Naturalizing the Soul & the Scientific Revolution

 

De Anima (On the Soul)
By Aristotle

 Book II                                                  Go to next


Part 1

Let the foregoing suffice as our account of the views concerning the soul which have been handed on by our predecessors; let us now dismiss them and make as it were a completely fresh start, endeavouring to give a precise answer to the question, What is soul? i.e. to formulate the most general possible definition of it.

We are in the habit of recognizing, as one determinate kind of what is, substance, and that in several senses, (a) in the sense of matter or that which in itself is not 'a this', and (b) in the sense of form or essence, which is that precisely in virtue of which a thing is called 'a this', and thirdly (c) in the sense of that which is compounded of both (a) and (b). Now matter is potentiality, form actuality; of the latter there are two grades related to one another as e.g. knowledge to the exercise of knowledge.

Among substances are by general consent reckoned bodies and especially natural bodies; for they are the principles of all other bodies. Of natural bodies some have life in them, others not; by life we mean self-nutrition and growth (with its correlative decay). It follows that every natural body which has life in it is a substance in the sense of a composite.

But since it is also a body of such and such a kind, viz. having life, the body cannot be soul; the body is the subject or matter, not what is attributed to it. Hence the soul must be a substance in the sense of the form of a natural body having life potentially within it. But substance is actuality, and thus soul is the actuality of a body as above characterized. Now the word actuality has two senses corresponding respectively to the possession of knowledge and the actual exercise of knowledge. It is obvious that the soul is actuality in the first sense, viz. that of knowledge as possessed, for both sleeping and waking presuppose the existence of soul, and of these waking corresponds to actual knowing, sleeping to knowledge possessed but not employed, and, in the history of the individual, knowledge comes before its employment or exercise.

That is why the soul is the first grade of actuality of a natural body having life potentially in it. The body so described is a body which is organized. The parts of plants in spite of their extreme simplicity are 'organs'; e.g. the leaf serves to shelter the pericarp, the pericarp to shelter the fruit, while the roots of plants are analogous to the mouth of animals, both serving for the absorption of food. If, then, we have to give a general formula applicable to all kinds of soul, we must describe it as the first grade of actuality of a natural organized body. That is why we can wholly dismiss as unnecessary the question whether the soul and the body are one: it is as meaningless as to ask whether the wax and the shape given to it by the stamp are one, or generally the matter of a thing and that of which it is the matter. Unity has many senses (as many as 'is' has), but the most proper and fundamental sense of both is the relation of an actuality to that of which it is the actuality. We have now given an answer to the question, What is soul?-an answer which applies to it in its full extent. It is substance in the sense which corresponds to the definitive formula of a thing's essence. That means that it is 'the essential whatness' of a body of the character just assigned. Suppose that what is literally an 'organ', like an axe, were a natural body, its 'essential whatness', would have been its essence, and so its soul; if this disappeared from it, it would have ceased to be an axe, except in name. As it is, it is just an axe; it wants the character which is required to make its whatness or formulable essence a soul; for that, it would have had to be a natural body of a particular kind, viz. one having in itself the power of setting itself in movement and arresting itself. Next, apply this doctrine in the case of the 'parts' of the living body. Suppose that the eye were an animal-sight would have been its soul, for sight is the substance or essence of the eye which corresponds to the formula, the eye being merely the matter of seeing; when seeing is removed the eye is no longer an eye, except in name-it is no more a real eye than the eye of a statue or of a painted figure. We must now extend our consideration from the 'parts' to the whole living body; for what the departmental sense is to the bodily part which is its organ, that the whole faculty of sense is to the whole sensitive body as such.

We must not understand by that which is 'potentially capable of living' what has lost the soul it had, but only what still retains it; but seeds and fruits are bodies which possess the qualification. Consequently, while waking is actuality in a sense corresponding to the cutting and the seeing, the soul is actuality in the sense corresponding to the power of sight and the power in the tool; the body corresponds to what exists in potentiality; as the pupil plus the power of sight constitutes the eye, so the soul plus the body constitutes the animal.

From this it indubitably follows that the soul is inseparable from its body, or at any rate that certain parts of it are (if it has parts) for the actuality of some of them is nothing but the actualities of their bodily parts. Yet some may be separable because they are not the actualities of any body at all. Further, we have no light on the problem whether the soul may not be the actuality of its body in the sense in which the sailor is the actuality of the ship.

This must suffice as our sketch or outline determination of the nature of soul.

 

Part 7

The object of sight is the visible, and what is visible is (a) colour and (b) a certain kind of object which can be described in words but which has no single name; what we mean by (b) will be abundantly clear as we proceed. Whatever is visible is colour and colour is what lies upon what is in its own nature visible; 'in its own nature' here means not that visibility is involved in the definition of what thus underlies colour, but that that substratum contains in itself the cause of visibility. Every colour has in it the power to set in movement what is actually transparent; that power constitutes its very nature. That is why it is not visible except with the help of light; it is only in light that the colour of a thing is seen. Hence our first task is to explain what light is.

Now there clearly is something which is transparent, and by 'transparent' I mean what is visible, and yet not visible in itself, but rather owing its visibility to the colour of something else; of this character are air, water, and many solid bodies. Neither air nor water is transparent because it is air or water; they are transparent because each of them has contained in it a certain substance which is the same in both and is also found in the eternal body which constitutes the uppermost shell of the physical Cosmos. Of this substance light is the activity-the activity of what is transparent so far forth as it has in it the determinate power of becoming transparent; where this power is present, there is also the potentiality of the contrary, viz. darkness. Light is as it were the proper colour of what is transparent, and exists whenever the potentially transparent is excited to actuality by the influence of fire or something resembling 'the uppermost body'; for fire too contains something which is one and the same with the substance in question.

We have now explained what the transparent is and what light is; light is neither fire nor any kind whatsoever of body nor an efflux from any kind of body (if it were, it would again itself be a kind of body)-it is the presence of fire or something resembling fire in what is transparent. It is certainly not a body, for two bodies cannot be present in the same place. The opposite of light is darkness; darkness is the absence from what is transparent of the corresponding positive state above characterized; clearly therefore, light is just the presence of that.

Empedocles (and with him all others who used the same forms of expression) was wrong in speaking of light as 'travelling' or being at a given moment between the earth and its envelope, its movement being unobservable by us; that view is contrary both to the clear evidence of argument and to the observed facts; if the distance traversed were short, the movement might have been unobservable, but where the distance is from extreme East to extreme West, the draught upon our powers of belief is too great.

What is capable of taking on colour is what in itself is colourless, as what can take on sound is what is soundless; what is colourless includes (a) what is transparent and (b) what is invisible or scarcely visible, i.e. what is 'dark'. The latter (b) is the same as what is transparent, when it is potentially, not of course when it is actually transparent; it is the same substance which is now darkness, now light.

Not everything that is visible depends upon light for its visibility. This is only true of the 'proper' colour of things. Some objects of sight which in light are invisible, in darkness stimulate the sense; that is, things that appear fiery or shining. This class of objects has no simple common name, but instances of it are fungi, flesh, heads, scales, and eyes of fish. In none of these is what is seen their own proper' colour. Why we see these at all is another question. At present what is obvious is that what is seen in light is always colour. That is why without the help of light colour remains invisible. Its being colour at all means precisely its having in it the power to set in movement what is already actually transparent, and, as we have seen, the actuality of what is transparent is just light.

The following experiment makes the necessity of a medium clear. If what has colour is placed in immediate contact with the eye, it cannot be seen. Colour sets in movement not the sense organ but what is transparent, e.g. the air, and that, extending continuously from the object to the organ, sets the latter in movement. Democritus misrepresents the facts when he expresses the opinion that if the interspace were empty one could distinctly see an ant on the vault of the sky; that is an impossibility. Seeing is due to an affection or change of what has the perceptive faculty, and it cannot be affected by the seen colour itself; it remains that it must be affected by what comes between. Hence it is indispensable that there be something in between-if there were nothing, so far from seeing with greater distinctness, we should see nothing at all.

We have now explained the cause why colour cannot be seen otherwise than in light. Fire on the other hand is seen both in darkness and in light; this double possibility follows necessarily from our theory, for it is just fire that makes what is potentially transparent actually transparent.

The same account holds also of sound and smell; if the object of either of these senses is in immediate contact with the organ no sensation is produced. In both cases the object sets in movement only what lies between, and this in turn sets the organ in movement: if what sounds or smells is brought into immediate contact with the organ, no sensation will be produced. The same, in spite of all appearances, applies also to touch and taste; why there is this apparent difference will be clear later. What comes between in the case of sounds is air; the corresponding medium in the case of smell has no name. But, corresponding to what is transparent in the case of colour, there is a quality found both in air and water, which serves as a medium for what has smell-I say 'in water' because animals that live in water as well as those that live on land seem to possess the sense of smell, and 'in air' because man and all other land animals that breathe, perceive smells only when they breathe air in. The explanation of this too will be given later.

 

On Sense and the Sensible
By Aristotle

From Section 1, Part 2

That without light vision is impossible has been stated elsewhere; but, whether the medium between the eye and its objects is air or light, vision is caused by a process through this medium.

Accordingly, that the inner part of the eye consists of water is easily intelligible, water being translucent.

Now, as vision outwardly is impossible without [extra-organic] light, so also it is impossible inwardly [without light within the organ]. There must, therefore, be some translucent medium within the eye, and, as this is not air, it must be water. The soul or its perceptive part is not situated at the external surface of the eye, but obviously somewhere within: whence the necessity of the interior of the eye being translucent, i.e. capable of admitting light. And that it is so is plain from actual occurrences. It is matter of experience that soldiers wounded in battle by a sword slash on the temple, so inflicted as to sever the passages of [i.e. inward from] the eye, feel a sudden onset of darkness, as if a lamp had gone out; because what is called the pupil, i.e. the translucent, which is a sort of inner lamp, is then cut off [from its connexion with the soul].

 

from Il Saggitore (The Assayer) 1623

By Galileo Galilei

Two Kinds Of Properties

In accordance with the promise which I made to Your Excellency, I shall certainly state my ideas concerning the proposition "Motion is the cause of heat," explaining in what way it appears to me to be true. But first it will be necessary for me to say a few words concerning that which we call "heat," for I strongly suspect that the commonly held conception of the matter is very far from the truth, inasmuch as heat is generally believed to be a true accident, affection, or quality which actually resides in the material which we feel to be heated. Now, whenever I conceive of any material or corporeal substance, I am necessarily constrained to conceive of that substance as bounded and as possessing this or that shape, as large or small in relationship to some other body, as in this or that place during this or that time, as in motion or at rest, as in contact or not in contact with some other body, as being one, many, or few--and by no stretch of imagination can I conceive of any corporeal body apart from these conditions. But I do not at all feel myself compelled to conceive of bodies as necessarily conjoined with such further conditions as being red or white, bitter or sweet, having sound or being mute, or possessing a pleasant or unpleasant fragrance. On the contrary, were they not escorted by our physical senses, perhaps neither reason nor understanding would ever, by themselves, arrive at such notions. I think, therefore, that these tastes, odors, colors, etc., so far as their objective existence is concerned, are nothing but mere names for something which resides exclusively in our sensitive body (corpo sensitivo), so that if the perceiving creatures were removed, all of these qualities would be annihilated and abolished from existence. But just because we have given special names to these qualities, different from the names we have given to the primary and real properties, we are tempted into believing that the former really and truly exist as well as the latter.

An example, I believe, will clearly explain my concept. Suppose I pass my hand, first over a marble statue, then over a living man. So far as the hand, considered in itself, is concerned, it will act in an identical way upon each of these objects; that is, the primary qualities of motion and contact will similarly affect the two objects, and we would use identical language to describe this in each case. But the living body, which I subject to this experiment, will feel itself affected in various ways, depending upon the part of the body I happen to touch; for example, should it be touched on the sole of the foot or the kneecap, or under the armpit, it will feel, in addition to simple contact, a further affection to which we have given a special name: we call it "tickling." This latter affection is altogether our own, and is not at all a property of the hand itself. And it seems to me that he would be gravely in error who would assert that the hand, in addition to movement and contact, intrinsically possesses another and different faculty which we might call the "tickling faculty," as though tickling were a resident property of the hand per se. Again, a piece of paper or a feather, when gently rubbed over any part of our body whatsoever, will in itself act everywhere in an identical way; it will, namely, move and contact. But we, should we be touched between the eyes, on the tip of the nose, or under the nostrils, will feel an almost intolerable titillation--while if touched in other places, we will scarcely feel anything at all. Now this titillation is completely ours and not the feather's, so that if the living, sensing body were removed, nothing would remain of the titillation but an empty name. And I believe that many other qualities, such as taste, odor, color, and so on, often predicated of natural bodies, have a similar and no greater existence than this.

A solid body and, so to speak, one that is sufficiently heavy, when moved and applied against any part of my body whatsoever, will produce in me the sensation which we call "touch." Although this sense is to be found in every part of the body, it appears principally to reside in the palm of the hand, and even more so in the fingertips, with which, we can feel the minutest differences of roughness, texture, and softness and hardness--differences which the other parts of the body are less capable of distinguishing. Some amongst these tactile sensations are more pleasing than others, depending upon the differences of configuration of tangible bodies; that is to say, in accordance with whether they are smooth or irregular, sharp or dull, flexible or rigid. And the sense of touch, being more material than the other senses and being produced by the mass of the material itself, seems to correspond to the element of earth.

Since certain material bodies are continually resolving themselves into tiny particles, some of the particles, because they are heavier than air, will descend; and some of them, because they are lighter than air, will ascend. From this, perhaps, two further senses are born, for certain of the particles penetrate two parts of our body which are effectively more sensitive than the skin, which is incapable of feeling the incursion of materials which are too fine, subtle, or flexible. The descending particles are received by the upper surface of the tongue, and penetrating, they blend with its substance and moisture. Thus our tastes are caused, pleasant or harsh in accordance with variations in the contact of diversely shaped particles, and depending upon whether they are few or many, and whether they have high or low velocity. Other particles ascend, and entering the nostrils they penetrate the various nodes (mammilule) which are the instruments of smell; and these particles, in like manner through contact and motion, produce savoriness or unsavoriness--again depending upon whether the particles have this or that shape, high or low velocity, and whether they are many or few. It is remarkable how providently the tongue and nasal passages are situated and disposed, the former stretched beneath to receive the ingression of descending particles, and the latter so arranged as to receive those which ascend. The arrangement whereby the sense of taste is excited in us is perhaps analogous to the way in which fluids descend through the air, and the stimulation of the sense of smell may be compared to the manner in which flames ascend in it.

There remains the element of air, which corresponds to the sense of sound. Sounds come to us indiscriminately, from above and below and from either side, since we are so constituted as to be equally disposed to every direction of the air's movements; and the ear is so situated as to accommodate itself in the highest possible degree to any position in space. Sounds, then, are produced in us and felt when (without any special quality of harmoniousness or dissonance) there is a rapid vibration of air, forming minutely small waves, which move certain cartilages of a certain drum which is in our ear. The various external ways in which this wave-motion of the air is produced are manifold, but can in large part be reduced to the vibrating of bodies which strike the air and form the waves which spread out with great velocity. High frequencies give rise to high tones; low frequencies give rise to low tones. But I cannot believe that there exists in external bodies anything, other than their size, shape, or motion (slow or rapid), which could excite in us our tastes, sounds, and odors. And indeed I should judge that, if ears, tongues, and noses be taken away, the number, shape, and motion of bodies would remain, but not their tastes, sounds, and odors. The latter, external to the living creature, I believe to be nothing but mere names, just as (a few lines back) I asserted tickling and titillation to be, if the armpit or the sensitive skin inside the nose were removed. As to the comparison between the four senses which we have mentioned and the four elements, I believe that the sense of sight, most excellent and noble of all the senses, is like light itself. It stands to the others in the same measure of comparative excellence as the finite stands to the infinite, the gradual to the instantaneous, the divisible to the indivisible, the darkness to the light. Of this sense, and all that pertains to it, I can pretend to understand but little; yet a great deal of time would not suffice for me to set forth even this little bit that I know, or (to put it more exactly) for me to sketch it out on paper. Therefore I shall ponder it in silence.

I return to my first proposition, having now shown how some affections, often reputed to be indwelling properties of some external body, have really no existence save in us, and apart from us are mere names. I confess myself to be very much inclined to believe that heat, too, is of this sort, and that those materials which produce and make felt in us the sense of heat and to which we give the general name "fire" consist of a multitude of tiny particles of such and such a shape, and having such and such a velocity. These, when they encounter our body, penetrate it by means of their extreme subtlety; and it is their contact, felt by us in their passage through our substance, which is the affection we call "heat." It will be pleasantly warm or unpleasantly hot depending upon the number and the velocity (greater or lesser) of these pricking, penetrating particles--pleasant if by their penetration our necessary perspiring is facilitated, unpleasant if their penetrating effects too great a division and dissolution of our substance. In sum, the operation of fire, considered in itself, is nothing but movement, or the penetration of bodies by its extreme subtlety, quickly or slowly, depending upon the number and velocity of tiny corpuscles of flame (ignicoli) and upon the greater or lesser density of the bodies concerned. Many bodies dissolve in such a manner that the major part of them becomes transformed into further corpuscles of flame; and this dissolution continues as further dissolvable material is encountered. But that there exists in fire, apart from shape, number, movement, penetration, and contact, some further quality which we call "heat," I cannot believe. And I again judge that heat is altogether subjective, so that if the living, sensitive body be removed, what we call heat would be nothing but a simple word. Since it is the case that this affection is produced in us by passage of tiny corpuscles of flame through our substance and their contact with it, it is obvious that once this motion ceases, their operation upon us will be null. It is thus that we perceive that a quantity of fire, retained in the pores and pits of a piece of calcified stone, does not heat--even if we hold it in the palm of our hand--because the flame remains stationary in the stone. But should we swish the stone in water where, because of its weight, it has greater propensity for movement and where the pits of the stone open somewhat, the corpuscles of flame will escape and, encountering our hand, will penetrate it, so that we will feel heat. Since, in order for heat to be stimulated in us, the mere presence of corpuscles of flame is not by itself sufficient, and since movement is required in addition, it is with considerable reason that I declare motion to be the cause of heat.

This or that movement by which a scantling or other piece of wood is burned up or by which lead and other metals are melted will continue so long as the corpuscles of flame, moved either by their own velocity or (if this be insufficient) aided by a strong blast from a bellows, continue to penetrate the body in question; the former will resolve itself into further corpuscles of flame or into ash; the latter will liquify and be rendered fluid like water. From a common-sense point of view, to assert that that which moves a stone, piece of iron, or a stick, is what heats it, seems like an extreme vanity. But the friction produced when two hard bodies are rubbed together, which either reduces them to fine flying particles or permits the corpuscles of flame contained in them to escape, can finally be analyzed as motion. and the particles, when they encounter our body and penetrate and tear through it, are felt, in their motion and contact, by the living creature, who thus feels those pleasant or unpleasant affections which we call "heat," "burning," or "scorching."

Perhaps while this pulverizing and attrition continue, and remain confined to the particles themselves, their motion will be temporary and their operation will be merely that of heating. But once we arrive at the point of ultimate and maximum dissolution into truly indivisible atoms, light itself may be created, with an instantaneous motion or (I should rather say) an instantaneous diffusion and expansion, capable--I do not know if by the atoms' subtlety, rarity, immateriality, or by different and as yet unspecifiable conditions--capable, I say, of filling vast spaces.

 

The World, or Treatise on Light

By Rene Descartes

 

Chapter 1: On the Difference Between Our Sensations and the Things That Produce Them

 

In proposing to treat here of light, the first thing I want to make clear to you is that there can be a difference between our sensation of light (i.e. the idea that is formed in our imagination through the intermediary of our eyes) and what is in the objects that produces that sensation in us (i.e. what is in the flame or in the sun that is called by the name of "light"). For, even though everyone is commonly persuaded that the ideas that are the objects of our thought are wholly like the objects from which they proceed, nevertheless I can see no reasoning that assures us that this is the case. On the contrary, I note many experiences that should cause us to doubt it.

 

You well know that words bear no resemblance to the things they signify, and yet they do not cease for that reason to cause us to conceive of those things, indeed often without our paying attention to the sound of the words or to their syllables. Thus it can happen that, after having heard a discourse, the sense of which we have very well understood, we might not be able to say in what language it was uttered. Now, if words, which signify nothing except by human convention, suffice to cause us to conceive of things to which they bear no resemblance, why could not nature also have established a certain sign that would cause us to have the sensation of light, even though that sign in itself bore no similarity to that sensation? Is it not thus that she has established laughter and tears, to cause us to read joy and sorrow on the faces of men?

 

But perhaps you will say that our ears in fact cause us to hear only the sound of the words, or our eyes to see only the countenance of him who laughs or cries, and that it is our mind that, having remembered what those sounds and that countenance signify, represents their meaning to us at the same time. To that I could respond that it is nonetheless our mind that represents to us the idea of light each time the action that signifies it touches our eye. But, rather than lose time in disputation, I would do better to adduce another example.

 

Do you think that, even when we do not pay attention to the meaning of words and hear only their sound, the idea of that sound, which forms in our thought, is anything like the object that is the cause of it? A man opens his mouth, moves his tongue, forces out his breath: in all these actions I see nothing that is not very different from the idea of the sound that they cause us to imagine. Also, most philosophers assure us that sound is nothing other than a certain vibration of air that strikes against our ears. Thus, if our sense of hearing were to report to our mind the true image of its object, then, instead of causing us to conceive of sound, it would have to cause us to conceive of the motion of the parts of air that then vibrate against our ears. But, because not everyone will perhaps want to believe what the philosophers say, I will adduce another example.

 

Of all our senses, touch is the one thought least misleading and most certain, so that, if I show you that even touch causes us to conceive many ideas that in no way resemble the objects that produce them, I do not think you will find it strange if I say that sight can do the same. Now, there is no one who does not know that the ideas of tickling and of pain, which are formed in our thought when bodies from without touch us, bear no resemblance whatever to those bodies. One passes a feather lightly over the lips of a child who is falling asleep, and he perceives that someone is tickling him. Do you think the idea of tickling that he conceives resembles anything in this feather? A soldier returns from battle; during the heat of combat he could have been wounded without being aware of it. But now that he begins to cool off, he feels pain and believes he has been wounded. A surgeon is called, the soldier's armor is removed, and he is examined. In the end, one finds that what he felt was nothing but a buckler or a strap, which was caught under his armor and was pressing on him and making him uncomfortable. If, in causing him to feel this strap, his sense of touch had impressed its image on his thought, there would have been no need of a surgeon to show him what he was feeling.

 

Now, I see no reason that forces us to believe that what is in the objects from which the sensation of light comes to us is any more like that sensation than the actions of a feather and of a strap are like tickling and pain. Nevertheless, I have not adduced these examples to make you believe absolutely that this light is something different in the objects from what it is in our eyes, but only so that you will doubt it and so that, forbearing from being preoccupied by the contrary, you can now better examine with me what light is.

 

Principles of Philosophy

Rene Descartes

From PART IV: Of the Earth

CXCVIII. That by our senses we know nothing of external objects beyond their figure [or situation], magnitude, and motion.

Besides, we observe no such difference between the nerves as to lead us to judge that one set of them convey to the brain from the organs of the external senses anything different from another, or that anything at all reaches the brain besides the local motion of the nerves themselves. And we see that local motion alone causes in us not only the sensation of titillation and of pain, but also of light and sounds. For if we receive a blow on the eye of sufficient force to cause the vibration of the stroke to reach the retina, we see numerous sparks of fire, which, nevertheless, are not out of our eye; and when we stop our ear with our finger, we hear a humming sound, the cause of which can only proceed from the agitation of the air that is shut up within it. Finally, we frequently observe that heat [hardness, weight], and the other sensible qualities, as far as they are in objects, and also the forms of those bodies that are purely material, as, for example, the forms of fire, are produced in them by the motion of certain other bodies, and that these in their turn likewise produce other motions in other bodies. And we can easily conceive how the motion of one body may be caused by that of another, and diversified by the size, figure, and situation of its parts, but we are wholly unable to conceive how these same things (viz., size, figure, and motion), can produce something else of a nature entirely different from themselves, as, for example, those substantial forms and real qualities which many philosophers suppose to be in bodies; nor likewise can we conceive how these qualities or forms possess force to cause motions in other bodies. But since we know, from the nature of our soul, that the diverse motions of body are sufficient to produce in it all the sensations which it has, and since we learn from experience that several of its sensations are in reality caused by such motions, while we do not discover that anything besides these motions ever passes from the organs of the external senses to the brain, we have reason to conclude that we in no way likewise apprehend that in external objects, which we call light, colour, smell, taste, sound, heat or cold, and the other tactile qualities, or that which we call their substantial forms, unless as the various dispositions of these objects which have the power of moving our nerves in various ways. [Footnote: "the diverse figures, situations, magnitudes, and motions of their parts."-- French.]

 

From PART II: Of the principles of material things 

LXIV. The only principles which I accept, or require, in physics are those of geometry and pure mathematics; these principles explain all natural phenomena, and enable us to provide quite certain demonstrations regarding them.

 

I will not here add anything about shapes or about the countless different kinds of motions that can be derived from the infinite variety of different shapes. These matters will be quite clear in themselves when the time comes for me to deal with them. I am assuming that my readers know the basic elements of geometry already, or have sufficient mental aptitude to understand mathematical demonstrations. For I freely acknowledge that I recognize no matter in corporeal things apart from that which the geometers call quantity, and take as the object of their demonstrations, i.e. that to which every kind of division, shape and motion is applicable. Moreover, my consideration of such matter involves absolutely nothing apart from these divisions, shapes and motions; and even with regard to these, I will admit as true only what has been deduced from indubitable common notions so evidently that it is fit to be considered as a mathematical demonstration. And since all natural phenomena can be explained in this way, as will become clear in what follows, I do not think that any other principles are either admissible or desirable in physics.