Acta eruditorum anno MDCCXII
pp 27-31

Date: January 1712

Translated from the Latin

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[AE p27]

Demonstratio de deo sive methodus ad cognitionem Dei naturalem brevis ac demonstrativa. Cui accedunt Epistolae quaedam Miscellaneae de Animae natura & immortalitate, de veritate Religionis Christianae, de universo &c. London: William Taylor, 1710. Quarto. Leipzig: Gleditsch and sons, 1712. Octavo.

[AE p28]

Since Mathematics began to be united with Philosophy a little over a half-century ago, many ingenious men have attempted to give us demonstrations of mathematical certainty even in metaphysical matters, and especially about God and the soul. Their intention should be praised, and the hope is that they can gradually reach their goal. But so far, the effort has seldom been rewarded with success. The ingenious author of this little book, Joseph Raphson, certainly has many excellent ideas (especially about the nature of the mind), as will soon be clear, but he also seems to move somewhat too freely in demonstrating them. Indeed, in the preface he says he approached the matter (namely the demonstration of God) by means of the briefest and most perspicuous arguments.1 And it should be admitted that although brevity is achieved, it would be desirable for there to be a similar degree of perspicuity. Accordingly, he will oblige us with his perspicacity if we might sometimes desire further explanation. He begins with definitions: "finite" (he says) "is designated whatever is actually circumscribed, whether in essence or in action (or in activity if you prefer) or in any other way, that is, that which has limits, in all respects, of its essence, its action etc."2 But in using "circumscribed" or "limited," he seems here to have substituted synonyms for "finite" rather than explained it. (Indeed, there are those who doubt whether every circumscribed thing is finite, for some people conceive a certain straight line which is infinite and yet circumscribed. For suppose an infinitely small straight line a and a regular straight line b, that is, LM beginning from some given point L, and let the straight lines a, b, c, and d be in continuous proportion, all beginning from the same given point L, and drawn along the same line through L and M; I say that the third line c will be infinite, but still circumscribed, because the fourth, d, is infinitely greater and extended further; although it too is not unbounded, but infinitely exceeded by the proportional fifth, and so on. Now although the author of the infinitesimal calculus does not in fact consider infinitely small quantities to be real,3 nor does he grant such consequences, there are others who do grant them, and therefore very different notions are asserted.) Moreover, our most illustrious author infers a corollary from his definition, namely that there cannot be two infinites in the same genus that are distinct in essence.4 But he does not explain what "in the same genus" is. Does it mean the same as "essence"? But if so, the proposition would be identical. [AE p29] He notes in a scholium that he is not concerned with the potential or mathematical infinite.5 But it can be doubted whether every mathematical infinite is potential. Therefore, from that point, he ought to have put forward a definition by means of which the infinite which concerns him would be distinguished from mathematical infinities. He defines being from itself as that which exists by the power of its own nature or essence, that is, that whose own nature involves existence, and therefore necessarily exists as a result.6
     He then postulates:

     (1) that something exists,
     (2) that every finite thing can be conceived as not existing,
     (3) that every greater or lesser finite thing in the same genus is admitted.7

But perhaps the followers of Epicurus will deny the second postulate, since they believe their atoms exist necessarily, and therefore while it can be imagined or conceived confusedly that they do not exist it cannot be conceived distinctly. These axioms follow:

     (1) Nothing can come from nothing,
     (2) nothing happens without a determinate cause,
     (3) whatever exists, exists either from itself or from another.8

Epicureans will say to the third axiom that eternal things like atoms and the void exist neither from themselves nor from another. Some will perhaps add to the third that something can exist partly from itself and partly from another, with the natures of many things concurring and mutually sustaining each other. There follows proposition 1: "A being from itself exists."9 The demonstration is this: "something exists, by postulate 1, but nothing can come from nothing, by axiom 1. Therefore something exists from itself. Therefore a being from itself, whatever that may be, exists."10 Here we openly admit that the evidence for this connection is lacking, nor is it readily apparent how it can be obtained by the form of the argument here. While our ingenious author endeavours to be brief, he is obscure, though he attempts to elucidate his demonstration in the scholium. Namely, if an opponent were to say that an existing being is produced from another and this in turn from another, and so on to infinity, his reply is that there must be an existing being from itself coeval with the infinite series of causes, otherwise non-being would become the cause of things, contrary to axiom 1.11 But all these things would require more meticulous confirmation. Opponents will say that an infinite series of non-necessary beings is sufficient for itself, for there is always a determinate cause present even if there is no first cause. Nor can he satisfy them except through another, higher and more general axiom which the illustrious author of the Theodicy has famously urged of late,12 with almost the whole work built upon it, namely that there is nothing without a sufficient reason why it is rather than is not; this must hold good [AE p30] whether a thing has a cause or not, or is eternal or not. For thus it is evident that no sufficient reason for existing is found in such a series, since the reason for it is always repeatedly sought.
     In proposition 4 our most illustrious author labours hard to prove that being from itself is infinite.13 He argues like this: being from itself is absolutely independent and necessarily possesses all perfections (by corollary 3 of proposition 3) and therefore possesses essence without limits too.14 But only these things were asserted in that third corollary: "the essence of being from itself possesses all the perfections which are the consequence of existence from itself, i.e. necessary existence."15 This certainly cannot be denied, though it proves nothing absolutely about all perfections. Therefore he does better when he tries to establish this same proposition 4 in two other ways; first in this way: "every finite thing (by postulate 2) can be conceived as not existing, but being from itself cannot be conceived as not existing, therefore being from itself is not finite."16 This syllogism is of good form, but since the postulate differs little from the conclusion, opponents will hardly accept it without proof, as we have already noted above. He gives a third proof of this sort: "being-unable-not-to-be belongs to being from itself" (correct) "but being-unable-not-to-be belongs to an actually infinite being" (which he says he has proved in a little book on real space, chapter 3), "therefore being from itself is actually infinite."17 Opponents will say that the form of this syllogism is problematic and they will deny that the argument succeeds unless it is first proved that being-unable-not-to-be belongs only to an infinite being. And I don't know whether the support the author tries to provide in the following words will resolve the objection: "because these two predicates18 are utterly unique, to show that being-unable-not-to-be is predicated of them [both] will hardly be worth the effort."19 I think he means that being from itself and infinite being are one and the same, and that therefore the consequence follows. But to prove this assertion was certainly worth a great deal of effort, though if he means something else then I do not sufficiently grasp his intention. And certainly in the end he tries to prove in proposition 5 that being from itself is unique,20 but there he supposes he has demonstrated that being from itself is infinite.
     Second part. Our most illustrious author thinks that God, or (which he now considers the same thing) being from itself, is infinitely extended, infinitely active, and endowed with an infinite intellect;21 he then cites the Cabalists [AE p31] and the younger of the van Helmonts in the Seder Olam;22 together with the Platonists he too divides the divine intellect into nous noeros [the contemplating intellect] and nous noetos [the contemplated intellect];23 the latter is exhibitive of things, the former perceptive,24 and he rightly thinks that the divine intellect is the ground of essences. Moreover, he adds that, although there are infinite possibles, it is still not possible that infinite systems of bodies actually and in all manner of ways coexist at the same time, on account of the impossibility of motion arising from the impenetrability of the same [bodies].25 But one doubts whether this argument is valid. Also, our most illustrious author rightly thinks that God is determined to act by his own perfection and that man acts most freely when he acts in accordance with reason.26
     In the third section he now attributes to God, to whom he has attributed infinite extension, holenmerianism (p69) (using Henry More's term),27 so that he is whole in each and every part, yet he considers it a contradiction to call God unextended.28 Moreover, he declares that, according to Augustine (book 4, chapter 12 and onwards of On the Literal Meaning of Genesis), creatures are continually produced by God.29 Many things may be said about the letters joined to this book,30 but we shall hold them over for next month.


1. Joseph Raphson, Demonstratio de deo sive methodus ad cognitionem Dei naturalem brevis ac demonstrativa. Cui accedunt Epistolae quaedam Miscellaneae de Animae natura & immortalitate, de veritate Religionis Christianae, de universo &c. (Leipzig: Gleditsch and sons, 1712), n.p.
2. Raphson, Demonstratio de deo, 10-11.
3. Leibniz is of course here referring to himself.
4. Raphson, Demonstratio de deo, 11.
5. Raphson, Demonstratio de deo, 12.
6. Raphson, Demonstratio de deo, 12.
7. Raphson, Demonstratio de deo, 12.
8. Raphson, Demonstratio de deo, 12-13.
9. Raphson, Demonstratio de deo, 13.
10. Raphson, Demonstratio de deo, 13.
11. Raphson, Demonstratio de deo, 13.
12. Again, Leibniz is referring to himself.
13. Raphson, Demonstratio de deo, 18.
14. Raphson, Demonstratio de deo, 18-19.
15. Raphson, Demonstratio de deo, 17.
16. Raphson, Demonstratio de deo, 19.
17. Raphson, Demonstratio de deo, 19.
18. Namely, "being from itself" and "actually infinite being."
19. Raphson, Demonstratio de deo, 19.
20. Raphson, Demonstratio de deo, 23.
21. Raphson, Demonstratio de deo, 33-46.
22. Namely Seder Olam,sive Ordo Seculorum ([Amsterdam], 1693); English translation: Seder Olam: or, the Order, Series, or Succession of All the Ages, Periods, and Times of the Whole World (London: Sarah Howkins, 1694). According to the title page of the English edition, the book was "Translated out of Latin by J. Clark, M. D. upon the leave of F. M. Baron of Helmont."
23. Raphson, Demonstratio de deo, 48.
24. For this distinction, see for example Henry More, Annotations upon the Two Foregoing Treatises, Lux Orientalis, or An Enquiry into the Opinion of the Eastern Sages concerning the Prae-existence of Souls; and the Discourse of Truth (London: J. Collins, 1682), 178-79.
25. Raphson, Demonstratio de deo, 50.
26. Raphson, Demonstratio de deo, 60-65.
27. Holenmerianism, a Greek term meaning "whole in parts", was coined by Henry More in his Enchiridium Metaphysicum (London, 1671), 367ff.
28. Raphson, Demonstratio de deo, 69.
29. Raphson, Demonstratio de deo, 74-75.
30. Some printings of Raphson's book contain ten of his letters in a long appendix (pp81-166). Leibniz's review of these letters appeared in the February 1712 issue of the Acta eruditorum, 62-69.

© Lloyd Strickland 2009, 2019