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CHAPTER XXXII.
POSSIBILITY OF THE PENETRATION OF BODIES

245. The more we meditate on the corporeal world, the more we discover the contingency of many of its relations, and the consequent necessity of recourse to a higher cause which has established them. Even those properties which seem most absolute cease to appear so when submitted to the examination of reason. What more necessary than impenetrability? Yet from the moment it is carefully analyzed, it becomes reduced to a fact of experience not founded on the nature of things, which consequently may exist or cease to exist without any contradiction.

246. Impenetrability is that property of bodies by which two or more cannot be in the same place at the same time. For those who do not make pure space a reality independent of bodies this definition has no meaning; for if place like pure space is nothing, to speak of the same place abstracted from bodies, is to speak of nothing. In that case, impenetrability can only be a certain relation either of bodies or of ideas.

247. Above all, we must distinguish the real order from the purely ideal. We may consider two kinds of impenetrability; physical impenetrability, and geometrical impenetrability. The physical is that which we see in nature; the geometrical that which is found in our ideas. Two balls of metal cannot be in the same place: this is physical impenetrability. The ideas of the two balls present two extensions which mutually exclude each other in the sensible representation: this is geometrical impenetrability. If we imagine two balls which perfectly coincide, they are no longer two, but only one; and if we imagine one ball to occupy a part of the other, we have a new figure, or, rather, one is considered as a portion of the other, and is consequently contained in the idea of the other, as a small ball inside of a larger ball. On either supposition the balls are regarded as penetrating each other in whole or in part; but by penetration is here meant only that there are certain parts in one, considered as pure space, which the other, also considered as pure space, occupies. Geometrical impenetrability exists only when the two objects are supposed to be separated, and only inasmuch as they are separated; in which case impenetrability is absolutely necessary, because penetration would be to confound what is by the supposition separated, and would imply separation and non-separation, which are contradictory. Therefore, geometrical impenetrability is no argument in favor of physical impenetrability; for the former exists only in case it is presupposed or required under pain of contradiction. The same would occur in reality; for if we suppose two bodies separated, they cannot be in the same place whilst they are separated, without a manifest contradiction. On this point, therefore, the ideal teaches us nothing as to the real.

248. Can penetration exist in reality? Can one ball of metal, for example, enter another ball of metal, as we make one geometrical ball enter another? We are not treating of the regular order of things which is repugnant to such suppositions, but of the essence of things. On this supposition, I maintain that there is no contradiction in making bodies penetrable, and that an analysis of this matter proves that the impenetrability of bodies is not essential.

We have seen that the idea of place as pure space is an abstraction. It is therefore an entirely imaginary supposition on which we give to every body a certain extension to fill a certain place, necessarily, and in such a manner that it is impossible for it to admit another body into the same place at the same time. The position of bodies in general is the sum of their relations; the particular extension of each body is only the sum of the relations of its parts among themselves, until we come by an infinite division to unextended or infinitesimal points.

The sum of the relations of indivisible or infinitesimal beings constitutes what we call extension and space, and all that is contained in the vast field of sensible representation. Who can assure us that these relations are not variable? Is our experience, perhaps, the limit of the nature of things? Evidently not. The universe was not planned after our experience, but our experience is obtained from the universe. To say that it contains, and can contain only what our experience sees in it, is to make the me the type of the universe; to affirm that its laws are derived from us, that they are emanations from our being. Foolish pride of an imperceptible atom, which appears for an instant on the great theatre of nature, and goes out like a spark of fire; foolish pride for a spirit which, despite its great idea of its own importance, feels that it is unable to withdraw itself from these laws and phenomena, which it pretends to consider as its own creation!

CHAPTER XXXIII.
A TRIUMPH OF RELIGION IN THE FIELD OF PHILOSOPHY

249. There are two things in extended objects: multiplicity and continuity. The first is absolutely necessary to extension; it supposes distinct parts, and that which is distinct cannot be identical without evident contradiction. The continuity represented in the sensible impression is not essential to extension, because it is only the result of a union of relations inseparable in the present order of sensibility, but not absolutely necessary in the order of reality. Transcendental philosophy rising above sensible representations, and leaving phenomena to enter on the contemplation of beings in themselves, nowhere discovers the necessity of these relations, and is obliged to consider them as simple facts which might cease to be without any contradiction. In this manner the correspondence of the phenomenon with the reality is saved, and the internal world harmonized with the external, but the subjective conditions of the former are not all transferred to the latter in such a way as to make what is necessary for our representations, absolutely necessary in itself.

250. Arrived at this point of transcendental philosophy, the mind beholds new worlds unfolded to its view. We rejoice to say that this discovers to us a new proof of the divinity of the Catholic religion, and teaches us to distrust that proud philosophy which finds a contradiction in every thing which it cannot understand.

251. There is a mystery which the Church celebrates with august ceremonies, and the Christian adores with faith and with love. The unbeliever sees the holy Tabernacle, and exclaims, in the pride of his ignorance: "Here is a monument of superstition; here man adores an absurdity."

As the present is a work of philosophy, not of theology, I might pass over without answering the objections of infidelity, but the occasion seems so well suited for the solution of some difficulties brought by light and superficial thinkers, that I am unwilling to pass them in silence. The nature of the work requires me to be brief in this discussion, though the subject is too important to be entirely omitted; the more so, as Catholic writers on philosophy have given their explanations on these points in what they considered the most seasonable place, and most frequently when treating of extension.

252. That the mystery of the Eucharist is a supernatural fact incomprehensible to man, and inexplicable by human words, is confessed by Catholics and acknowledged by the Church. We cannot, therefore, give a philosophical reason to explain this secret; no one was ever so vain as to attempt it. We can only examine whether the mystery is absurd and intrinsically contradictory; for if it were, it would not be a truth but an error, because divine omnipotence does not extend to what is absurd. The question is, whether the fact, although beyond the laws of nature, is intrinsically possible; for then it belongs to the field of criticism. If the incredulous man admits God, he must admit his omnipotence; the discussion must then be, not whether God can perform this miracle, but whether he has performed it.

253. The objections brought against the Eucharist may be reduced to the following: a body exists without the conditions to which other bodies are subject; it produces none of the sensible impressions which we receive from other bodies; and is in many places at the same time. To answer these objections, let us first determine our ideas.

254. The doctrines explained in the theory of sensations in this volume, show how false it is to say that the Eucharist is impossible. Under the sacred species is a body which does not affect our senses; here is a miracle, but not an impossible thing. I have shown that there is no necessary relation between bodies and our sensibility. The connection which now exists cannot be explained by any intrinsical property of spirits and bodies; we must, therefore, recur to a higher cause which freely established these relations. The same cause can suspend them. From this point of view the question becomes this: Can the power of God make a body which shall not produce the phenomena of sensibility, and suspend the laws which he was free to establish? Thus presented, the question cannot bear two answers. It must be answered in the affirmative, or the omnipotence of God is denied.

255. Those who attempt to show the impossibility of our dogma, must prove the following propositions:

I. Passive sensibility is so essential to bodies that they cannot lose it without destroying the principle of contradiction.

II. The relations of our organs [to] objects are intrinsically immutable.

III. The transmission of the impressions of the organ to the sensitive faculties of the soul is equally essential, and can fail under no supposition.

If they do not prove the truth of these three propositions, all the objections founded on the phenomena of sensibility fall to the ground. If one only is not proved, all the objections are solved; for it is evident that the phenomena of sensibility may be altered by three causes:

I. By the absence of the dispositions necessary to the body, that it may be the object of sensibility.

II. By the interruption of the ordinary relations between our organs and the body.

III. By the failure of the transmission of the impressions of the organ to the sensitive faculties.

Consequently, if one of the first propositions is false, the doubter is reduced to silence.

256. Whoever should attempt to prove these three propositions, not only would fail, but the attempt would prove his ignorance of the phenomena of sensibility, and that his philosophy on this point is the notions of the vulgar. It is not necessary to be a philosopher, it is sufficient to have acquired a very slight knowledge of philosophy to see that such an attempt would suppose a complete ignorance of the history of philosophy. At any rate, I need not insist on this point; for I have treated these questions at length in the last two books of this volume.

257. The solution there given ought to suffice to answer satisfactorily the objection founded on the particular state of a body without the conditions of extension which we find in others. From the moment that we suppose the correspondence of a body with our senses to be suspended, as these are the only means by which we are informed of what passes in the external world, it is impossible for us to affirm that there is any absurdity in that of which we have no experience. We perceive extension only by sensation, therefore we can say nothing in relation to the extension of an object of which we have no sensation. But although this answer should cut short all objections, I shall not confine myself to this alone.

258. What is extension? In reality it is the sum of the relations of the beings which compose the extended object. These relations, as I have proved, are not intrinsically necessary: therefore God can alter them. Thus this question comes to the same point as the preceding: can the power of God suspend, alter, or entirely take away relations which are not intrinsically necessary? Evidently it can. The difficulty then is not as to what could have been, but as to what is. Again we find ourselves out of the field of philosophy in that of facts, or the examination of the motives of credibility.

259. The other objection founded on the impossibility of body being in several places at the same time, though in appearance more difficult, amounts to the same as the former. To be in a place, as we now understand it, is to have a particular extension, with the ordinary form and relations with respect to the extension of other bodies. If we suppose a body with extension subject to other conditions, without the ordinary relation to the extension of other bodies, we destroy the supposition on which we base the impossibility of a body being at the same time in several places. Therefore, as we have proved that the omnipotence of God can alter and even take away these relations, there is no contradiction in admitting the destruction of the results which proceed from these relations.

260. This is why the distinction of the scholastics between two classes of extension: in ordine ad se, et in ordine ad locum, or quantitative and sacramental extension, though to the eyes of a superficial philosophy it might appear to be an empty subtlety, invented for the purpose of avoiding the difficulty, is nevertheless a profound observation, confirmed by the analysis of the reality and the phenomenon in the sensible order. I do not mean by this to say that when this distinction was made in the schools, they understood perfectly all the truth and philosophical nicety which it involves; nor that the distinction was always accompanied by the critical analysis which belongs to it. At present I abstract the merit of the men and regard only the thing. The less philosophical intelligence we suppose in those who used the distinction, the more admirable appears that religion which inspires its defenders with fruitful thoughts which the ages to come might unfold. The philosophical schools disputed warmly on extension, on accidents, and on the sensitive faculties: the Catholic dogma taught a truth which was contrary to all appearances, it stimulated them to examine more profoundly the distance of the phenomenon from the reality, the difference between the contingent and the necessary; the mystery which the Church taught introduced into philosophy questions which without it would probably never have occurred to man's understanding.

261. Bacon expressed a profound truth when he said that a little philosophy carried its possessor from religion, and a great deal of philosophy leads him to it. A careful study of the objections brought against Christianity, lays bare a truth confirmed by the history of eighteen centuries; the most weighty objections against Catholicity, instead of proving any thing against it, involve a proof which confirms it. The secret for discovering this proof, is to go to the bottom of the objection, and examine it under all its aspects. Original sin is a mystery, but it explains the whole world; the Incarnation is a mystery, but it explains the traditions of the human race; faith is full of mysteries, but it satisfies one of the greatest necessities of reason; the history of the creation is a mystery, but this mystery clears up chaos, throws light on the world, and is the key to the history of mankind; all Christianity is a collection of mysteries, but these mysteries are connected by a secret union with all that is profound, grand, sublime, or beautiful in heaven or earth; they are connected with the individual, with the family, with society, with God, with the understanding, with the heart, with languages, sciences, and art. The investigator who rejects religion and even seeks means to oppose it, finds it at the entrance as at the outlet of the mysterious ways of life; at the cradle of the infant as in the shadow of the tomb; in time as in eternity; explaining every thing by a word; listening unmoved to the wanderings of ignorance and the sarcasms of unbelief, patiently awaiting till the course of ages shall acknowledge its truth, which existed before all ages.

CHAPTER XXXIV.
CONCLUSION AND SUMMING UP

262. Before passing to another subject, let us fix our attention for a few moments on the nature and origin of the idea of extension. We shall thus collect the fruit of the preceding investigations, and prepare the way for those which follow.

The scientific fruitfulness of this idea to our mind proves how distant sensible impressions are from intellectual perception. We cannot know whether this idea existed in our mind before the sensible impression; if it did exist we were not conscious of it, and in this respect it is affirming a gratuitous proposition to say that it is an innate idea. What we can safely say, is, that there are two distinct orders of internal phenomena, that sensation could not have produced the idea, that this idea is immeasurably superior to the external impression, or even the internal sensitive intuition, and that if it did not already exist in the mind, it was not produced by sensation as an effect is produced by its cause.

263. Here we make an important transition from the order of sensations, to the order of ideas, and discover in our mind a new class of facts. It matters little whether these facts exist before the impression, or result from its presence. In the first case, we see in the mind a deposit of germs which need only the warmth of life in order to be developed; in the second, we find in the mind a fertility which produces these germs. In either case we find a being of a privileged nature, a sublime being which by a single leap rises above the region of matter, and awakened by the external impression, arises to a new life which this world cannot contain.

264. In this sense there are innate ideas; ideas which sensation could not have produced. In this sense all general and necessary ideas are innate; for sensation could not produce them. Sensation is never any thing more than a phenomenon, a particular and contingent fact, and consequently incapable of producing general ideas, or the ideas of the necessary relations of being. Sight, or the imaginary representation of a triangle, is a contingent phenomenon which tells us nothing of the necessary relations of the sides and angles to each other. In order to perceive these relations, this necessity, something else is required. This something else, call it innate ideas, force, fecundity, or activity of the mind, or any thing you please, exists, and could not have been produced by sensation, but belongs to a higher order distinct from sensible phenomena.

265. After such long investigations of the phenomena of sensation, we at last find an idea; it is the idea of extension, the foundation of all the mathematical sciences and of their application to the laws of nature.

The human mind, in all its relations with the material world, seems to have one great idea, that of extension, which, modified in infinite ways, is the origin of all the sciences which relate to matter. The whole material world rests on this idea, and all knowledge of material objects proceeds from it. It is a pure idea in its necessary relations and in its necessary branches. It is a light given to the lord of creation that he may know and admire the prodigies of nature.

266. We find the same wonderful simplicity amidst so complicated a multiplicity in another order of ideas. Hence we infer that the whole edifice of the sciences and all human knowledge are founded on a small number of ideas, perhaps on two alone. These ideas are not sensible representations, they are the objects of pure intuitions; they cannot be decomposed, but they may be applied to an infinite variety of things; they are not explained by words, as a union including various conceptions; by them a mind acts on another mind, not to teach it any thing, but to make it concentrate its activity in order to note what it contains within itself, and learn, in a certain measure, what it already knows.

Try to explain extension, the idea by which we perceive this order which we cannot express in words, but on which we found sensible experience and geometrical science, and you can find no expression. Will you define it to be "parts outside of parts?" But what are parts, and what does outside mean, if you have not the idea of extension? Take any extended thing, make your mind concentrate itself and exercise its activity in generalization. Is this triangle a quadrilateral? No. Are they both extended? Yes. Is this surface a solid? No. Are they both extended? Yes. Are all triangles different from quadrilaterals? Yes. Have all surfaces and solids extension? Yes. How do you pass from one fact to all the facts of the same kind, from the contingent to the necessary? Have you explained what extension is? No. Have you shown what there is common to all these different things? No. All that you have done then is to arouse the activity of your mind, and to make it direct its attention to the general idea of extension, and the mind applies this idea to various things which are different, yet have something in common, it applies the different modifications of this idea to various things which have something in common, and finds them different. You have not taught the truths of geometry to the mind, but have awakened them in it, whether they already existed in it, or the mind had the faculty of producing them.

267. Let us now collect the result of the investigations we have made. I do not give an equal value to all the propositions which follow. I have explained my opinion of each in its proper place, but I consider it well to sum them all up here in order to assist the understanding and help the memory.

I. There is immediate certainty of our relations with beings distinct from us.

II. There is certainty of the existence of an external world.

III. The external world in relation to us, is only an extended being which affects us, and is subject to constant laws which we may determine.

IV. We have the idea of extension.

V. The idea of extension is excited by sensations, but it is not confounded with them.

VI. The idea of extension is the basis of all our cognitions of bodies.

VII. The idea of extension should not be confounded with the imaginary representation of extension.

VIII. An extended space which is nothing real, is an absurdity.

IX. Space is nothing real distinguished from the extension of bodies.

X. Where there are no bodies, there are no distances.

XI. Motion is the change of the positions of bodies among themselves.

XII. There is not and cannot be vacuum of any kind.

XIII. The idea of space is the idea of extension in the abstract.

XIV. The imagination of an unlimited space is only an attempt of the imagination to follow the understanding in the abstraction of extension. It also arises from our habit of seeing through transparent mediums, and moving in fluids whose resistance is not perceptible.

XV. As all that we know of bodies is, that they are extended and affect us, whatever has these two conditions is to us a body.

XVI. But as we do not know the essence of bodies, we do not know whether a body can exist without extension.

XVII. Neither do we know what modifications the extension of one body may be subject to, with respect to others.

XVIII. The elements of which bodies are composed are unknown to us.

XIX. The approximation of some bodies to others, and the gravitation which results from it, seem to be the necessary effect of their present relations.

XX. The necessity of approximation does not suffice to explain the laws of motion, or their beginning, or their continuation.

XXI. The idea of space is not an absolutely necessary condition of sensation.

XXII. The idea of extension has a real objectiveness.

XXIII. The transition from the subjective to the objective in relation to extension is a primitive fact of our nature.

XXIV. Therefore bodily phenomena have a real existence outside of us.

XXV. Therefore a real certainty, scientific as well as phenomenal, arises from the testimony of the senses.

XXVI. Reason justifies the instinct of nature when it examines the relation of subjectiveness with objectiveness in sensations.

XXVII. Geometry considers extension in the abstract; but with the certainty that when the principle exists in the real order, the consequences cannot fail to be produced, and that the consequences will be more or less exact in proportion as the principle is more or less exactly realized.

XXVIII. Notwithstanding our certainty of the existence of the external world we do not know its essence.

XXIX. We do not know what this world is when seen by a pure spirit.

XXX. Sensible intuition, to which our geometry relates, does not constitute the essence of scientific knowledge, and may be separated from it.

XXXI. A change in the relations of corporeal beings among themselves, and with our sensitive faculties, is not intrinsically impossible.