fifth edition of the work, published in A collection of philosophical writings of Dr. Henry More, 4th edn (London 1712). Each work in this volume is separately paginated. The quotation is from Book I, ch. 3, p. 13.

22  AA, p. l4.

23  ibid., p. 16.

24  ibid., Book I, ch. 8.

25  Something which emerges in their correspondence and in More’s prefatory remarks to his poem Democritus Platonissans (1647).

26  Drafts for the ‘Essay concerning human understanding’, and other philosophical writings, ed. P. H. Nidditch and G. A. J. Rogers, vol. I (Oxford 1990), p. 1.

27  The central document here is one of Locke’s notebooks now in the British Library, Add. MS 32,554. This notebook is often described as a Commonplace Book for 1660, though this is certainly to misdescribe it, as many of its entries were made later than 1660. In it Locke cites passages from many sources in his reading, including Boyle and Descartes. He lists thirty-six definitions of terms taken from several of Descartes’s works, including the Dioptrique, the Météores, the Meditationes, and the Principia philosophiae.

28  An essay concerning human understanding, ed. P. H. Nidditch (Oxford 1975) I. i. 2, p. 44, cited hereafter as Essay.

29  Lady Masham to Jean Le Clerc, in a letter written after Locke’s death, now preserved in the Remonstrants’ Library, Amsterdam. I am grateful to the late Esmond de Beer for a sight of his copy. Locke also indicated such a debt in his correspondence with Stillingfleet, The works John Locke, in ten volumes (London 1823), vol. 4, pp. 48-9.

30  Drafts, vol. 1, p. 78

31  ibid, p. 80.

32  An early draft of Locke’s Essay together with excerpts from his journals, ed. R. I. Aaron and J. Gibb (Oxford 1936), pp. 111-12.

33  A year earlier Locke had listed in his journal a list of Descartes’s works, under the heading Cartesii opera omnia. His journal entries and letters of the period reflect his deep interest in matters of scientific, medical and philosophical concern as he found them in France.

34  Drafts, vol. 1, p. 249.

35  ibid. Since Cantor we have come to appreciate that Locke’s ‘absurdity’ is no absurdity at all.

36  For example he uses the same example of adding two infinities together that we have just seen in Draft B. See Drafts, vol. 2 (Oxford forthcoming): Draft C, ch. 20, section 3. Cf. Essay, II. xvii, 13, p. 217, where the example appears in the published text.

37  Essay, II. xvii. 5, p. 212.

38  ibid., II. xvii, 6, pp. 212-13.

39  ibid., II. xvii. 20, p. 222.

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