Koyre, Alexandre. From the Closed World to the Infinite Universe.  Baltimore: Johns Hopkins UP, 1957.

(excerpted by Clifford Stetner) 





…seventeenth century…replacement of the concern for the other world and the other life by preoccupation with this life and this world.


…discovery, by man’s consciousness, of its essential subjectivity and, therefore, in the substitution of the subjectivism of the moderns for the objectivism of the mediaevals and ancients…


…mediaeval and ancient man aimed at the pure contemplation of nature and of being, the modern one wants domination and mastery.


…exemplified by Montaigne, by Bacon, by Descartes, or by the general spread of skepticism and free thinking.



This scientific and philosophical revolution—it is indeed impossible to separate the philosophical from the purely scientific aspects of this process: they are interdependent and closely linked together—can be described roughly as bringing forth the destruction of the cosmos, that is, the disappearance, from philosophically and scientifically valid concepts, of the conception to the world as a finite, closed, and hierarchically ordered whole (a whole in which the hierarchy of value determined the hierarchy and structure of being, rising from the dark, heavy and imperfect earth to the higher and higher perfection of the stars and heavenly spheres), and its replacement by an indefinite and even infinite universe which is bound together by the identity of its fundamental components and laws, and in which all these components are placed on the same level of being.  This in turn, implies the discarding by scientific thought of all considerations based upon value-concepts, such as perfection, harmony, meaning and aim, and finally the utter devalorization of being,



…shift from geocentrical to heliocentrical conceptions…


…mathematization of nature and its concomitant and convergent emphasis upon experiment and theory.


Bacon and Hobbes, Pascal and Gassendi, Tycho Brahe and Huygens, Boyle and Guericke…





the conception of the infinity of the universe, like everything else or nearly everything else, originates, of course, with the Greeks…


…Greek atomists which became better known through the newly discovered Lucretius…


…rejected by the main trend, or trends, of Greek philosophical and scientific thought—the Epicurean tradition was not a scientific one—and that for this very reason, though never forgotten, they could not be accepted by the mediaevals.



…the influences we are submitting to; our intellectual ancestors are by no means given to, but are freely chosen by, us.


…it was Nicholas of Cusa, the last great philosopher of the dying Middle Ages, who first rejected the mediaeval cosmos-conception and to whom, as often as not, is ascribed the merit, or the crime, of having asserted the infinity of the universe.


Christina of Sweden, who doubted whether, in the indefinitely extended universe of Descartes, man could still occupy the central position..


Chanut…”the Cardinal of Cusa and several other divines have supposed the world to be infinite, without ever being reproached by the Church; on the contrary, it is believed that to make His works appear very great is to honor God.”


…Nicholas of Cusa denies the finitude of the world and its enclosure by the walls of the heavenly spheres.  But he does not assert its positive infinity…



…as carefully and as consistently as Descartes…


… “infinite,”…he reserves for God…


His universe is not infinite (infinitum) but “interminate” (interminatum)…


It cannot therefore, be the object of total and precise knowledge, but only that of a partial and conjectural one.


…partial—and relative—character of our knowledge…


…the docta ignorantia…(1440)


The universe of Nicholas of Cusa is an expression or a development (explicatio)…of God—imperfect and inadequate because it displays in the realm of multiplicity and separation what in God is present in indissoluble and intimate unity (complicatio)…



…every singular thing in the universe represents it—the universe—and thus also God, in its own particular manner…


The metaphysical and epistemological conceptions of Nicholas of Cusa, his idea of the coincidence of the opposites in the absolute which transcends them, as well as the correlative concept of learned ignorance as the intellectual act that grasps this relationship which transcends discursive, rational thought…



NC… “The world has no circumference, because if it had a center and a circumference, and thus had a beginning and end in itself, the world would be limited in respect to something else, and outside the world there would be something other, and space, things that are wholly lacking in truth.  Since, therefore, it is impossible to enclose the world between a corporeal centrum and a circumference, it is [impossible for] our reason to have a full understanding of the world, as it implies the comprehension of God who is the center and the circumference of it.”



…I believe that we can understand it as expressing, and as stressing, the lack of precision and stability in the created world.  Thus, there are no stars exactly on the poles, or on the equator of the celestial sphere.  There is no fixed constant axis; the eighth, as well as all the other spheres, perform their revolutions around axes that continuously shift their positions.  Moreover, these spheres are by no means exact, mathematical (“true”) spheres, but only something which we should today call “spheroids”; accordingly, they have no center, in the precise meaning of this term.  It follows therefore that neither the earth, nor anything else, can be placed in this center, which does not exist, and that thus nothing in this world can be completely and absolutely at rest.



…neither the daily rotation around its axis, nor the annual revolution around the sun, but a kind of loose orbital gyration around a vaguely determined and constantly shifting center.



…world-image of a given observer is determined by the place he occupies in the universe; and as none of these places can claim an absolutely privileged value (for instance, that of being the center of the universe), we have to admit the possible existence of different, equivalent world-images, the relative—in the full sense of the word—character of each of them, and the utter impossibility of forming an objectively valid representation of the universe.



… “wherever the observer be he will believe himself to be in the center.”


… “this earth really moves, though it does not appear to us to do so, because we do not apprehend motion except by a certain comparison with something fixed.”


… “seem to the observer, whether he be on the earth, or on the sun or on another star, that he is in the quasi-motionless center and that all the other [things] are in motion, he will certainly determine the poles [of this motion] in relation to himself; and these poles will be different for the observer on the sun and for the one on the earth, and still different for those on the moon and Mars.


… “Thus, the fabric of the world (machina mundi) [world-machine] will quasi hav its center everywhere and its circumference nowhere, because the circumference and the center are God, who is everywhere and nowhere.”



… “For all motion of the parts is towards the perfection of the whole…”


… “all shapes towards the spherical one, as we see in the parts of animals, in trees, and in the sky. But one motion is more circular and more perfect than another, and it is the same with shapes.


… “a sphere of which the center is everywhere, and the circumference nowhere.”


after Giordano Bruno, who drew his chief inspiration from him, that Nicholas of Cusa achieved fame as a forerunner of Copernicus, and even of Kepler, and could be quoted by Descartes as an advocate of the infinity of the world.



…anticipations of later discoveries, such, for instance, as the flattened form of the earth, the elliptic trajectories of the planets, the absolute relativity of space, the rotation of the heavenly bodies upon their axes.



Cusa … “Neither is this earth a proportional, or aliquot part of the world, for as the world has neither maximum, nor minimum, neither has it a moiety, nor aliquot parts, any more than a man or an animal [has them]; for the hand is not an aliquot part of the man, though its weight seems to have a proportion to the body.”



…no center of perfection in respect to which the rest of the universe would play a subservient part…


…earth in its way is just as perfect as the sun, or the fixed stars.



… “God is the center and the circumference of all the stellar regions…in every region inhabitants of diverse nobility of nature proceed from Him…”



…dissolution, or resolution, of a being into its constitutive elements and their reunification into something else, a process that may take place-and probably does take place—in the whole universe just because the ontological structure of the world is, fundamentally, everywhere the same.



…no longer the medieval cosmos.  But it is not yet by any means, the infinite universe of the moderns.


Palingenius, [Zodiacus (1534)] who is deeply influenced by the Neoplatonic revival of the fifteenth century and who therefore rejects the absolute authority of Aristotle…



…creatures doth the skies containe, and every starre beside

Be heavenly townes and seates of Saints, where Kings and Commons bide.

Not shapes and shadows vain of things (as we have present here)

But perfect Kings and people eke, all things are perfect there.



…Therefore the reigne and position of the world consists in three,

Celestiall, Subseclestiall which with limits compast bee:

The Rest no boundes may comprehend which bright aboue the Skye.

Doth shine with light most wonderfull…



Palingenius does not accept this theory which makes light dependent on matter and thus material itself.


…it is God’s heaven, not God’s world, that Palingenius asserts to be infinite.






Palingenius and Copernicus are practically contemporaries.


De revolutionibus orbium coelestium [ca. 1534]

…all those centuries during which Aristotelian cosmology and Ptolemaic astronomy dominated Western thought.  Copernicus, of course, makes full use of the mathematical techniques elaborated by Ptolemy…


…goes back beyond him, and beyond Aristotle, to the golden age of Pythagoras and Plato.


…according to Rheticus, his pupil and mouthpiece, it is


…following Plato and the Pythagoreans, the greatest mathematicians of that divine age, that [he] thought that in order to determine the cause of the phenomena, circular motions have to be ascribed to the spherical earth.


…removing the earth from the center of the world and placing it among the planets, undermined the very foundations of the traditional cosmic world-order with its hierarchical structure and qualitative opposition of the celestial realm of immutable being to the terrestrial or sublunar region of change and decay.



…it is on account of its supreme perfection and value—source of light and of life—that the place it occupies in the world is assigned to the sun: the central place which, following the Pythagorean tradition and thus reversing completely the Aristotelian and mediaeval scale, Copernicus believes to be the best and most important one.  Thus, though the Copernican world is no more hierarchically structured (at least not fully: it has, so to say, two poles of perfection, the sun and the sphere of the fixed stars, with the planets in between), it is still a well-ordered world.  Moreover, it is still a finite one.


…natural to interpret Copernicus this way, that is, as an advocate of the infinity of the world, all the more so as he actually raises the question of the possibility of an indefinite spatial extension beyond the stellar sphere, though refusing to treat that problem as not scientific and turning it over to the philosophers.



…Copernicus, who believed in the existence of material planetary spheres because he needed them in order to explain the motion of the planets, believed also in that of a sphere of the fixed stars which he no longer needed.


…Copernicus tell us quite clearly that


…the universe is spherical; partly because this form, being a complete whole, needing no joints, is the most perfect of all; partly because it constitutes the most spacious form which is thus best suited to contain and retain all things; or also because all discrete parts of the world, I mean the sun, the  moon and the planets, appear as spheres.


****a four dimensional hyper-torus reflects the perfect symmetry that mediaeval thinkers had only vocabulary to conceive as sphere



…he never tells us that the visible world, the world of the fixed stars, is infinite, but only that it is immeasurable (immensum)…


world of Copernicus would remain a finite one, encompassed by a material sphere or orb, the sphere of the fixed stars—a sphere that has a centrum, a centrum occupied by the sun.



“… the first and the supreme of all [spheres] is the sphere of the fixed stars which contains everything and itself and which, therefore, is at rest.  Indeed, it is the place of the world to which are referred the motion and the position of all other stars.  Some [astronomers] indeed, have thought that, in a certain manner, this sphere is also subjected to change: but in our deduction of the terrestrial motion we have determined another cause why it appears so.  [After the sphere of the fixed stars] comes Saturn, which performs its circuit in thirty years.  After him, Jupiter, which moves in a duodecennial revolution.  Then Mars which circumgirates in two years.  The fourth place in this order is occupied by the annual revolution, which, as we have said, contains the earth with the orb of the Moon as an epicycle.  In the fifth place Venus revolves in nine months.  Finally, the sixth place is held by Mercury, which goes around in the space of eighty days.  but in the center of all resides the Sun.  who, indeed, in this most magnificent temple would put the light in another, or in a better place than that one wherefrom it could at the same time illuminate the whole of it?  therefore it is not improperly that some people call it the lamp of the world, others its mind, others its ruler.  Trismegistus [calls it] the visible God, Sophocles’ Electra, the All-Seeing.  Thus, assuredly, as residing in the royal see the Sun governs the surrounding family of the stars.”



…Copernican world as compared to the mediaeval one—its diameter is at least 2000 greater.


…even the Aristotelian or Ptolemaic world was by no means that snug little thing that we see represented on the miniatures…


…20,000 terrestrial radii, such was the accepted figure…about 125,000,000 miles.


…it is somewhat easier, psychologically if not logically, to pass from a very large, immeasurable and ever-growing world to an infinite one than to make this jump starting with a rather big, but still determinably limited sphere: the world-bubble has to swell before bursting.



…rather short time after Copernicus some bold minds made the step that Copernicus refused to make, and assert that the celestial sphere, that is the sphere of the fixed stars of Copernican astronomy, does not exist, and that the starry heavens, in which the stars are placed at different distances from the earth, “extendeth itself infinitely up.:


…Giordano Bruno who, drawing on Lucretius and creatively misunderstanding both him and Nicholas of Cusa, first made this decisive step.


Perfit Description of the Caelestiall Orbes according to the most aunciene doctrine of the Pythagoreans lately revived by Copernicus and by Geometricall Demonstrartions approued, which Thomas Digges, in 1576, added to the Prognostication euerlasting of his father Leonard Digges, this honor, at least partially, must be ascribed to him.


… “Of which lightes Celestiall it is to bee thoughte that we only behoulde sutch as are in the inferioure partes of the same Orbe, and as they are hygher, so seeme they of lesse and lesser quantity, even tyll our syghte beinge not able farder to reache or conceyve, the greatest part rest by reason of their wonderfull distance inuisible vnto vs.  And this may well be thought of vs to be the gloriouse court of ye great god, whose vnsercheable works inuisible we may partly by these his visible coniecture…”


…Thomas Digges puts his stars into a theological heaven; not into an astronomical sky.



Palingenius, it is true, places his heaven above the stars, whereas Thomas Digges puts them into it.


needless to say, there is no place for Paradise in the astronomical world of Copernicus.


…it was Bruno who, for the first time, presented to us the sketch, or the outline, of the cosmology that became dominant in the last two centuries…


…Lovejoy…it is Giordano Bruno who must be regarded as the principal representative of the doctrine of the decentralised, infinite and infinitely populous universe…preached it throughout western Europe with  the fervour of an evangelist…



…De immenso et innumerabilibus…“There is a single general space, a single vast immensity which we may freely call Void: in it are innumerable globes like this on which we live and grow; this space we declare to be infinite, since neither reason convenience, sense-perception nor nature assign to it a limit.  For there is no reason, nor defect of nature’s gifts, either of active or passive power to hinder the existence of other worlds throughout space, which is identical in natural character with our own space, that is everywhere filled with matter or at least ether.”


We have, of course, heard nearly similar things from Nicholas of Cusa.



Nicholas of Cusa simply states the impossibility of assigning limits to the world, Giordano Bruno asserts, and rejoices in, its infinity…


… “For he who speaketh of emptiness, the void or the infinite ether, ascribeth to it neither weight nor lightness, nor motion, nor upper, nor lower, nor intermediate regions; assuming moreover that there are in this space those countless bodies such as our earth and other earths, our sun and other suns, which all revolve within this infinite space, through finite and determined spaces or around their own centres.  Thus we on the earth say that the earth is in the centre…just as we say that we are at the centre of that [universally] equidistant circle, which is the great horizon at the limit of our own encircling ethereal region, so doubtlessly the inhabitants of the moon believe themselves at the centre [of a great horizon]”


… “From various points of view these may all be regarded either as centres, or as points on the circumference, as poles, or zeniths…”


… “the earth is not in the centre of the Universe; it is central only to our surrounding space.”



…Bruno uses the principle of plenitude in an utterly ruthless manner, rejecting all the restrictions by which mediaeval thinkers tried to limit its applicability…


…Bruno’s God, the somewhat misunderstood infinitas complicata of Nicholas of Cusa, could not but explicate and express himself I an infinite, infinitely rich, and infinitely extended world.



… “This science does not permit that the arch of the horizon that our deluded vision imagineth over the Earth and that by our phantasy is feigned in the spacious ether, shall imprison our spirit under the custody of a Pluto or at the mercy of a Jove.  We are spared the thought of so  wealthy an owner and subsequently of so miserly, sordid and avaricious a donor.”


The displacement of t the earth from the centrum of the world was not felt to be a demotion.  Quite the contrary: it is with satisfaction that Nicholas of Cusa asserts its promotion to the rank of the noble stars; and, as for Giordano Bruno, it is with a  burning enthusiasm—that of a prisoner who sees the walls of his jail crumble—that he announces the bursting of the spheres that separated us from the wide open spaces and inexhaustible treasures of the ever-changing, eternal and infinite universe.


Nicholas of Cusa states that immutability can nowhere be found in the whole universe; Giordano Bruno goes far beyond this mere statement; for him motion and change are signs of perfection and not a lack of it.  an immutable universe would be a dead universe; a living one must be able to move and to change.


“There are no ends, boundaries, limits of walls which can defraud or deprive us of the infinite multitude of things.  Therefore the earth and the ocean thereof are fecund; therefore the sun’s blaze is everlasting, so that eternally fuel is provided for the voracious fires, and moisture replenishes the attenuated seas.  For from infinity is born an ever fresh abundance of matter.  Thus Democritus and Epicurus, who maintained that everything throughout infinity suffereth renewal and restoration, understood these matters more truly that those who at all costs maintain a belief in the immutability of the Universe, alleging a constant and unchanging number of particles of identical material that perpetually undergo transformation, one into another.”



…a century later Leibniz—who certainly knew Bruno and was influenced by him—was to call the principle of sufficient reason, which supplements the principle of plenitude and, in due time, superseded it; and the decisive shift (adumbrated indeed by Nicholas of Cusa) from sensual to intellectual cognition in its relation to thought (intellect)


on The Infinite Universe and the Worlds…Bruno (Philotheo) asserts that sense-perception, as such, is confused and erroneous and cannot be made the basis of scientific and philosophical knowledge.


***brings back Platonism



… “It is the part of the intellect to judge yielding due weight to factors absent and separated by distance of time and by space intervals.  And in this matter our sense-perception doth suffice us and doth yield us adequate testimony, since it is unable to gainsay us…”



“… truth is in but a very small degree derived from the senses as from a frail origin, and doth by no means reside in the senses.

Elp.—Where then?

Phil.—In the sensible object as in a mirror; in reason by process of argument and discussion.  In the intellect either through origin or by conclusion.  In the mind, in its proper and vital form.”


…principle of sufficient reason…Bruno’s space, the space of an infinite universe and at the same time the (somewhat misunderstood) infinite “void” of Lucretius, is perfectly homogeneous and similar to itself everywhere: indeed, how could the “void” space be anything but uniform—or vice versa , how could the uniform “void” be anything but unlimited and infinite?



“Philotheo—Thus, let the surface be what it will, I must always put the question: what is beyond?  If the reply is nothing, then I call that the void, or emptiness.  And such a Void or Emptiness hath no measure nor outer limit, though it hath an inner; and this is harder to imagine than is an infinite or immense universe.  Fir if we insist on a finite universe, we cannot escape the void.”


“Fracastoro—It certainly appeareth to me not so.  For where there is nothing there can be no differentiation; where there is no differentiation there is no distruction of quality and perhaps there is even less of quality where there is nought whatsoever.”


Thus the space occupied by our world, and the space outside it, will be the same.


…not only space, but also being in space is everywhere constituted in the same way, and that if in our part of the infinite space there is a world, a sun-star surrounded by planets, it is the same everywhere in the universe.  Our world is not the universe, but only this machina, surrounded by an infinite number of other similar of analogous “worlds” –the worlds of star-suns scattered in the etheric ocean of the sky.



…the limitation of God’s creative action is unthinkable.  In this case, the possibility implies actuality.  The infinite world can be; therefore it must be; therefore it is.


…the Aristotelian adversary of Bruno, Elpino, now  converted to his views, formulates it:


… “universe may have extended its capacity in order to contain may bodies such as those we name stars…”



Bruno…Philo… “we discern only their largest suns, immense bodies.  But we do not discern the earths because, being much smaller they are invisible to us.  Similarly, it is not impossible that other earths revolve around our sun and are invisible to us either on account of greater distance or smaller size…”



…God needs an infinite space in order to place in it this infinite world.



Giordano Bruno, I regret to say, is not a very good philosopher.  The blending together of Lucretius and Nicholas of Cusa does not produce a very consistent mixture…he is a very poor scientist, he does not understand mathematics, and his conception of the celestial motions is rather strange.  My sketch of his cosmology is, indeed somewhat unilateral and not quite complete.  As a matter of fact, Bruno’s world-view is vitatlistic, magical; his planets are animated beings that move freely through space of their own accord like those of Plato or of Pattrizzi.”



… “that there are any real, and, as it were, adamantine spheres?  No one has ever proved this as a fact; nor is there a doubt but that just as the planets are at unequal distances from the earth, so are those vast and multitudinous lights separated from the earth by varying and very remote altitudes…”





…the infinity of the universe…can never be based on empiricism.  This was very well understood by Kepler who rejects it therefore…


Indeed, Kepler, a devout though somewhat heretical Christian, sees in the world an expression of God, symbolizing the Trinity and embodying in its structure a mathematical order and harmony.


Kepler is writing in 1606…



…Kepler…”Finally, even if you extend the place without stars to infinity, it is certain that wherever you put a star into it, you will have a finite interval and a finite circumference determined by the star; thus, those who say that the sphere of the fixed stars is infinite commit a contradiction…



…the telescope—used by Galileo…seemed to him to confirm his own finitistic world-view and to bring new data in favor of the unicity of the solar system and of the essential distinction of our moving world and the motionless congeries of the fixed stars.



Epitome astronomiae Copernicanae, the last, and the most mature, great work of Kepler.


What is to be held concerning the shape of the sky?


The reply is given:


“though we cannot perceive with our eyes the matter of the etheric aura, there is nothing, however, to prevent us from believing that it is spread through the whole amplitude of the world on all sides surrounding the elementary sphere.  That the army of the stars completely encircles the earth and thus forms a certain quasi-circular vault is clear for the fact that, while the earth is round, men, wherever they go, see the stars above their heads, as we do.”



If there is no more certain knowledge concerning the fixed stars, it would seem that their region is infinite; nor will this our sun be anything other than one of the fixed stars, larger and better seen by us, because [it is] nearer to us than the fixed stars; and in this case around any one of the fixed stars there may be such a world as there is around us; or, which is exactly the same, among the innumerable places in that infinite assembly of the fixed stars.



“This [the infinity of the world] indeed [was asserted] by Bruno and some others.  But [even] if the centers of the fixed stars are not on the same spherical surface, it does not follow that the region in which they are dispersed is everywhere similar to itself.  As a matter of fact, in the midst of it [the region of the fixed stars] there is assuredly a certain immense void, a hollow cavity, surrounded in close order by the fixed stars, enclose and circumscribed as by a wall or vault; it is in the bosom if this immense cavity that our earth with the sun and the moving stars [planets] is situated.”





We have already seen that the invisibility for the human eye of the fixed stars discovered by Galileo, and, accordingly, the role of his perspicillum in revealing them could be interpreted in two different ways:  it could be explained by their being (a) too small to be see, (b) too far away.  The perspicillum would act in the first case as a kind of celestial microscope, in enlarging, so to say the stars to perceivable dimensions; in the second it would be a “telescope” and , so to say, bring the stars nearer to us, to a distance at which they become visible.  The second interpretation, that which makes visibility a function of the distance, appears to us now to be the only one possible.  Yet this was not the case in the seventeenth century.  As a matter of fact both interpretations fit the optical data equally well and a man of that period had no scientific, but only philosophical, reasons for choosing between them.


…seventeenth century thinking rejected the first interpretation and adopted the second.



Finiteness or the infinity of the universe, the great Florentine, to whom modern science owes perhaps more than to any other man, takes no part.


…in contradistinction to Ptolemy, Copernicus and Kepler, he does not admit the limitation of the world or its enclosure by a real sphere of fixed stars.



 …in opposition to Ptolemy, Copernicus and Kepler, and in accordance with Nicholas of Cusa and Giordano Burn, Galileo rejects the conception of a center of he universe where the earth, or the sun, should be placed, “the center of he universe which we do not know where to find or whether it exists at all.”  He even tells us that “ the fixed stars are so many suns.” Dialogue on the Two Greatest World-Systems



…the fate of Bruno, the condemnation of Copernicus in 1616, his own condemnation in 1633 incited him to practice the virtue of prudence…



…never could completely free himself from the obsession of circularity – his planets move circularly around the sun without developing any centrifugal force…


…not Galileo, in any case, nor Bruno, but Descartes who clearly and distinctly formulated principles of the new science, its dream de reductione scientiae ad mathematicam, and of the new, mathematical, cosmology.



…Descartes’ God, in contradistinction to most previous Gods, is not symbolized by the things He created; He does not express Himself in them.  There is no analogy between God and the world; no imagines and vistigia Dei in mundo; the only exception is our soul…


…this world, He created it by pure will, and even if He had some reasons for doing it, these reasons are only known to Himself; we have not, and cannot have, the slightest idea of them…


…world of Descartes, is by no means the colorful, multiform and qualitatively determined world of the Aristotelian, the world of our daily life and experience – that world is only a subjective world of unstable and inconsistent opinion based upon the untruthful testimony of confused and erroneous sense-perception – but a strictly uniform mathematical world, a world of geometry made real about which our clear and distinct ideas give us a certain and evident knowledge.  There is nothing else in this world but matter and motion; or, matter being identical with space or extension, there is nothing else but extension and motion.



…”nature of body, taken generally, does not consist in the fact that it is a hard, or a heavy, or a colored thing, or a thing that touches our senses in any other manner, but only in that it is a substance extended I length, breadth and depth…


…the void, according to Descartes, is not only Physically impossible, it is essentially impossible.


Contradictio in adjecto, an existing nothing.  Those who assert its existence, Democritus, Lucretius and their followers, are victims of false imagination…


…distance is not a length breadth or depth of nothing but of something, that is of substance or matter, a “subtle” matter, a matter that we do not sense…



Bodies are not in Space, but only among other bodies; the space that they “occupy” is not anything different from themselves:



“…we must conclude the same about the space supposed to be void:  namely that , as there is in it some extension, there is necessarily also some substance.”



To assign boundaries to it becomes not only false, or even absurd, but contradictory.  We cannot posit a limit without transcending it in this very act..  We have to acknowledge therefore that the real world is infinite, or rather…indefinite.


“…wherever we imagine such limits, we always not only imagine beyond them some indefinitely extended spaces, but we even perceive them to be truly imaginable…”



The old opposition of the earthly world of change and decay to the changeless world of the skies which, as we have seen, was not abolished by the Copernican revolution, but persisted as the opposition of he moving world of the sun and planets to the motionless, fixed stars, disappears with trace.


…as in the universe of Giordano Bruno (it is a pity that Descartes does not use Bruno’s terminology) – there are an infinite number of subordinate and interconnected systems, such as our system with its sun and planets…


“…even if the worlds were infinite, it is impossible that they should not be constituted from one and the same matter; and therefore, they cannot be many, but only one…”



Like Nicholas of Cusa two centuries before him, he applies the term “infinite” to God alone.  God is infinite.  The world is only indefinite.


The idea of the infinite plays an important part in the philosophy of Descartes, so important that Cartesianism may be considered as being wholly based upon that idea.



…we shall never burden ourselves with disputes about the infinite.  Indeed, as we are finite, it would be absurd for us to want to determine anything about it, to comprehend I, and thus to attempt to make it quasi-finite.


…because it is impossible to imagine such a number of stars that we should believe God could not create still more, we shall assume that their number is indefinite.



…the limitations of our reason manifest themselves in assigning limits to the world…


…Descartes, as we shall see in  a moment, had really very good reasons for opposing the “infinity” of God to the “indefiniteness” of the world, the common opinion of his time held that it was a Pseudo-distinction, made for the purpose of placating the theologians.





Henry More was a one of the first partisans of Descartes in England even though ,as  a matter of fact, he never was a Cartesian and later in life turned against Descartes and even accused the Cartesians of being promoters of atheism.


…series of extremely interesting letters…


…difficult to understand or to admit the radical opposition established by Descartes between body and soul.  How indeed can a purely spiritual soul, that is, something which, according to Descartes, has no extension whatever, be joined to purely material body, that is, to something which is only and solely extension?  Is it not better to assume that the soul, though immaterial, is also extended; and that everything,  even God, is extended?  How could He otherwise be present in the world?



…More… “…he is omnipresent and occupies intimately the whole machine of the world as well as its singular particles.  How indeed could He communicate motion to matter, which He did once, and which according to you, He does even now, if He did not touch the matter of the universe in practically the closest manner, or at least had not touched it at a certain time?  Which certainly He would never be able to do if He were not present everywhere and did not occupy all spaces.  God, therefore, extends and expands in this manner; and is, therefor, and extended thing (res).


…More suggests secondly that matter, being necessarily sensible, should be defined only by its relation to sense….




But if Descartes insists on avoiding all reference to sense-perception, then matter should be defined by the ability of bodies to be in mutual contact, and by the impenetrability which matter possesses in contradistinction to spirit.


Why should not God be able to destroy all matter contained in a certain vessel without—as Descartes asserts—its walls being obliged to come together?  Descartes, indeed, explains that to be separated by “nothing” is contradictory…


…More is not convinced, all the more so as ‘learned Antiquity”—that is Democritus, Epicurus, Lucretius—was of quite a different opinion.


…pressure of matter outside them.  But if that happens, it will be because of a natural necessity and not because of a logical one.


…will not be absolutely void, for it will continue to be filled with God’s extension.  It will only be void of matter, or body…


In the third place Henry More does not understand the “singular subtlety” of Descartes’ negation of the existence of atoms, of his assertion of the indefinite divisibility of matter…



…imply, an imperfection (thus, for instance, God cannot lie and deceive), or because it would make no sense.  It is just because of that, Descartes asserts, that even God cannot make a void, or an atom.



…Neoplatonist, More…influenced by the tradition of Greek atomism…


…Democritus Platonissans…


What he wants is just to avoid the Cartesian geometrization of being, and to maintain the old distinction between space and the things that are in space; that are moving in space and not only relatively to each other, that occupy space…


…impenetrability—by which they resist each other and exclude each other from their “places.”


…Democritian conceptions…


…his space is not the infinite void of Lucretius: it is full, and not full of “ether” like the infinite space of Bruno.  It is full of God, and in a certain sense it is God Himself…


“…I do not understand your indefinite extension of the world…


If you understand extension to be infinite simpliciter, why do you obscure your thought by too low and too modest words?  If it is infinite only in respect to us, extension, in reality, will be finite…




…Descartes replies—and his answer is surprisingly mild and courteous—that it is an error to define matter by its relation to senses, because by doing so we are in danger of missing its true essence, which does not depend on the existence of men had which would be the same if there were no men in the world; that, moreover, if divided into sufficiently small parts, all matter becomes utterly insensible…


…unnecessary to postulate a special property of impenetrability in order to define matter because it is a mere consequence of its extension.


“I am not in the habit of disputing about words, and therefore if somebody wants to say that God is, in some sense, extended because he is everywhere, I shall not object.   But I deny that there is in God, in an angel, in our soul, and in any substance that is not a body, a true extension,, such as is usually conceived by everybody.



…God, or to our souls, which are not objects of imagination, but of pure understanding, and have no separable parts, especially no parts of determinate size and figure.  Lack of extension is precisely the reason why God, the human soul, and any number of angels can be all together in the same place...we must boldly assert “that God can do all that we conceive to be possible but not that He cannot do what is repugnant to our concept.”


…we say simply that all that implies contradiction.  Descartes’ attempt to save God’s omnipotence and, nevertheless, to deny the possibility of void space as incompatible with our manner of thinking, is, to say the truth, by no means convincing.



…it is not only repugnant to our thought, but impossible that something of which we clearly see that it implies contradiction be real.


…Descartes assures him that it is not because of:


“…an affectation of modesty, but as a precaution, and, in my opinion a necessary one, that it call certain things indefinite rather than infinite.  For it is God alone whom I understand positively to be infinite…you imagine beyond this one a certain divine extension, which would stretch farther than the extension of bodies, and thus suppose that God has partes extra partes, and that he is divisible, and, in short, attribute to Him all the essence of corporeal being.”



…even if the world had these limits which we are unable to find, there certainly would be nothing beyond them, or, better to say, there would be no beyond.


…maintain the distinction between the “intensive” infinity of God, which not only excludes all limit, but also precludes all multiplicity, division and number, from the mere endlessness, indefiniteness, of space, or of the  series of numbers, which necessarily include and presuppose them.


…asserted not only by Nicholas of Cusa, but even by Bruno.  Henry More does not deny this distinction; at least not completely.



…More…the world is finite or infinite, tertium non datur.  And if we admit, as we must, that God is  infinite and everywhere present, this “everywhere” can only mean infinite space.  In this case, pursues More, re-editing an argument already used by Bruno, there must also be matter everywhere, that is, the world must be infinite.


“You can hardly ignore that it is either simpliciter infinite or, in point of fact, finite…Yet if one recognizes God to be positively infinite (that is, existing everywhere), as you yourself rightly do, id do not see whether it is permitted to the unbiassed reason to hesitate to admit forthwith also that He is nowhere idle, and that with the same right, and with the same facility with which [He created] this matter in which we live, or that to which our eyes and our mind can reach, he produced matter everywhere.”



…the particle “only” (tantum) clearly excludes all real infinity of the thing which is said to be infinite only in respect to us, and therefore in reality the extension will be finite…


…More…God’s extension, is infinite.  On the other hand, the material world may, perhaps, be finite.  After all, nearly everybody believes it…


Could Descartes not tell  what would happen, in this case, if somebody sitting at the extremity of the world pushed his sword through the limiting wall?  On the one hand, indeed, this seems easy, as there would be nothing to resist it; on the other, impossible, as there would be no place where it could be pushed.


Descartes’ answer…does not understand his…Descartes’, great discovery, that of the essential proposition between mind and extension…



“…he does not conceive any extension of substance in God, in the angels, or in our mind, but only an extension of power……prejudice which makes us suppose all substance, even that of God, to be something that can be imagined.”


…intermundium “…implies a contradiction to conceive a duration between the destruction of the first world and the creation of the second one; for, if we refer this duration or something similar to the succession of God’s ideas, this will be an error of our intellect and not a true perception of something.”



…eternity, replacing it by mere sempiternity…making Him an extended thing…God is menaced with losing his transcendence, with becoming immanent to the world.


…Descartes’ God…not the Christian God, but a philosophical one.  He is, nevertheless, God, not the soul of the world that penetrates, vivifies and moves it.


…God has nothing in common with the material world.  He is a pure mind an infinite mind…of which spatial extension is neither an image nor even a symbol.



“It is repugnant to my mind, or what amounts to the same thing, it implies a contradiction, that the world be finite or limited…”


More…persisted, therefore, in believing “with all the ancient Platonists” that all substance, souls, angels and God are extended, and that the world, in the most literal sense of this word, is in God just as God is in the world.



…Descartes…to assert the indefiniteness of the world, or of space, does not mean, negatively, that perhaps it has limits that we are unable to ascertain,; it means, quite positively, that tit has none because it would be contradictory to posit them.


…maintain the identification of extension and matter…


…contention that the physical world is an object of pure intellection and, at that same time, of imagination—the precondition of Cartesian science—and that the world, in spite of its lack of limits, refers us to God as its creator and cause.


…Duns Scotus, who could accept the famous Anselmian a priori proof of the existence of God (a proof revived by Descartes) only after he had “colored” it by substituting the concept of the infinite being (ens infinitum)for the Anselmian concept of a being than which we cannot think of a greater (ens quo maius cogitari nequit).  Infinity thus—and it is particularly true of Descartes whose God exists in virtue of the infinite “superabundance of His essence” which enable him to be His own cause (causa sui)


The distinction, or opposition, between God and creature is parallel and exactly equivalent to that of infinite and of finite being.





…1655 and also in 1662, Henry More was hesitating between various solutions of the problem of space.  Ten years later his decision is made, and the Enchiridium metaphysicum  (1672) not only asserts the real existence of infinite void space against all possible opponents, as a real precondition of all possible existence, but even presents it as the best and most evident example of non-material—and therefore spiritual reality and thus as the first and foremost, though of course not unique, subject-matter of metaphysics.



…by his denial both of void space and of spiritual extension, Descartes practically excludes spirits, souls, and even God, from his world…


…in spite of his having invented or perfected the magnificent a priori proof of the existence of God, which Henry More embraced enthusiastically and was to maintain all his life, Descartes, by his teaching, leads to materialism and, by his exclusion of God from the world, to atheism.


…derisive nickname of nullibists.



…More, who in his youth had been such an inspired and enthusiastic adherent of the doctrine of the infinity of the world (and of worlds), became more and more adverse to it, and would have liked to turn back to the “Stoic” conception of a finite world in the midst of an infinite space, or, at. Least, to join the semi-Cartesians and reject Descartes’’ infinitization of the material world.



“Space,” or “inner locus,” is something extended.  Now, extension, as the Cartesians are perfectly right in asserting, cannot be an extension of nothing:  distance between two bodies is something real, or, at the very least, a relation which implies a fundamentum reale.  The Cartesians, on the other hand, are wrong in believing that void space is nothing.  It is something, and even very much so.  Once more it is not a fancy, or a product of imagination, but a perfectly real entity. The ancient atomists were right in asserting its reality and calling it an intelligible nature.



…Gassendi, who claims that space and time are neither substances nor attributes but simply space and time…



More…”I, on the contrary, since I have so clearly proved that Space or internal place (locus) is really distinct from matter, conclude therefrom that it is a certain incorporeal subject or spirit, such as the Pythagoreans once asserted it to be.”


Descartes was right in looking for substance to support extension.  He was wrong in finding it in matter. 


…it is not matter..  it is  Spirit; not a spirit, but the spirit, that is, God.



about twenty titles which the metaphysicians attribute to God and which fit the immobile extended [entity] or internal place (locus).


One, Simple, Immobile, Eternal, Complete, Independent, Existing in itself, Subsisting by itself, Incorruptible, Necessary, Immense, Uncreated, Uncircumscribed, Incomprehensible, Omnipresent, Incorporeal, All-penetrating, All-embracing, Being by its essence, Actual Being, Pure Act.



Absolute space is infinite, immovable, homogeneous, indivisible and unique.  These are very important properties which Spinoza and Malebranche discovered almost at the same time as More…



The list of “attributes” common to God and to space, enumerated by Henry More, is rather impressive…


…separate matter and space, raise the latter to the dignity of an attribute of God, and of an organ in which and through which God creates and maintains His world, a finite world, limited in space as well as in time…


“And in order not to dissimulate anything, this seems to be the best argument for demonstrating that the Matter of the World cannot be absolutely infinite but only indefinite, as Descartes has said somewhere, and to reserve the name of infinite for God alone.  Which must be asserted as well of the Duration as of the Amplitude of God  both are indeed absolutely infinite; those of the World, however, only indefinite…that is, in truth, finite.  In this way God is duly, that is, infinitely, elevated above the Universe, and is understood to be not only by an infinite eternity older that the world, but also by immense spaces larger and more ample than it.