Not only the existence of material nature is of course obvious but its main characteristic is even translated in a definition. We indeed say that a body is a substance with a triple extension or three-dimensional and we usually designate as full the space which is occupied by this body. This judgement results from the fact that inside any vessel one can set either earth or water or any other body either fluid or dense. We thus say that the capacity of the vessel is filled with one or the other of the said bodies. Consequently, we conceive the capacity of the vessel as distinct and different from the bodies which fill it.

From the preconceived nature and character of what is full we understand at once that the nature of the vacuum or of what is empty consists in that the capacity of a vessel is absolutely deprived of any body which could fill it. This vacuum actually can be conceived in two ways. It can indeed be supposed to be an immaterial entity, although not indivisible, but extended and occupying all the capacity of the vessel in its three dimensions. It can also be conceived as pure absence of bodies and as absolutely nothing. The explanation given by Pythagoras, Democritus, Epicure and others for the former concept and which seems to prove and confirm this opinion is that the capacity of the vessel taken in itself seems to retain the same dimensions or rather dimensions equal to those of the body filling it after that the body filling and occupying it has been removed either in fact or in imagination. This, they say, verifies that the material dimensions match exactly the dimensions of this space. They actually claim that they cannot conceive this capacity, or a space completely deprived of dimensions, since they concede that it has an entity, although immaterial. Consequently, they admit not only these small spaces delineated by the particles of bodies but also all the separate spaces outside this sensible world. But it is worth noting that this separate empty space must be admitted as being expanded and extended infinitely in every direction. There is indeed no reason to admit it close to the extreme material surface of the world and not beyond, in places more and more distinct and remote from this surface of the world. Moreover, this nature or immaterial spatial entity must be conceived not only as infinite but also as non-created and eternal since these spatial dimensions existed before the creation of the world, i.e. in times past there were already immaterial length, width and depth. The ancients admitted that very willingly without any reluctance together with the existence of the whole world since eternity. It is surprising how much this worries the true supporters of this opinion. They are forced to sustain an actual entity such as is this spatial entity, not only extended infinitely but even pre-existing from eternity and independent of God creator. Others, more cautious, do not fear to admit that this spatial entity is, not only finite, but also created by God from the beginning of the world. It is usually objected to these, that beyond the confines of the world and of this immaterial space, and before the creation of the world, the concept of an immaterial extension inside and outside the site in which the world and its space were created cannot be eliminated since they say that the said dimensions are not nothing. Consequently, this spatial entity must necessarily be admitted everywhere before the world created from eternity and outside the sensible world. From this it results that an empty space can in no way be admitted or, if it is, it has no immaterial entity. Hitherto thus, vacuum can be admitted in so far as it is conceded to be an absolute absence and nothing. In this sense, we shall see whether it can and must be admitted in nature.

Firstly, the arguments of Aristotle against the existence of vacuum and for the existence of fullness must be examined, as they are found in 4 Physic. Chapters 6, 7 and 8.

Against the ancients who supposed vacuum so that movements of bodies could occur in nature, Aristotle said: Even if there is no separable space besides the bodies which move, movement can occur. This appears in the whirling of continuous environments as well as of liquids.

This assertion, however, seems not only insufficient but even valueless. Although there is seemingly no need of vacuum in the circular movement of a solid wheel, the principal problem does not concern the circular movement but the straight movement or a movement along irregular curves in a fluid. In this movement it does not seem and it is not demonstrated that parts of the fluid can run between other parts unless they rub against each other, rotate and admit between them countless small empty spaces. In the last part of this chapter we will indeed show that vacuum must necessarily be admitted so that a fluid or a dense body can move through a fluid. But so far it is enough to have shown that it is not evident and that it was not demonstrated that vacuum is not necessarily required in a movement carried out in fluids. Secondly, it is not vacuum which is the cause of movement but Nature. Therefore there is no vacuum. It can be answered to this that nobody, unless mad and out of his senses, ever dreamed that vacuum, i.e. nothing, is the positive cause carrying out movement. The ancients certainly said that movement is caused by nature, or by an external impulsive cause, but vacuum is necessary as the place in which movement can occur. Consequently, the argument of Aristotle does not silence the supporters of vacuum.

Thirdly, he says: that, to those who say that vacuum is necessary it occurs that it is the contrary of movement. Indeed, if there was vacuum, nothing could move in it since it is not where it can be moved more or less, and indeed what is empty is deprived of any difference, i.e. there is there no upwards, nor downwards, nor in front, nor behind, etc. It can be answered to this that movement as such means only migration and displacement. This can occur in a fluid but also in an empty space, in any direction assigned by the impressed motive force. Thus, although in vacuum the infinite possible directions are not determined nor have their own names, they can be ascribed and thus movement be carried out in any direction.

Fourthly, he says: projectiles move because, when they are not touched, they continue their dash or, because they are pushed by air more quickly than by their throwing. In vacuum, none of this is possible and nothing can move except what is being carried. To show the shortcoming of the argument of Aristotle, let us suppose that no projection can occur in vacuum as a result of the absence of a fluid environment. This does not mean that vacuum cannot exist. Only natural movement would remain in vacuum whereas this could occur together with projection in a space full of fluid. Aristotle did not show this to be absurd. By the way, it is most untrue that projectiles are moved by the fluid environment after leaving the throwing subject. They are moved forwards by the motive force transmitted to them. Consequently, projection could occur in vacuum much better than in a space full of fluid since the motive force impressed in the projectile is in no way impeded by empty space whereas it is very much impeded and slowed down by a fluid environment.

Fifthly, nobody can say why what moves stops somewhere, why indeed here rather than there. Therefore, it must either be immobile or move ad infinitum if something does not impede it more powerfully. The best answer is that the argument proceeds from the fact that there is neither cause nor reason why an impetus, once impressed in a mobile, is slowed down or extinguished. Consequently, the mobile will stop nowhere nor remain immobile. It will move ad infinitum in vacuum unless another external body impedes its movement. I do not see what inconvenience results from this and why he must consequently deny the existence of an empty space. Sixthly, bodies are thought to move in vacuum because vacuum yields. But vacuum gives way everywhere.

If this argument was valid, unquestionably since sea water yields to the motive force of a fish with an equal facility everywhere, this would allow to infer that the fish moves at the same time in all directions, namely upwards, downwards, forwards, backwards, to the right, to the left, etc. Thus a legitimate inference is that, since the space gives way everywhere, the mobile is free to move in any direction, actually in that in which it is impelled by its motive force. Thus no inconvenience results. Therefore, vacuum is not eliminated. We met the other arguments of Aristotle partly in Chap. 10. We shall answer to the other ones below.

Meanwhile one can wonder how the disciples of Aristotle are so firmly convinced by arguments of this kind that none of them dares assert that God the best and the greatest in His infinite virtue could not heap up some small vacuum space in the nature of things.

But let us proceed to the argument which is found in the mouth of all the moderns. It is most obvious, they say, that there is no vacuum in the nature of things. They conclude that from countless experiments which show that many bodies move against their own and natural tendency, in order to prevent vacuum and, when there is no body available to fill a cleft or a space which should remain empty, then whatever external force is used, the separation and cleft cannot be created.

Firstly, if the sheets of a table are compressed or if the piston of a siphon or of a syringe is pushed to the bottom, they cannot be retrieved if the lower orifice is closed or the subjacent and adjacent water rises against nature so that no intercepted empty space remains.

The same happens with pumps and with the machines of Ctesibius which are commonly called water organs. In these also, when the piston is pulled, the subjacent water simultaneously rises.

Secondly, in a water-clock full of water, when the upper orifice is sealed, water does not flow out from the open lower small hole, by fear of the vacuum which would have to remain in the cavity of the vessel.

Thirdly, similarly, if air is excluded from a cupping-glass by a flame or otherwise and the cupping-glass is applied on the flesh, flesh itself and blood surge to refill this space.

Based on these and other experiments of the same kind, they think to have proved most evidently that nature abhors vacuum. They care only about the cause of such movement by which the parts of the universe arrive to avoid vacuum. It is amazing how much they worry about that. Some indeed say that God directly, others that Nature, impels heavy bodies against their innate virtue in order to prevent vacuum. Others say that the parts of the universe, besides their own innate force, have a new faculty to move whenever the opportunity requires it for the good of the universe. In other words, water has an innate principle of gravity which always acts by compressing and moving downwards. But whenever there is an urgent need, when a risk of a cleft and of a vacuum space occurs in the universe, then another new virtue also innate in water impels this upwards in order to cure a universal evil.

If a direct action of God is admitted in this instance, it will unquestionably be a miraculous, unnatural operation. Indeed all natural actions, although requiring an universal divine concurrence, are nevertheless exerted by physical and natural organs and instruments. If actually this new virtue is considered as being innate for all natural bodies, such faculty is of course not different from that which is found in animals since so much prudence cannot be conceived as providing a medicine against a universal evil without that water for instance perceives and feels this evil and thus moves and attempts at preventing it. In that indeed natural operations are different from animal ones: they occur continuously and uninterruptedly as a result of a blind necessity and not actually when needed. Thus compression and fall of heavy bodies always occur. When fire for example attempts at destroying water, water pushed by necessity never escapes nor tries to avoid the danger. In summary, one cannot imagine how water forgets its own nature and rises when there is an imminent risk of vacuum. Nature does not perceive such risk and has no organs or instruments apt at carrying out this new operation in this instance of need only while not caring for it all the rest of the time and exerting then its own gravity.

It must be seen in what consists the shortcoming of the reasoning of the peripatetics when they say that one always sees that natural bodies arrive to prevent vacuum even if they have to move against their nature, and thus that nature itself abhors vacuum. It is not denied that obviously water rises whenever a space is emptied above. But it is denied that water ascends spontaneously in order to prevent vacuum. Of course we can never be sure whether water moves upwards spontaneously in this case of need unless it appears that water is not impelled upwards by another cause. But the peripatetics have never proved this. In this instance, water, if it were impelled upwards by another physical cause, would not arrive by itself but only by accident to refill the emptiness. It would actually move by itself forced as a result of the violence and impulse with which it is provided by the impelling cause.

For clearer understanding, two unequal weights are set in a balance and the palm of a hand is superimposed on the lighter one so as to prevent tipping of the balance. No doubt, if the hand is raised little by little, the smaller weight will rise also, adhering to the hand. If, from the fact that the lighter weight appears to rise, somebody inferred that this weight forgets its own nature for the good of the universe and moves upwards to refill the space, he would of course be wrong and misled in his reasoning, since the rising is produced by a physical and necessary cause, namely by the heavier weight at the opposite side. Imagine now that the heavier weight on the balance is hidden. If, on the other hand, it is obvious that a heavier weight is acting there, even if it is inconspicuous, it would be ridiculous to resort to miracles and to machines by assigning to the raised lighter weight feeling and perception in order to provide a medicine against an imminent universal evil. Consequently, all this huge mass of arguments comes to nothing if we show that water and other heavy bodies, when rising to refill an empty space, are actually impelled in a balance or a siphon by an opposite heavier weight which is always present and acts in such instance. Then the rising having a necessary cause cannot be attributed to this prudent knowledge, or rather to a fanciful one.

To show this as clearly as possible, a siphon ABCD is supposed to be filled with water (Table 11.​3, Fig. 5). Its arms AB and DC are vertical. Then the piston EFG and the pipe DC form a syringe. The piston is pushed down in the pipe until its base FG reaches the bottom C of the pipe. Then the water BC appears to play the role of a balance. At one extremity B a heavy mass of water AB is superimposed. At the other extremity C a thin layer of water FC remains. Therefore, if its other portion FD up to the horizontal AD were full of air or absolutely empty, no doubt the water FC would rise towards D, not spontaneously, but pushed by the opposite heavier weight of water AB. In the imaginary fluid balance BC, the part B more compressed by the heavier weight of the water above AB must expel upwards the lighter mass of water FC until this is balanced on the horizontal plane AD. After these premises, the piston EFG is pulled upwards so that its base FG is brought up to the top D of the pipe in such a way, however, that the piston FG touches perfectly the inner surface of the pipe and no cleft remains through which the air above could enter. Then in the space FD neither air nor any other body would remain whereas the opposite pipe AB is full of water. This unquestionably, by its natural gravity, will impel the water upwards from F up to D. The only cause is that in the balance BC the heavier weight of the water AB must impel the opposite lighter weight upwards. In this operation would it not be stupid to claim that the water FC rises to occupy the space FD against the natural tendency of its gravity, in order to refill this space so that no empty space be admitted in nature? The physical and actual cause of this operation cannot be questioned. It is the heavier weight of the water AB on the opposite side which in a siphon or in a balance is able by a mechanical necessity to impel the water FC upwards up to D.

It is no longer a solid siphon ABCD which is used but only a copper syringe EDC (Table 11.​3, Fig. 6). This syringe is lowered vertically in a vessel RSTV with its orifice downwards until this lower orifice C is close to the bottom of the vessel. The water in the cavity of the syringe CF cannot rise unless the adjacent water IB descends to fill the subjacent space left by the water FC. The portion of adjacent water closest to the bottom of the syringe IB can be lowered only if the next parts vertically above it AI are all lowered successively one after the other until the former portion arrives at the surface RV of the water. Thus in this instance it is as if there were two columns of water, one AIB which compresses and moves downwards and the other which is the portion of water CF together with the piston FE and the water above EH, which is supposed to move upwards in the opposite direction. Both are supported and sustained by the lower layer of water BC which plays the role of a balance. If the moments with which the extremities of the fluid balance BC are compressed by the columns AB and HC are equal, then unquestionably there is equilibrium and immobility: none of the columns is pushed upwards by the other. But, if the piston EFG is pulled upwards from the bottom of the syringe up to D, unquestionably the subjacent water CF will rise through the cavity of the syringe always adhering to the piston, not as a result of fear of vacuum but because of being pushed by the heavier weight of the opposite column of water AB. This is a mechanical necessity.

A bowl MNO full of mercury is set at the bottom of the vessel RSTV (Table 11.​3, Fig. 7). The lower orifice C of a syringe is pushed below its surface MO. When the piston EFG is pulled the mercury also will rise in the syringe CD, not spontaneously to refill the vacuum, but pushed by the heavier weight of the column of water AB. The rising of the mercury will continue until equilibrium is achieved between the moment of the water and the mercury. If the height of the column of water AB is 18 cubits, the height of a column of mercury of the same diameter must be about two cubits and a half. This is the highest level at which the mercury can rise in the syringe. If the piston is raised further by the force of the hand, the mercury remains and will remain at this height. An empty space without mercury, water or air will remain rather than the mercury being raised one hair higher. From this it is deduced, not only that mercury rises inasmuch and as long as it is impelled by the opposite weight of the fluid AB. Moreover it is clear that it does not rise spontaneously to refill a space deprived of mercury or empty since it does not pass over the limit of two and a half cubits and is not disturbed by the fact that the upper space remains empty of mercury.