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Locke’s attack on the theory of innate knowledge provoked a comprehensive response from the German philosopher Gottfried Leibniz, in his New Essays on Human Understanding (Nouveaux Essais sur l’entendement humain), written in French and completed in 1704 (but not published until 1765, some fifty years after the author’s death). Leibniz agrees with Locke that sensory stimulation is necessary for the acquisition of knowledge. But he argues that it is not, by itself, sufficient. The senses merely elicit or activate what is already in a certain sense present within us – ‘living fires or flashes of light hidden inside us but made visible by the stimulation of the senses, as sparks can be struck from a steel’. Leibniz goes on to cite the necessary truths of mathematics as support for his version of the theory of innateness: the truth of such propositions ‘does not depend on instances, nor consequently on the testimony of the senses’. Readers may well see a parallel here with the earlier arguments of Plato in the Meno (extract 1, above). Although sensory stimulation (the drawing of a visible diagram in the sand) helped the slave boy to see the result concerning the square on the diagonal, the truth of the proposition in question does not in any way depend on such experiments or observations or ‘instances’; it can be demonstrated quite independently of experience. Reflection on the universal and necessary nature of truths of this kind leads Leibniz to the conclusion that proof of necessary truths such as those of mathematics ‘can only come from inner principles’.

Locke, as is clear from our previous passage (extract 5), had objected that if such truths were indeed imprinted in the mind from birth, one would surely expect young children to be aware of them – which in many cases they patently are not. To this Leibniz replies that although present in the mind, such principles are not like notices conspicuously posted on a ‘notice board’: it often needs diligent attention for us to achieve the kind of explicit awareness that makes us recognize their truth. Against Locke’s image of the mind as a tabula rasa or blank sheet, Leibniz compares the mind to a block of marble – one that is not homogenous but already veined in a certain pattern: the sculptor’s blows (corresponding to the stimulation of the senses) are certainly necessary, but they serve to uncover a shape that is already present in the structure of the stone. There follows an interesting discussion of the way in which the cognitive activities of the human mind seem to transcend entirely the straightforward ‘stimulus-response’ capacities of animals. The beasts, as Leibniz puts it, are like ‘simple empirics’: their awareness of things is limited to particular sensory images and impressions. Humans, by contrast, ‘are capable of demonstrative knowledge’ – that is, they can use their reason to establish universal and logically necessary truths (like those of mathematics). Leibniz’s innatism thus proclaims the power of human reason to achieve knowledge that goes wholly beyond what can be derived from sensory data: ‘What shows the existence of inner sources of necessary truths is also what distinguishes man from beast.’

The Essay on the Understanding, produced by an illustrious Englishman, is one of the finest and most admired works of the age. Since I have thought at length about the same subject and about most of the topics which are dealt with in it, I have decided to comment upon it. I thought that this would be a good opportunity to publish something entitled New Essays on the Understanding and to gain a more favourable reception for my thoughts by putting them in such good company. I thought too that I might benefit from someone else’s labour, not only to lessen mine (since it is easier to follow the thread of a good author than to do everything by one’s own efforts), but also to add something to what he has produced for us, which is always easier than to start from the beginning. It is true that my opinions frequently differ from his, but far from denying the merit of this famous writer I testify in his favour by showing where and why I differ from him, when I find that on certain significant points I have to prevent his authority from prevailing over reason.

Indeed, although the author of the Essay says hundreds of fine things which I applaud, our systems are very different. His is closer to Aristotle and mine to Plato, although each of us parts company at many points from the teachings of both of these ancient writers. He is more popular whereas I am sometimes forced to be a little more esoteric and abstract – which is no advantage for me, particularly when writing in a living language. However, I think that by using two speakers, one of whom presents opinions drawn from that author’s Essay and the other adds my comments, the confrontation will be more to the reader’s taste than a dry commentary from which he would have to be continually turning back to the author’s book in order to understand mine. Nevertheless it would be well to compare our writings from time to time, and to judge of his opinions only from his own book even though I have usually retained its wording. I am afraid that the obligation to follow the thread, when commenting on someone else’s treatise, has shut out any hope of my attaining to the charms of which dialogue is capable; but I hope that the matter will make up for the shortcomings of the manner.

Our disagreements concern points of some importance. There is the question whether the soul in itself is completely blank like a writing tablet on which nothing has as yet been written – a tabula rasa – as Aristotle and the author of the Essay maintain, and whether everything which is inscribed there comes solely from the senses and experience; or whether the soul inherently contains the sources of various notions and doctrines, which external objects merely rouse up on suitable occasions, as I believe and as do Plato … and all those who understand in this sense the passage in St Paul where he says that God’s law is written in our hearts (Romans, 2: 15). The Stoics call these sources ‘Prolepses’, that is fundamental assumptions or things taken for granted in advance. Mathematicians call them common notions or koinai ennoiai. Modern philosophers give them other fine names … ‘seeds of eternity’ and also zopyra – meaning living fires or flashes of light hidden inside us but made visible by the stimulation of the senses, as sparks can be struck from a steel. And we have reason to believe that these flashes reveal something divine and eternal: this appears especially in the case of necessary truths. That raises another question, namely whether all truths depend on experience, that is on induction and instances, or if some of them have some other foundation. For if some events can be foreseen before any test has been made of them, it is obvious that we contribute something from our side. Although the senses are necessary for all our actual knowledge, they are not sufficient to provide it all, since they never give us anything but instances, that is particular or singular truths. But however many instances confirm a general truth, they do not suffice to establish its universal necessity; for it does not follow that what has happened will always happen in the same way. For instance, the Greeks and Romans and all the other nations on earth always found that within the passage of twenty-four hours day turns into night and night into day. But they would have been mistaken if they had believed that the same rule holds everywhere, since the contrary was observed during a stay in Novaya Zemlya. And anyone who believed that it is a necessary and eternal truth at least in our latitudes would also be mistaken, since we must recognize that neither the earth nor even the sun exist necessarily, and that there may come a time when this beautiful star no longer exists, at least in its present form, nor its whole system.

From this it appears that necessary truths, such as we find in pure mathematics and particularly in arithmetic and geometry, must have principles whose proof does not depend on instances nor, consequently, on the testimony of the senses, even though without the senses it would never occur to us to think of them. This distinction must be thoroughly observed, and Euclid understood that so well that he demonstrates by reason things that experience and sense-images make very evident. Logic also abounds in such truths, and so do metaphysics and ethics, together with their respective products, natural theology and natural jurisprudence; and so the proof of them can only come from inner principles, which are described as innate.

It would indeed be wrong to think that we can easily read these eternal laws of reason in the soul, as the Praetor’s edict can be read on his notice-board, without effort or inquiry; but it is enough that they can be discovered within us by dint of attention: the senses provide the occasion, and successful experiments also serve to corroborate reason, somewhat as checks in arithmetic help us to avoid errors of calculation in long chains of reasoning.

It is in this same respect that man’s knowledge differs from that of beasts: beasts are sheer empirics and are guided entirely by instances. While men are capable of demonstrative knowledge, beasts, so far as one can judge, never manage to form necessary propositions, since the faculty by which they make sequences is something lower than the reason which is to be found in men. The sequences of beasts are just like those of simple empirics who maintain that what has happened once will happen again in a case which is similar in the respects that they are impressed by, although that does not enable them to judge whether the same reasons are at work. That is what makes it so easy for men to ensnare beasts, and so easy for simple empirics to make mistakes. Even people made cunning by age and experience are not proof against this when they trust too much to their past experience; as has happened to various people engaged in civil or military affairs, through their not taking sufficiently to heart that the world changes and that men become cleverer and find hundreds of new tricks – whereas the deer and hares of our time are not becoming craftier than those of long ago. The sequences of beasts are only a shadow of reasoning, that is, they are nothing but a connection in the imagination – a passage from one image to another; for when a new situation appears similar to its predecessor, it is expected to have the same concomitant features as before, as though things were linked in reality just because their images are linked in the memory. It is true, moreover, that reason counsels us to expect ordinarily that what we find in the future will conform to long experience of the past; but even so, this is no necessary and infallible truth, and it can fail us when we least expect it to, if there is a change in the reasons which have been maintaining it. This is why the wisest men do not trust it so implicitly that they neglect to probe somewhat, where possible, into the reason for such regularities, in order to know when they will have to allow exceptions. For only reason is capable of establishing reliable rules, of making up the deficiencies of those which have proved unreliable by allowing exceptions to them, and lastly of finding unbreakable links in the cogency of necessary inferences. This last often provides a way of foreseeing events without having to experience sensible links between images, as beasts must. Thus what shows the existence of inner sources of necessary truths is also what distinguishes man from beast.

Perhaps our gifted author will not entirely disagree with my view. For after devoting the whole of his first book to rejecting innate illumination, understood in a certain sense, he nevertheless admits at the start of his second book, and from there on, that ideas which do not originate in sensation come from reflection. But reflection is nothing but attention to what is within us, and the senses do not give us what we carry with us already. In view of this, can it be denied that there is a great deal that is innate in our minds, since we are innate to ourselves, so to speak, and since we include Being, Unity, Substance, Duration, Change, Action, Perception, Pleasure, and hosts of other objects of our intellectual ideas? And since these objects are immediately related to our understanding and always present to it (although our distractions and needs prevent us being always aware of them), is it any wonder that we say that these ideas, along with what depends on them are innate in us? I have also used the analogy of a veined block of marble, as opposed to an entirely homogeneous block of marble, or to a blank tablet – what the philosophers call a tabula rasa. For if the soul were like such a blank tablet then truths would be in us as the shape of Hercules is in a piece of marble when the marble is entirely neutral as to whether it assumes this shape or some other. However, if there were veins in the block which marked out the shape of Hercules rather than other shapes, then that block would be more determined to that shape and Hercules would be innate in it, in a way, even though labour would be required to expose the veins and to polish them into clarity, removing everything that prevents their being seen. This is how ideas and truths are innate in us – as inclinations, dispositions, tendencies, or natural potentialities, and not as actions; although these potentialities are always accompanied by certain actions, often insensible ones, which correspond to them.

Our gifted author seems to claim that there is nothing potential in us, in fact nothing of which we are not always actually aware. But he cannot hold strictly to this; otherwise his position would be too paradoxical, since, again, we are not always aware of our acquired dispositions or of the contents of our memory, and they do not even come to our aid whenever we need them, though often they come readily to mind when some idle circumstance reminds us of them, as when hearing the opening words of a song is enough to bring back the rest. So on other occasions he limits his thesis to the statement that there is nothing in us of which we have not at least previously been aware. But no one can establish by reason alone how far our past and now perhaps forgotten awarenesses may have extended, especially if we accept the Platonists’ doctrine of recollection which, though sheer myth, is entirely consistent with unadorned reason. And furthermore, why must we acquire everything through awareness of outer things and not be able to unearth anything from within ourselves? Is our soul in itself so empty that unless it borrows images from outside it is nothing? I am sure that our judicious author could not approve of such a view. Where could tablets be found which were completely uniform? Will a perfectly homogeneous and even surface ever be seen? So why could we not also provide ourselves with objects of thought from our own depths, if we take the trouble to dig there? Which leads me to believe that fundamentally his view on this question is not different from my own or rather from the common view, especially since he recognizes two sources of our knowledge, the senses and reflection.