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The Fairy Tale of the Green Snake and the Beautiful Lily

Johann Wolfgang von Goethe, Thomas Carlyle, Rudolf Steiner

The Pictorial Key to the Tarot

Arthur Edward Waite

Letters on the Aesthetical Education of Man

Friedrich Schiller

Further Adventures of an Irish R. M.

Edith Somerville and Martin Ross

The Philosophical Works of Leibnitz ...

by Gottfried Wilhelm Freiherr von Leibniz


Proposition 6. One substance cannot be produced by another substance, for two substances, by Prop. 5, do not possess the same attribute, therefore they have nothing in common, by Prop. 2; therefore, it cannot be that one is the cause of the other, by Axiom 5. The same in other words and more briefly: Because what is conceived through itself cannot be conceived through another as cause, by Axiom 4. But I reply, that I grant the demonstration, if substance is understood as a thing which is conceived through itself; it is otherwise if it is understood as a thing which is in itself, as men commonly understand it, unless it be shown that to be in itself and to be conceived through itself are the same thing.

Proposition 7. Existence belongs to the nature of substance. Substance cannot be produced by anything else, Prop. 6. Therefore it is the cause of itself; that is, by Def. 1, its essence involves existence. He is not unjustly censured because sometimes he employs cause of itself as a definite something to which he ascribes a peculiar signification, Def. 1; sometimes he uses it in the common and vulgar meaning. Nevertheless, the remedy is easy, if he converts this Def. 1 into an Axiom and says: Whatever is not by another, is by itself or of its own essence. But here other difficulties still exist: the reasoning, namely, is valid only when it is posited that substance can exist. For it is then necessary that, since it cannot be produced by another, it exists by itself, and thus necessarily exists; but it must be demonstrated that it is a possible substance; that is, that it can be conceived. It seems that it can be demonstrated from the fact that if nothing can be conceived through itself nothing also can be conceived through another, and hence nothing at all can be conceived. But that it may be shown distinctly, we must consider that if a is posited as conceived through there is in the conception of a itself the conception of b itself. And again, if b is conceived through c, there is in the conception of b the conception of c itself, and thus the conception of c itself will be in the conception of a itself, and so on to the last. But if any one reply that the last is not given, I answer, neither is the first, which I thus show. Because in the conception of that which is conceived through another there is nothing except what belongs to the other, so step by step through many there will either be nothing at all in it or nothing except what is conceived through it itself; which demonstration, I think, is wholly new but infallible. By this means we can demonstrate that what is conceived through itself can be conceived. But nevertheless, thus far it can be doubted whether it be possible in the way in which it is here assumed to be possible, certainly not for that which can be conceived, but for that of which some cause can be conceived, to be resolved into the first. For those things which can be conceived by us, nevertheless cannot therefore all be produced, on account of others which are preferable with which they are incompatible. Therefore, being which is conceived through itself must be proved to be in actual existence by the additional evidence that because those things exist which are conceived through another, therefore that also through which they are conceived, exists. You see what very different reasoning is needed for accurately proving that a thing exists through itself. However, perhaps there is no need of this extreme caution.

Proposition 8. Every substance is necessarily infinite, since otherwise it would be limited by another of the same nature, by Def. 2, and two substances would be given with the same attribute, contrary to Prop. 5. This proposition must be understood thus: A thing which is conceived through itself is infinite in its own kind, and thus is to be admitted. But the demonstration labors not only with obscurity as respects this is limited, but also with uncertainty, by reason of Prop. 5. In the scholium he has excellent reasoning to prove that the thing which is conceived through itself is one, of course after its kind, since many individuals are posited as existing, therefore there ought to be a reason in nature why there are so many, not more. The reason which accounts for there being so many accounts for this one and that one; hence also for this other one. But this reason is not found in one of these rather than in another. Therefore it is outside of all. One objection might be made, if it were said that the number of these is boundless or none, or that it exceeds every number. But it can be disposed of, if we assume only some of these and ask why these exist, or, if we posit more having something in common, for example existing in the same place, why they exist in this place.

Proposition 9. The more reality or being a thing has the greater the number of its attributes. [He ought to have explained what is meant by reality or being, for these terms are liable to various significations.] Demonstration: It is clear from Def. 4. Thus the author. It seems to me not to be clear from it. For one thing may have more of reality than another, as what is itself greater in its own kind, or has a greater part of some attribute; for example, a circle has more extension than the inscribed square. And still it may be doubted whether there are many attributes of the same substance, in the way in which the author employs attributes. I confess, however, that if this be admitted and if it is posited that attributes are compatible, substance is more perfect according as it has more attributes.

Proposition 10. Each particular attribute of the one substance must be conceived through itself, by Defs. 4 and 3. But hence it follows, as I have several times urged, that there is but a single attribute of one substance, if it expresses the whole essence.

Proposition 11. God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essence, necessarily exists. He offers three demonstrations of this. First, because he is substance; therefore, by Prop. 7, he exists. But in this he supposes both that substance necessarily exists, which, up to Prop. 7, was not sufficiently demonstrated, and that God is a possible substance, which is not equally easy to demonstrate. Second. There must be a reason as well why a thing is as why it is not. But there can be no reason why God does not exist, not in his own nature for it does not involve a contradiction; not in another, for that other will either have the same nature and attribute, and hence will bo God, or will not have them and hence will have nothing in common with God, and thus it can neither posit nor prevent his existence. I reply, 1st, that it is not yet proved that the nature of God does not involve a contradiction, although the author says it is absurd to assert, without proof, that it does. 2d. There might be something having the same nature with God in some things, not in all. Third. Finite beings exist (by experience); therefore if the infinite does not exist there will be beings more powerful than the infinite being. It may bo answered, if it implies anything, infinite being will have no power at all. I need say nothing of the impropriety of calling the potentiality of existence a power.

Propositions 12 And 13. Iso attribute of substance can be conceived, from which it would follow that substance can be divided; or substance taken absolutely is indivisible. For it will be destroyed by division and the parts will not be infinite and hence not substances. Many substances of the same nature would be given. I grant it of a thing existing through itself. Hence the corollary follows that no substance, and therefore no corporeal substance is divisible.

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