De Moor VIII:34: The Finitude of the World

The World truly has Limits to its Extension.  That the World is Finite, our AUTHOR asserts in this §, not only against some Ancient Philosophers, concerning which PLUTARCH, in book II de placitis Philosophorum, chapter I, speaks:  Δημόκριτος καὶ Ἐπίκουρος καὶ ὁ τούτων μαθητὴς Μητρόδωρος, ἀπείρους κόσμους ἐν τῷ ἀπείρῳ κατὰ πᾶσαν περίστασιν, Democritus, Epicurus, and their disciple, Metrodorus, asserted infinite World in the infinite according to all circumstances….  Σέλευκος ἄπειρον τὸν κόσμον.  Διογένης τὸ μὲν πᾶν, ἄπειρον, τὸν δὲ κόσμον πεπρώνθαι, Seleucus [asserted] an infinite World:  Diogenes an infinite Universe, but a finite World.  But the same thing is to be maintained against Descartes and his followers, whose expressions LEYDEKKER excerpted from their very own writings, Face Veritatis, locus VI, question IV:  The World actually fills up all imaginable space, so that no place or space is able to be conceived, in which new world could be placed.  In actuality the World has consequently such extension, that we are not able to conceive something greater than it.  We ought not so to conceive of the border of the World; for, should we do this, we would be conceiving of an extension greater than that which belongs to the world.  The World is so great, in which we are not able to discover or to conceive with the intellect boundaries.  Neither does that proceed from the weakness of the human mind, but from the positive conception, whereby we experience in ourselves such an idea of the World, that we are able to imagine no boundaries to it.  Since this idea of the World did not arise from prejudices, nor was drawn from another source, it is necessary, that it was indited in us by God, and is consequently true and rightly representing the nature of it.  We deny that the World is finite, and that the infinity of the extension of the World implies a contradiction.  Indeed, contrarwise, it is repugnant, or, which is the same thing, implies a contradiction to our conception, that the World is finite or bounded.  All these are the very words, either of DESCARTES, or of WITTICH or BURMAN:  compare VRIESIUS, explainly very distinctly the mind of Descartes, and painstakingly uncovering his κρησφύγετα/retreats, in his Dissertatione de Infinito, posterior Section, which is de Extensione Infinita, § 20-30.  Now, this assertion, that the World is infinite in Extension, with many others, the Curators of the Leiden Academy prohibited to be taught or defended, January 16, 1676.  What HEIDANUS thought worthy of attention concerning the same, see in his Consideratien, etc., pages 94-96.  The warnings of WITSIUS against this thesis of Descartes, too boldly defended by Wittich, see in his tractate, Twist des Heeren met zynen Wyngaard, chapter XXI, pages 271, 274-276.  The whole controversy of this paragraph treated at length, see also in the Most Illustrious VAN MASTRICHT’S Gangrænam Novitatum Cartesianarum, posterior Section, chapter XX, § 3-18, pages 362-379; add also his Vindicias Veritatis et Authoritatis Sacræ Scripturæ adversus Wittichium, chapter VII, § 27, pages 149-167; likewise LEYDEKKER’S Facem Veritatis, locus VI, question IV, pages 269-282.

LEYDEKKER notes that the πρῶτον ψεῦδος, fundamental error, of the Cartesians in this controversy is the impugning of Possible Spaces; so that they rather prefer to imagine an Infinite World, and to convert all possible Spaces into true and real Spaces, than conceive of possible Spaces beyond the World unto the glory of God’s Immensity, Power, and Infinitude.  To which one may add another πρῶτον ψεῦδος, fundamental error, that, unless the Infinite Extension of the Universe be supposed, the matter of Descartes’ vortices shall move away from their centers, and the whole machine of the world shall disappear into scattered atoms and wandering dust, as HENRY MORE warned Descartes in his Epistolis Cartesii, part I, epistle LXVI, page 180.

Johannes a Marck

When our AUTHOR asserts that the World has Bounds to its Extension, he wishes to preclude the inane distinction between Finitude of Perfection and of Extension, as if the former were indeed applicable to the World, but the latter not; to which tend those words of DESCARTES, Epistle LXIX ad Henricum Morum, part I, page 206:  I would not dare to call the World Infinite, because I perceive that God is greater than the World, not with respect to extension, which, as I have often said, I understand to be no property of God, but with respect to perfection.  Now, when the followers of Descartes, in order to uphold the opinion of their Master, employ that distinction concerning the World, Infinite indeed with respect to Extension, but not with respect to Perfection, the Infinity of which is applicable to God alone; they imitate the Jesuits, who, so that in order to please Aristotle they might assert that the Eternity of the World is possible, distinguish between Infinity of Perfection and Infinity of Duration, the latter of which they think to be able to be applicable to the World without the former.  In a similar manner, as Julius Cæsar Vaninus[1] was also distinguishing between Infinite in power and Infinite in age, of which the formed he believes is to be attributed to God alone, the latter even to the World, Dialogue VI de Cœli Æternitate:  Therefore, the Heaven (says he) is to be said to be finite in magnitude and power, but infinite in duration; because God was not able to make another God, but He would have done it, if He had made an infinite in power; and so He made an infinite in age, because this alone was able to appear as the perfection of the Creature.

But, 1.  the Finite bears no Proportion to the Infinite, such that it is proper that what is Infinite in one way is Infinite in every way, and vice versa; neither is a mixture of the Finite with the Infinite able to obtain in the same subject.  2.  When also, as those contend with whom it is here disputed, extension itself constitutes the essence of a body, it is manifest, that infinity of extension and of essence proceed here with equal step.  And, while what is infinite in Essence is necessary such in all attributes (as which things by their nature follow the condition of the subject), it appears that infinity is to be attributed to the World either in no way, or in every way.

Wittich

Although we are not able to determine its Definite Magnitude.  Whence the World, which we assert to be Finite in itself, is at the same time able to be called Indefinite by us, since we are not able precisely to indicate and determine the Bounds of the World, Where they are, and how great its Extension might be.  But it is little help to Descartes and his followers, that they pronounce the World, not Infinite (for, they hardly dare openly to make use of that term, but they rather carefully abstain from the same, when they speak of the World), but only Indefinite.  For, while they are unwilling to call the World Infinite, yet at the same time they deny the same to be Finite; whence it appears that they fasten new and unaccustomed signification to terms, so that among those unskillful in the matter deceit and hurtfulness of opinion might be able the more easily to lie hidden.  WITTICH, Theologia pacifica, chapter VIII, § 89, says:  Whoever determines the World to be Indefinite does indeed deny it to be Finite, but for this reason he does not ascribe Infinity to the World.  He then adds, § 90, speaking on behalf of Descartes:  What circumspection is able to be greater, than to be so painstakingly careful to avoid confusing God with creatures, that thou wouldest determine to make use even of different words concerning God and creatures?...  Descartes…says that only God is infinite, and thinks that all other things are to be called indefinite rather than infinite:  …He attributes extension to the World, …he judges that no greater extension is able to be conceived than the extension of the World; he contemplates by what name that extension is to be denominated, which he does not discover with the finite, yet does not want to call infinite, so that he might keep the name of the infinite for God alone.  Thus he discourses on those things that he had cited out of Descartes, § 89, where he introduces him writing in Epistle LXIX ad Henricum Morum:  I say, therefore, that the World is indeterminate or indefinite, because I recognize no boundaries to it:  but I would not dare to call it Infinite, because I perceive that God is greater than the World…with respect to perfection.  And in Epistle XXXVI, part I, pages 80, 81:  To say that a thing is infinite, it is necessary that we have a reason causing us to acknowledge it as such, which we are only able to have concerning God alone; but to say that it is indefinite, it is sufficient that we have no reason whereby we might be able to prove that it has limits.  Thus it appears to me, that we are not able to prove, nor even to conceive, that there are limits on the matter of which the world is composed.  Adding still a little farther on:  But I am not, therefore, able to deny that perhaps the limits are able to be known by God, although they are incomprehensible to me.  That is, while they, denying the World to be Finite, nevertheless dare not to call it Infinite, but rather pronounce it Indefinite, however they might sometimes speak less harshly; they appear by Infinite to understand Infinite in Perfection, but by Indefinite Infinite Extension:  which even Wittich expressly indicates, Dissertation I de Abusu Sacræ Scripturæ, chapter I, article X, with the words cited by MASTRICHT in his Vindiciis Veritatis et Authoritatis Sacræ Scripturæ adversus Wittichium, chapter VII, § 27, page 151:  The Infinity of God is of another sort than the Infinity of the World:  the former is of Perfection, whereby it is signified, that God has omnimodal perfection, and greater than any creatures is able to apprehend by its own contemplation:  the latter of Extension, which in no way is able to be applied to God, indeed, overthrows the former.  Which, 1.  distinction between the Infinite of Extension and of Perfection is not able to be admitted, as we have already observed.  2.  It is to be observed, that the Finite and the Infinite are contradictories, and that this division is absolute; such that the World ought to be either Finite or Infinite, neither is the Indefinite able to be admitted as some Middle thing actually diverse from the Finite and the Infinite.  3.  Therefore, no created thing is said to be Indefinite with respect to itself, but only with respect to our knowledge; and so, when we call the World Indefinite, it comes completely to be referred to our knowledge; and thus we signify, that we are not able to define where the Boundaries of the World are, but which we otherwise know to be Finite:  compare VRIESIUS, in his Dissertatione de Infinito, posterior Section, § 28-30.  And so we readily acknowledge that the World is Indefinite in this sense, but at the same time we affirm that it is also Finite, against which the Cartesians argue.  Which now, with our Author, we further demonstrate:

α.  From express Passages:  1 Kings 8:27, in which the Immensity of God is made known from this, that it is not contained by the bounds of the created World; and so the Heaven of Heavens is considered as standing open to the broadest possible extent, but at the same time as the final and supreme boundary of the World, comprehending all inferior things in its embrace.  In Isaiah 48:13 also, it is affirmed that the Heavens have a measure known to God.

It is not permitted, adds our AUTHOR in his Compendio, without insane incredulity to pretend Bodies Higher than the Supreme Heaven.  Since, besides the Lower Earth with the visible Heavens, and the Supreme Heaven, neither Moses, painstakingly surveying the work of Creation, nor the whole Scripture make mention of anything created by God.  However, our AUTHOR thus considers again the trifles of the Cartesians, who conceive of what we call Possible Spaces beyond the World as real Spaces, and hence write, for example, with WITTICH, Theologia pacifica, chapter VIII, § 86, that we say that the World, unto which pertain the Heavens of Heavens, is extended indefinitely, and what things others say that they conceive as Imaginary Spaces beyond the World, those we say are real and pertain to this very World….  But how far that body, which Scripture calls the Heavens of Heavens, might extend itself; or whether or not beyond that other bodies, which are not the Heavens of Heavens, are to be conceived, we leave undetermined, etc.

β.  A reason is added,

              א.  From the Nature of a Body, which

                             1.  Consists of finite Parts.  But what consists of finite Parts, that whole has to be finite; since, a.  finite Parts are not able to give to the whole what they themselves do not have:  and, b.  a Part’s proportion is entirely according to its Whole; but there is no proportion of the Finite to the Infinite, since the Finite, taken however many times, shall never equal or exceed the amplitude of the Infinite.  Thus there is a proportion between four and nine, between three and nine; because four, taken three times, exceeds nine, but three, taken three times, equals nine.  There is a proportion between a grain of sand and the whole earth, because myriads of grains of sand, multiplied one hundred thousand times and gathered into one, are able to be multiplied to the extent that they equal, indeed exceed, the whole mass of the earth.  But between the Finite and the Infinite there is no proportion:  for, even if a certain Finite thing be multiplied a hundred thousand times or more, it will never rise to the Infinite.  c.  No part, in that it is a part, is able to be infinite; therefore, whatever part you might take, it will be finite:  why, if all parts be conjoined, will they not remain finite?  Now, parts conjoined make a whole; therefore, the whole, consisting of those parts, has to be finite, and consequently also the World, which actually consists of the same parts.

                             2.  And is of a certain amount.  The corporeal Universe necessarily has its own Quantity and Dimension, length, breadth, and depth.  a.  But whatever is extended has a part beyond a part; every part has a limit; therefore, whatever extension has a limit.  b.  Whatever has three Dimensions, that is certainly able to be measured; and what is able to be measured, that undoubtedly has limits.  There is the implication that there are three Dimensions in a body of infinite Extension, lest three infinites be conceived in the one infinite.  On this Argument taken from the Nature of Bodies, compare carefully VRIESIUS’ Dissertationem criticam de Extensione Infinita, § 31-36.

              ב.  From the Glory of God, who, because He is Infinitely Perfect, with respect to the Where is also Infinite or Immense; for whatever is Infinite in any way, that is Infinite in every way:  but, because God alone is Infinitely Perfect, therefore also ought the glory of Immensity to be left to Him alone:  and, on the other hand, the World, finite in Perfection, ought to be said to be finite in Extension also; because what is Finite in any way, that is Finite in every way, neither is any mixture of the Finite and the Infinite, things having no proportion, able to be granted in the same subject:  see VRIESIUS, Dissertatione critica de Extensione Infinita, § 38-41, where from a consideration of th diverse Perfections of the divine Essence he confutes the Infinite Extension of the World.

              ג.  From the easy transition from the Immensity of the World to the assertion of the Eternity of the same; since, 1.  what is Infinite in Extension ought likewise to be Infinite in Duration, for the same reason, that whatever is Infinite in any way, that ought to be Infinite in every way.  2.  Should the Cartesians deny the finite Extension of the World, neither should the acknowledge Possible Spaces beyond the World; for the same reason, they ought to deny its finite Duration and to acknowledge the World as Eternal:  since otherwise they would be bound to admit Possible Spaces before the World, which the created World now occupies.  Whence now, our AUTHOR adds, the voices of some are heard, who assert the Possible Eternity of the World, that are hardly able to be refuted.  That is, thus BURMAN, Synopsi Theologiæ, book I, chapter XLI, § 24:  Although we ourselves think that those, who assert the possible Eternity of the World, are hardly refuted; yet we prefer to join with those that deny that anything was able to be created without a principal time.  But how odious is the error of those that affirm an Eternal World; how contradictory it is to relate that the World was able to be created from Eternity, or that it was possible, that the World might exist by Creation from Eternity, we have seen above, § 13, 19:  compare also VRIESIUS, Dissertatione critica de Extensione Infinita, § 37; ANTONIUS HULSIUS,[2] Theologiæ hypotheticæ, part I, Disputation XXX, § 17, part 2, pages 386-388.  It is sufficiently apparent from the things said, that Hobbes[3] speaks to no purpose, who thinks that no absurdity is going to follow, whether the World is thought to be finite or infinite, in Physicis, part IV, chapter XXVI:  compare COCQUIUS’[4] Hobbesianismi Anatomen, locus VII, chapter XIV, pages 134, 135.

Objection 1:  The Heavens are not able to be measured, Isaiah 40:12; Jeremiah 31:37.  Our AUTHOR rightly Responds:  α.  Not by Men, but indeed by God, concerning whom the contrary is thereafter expressly affirmed, Isaiah 48:13:  similarly what is found in Proverbs 25:3 ought to be understood with respect to men, not with respect to God, since concerning Him we also have Proverbs 21:1; 16:2.  β.  And the same is said concerning the Earth and the Waters, which certainly have bounds, Job 28:4, 5; Proverbs 30:4.

Objection 2:  There is in us the Idea of the World extended Infinitely.  Response:  α.  If you represent to yourself such an Idea of the World, you are deceived by false Imagination, which with complete temerity you hold as an Idea indited in you by God:  since from the things said above with a completely clear Perception I discern, that the World has to be Finite, and that Extension unto the Infinite verily asserts a contradiction in terms.  β.  If you imagine Nothing beyond the created World by way of real Space, and hence you form for yourself an Idea of the World or Being Extended unto the Infinite; this is done contrary to the truth of the matter, from imbecility of mind, desiring some Positive conception of Nothing:  which sort of false Imagination you rashly ascribe in turn to an Idea indited in you by God Himself.  γ.  Our thoughts are not the measure of things.  δ.  But if no Possible Spaces are able to be granted beyond the World, and so we ought to propose to ourselves Spaces true and real in the place of the same, and to deny boundaries to the World; neither shall the Eternal World be Annihilable even by divine Power, since otherwise either before the creation of the World, or after the Annihilation of the same, Possible Spaces of this sort would have to be acknowledged.

Should you say, that the World is not able to be affirmed as Finite, because every finite is shut up in the Space of another surrounding Body.  I Respond, that It is not necessary to constitute the nature of a Finite, because every Body is Finite of itself and its own determinate quantity:  for, whatever extends to a certain extent and not farther, and so a greater than which is able to be conceived, the same is Finite:  compare VRIESIUS, Dissertatione critica, § 45, 46, who in § 44 looses the Objection of Descartes thence sought, that whoever contemplates a Finite Extension of the World, thinks too highly of himself, and less magnificently of God.  And then, in § 47, 48, he shows, that the Immensity of the divine Omnipotence concludes nothing for possible Infinite Extension.  See also the Monitum against Spatium Infinitum of the Most Illustrious HORTHEMELS as President, subjoined to the Disputationi of the Illustrious GISBERT BONNET de Notitia eorum, quæ Mens humana nec directe nec positive cognoscere potest, K.

[1] Lucilio Vanini (1585-1619) was an Italian physician, philosopher, and radical free-thinker.  He asserted a naturalistic determinism, and was an early proponent of biological evolution.

[2] Antonius Hulsius (1615-1685) was a Dutch Reformed philologist and theologian.

[3] Thomas Hobbes (1588-1679) was an English philosopher, remembered for his work in political philosophy and social contract theory.  He was also interested in theology, but heterodox in his beliefs, denying incorporeal substance (reducing all things to matter and motion), and the divine inspiration of the Biblical prophets.

[4] Gisbertus Cocquius (1630-1708) of Utrecht was a Reformed thinker and doctor of philosophy; he opposed Hobbes.