Jacques Maritain Center: Thomistic Institute

Does Void Exist?: The Thomistic Rejection of its Presence in the Natural World

Mario Enrique Sacchi
Member of the Pontifical Roman Academy of
St. Thomas Aquinas and of Catholic Religion

Buenos Aires.

The natural philosophy of Saint Thomas Aquinas holds that every body existing in this world is contained in its own place and that every place is occupied by a material body(1). This Thomistic thesis alludes restrictively to material bodies, to the same sensible substances composed of matter and form which we know by means of sense perception. The mathematical bodies which geometry is concerned with are excluded from Aquinas' thesis because although these entities are understood through an analogical intellection with regard to physical bodies they lack sensible matter utterly in reducing themselves to merely extensive quantities(2). Moreover, places occupied by material bodies are recipients whose subjects are also of a material kind, hence they cannot be assimilated to geometrical spaces incapable of containing anything endowed with a sensible nature(3).

St. Thomas was aware of the extraordinary difficulties of a philosophical explanation of his theory. The main reason for these difficulties lies in our complicated knowledge of the nature of place. This knowledge is threatened constantly by the interference of something that men tend to confuse with a place and sometimes they invoke it as a substitute for the place itself: the space. That is why they often say "there is no space here" as if it were equivalent to saying "there is no place here". Men also attribute frequently to the space a role destined to substitute the place's when it is said that "the Earth occupies a very small space in the whole universe". But the identification of space and place is rejected in Aquinas' physical speculation and, for a still stronger reason, he also refuted the substitution of the latter by the former. St. Thomas' most relevant argument for rejecting these criteria is of capital importance: whereas place belongs to the order of nature, space is no more than a being of reason which, although founded in sensible beings existing ad extra, is something foreign to the material world. Sensible bodies need to be received and conserved in their own places, but they have no need to occupy a space which plays neither a receptive nor a conserving role. In that respect the notion of space reiterates redundantly and fictitiously the concept of place(4).

St. Thomas observed that the imagination of space gave rise to several errors in the investigation of nature which promoted untenable cosmological systems, such as the model of a universe contained within an infinite spatial receptacle. The infinity of space has been outlined as an immediate consequence of the aim of identifying it with a place. We can point out this consequence in analysing the meaning of the widely generalized opinion which reads as follows: "Place is the part of space occupied by a body". Isaac Newton himself held this opinion in his Principia as it were an evident axiom of physics(5). Now then, if every body were occupying a place in a space, this space would then be an extrinsic container whose dimensions exceed the dimensions of all the bodies actually placed in itself. But material bodies multiply incessantly and they occupy places which are always exceeded by the space they are contained in. Then, if there always were a larger space capable of receiving all the new bodies which are constantly coming into existence, would it be reasonable to think that it would have an infinite extension? Aquinas also rejected this opinion because in our universe there is no infinite thing in act(6). Furthermore, it is impossible that the universe be contained within a spatial extension devoid of material nature since the world includes all the sensible bodies as a whole, but this totality is finite in number(7).

Most philosophers who have affirmed the natural existence of space have also asserted that every place occupied by a physical body would be a filled space while spaces where there are no located bodies would be empty. According to this theory, space would be divided into a portion full of matter and into another portion empty of any content, although this void could potentially be filled by the reception of material substances. At all events its dimensions would undergo no modifications, for the spatial dimensions, now full, now empty, are the same. The inner space of a bottle does not change when a fluid fills its receptive capacity, for this capacity remains the same if the liquid is not present within the bottle.

St. Thomas emphasized that this conception of space has no correlate in the external world. For space is reduced to its extensive dimensions, it is absolutely indifferent to nature. The bottle is made of glass, but the liquid which fills its capacity is water, oil or wine while its inner space does not go beyond a mathematical abstraction of its extensive quantity, e.gr. a gallon. But a gallon of what? A gallon of any fluid and even of none because the geometrical measurements of volumes are considered by leaving the sensible matter aside and are restricted to quantitative dimensions of mathematical bodies. That is why we cannot accept the definition of a substance as a res extensa propounded by Descartes(8). There are two reasons for rejecting this bad definition: firstly, because extension is predicated of every body, but there are bodiless substances and therefore extension cannot be predicated of their entities; secondly, because an extensive thing qua extensa is not a substantial being in itself, at least necessarily, and so a cylinder can be the object of a mathematical measurement of its extensive dimensions not being itself a substance or an ens per et in se. In short, Descartes overlooked that a bodily substance is not a mere extensive quantity, but a being consisting essentially of sensible matter.

The Thomistic speculation on place displaced the erroneous doctrines which affirm the existence of space in the natural world. In contrast to space, place is a natural entity, not a mathematical one. Place is predicated of material bodies which contain other sensible bodies. Aristotle has defined it as "the innermost motionless boundary of what contains"(9). This definition implies that place is the boundary which is in an immediate contact with the external surfaces of bodies contained within its own dimensions; for instance, the internal surface of the bottle which the external surface of a contained fluid is in contact with. Then place is not the whole body of the bottle as such, but only its inner surface which determines the location of a contained liquid in a certain position. The position gotten by the content in the place where it is duly received is that which the Scholastic philosophy of nature has called ubi(10).

Aquinas has always stated that place does not identify with space. Space consists of extensive dimensions indifferent to all material natures and we can conceive of it as being filled with matter or as an empty receptacle, but the same is not true of place. Place pertains to a sensible body invariably and participates its own material nature. Moreover, a place is always replete with corporeal matter(11). Whether the contents of a bottle spill or not, the recipient will never remain empty because the place once full of water, oil or wine is now full of air. In fact, there is no place in the material world devoid of a bodily content just as there is no sensible body which does not occupy its proper place. Hence it follows that Thomistic natural philosophy rejects the existence of a void as something absolutely impossible.

St. Thomas' rejection of a void was objected to with two main arguments based on the apparent existence of intramundane spaces --viz. the interastral zones existing between planets and stars-- and also on the apparent existence of an extramundane space beyond the material universe. Both these objections can be synthesized in these statements: 1) since there are no evidences of the material nature which the interastral regions would consist of, it must be affirmed that these regions are empty spaces; and 2) provided that the world includes the sensible substances in their entirety, all these sensible substances --the world itself-- must be contained in some place because it is not likely that it would be hanging in a nothingness, so that it is necessary that it would be installed in a determined place in space.

Aquinas answered the first objection to his thesis by affirming that neither the apparent emptiness of the interastral zones nor our present ignorance of the material entity which could exist in themselves justifies that we reject the presence of a sensible matter there(12). It is true that these regions sometimes show themselves as dark and sometimes light, a fact which reveals that there are boundaries where the qualitative virtues of light irradiate, but no quality can subsist by itself, i.e. without a substantial support where it would have its subject of inherence. Therefore, something of material nature must be there with the sufficient aptitude to receive the presence of light waves and allow their propagation in these same regions. Now, what is this thing? St. Thomas does not know, but we do not either. No hypothesis set forth by modern mathematical physics about the nature of the interastral boundaries goes further than the conjectural affirmation of the existence of a field suitable for the propagation of gravitatory forces and electromagnetic waves. Again, what is the nature of this field? Nobody up to now has satisfactorily solved the enigma locked in this question.

The second objection to Aquinas' thesis is resolved efficaciously by his natural philosophy. St. Thomas said that the world occupies no place. It contains in itself all the matter actually existing and all the places containing sensible bodies as a consequence(13). As the world comprises the sum of all these places, and due to the fact that place is always an extrinsic container of material bodies, it has no location because there is no place outside the world itself. If it occupied a place in a space, as a lot of men think, it would be necessary that there exist an extrinsic material receptacle to receive it with certain dimensions that at all events must be equal to those of the world. On the other hand, the existence of such an extramundane space would also imply the absurd existence of material things outside the universe, but there is no world outside the world itself. In truth, the imagination of an extramundane space where the world would be contained rests on the unfounded assumption of those who assign a single mass to the universe, as if the world were an individual matter whose conservation requires the existence of a locating recipient, but it is not so. Our material world is not a substantial entity, as on the contrary every sensible thing which is by itself and in itself is. It is the order of all the material individuals whose unity arises from the relationship existing between themselves with the whole universe where they are inserted. Thus if there were an extramundane space outside the material world, this space would be empty of matter and the material universe would be contained in a void. Thereby St. Thomas did not hesitate in rejecting the existence of the void vis-à-vis the incoherence of such an opinion.

Aquinas not only rejected the existence of an extrinsic void with respect to material bodies, but also its presence inside corporeal things(14). His rejection of the natural existence of a void has been laid aside by many authors who thought that the existence of empty spaces would be necessary to explain some processes which happen inside material bodies, such as condensation and increase. At first glance the condensation of matter seems to be a sort of internal contraction of its parts which would pass to fill some supposedly empty spaces, and so every condensed body would acquire a compacter organization than that which it had before. But Thomistic philosophy disagrees with this viewpoint because condensation does not occur in this way. On the one hand, it is impossible that the inner parts of a body move to fill empty spaces for the location of every sensible thing needs the reception of its dimensions into bodily boundaries full of matter, but the void, according to its own definition, is a bodiless space and thus unable to contain a material being. On the other hand, granted the impossibility that the integral parts of sensible bodies can be contained in empty spaces, the process of condensation does not happen through the successive filling of these spaces, but by means of the elimination of the weakest or the least solid components of the bodies discharged by the expulsive force of the toughest ones. Therefore, condensation is not the exclusion of non-existent empty intra-corporeal spaces. It is the result of the presence of a larger quantity of matter within the same dimensions of a body from which the parts that keep it in a lesser stage of intrinsic density and cohesion were expelled(15).

Neither does the augmentative motion of living natures imply the existence of a void. There were philosophers and biologists who have described the increase of material bodies in such a way that it was reduced to a pure addition of some substances to others. For example, sometimes nutrition has been understood as an addition of external substances which would come to occupy empty spaces inside the body that is being fed. In this case, one could think that the increase of a material body by means of nutrition would involve a yuxtaposition of numerous corporeal substances. That is why this opinion is not very far from the ordinary impression which men have of the sensation of hunger. Men commonly think that hunger is caused by a certain gastric vacuum and therefore every one says "I am hungry" as it were equivalent to "I am empty". But St. Thomas also rejected this opinion. Nutrition does not consist of an addition of external substances which join to a corporeal matter that is being fed, but of an assimilation (fieri simile) which requires the conversion of the assimilated substances to the substance of the assimilating body. This assimilation needs to be made through a special motion that Thomistic natural philosophy calls alteratio, but there is no objection to mentioning it with the modern term chemical compound. Hence there is not an empty space in a body which increases itself by means of the incorporation of other substances into its own matter, although through this incorporation the assimilated substances lack their substantial conditions of beings in act and become themselves the true substance of that assimilating body, so that its increase is an enrichment which follows the chemical combination of the elements of the assimilating body and of those ones supplied by the assimilated substances. The empirical verification of this Thomistic thesis is unanswerable: providing that 1 litre of water weighs 1 kg, a human body that ingests it neither increase its volume in 1 litre nor its weight in 1 kg for the substance of the water does not add itself to the substance of that body, but it alterates in lacking to be water by its conversion in human flesh and blood(16).

St. Thomas has rejected vigorously an inner void as an extrinsic one as well. He was persuaded that the existence of a vacuum in the natural world stems only from a mental construction which produces indeed a fictitious entity. The human imagination of the existence of a void arises from the previous imagination of the space as a res extensa reduced to mere quantitative dimensions and indifferent to any sensible content. But since a non-sensible space is unable to receive the presence of material bodies, they must be contained properly in their own places. This is the reason why Aquinas has said that the existence of place as something which is not an external space also excludes the existence of a void(17). Place is the boundary where material bodies are contained and conserved in whereas space is reduced to mere extensive dimensions which we imaginate as they were being superposed to the dimensions of place. But place predicates of containing bodies endowed with sensible matter, which cannot be predicated of a void for its definition means a space where there is no material body. However the boundaries containing sensible bodies not only are full of matter, but they also are the only ones capable of containing them. The existence of place does not endure the concomitant existence of a void because in our universe there are neither immaterial receptacles nor bodies located in spaces bereft of sensible matter.

St. Thomas also pointed out that the existence of a void would hinder the knowledge of the causes of motion and rest of all the things which move themselves naturally(18). Sensible bodies move from a place to another finding in each one of themselves the appropriate boundaries for their rest. Then our knowledge of the causes of motion and rest relies immediately on our intellection of places filled of the bodies which occupy them successively for we should not understand that causes if we have no apprehension of the differences existing between their successive locations. But the knowledge of the places where movable beings are contained successively requires the perception of the material bodies which the locating boundaries are predicated of. This is so because every location is known by means of a perception both of the diversity of the locating body and of the body located within its boundaries. This knowledge would be impossible if an empty space would exist, for its privation of matter impedes the reception of material bodies and the apprehension of its diversity with respect to movable substances as well(19).

One of the outstandingest teachings of Thomistic natural philosophy regarding the non-existence of an empty space in the world holds the mutual exclusion of void and motion: Si est vacuum non est motus. St. Thomas has demonstrated this thesis in saying that local motion needs a plurality of places where movable bodies were received and contained; otherwise it would be impossible that these bodies move from place to place. Now then, if material bodies need to be located successively in a plurality of places as a conditio sine qua non for their motion, the existence of an empty space becomes quite impossible for they would lack locating boundaries where they can exercise such an act and where they must be contained necessarily(20).

It is very interesting to recall an Aquinas' approach to ballistics. As he has noted, the motion of all kind of missiles cannot occur in an empty space. Let us consider a stone thrown onwards by the thrust of a man's hand. In this case, as in every similar one, the mover and the moved are simultaneous. The local motion of the stone goes on in spite of the fact that the hand of that man stopped propelling it. Now what would happen if the boundary where the stone is moving were an empty space? No doubt, the stone cannot be neither contained nor conserving in a vacuum, so that it could move itself in the measure that the man's hand propelled it continuously; on the contrary, the stone would fall to the ground. But our proper experience tells us that it does not happen so. The initial impulse of the hand that has thrust the stone propels it to cover a certain distance in occupying succesive places in the atmosphere along its trajectory until the cessation of the driving force causes its fall. Therefore, as the stone needs a material boundary to be contained and to move itself, the existence of a void would hinder it to exercise its local motion(21).

St. Thomas remarked that the existence of an extracorporeal vacuum would turn unnecessary the location of material bodies. It is obvious that every sensible body has its own dimensions founded on the extensive quantity of its substance. The extrinsic measure of these dimensions is the place where such a body is contained and thus the dimensions of the body located in its own place and the dimensions of the locating boundary are equal. But an assumed empty space lacks extensive dimensions because it is not a material receptacle. As Aquinas accurately saw, the notions of an empty space and of a sensible body exclude themselves mutually. Of course, the presence of a sensible body in an empty space would indicate that its dimensions would need no extrinsic measures because a void is a measure of nothing, but in this circumstance we would think that place would not be necessary for the reception and conservation of material substances. Certainly this thought is incompatible with the clearest evidences perceived in our natural world, where we can observe that every body occupies its own place. Again, it is true that it does not occupy an empty space(22).

St. Thomas has drawn attention to the impossibility of a sensitive knowledge of an empty space whether it would exist in the external world. A vacuum is something devoid of sensible matter, but such a thing cannot be an object of our senses. The inferior apprehensive powers of human soul can perceive objects possessing a material entity proportionated to the their own cognitive capacities only. Now, how should we know by means of our senses an empty space deprived of sensible matter that, inasmuch as non-sensible, is not itself an object detectable through sense perception? It is obvious that we have no sensitive knowledge of non-sensible things. That is why natural sciences does not deal fittingly with a so-called empty space for its subject is the movable being, a bodily entity which cannot be bereft of sensible matter(23).

The reasons which led Aquinas to deny the existence of a void in the natural world require a thorough review of physical theories that persist in affirming it. The necessity of this review is brought to light when we realize that the affirmation of an empty space is nothing but a postulate derived from human imagination. In fact nobody has ever had an experience of a void. As its definition shows it as an space bereft of a sensible body, an incorporeal vacuum would be either an immaterial thing, such as the spiritual substances are, or a pure being of reason whose existence cannot be exercised outside the human mind. The first alternative is inadmissible because the incorporeal spirits, which cannot be investigated by natural sciences, are not empty substances. Then we must accept the second one: vacuum is a being of reason with a fundamentum in re. But physics does not deal with beings of reason for this kind of things does not belong to the genus of sensible substances.

The steady resort of phycisists to the existence of an empty space is a barren method for researching the natural world. Physical knowledge is bound to sensible experience, but it would be impossible without the objective presence of material things. As it has been said, men have no experience of a void, i.e. of a thing defined as something bereft of a corporeal content. An empty space implies a privation of a sensible body, so that the existence of an immaterial place is absolutely impossible in our material universe for such a supposed place of the material world would be out of the kingdom of matter.

However, it is not right to say that the expression "empty space" involves an intrinsic contradictio in terminis because our imagination of a space allows to understand it as it were either full of matter or devoid of itself. We can conceive an empty space or a void in the same way that we can conceive a horse whose head, instead of being an equine's, is a man's head, and so we conceive a centaur. Nevertheless, the human understanding of an empty space, as well as our conception of the centaur, has no correlate in the world of sensible nature because in our bodily universe there is nothing which can be a pure extension lacking matter. The foundation of the notion of an empty space lies in the existence of sensible things whose vacuity is merely apparent or whose experience cannot be obtained directly or naturally by means of our sensitive powers, but sensible things remain material ones despite of the obstacles to their human perception. A typical example of their sensible objectivity, but also of the difficulties in apprehending them, may be appreciated both in the cases of the radiations which we cannot perceive without the aid of very refined instruments and of the gravitatory and electromagnetic fields such as they were suggested by Einstein in the context of his theory of general relativity(24).

The postulate of the existence of a void in the natural world involves a great challenge to the human science, but there were no experiment which had confirmed it. Pascal has tried out to verify the existence of a vacuum in finding inspiration in a test made by Torricelli beforehand; however, his attempt failed because a mechanicist prejudice infiltrated into his cosmological views led him to scorn the deep significance of the horror vacui which nature exudes universally(25). It does not mean that the failure of Pascal's essay could be surmounted through a more perfect expedient than that he used in the seventeenth century for all the attempts to prove the existence of an empty space are fruitless. It is absurd that men endeavour to prove the existence within the boundaries of the material world of something which does not exist there inasmuch as it is a privation of a bodily nature.

The unfounded assumption of the existence of an empty space is often a prelude to many physical doctrines which start from its affirmation not foreseeing the risks of such a position. We can find one of the most illustrative examples of this attitude in the mathematical model of the universe where it is supposed that light would propagate in a void at a given velocity. This mathematical model got a generalized approval from modern phycisists, but it contains a defect which was also transfered to Einstein's theory of special relativity.

As it is known, Einstein's criticized the addition theorem for velocities enunciated in classical physics. According to this theorem, if we consider a man walking in a wagon of a train at 2 miles/hour in the same direction of this train running at 50 miles/hour with respect to the rails, the man's velocity with respect to the rails would result from the addition of his own speed and that of the train's, e.g. 52 miles/hour. But Einstein said that this theorem is not applicable to the calculus of the velocity of light. He gave the following example with the aim of showing it: be a train running on the rails at 50 miles/hour and a beam of light which propagates in an empty space in the same direction at a speed c with respect to the rails. Now then, according to that theorem, the velocity of light with respect to the moving train must result from c minus the train's speed, and so it would uccur that c would be minor than c itself, but it is absurd for c cannot be minor than c itself(26).

However, Einstein's criticism of the addition theorem for velocities contains several defects. On the one hand, that what is to be calculated in the first example is the velocity of a man with respect an unmovable body --the rails--, whereas in the second one the light's speed is compared with regard to a moving thing --the train running on the rails. On the other hand, although Einstein has omitted explicitly to mention the existence of an absolute space as a point of reference for the velocity of light --for it was demanded to him owing to his own rejection of the absolute space held by classical physics--, nevertheless he has admitted its existence implicitly because the propagation of light at a uniform velocity c is postulated necessarily with respect to an absolute space, but a void or an empty space is really an absolute one. Now, if there is no void in our natural world, and providing that the velocity of every moving thing needs a comparison of its motion with a material point of reference, to what an extent can physics insist in choosing arbitrarily a fictitious vacuum to calculate the light's speed?

Perhaps the key to understand the reason why physics does not reach a definitively exact measure of light's velocity in a void can be found in this question. Many physicists think that this lack of exactness be due to the defects of the instruments used to mesure it or to the unpreciseness of human calculations, but from what it has been said it seems logical to infer that the search for a uniform velocity of light in a vacuum is very close to an utopia. If there is no empty space in our world, light propagates across boundaries undefectively full of matter. Now, if it is so, the differences of light's speed found by means of physical experiments must be attributed to the natural resistance which it runs into the bodily universe where their waves irradiate. This is the reason why Thomistic philosophy raises a serious objection to the famous formula E mc2 popularized by Einstein's theory of relativity, for if light does not propagate in a vacuum, but in a space which is always and invariably full of sensible matter, the validity of this formula seems to be extremely questionable because the constant c, which means universally the speed of light in a void, is something conceivable by our mathematical intellection, but it has no correlate in the material world because there are no empty spaces here(27).

If light would propagate in an empty space, it only would be possible in the case that it would be a material substance of the same genus predicated of sensible bodies for its entity must exist by itself and in itself. Of course, a void cannot be a subject of nothing. Moreover, it would be necessary that it subsist separately, e.g. outside of any containing body, for in a vacuum, in accordance with its definition, nothing is contained. Finally, it would be also necessary that light were its own act of propagating as there is no light which does not propagate constantly, hence it would be a thing whose propagation would be its own essence. These outcomes would be unavoidable if anybody thinks that light irradiates in an empty space, but Thomistic philosophy has many reasons to reject them.

The light cannot propagate in a void as it were a separate being. If it were so, this vacuum would become the same absolute space described in Newton's Principia. Moreover, in this case the sensible entity would correspond to a substance or a material body that would be capable of subsisting in a void independently of a containing subject, a fact which is discarded by both Aquinas' philosophy and modern mathematical physics. But St. Thomas had also a powerful metaphysical motive to reject the possibility of a propagation of light in an a void, for if light were a being which would exist in a vacuum as a permanent act of propagating itself, as it was conjectured above, this act must subsist as something identical to the essence of light. In the spirit of Thomistic metaphysics this last alternative is plainly pantheistic because only in the divine being the essence is its own subsisting act or a pure act identical to God's nature.

Pantheism is not a strange redundancy of many physical speculations. Sometimes the absolute space of classical physics was qualified as a divine thing, such as Newton himself thought about what he called a sensorium Dei(28). But a void has always the own attributes of an absolute space because it has no determinate nature and no limited dimensions, and so we conceive it as it were a motionless boundary which would be able of containing sensible bodies. That is why Thomistic natural philosophy has right on his side in asking where we can find such a thing in our finite and movable natural world.

Mario Enrique Sacchi
Member of the Pontifical Roman Academy of
St. Thomas Aquinas and of Catholic Religion

Buenos Aires.


The works of St. Thomas Aquinas cited in this article were quoted according to the following editions:

Compendium theologiae. Leonine Edition, vol. xlii/a.

De malo. Cura et studio P. Bazzi O. P. et P. M. Pession O. P., in Questiones disputatae, vol. ii

De potentia. Cura et studio P. M. Pession O.P., in Quaestiones disputatae, vol. ii.

De spiritualibus creaturis. Cura et studio M. Calcaterra O. P. et T. S. Centi O. P., in Quaestiones disputa- tae, vol. ii.

De veritate. Leonine Edition, vol. xxii/ 1-3.

Expositio super librum Boethii De Trinitate. Ad fidem codicis autographi nec non ceterorum codicum manu scriptorum recensuit B. Decker, editio photomechanice iterata (Leiden: E. J. Brill, 1965).

In Aristotelis libros De caelo et mundo expositio. Leonine Edition, vol. iii.

In Aristotelis libros Meteorologicorum expositio. Leonine Edition, vol. iii.

In Aristotelis librum De anima commentarium. Cura et studio A. M. Pirotta O. P. (Turin-Rome: Mariet- ti, 1959).

In duodecim libros Metaphysicorum Aristotelis expositio. Editio iam a M.-R. Cathala O. P. exarata retracta- tur cura et studio R. M. Spiazzi O. P. (Turin-Rome: Marietti, 1950).

In librum Beati Dionysii De divinis nominibus. Cura et studio C. Pera O. P. Cum introductione historica P. Caramello et synthesi doctrinali C. Mazzantini (Turin-Rome: Marietti, 1950).

Quaestiones disputatae. Ed. 9a (Turin-Rome: Marietti 1953).

Quaestiones quodlibetales. Cura et studio R. M. Spiazzi O. P. (Turin-Rome: Marietti 1956).

Sancti Thomae Aquinatis, Doctoris Angelici, Ordinis Praedicatorum, Opera omnia iussu impensaque Leonis xiii P. M. edita. Cura Fratrum Praedicatorum (Rome: Commissio Leonina, 1882ff.) (Leonine Edit- ion).

Scriptum super libros Sententiarum magistri Petri Lombardi epsicopi Parisiensis. [In i et ii Sent.] Editio nova curâ P. Mandonnet O. P. (Paris: P. Léthielleux Éditeur, 1929).

Scriptum super Sententiis magistri Petri Lombardi. [In iv Sent.] Recognovit atque iterum edidit M. F. Moos O. P. (Paris: P. Léthielleux, 1947).

Summa contra Gentiles. Cum commentariis Francisci Sylvestris Ferrariensis O. P. Leonine Edition, vol. xii-xv.

Summa theologiae. Cum commentariis Thomae de Vio Cardinalis Caietani O. P. Leonine Edition, vol. iv-xii.

Super Evangelium S. Ioannis lectura. Cura et studio R. Cai O. P., 5th ed. (Turin.Rome: Marietti, 1965).

1. Cf. In iv Phys., lect. 7, nn. 4 et 7; lect. 9, nn. 2 et 6; lect. 23, n. 2; In i De caelo et mundo, lect. 10, n. 2; lect. 14, n. 8; lect. 15, n. 8, lect. 18, nn. 8-9; lect. 20, n. 6; In ii De anima, lect. 23, n. 535; In xi Metaphys., lect. 10, n. 2352; lect. 11, n. 2373; In Boeth. De Trinit. q. 4 a. 3 ad 2um; In ii Sent. dist. 14 q. 1 a. 1 sed contra 1; dist. 17 q. 1 prol.; Quodlib. vi q. 2 a. 2 obi. 2a et resp.; Summ. c. Gent. ii 35; et passim.

2. "Quanto, prout quantum est, non debetur proprie locus, nec per consequens potentia ad ubi; sed prout habet determinatam naturam" (In ii Sent. dist. 2 q. 2 a. 2 ad 3um).

3. "Locus et locatum sunt proprietates corporum naturalium, inquantum huiusmodi" (In xi Meta-phys., lect. 10, n. 2330). Cf. In Evang. Ioannis, cap. 1, lect. 1; In iii Phys., lect. 6, n.6; In ii Meteorol., lect. 2, n. 2; In ii De anima, lect. 3, n. 257; In De mem. et remin., lect. 6, n. 6; In xi Metaphys., lect. 10, nn. 2339, 2343-2344 et 2349; In xii Metaphys., lect. 2, n. 2436; In ix De div. nomin., lect. 2, n. 816; In i Sent. dist. 37 q. 2 a. 1 sed contra; q. 2 a. 1 obi. 5a et resp.; q. 3 a. 3 resp.; In ii Sent. dist. 2 q. 1 a. 3 sed contra 1; q. 2 a. 2 ad 3um; dist. 12 q. 1 a. 5 obi. 1a et ad 2um; dist. 14 q. 1 a. 1 sed contra 1; dist. 15 q. 2 a. 1 ad 4um; dist. 17 q. 3 a. 1 sed contra 2; In iv Sent. dist. 49 q. 3 a. 1 qla. 1a resp.; Quodlib. xi q. 1 a. 1 obi. 3a; De potent. q. 3 a. 10 obi. 10a; De malo q. 1 a. 1 obi. 4a; Summ. c. Gent. iii 23 et iv 59; Summ. theol. i q. 8 a. 2 resp. et a. 4 ad 2um; q. 68 a. 3 obi.1a; q. 110 a. 3 obi. 1a; i-ii q. 31 a. 7 obi. 1a; iii q. 76 a. 6 ad 1um.

4. Cf.In iii Phys., lect. 7, n. 6; lect. 13, n. 4; In iv Phys., lect. 6, nn. 6-9; lect. 8, nn. 2-4 et 6; lect. 11, n. 2; lect. 12, n. 14. See M. E. Sacchi, "La teoría del espacio en la física de Santo Tomás de Aquino": Sapientia li (1996) 517-563, and Id., El espacio enigmático (Buenos Aires: Basileia, 1998), chap. vi: "La diversidad del espacio y del lugar", pp. 106-128.

5. Cf. I. Newton, Naturalis philosophiae principia mathematica, new ed. (Amstelodami, 1723), Scholion post definitiones, p. 9. We have previously noted (cf. El espacio enigmático, pp. 106-108) the impossibility of taking this common opinion back to Aristotle's natural philosophy in spite of the suggestions of Duhem and Ross. See P. Duhem, Le système du monde. Histoire des doctrines cosmologiques de Platon à Copernic, new. ed. (Paris: Hermann, 1988), vol. i, pp. 197-198; and Aristotle's Physics. A Revised Text with Introduction and Commentary by W. D. Ross, 3rd rpt. (Oxford: Clarendon Press, 1966), p. 53.

6. "Nihil quod est praeter Deum, potest esse infinitum" (Summ. theol. i q. 7 a. 2 sed contra). Cf. the context of this question 7 of the Pars prima in its entirety.

7. "[Non est extra mundum] aliquem locum in rerum natura existentem, sed imaginabilem tantum: alioquin esset ponere locum extra caelum, cuius est magnitudo finita, habens principium et finem [...] Sicut ergo, cum dicimus extra mundum non esse nisi Deum, non ponimus aliquam dimensionem extra mundum; ita cum dicimus ante mundum nihil fuisse, non ponimus aliquam successivam durationem ante mundum" (In viii Phys., lect. 2, n. 20). "Est falsum [...] quod sint plures mundi" (In i De caelo et mundo, lect. 16, n. 4). "Impossibile est esse multos mundos" (Ibid., lect. 18, n. 9). "Extra caelum non est possibile existere aliquod corpus [...]; ergo extra caelum non est locus" (Ibid., lect. 21, n. 7).

8. "Extensio constituit essentiam corporis" (R. Descartes, Lettre à Arnauld, 4 juin 1648, in Oeuvres de Descartes, ed. by Ch. Adam et P. Tannery [Paris: Léopold Cerf 1897-1910], vol. v, p. 193).

9. Phys. 4: 212 a 20-21, transl. by R. P. Hardie and R. K. Gaye, 6th rpt. (Oxford: Clarendon Press, 1970 ), in The Works of Aristotle Translated into English. Under the Editorship of W. D. Ross, vol. ii, ad locum. See H. Bergson, Quid Aristoteles de loco senserit (Paris: Félix Alcan, 1889); C. Piat, Aristote, 2nd ed. (Paris: Félix Alcan 1912); A. E. Taylor, A Commentary on Plato's Timaeus (Oxford: Clarendon Press, 1928), pp. 664-677: "Aristotle's Doctrine of Space"; M. Dehn, "Raum, Zeit, Zahl bei Aristoteles vom mathematischen Standpunkts aus": Scientia lx (1936) 12-21 und 69-74; A. Sesmat, "La théorie aristotélicienne du lieu": Revue de Philosophie xxxviii (1938) 477-500; J. Moreau, L'espace et le temps selon Aristote (Padova: Antenore 1965); V. Goldschmidt, "La théorie aristotélicienne du lieu", in Mélanges de philosophie grecque offerts à Mgr A. Diès par ses élèves, ses collègues et ses amis (Paris: Librairie Philosophique Joseph Vrin 1956), pp. 79-120; and M. E. Sacchi, El espacio enigmático, pp. 103-128.

10. The proper notion of the category of the ubi raises many problems in Scholastic philosophy. Thomistic authors conceive it as the presence of a thing in its own place, such as St. Thomas defined it in the thirteenth century: "Ubi enim est in loco esse" (In i Sent. dist. 37 q. 2 a. 3 ad 2um); and also with this words: "Nihil aliud significat esse ubi, nisi esse in loco" (In xi Metaphys., lect. 12, n. 2376). Cf. In iii Phys., lect. 5, n. 15; In v Metaphys., lect. 9, n. 892; lect. 17, n. 1005; De potent. q. 10 a. 1 resp.; De spirit. creat. a. 1 sed contra 3.

11. "Oportet ostendere quod non sit aliquod spatium sine corpore sensibili" (In iv Phys., lect. 9, n. 5). "Possibile enim est locum evacuari ab hoc corpore, non ut sit totum vacuum: remanet enim plenus alio corpore" (In ix Metaphys., lect. 5, n. 1831). "Quamvis dimensiones per se non possent replere locum, tamen corpus naturale ex hoc quod eius materia intelligitur subiecta dimensionibus habeat quod repleat locum" (In Boeth. De Trinit. q. 4 a. 3 ad 7um). "Locata sunt in loco inquantum replent locum [...] Corpus enim dicitur replere locum, inquantum non compatitur secum aliud corpus [...]", but the located bodies "replent omnia loca" (Summ. theol. i q. 8 a. 2 resp.). "Plura enim corpora non possunt esse in eodem loco, quia replent locum [...] Solum corpus replet locum, ut non sit vacuum" (Ibid., q. 52 a. 3 obi.1a). "Nullus locus est qui non sit plenus sensibile corpore" (Ibid., q. 53 obi. 2a). "In omni loco est aliquod corpus, cum nihil sit vacuum in natura" (Ibid., iii q. 57 a, 5 obi. 3a). "Omne quod replet locum aliquem, est in eo localiter" (Ibid., q. 76 a. 5 obi. 2a).

12. "Apparet quod illud spatium in quo stellae moventur, non potest esse vacuum, eo quod impossibile est esse vacuum in natura [...] Relinquitur ergo quod totum illud spatium in quo stellae videntur moveri, est plenum caelesti corpore, quod pertinet ad ipsam substantiam sphaerarum" (In ii De caelo et mundo, lect. 13, n. 3).

13. Cf. In iv Phys., lect. 8, n. 7; In v Phys., lect. 5, n. 2; In ii De caelo et mundo, lect. 20, n. 7; In xii Metaphys., lect. 5, n. 2498; In ii Sent. dist. 8 q. 1 a. 4 qla. 4a resp.; Comp. theol. i 98; Quodlib. v q. 1 a. 1 resp.; Quodlib. vi q. 2 a. 2 obi. 2a; Summ. c. Gent. ii 35-36; Summ. theol. i q. 8 a. 4 ad 3um; q. 46 a. 1 ad 4um et 8um; q. 49 a. 3 resp.; q. 66 a. 4 ad 5um.

14. "Quia vacuum est locus privatus corpore, et determinatum est de loco quomodo sit et quomodo non sit (dictum est enim quod locus non est aliquod spatium, sed terminus continentis); manifestum est etiam quod neque vacuum est spatium separatum a corporibus, neque intrinsecum corporibus [...] Et hoc ideo, quia ponentes vacuum quocumque istorum modorum, volunt quod vacuum non sit corpus, sed spatium corporis. Ideo enim videbatur esse spatium, ita et vacuum, quia locus aliquid est: et si locus videbatur esse spatium, ita et vacuum. Si ergo locus non est aliquod spatium praeter corpora, neque vacuum potest esse spatium praeter corpora. Et cum de ratione vacui sit quod sit spatium praeter corpora [...], sequitur quod vacuum non sit" (In iv Phys., lect. 10, n. 11).

15. "Contingit quod corpora condensari, et partes corporis subintrare sibi invicem, non propter hoc quod pars subintrans vadat in locum vacuum; sed ideo quia erant aliqua foramina, plena aliquo corpore subtiliori, quod facta condensatione elabitur: sicut quando aqua colliditur et inspissatur, aer qui intus erat, excluditur. Et haec maxime apparent in spongia, et in huiusmodi corporibus porosis. Haec igitur solutio non ostendit causam condensationis [...], sed ostendit quod etiam per hunc modum manifeste excludi potest necessitas vacui" (In iv Phys., lect. 10, n. 12).

16. "Alimentum non sic transit in id quod augetur, quasi sit aliud corpus ab ipso; sed quia convertitur in substantiam eius, sicut ligna apposita igni, convertuntur in ignem" (In iv Phys., lect. 10, n. 13). See also n. 14. As we can see, this Thomistic thesis extends to the biological field the anti-mechanicist position of his conception of bodily things. In this sense, once more St. Thomas shows himself as a loyal follower of Aristotle's natural philosophy.

17. "Oportet iterum dicere quod non est vacuum separatum [...] quia hoc etiam aliqualiter ostensum est ex parte loci: si enim locus non sit spatium, sequitur quod vacuum nihil sit" (In iv Phys., lect. 11, n. 2).

18. "Si ponatur vacuum esse, non potest assignari causa motus naturalis et quietis naturalis" (In iv Phys., lect. 11, n. 3).

19. "Manifestum est enim quod corpus naturale movetur ad locum suum naturalem et quiescit in eo naturaliter, propter convenientiam quam habet cum ipso, et quia non convenit cum loco a quo recedit. Sed vacuum non habet aliquam naturam per quam possit convenire vel disconvenire a corpore naturali. Si ergo ponatur aliquod vacuum, quasi quidam locus privatus corpore, non poterit assignari ad quam partem illud corpus naturaliter moveatur [...] Illi qui ponunt vacuum, et ponentes locum esse spatium, non possunt assignare quomodo aliquid moveatur et quiescat secundum locum: sed etiam non possunt convenienter assignare quomodo aliquid sit in loco vel in vacuo. Si enim locus ponatur esse spatium, oportet quod totum corpus inferatur in illud spatium; et non sicut accidit apud ponentes locum esse terminum corporis continentis, quod locatum est in loco sicut in aliquo separato et seorsum existente: quia si pars alicuius corporis non ponatur seorsum ab ipso corpore, non erit in eo sicut in loco, sed sicut in toto. Est igitur de ratione loci et locati, quod locus seorsum sit a locato. Et hoc non accidit si spatium sit locus, in quod totum mergitur totum corpus. Non igitur spatium est locus. Et si spatium non est locus, manifestum est quod vacuum non est" (Ibid.).

20. Cf. In iv Phys., lect. 11, n. 4. For a comparison of Averroes' and St. Thomas' doctrines with regard this matter, see the article of J. A. Weisheipl O. P., «Motion in a Void: Aquinas and Averroes», in St. Thomas Aquinas 1274-1974. Commemorative Studies (Toronto: Pontifical Institute of Mediaeval Studies, 1974), vol. i, pp. 467-488.

21. "Oportet enim movens et motum simul esse [...]; et tamen illud quod proiicitur, invenitur moveri etiam postquam separatum est a proiiciente, sicut apparet in lapide proiecto, et sagitta emissa per arcum. Nunc igitur supposito quod vacuum non sit, solvitur ista dubitatio ex parte aeris, quo medium repletur. Et hoc dupliciter. Dicunt enim quidam quod ea quae proiiciuntur, movetur etiam postquam non tanguntur a proiiciente, propter antiperistasim, idest reprecussionem vel contra-resistentiam: aer enim motus repercutitur ad alium aerem, et ille ad alium, et suic deinceps; et per talem repercussionem aeris ad aerem movetur lapis. Alii vero dicunt quod ideo est, quia aer, qui continuus existens a proiiciente impellitur, velocius impellit corpus proiectum, ut puta lapis vel aliud huiusmodi, cadere deorsum; sed fertur secundum impulsionem aeris. Nulla autem istarum causarum posset poni, si esset vacuum; et ita corpus proiectum nullo modo ferretur nisi quandiu veheretur, puta a manu proiicientis, ed statim emissus a manu caderet; cuius contrarium videmus. Non ergo est vacuum" (In iv phys., lect. 11, n. 6).

22. "Cubus, qui transmutatur et ponitur in spatium vacuum, habet hoc quod habent omnia alia corpora, scilicet dimensiones. Si ergo dimensiones corporis cubici non differunt a dimensionibus loci secundum rationem, quare oportet facere aliquem locum corporibus extra proprium corpus uniuscuiusque, si locus nihil aliud est quam corpus impassibile, idest absque passionibus sensibilibus? Ex quo enim corpus habet proprias dimensiones, ad nihil videtur esse necessarium quod ponatur circa ipsum aliquae aliae dimensiones spatii aequalis suis dimensionibus. Accidit igitur, si ponatur vacuum vel locus esse quoddam spatium separatum, quod non est necessarium corpora esse in loco" (In iv Phys., lect. 13, n. 2).

23. "Si aliquid esse vacuum, oporteret quod manifestaretur in istis mobilibus. Sed nunquam apparet aliquid vacuum infra mundum: quia plenum aere, quod videtur vacuum, non est vacuum. Aer enim est aliquid, licet visu non percipiatur. Quia si etiam pisces essent ferrei, et haberent similem apparentiam cum aqua, non posset aqua discerni ab eis per visum; nec tamen sequeretur quod aqua non esset, vel etiam pisces: quia non solum visu, sed etiam tactu discernitur illud quod tangitur. Et sic patet aerem aliquid esse: quia tactu percipitur calidus vel frigidus. Ex his igitur apparet quod vacuum non sit aliquod spatium separatum, neque infra mundum neque extra mundum" (In iv Phys., lect. 13, n. 3).

24. See A. Einstein, The Meaning of Relativity, transl. By E. Plimpton Adams, E. G. Straus and S. Bargmann, 5th ed. (Princeton University Press: Princeton 1956), Appendix ii: "Relativistic Theory of the Non-Symetric Field", pp. 133-166.

25. "Qu'une force plus grande de si peu que l'on voudra, que celle avec laquelle l'eau de la hauteur de trente et un pieds tend à couler en bas, suffit pour faire admettre du vide, et même si grand que l'on voudra: c'est-à-dire, à faire désunir les corps d'un grand intervalle que l'on voudra: pourvu qu'il n'y a point d'autre obstacle à leur séparation, ni à leur éloignement, que l'horreur que la nature a pour le vide» (B. Pascal, Expériences nouvelles touchant le vide, in Oeuvres complètes, ed. by J. Chevalier [Paris: Librairie Gallimard, 1954], p. 370). Cf. M. E. Sacchi, El espacio enigmático, pp. 8-11.

26. See A. Einstein, Über die spezielle und die allgemeine Relativitätstheorie, 23th ed. (Friedrich Vieweg & Sohn: Braunschweig-Wiesbaden 1992), pp. 10-13.

27. Cf. M. E. Sacchi, El espacio enigmático, pp. 169-171.

28. Cf. I. Newton, Naturalis philosophiae principia mathematica, Book iii, schol. gener., p. 483.