A Memoir- the Testament
Page 67
The mind, therefore, is the inner eye of man, it’s by this eye that he sees and knows all things; but this eye must not see itself, or know itself, since it is the first principle of all sight, of all knowledge, and of all feeling. And, since nobody is surprised at the fact that men don’t see their own eyes, although they see everything else with their eyes, in the same way it seems there should be no reason to be so surprised that men don’t clearly know the nature of their mind and their thoughts, although it’s by their mind, by their thoughts, and by their feelings that they know and perceive everything else, since this mind itself, which is in them, is the first principle of all their thoughts, of all their knowledge, and all their feelings. There is a maxim in morality which says that the principle of merit does not fall under merit: principium meriti not cadit sub merito. The same thing applies to sight, knowledge, and feeling. And, as we already know that the principle of sight doesn’t fall under sight, we should definitely also expect that the principle of feeling shouldn’t fall under feeling, or the principle of knowledge under knowledge; and we shouldn’t doubt that this is the reason why we know the nature of our mind and the nature of our thoughts and feelings so poorly.
But, no matter how we approach the problem we have in knowing them, we all know and we are all certain that we ourselves think, that we imagine, that we reason, that we have ideas of many things and that we have various feelings of good and evil within ourselves, we can’t doubt this at all. We also know that it’s with our heads and especially our brain that we think, that we imagine and reason, as we know that it’s with our eyes that we see and that it’s with our ears that we hear, and that it’s by our nose that we sniff odors, that it’s with our tongue that we discern taste, flavors, and that it’s properly with our hands that we touch, and finally, that it’s by all the parts of the body that we have feeling. We always have the experience of all that and we can’t doubt it.
But, since we also know that we often have or that we might often have ideas of many things which don’t exist, it is clear and obvious that the ideas we might have of many things, that we might imagine and represent in our brain, are not always proofs that those things are actually as we imagine them. It’s only the necessary ideas that we can’t erase from our mind, which are truly a convincing proof of the existence of these things, that we conceive by ideas and of which we have such ideas. We couldn’t, for example, if we reflected on them, erase from our mind the idea we have of an infinite extension; the mere idea we have of it, which we can’t erase from our mind, is a clear proof that it is actually and truly infinite, as we conceive it; for we can’t conceive that this extension would be limited and not infinite; because, if it weren’t truly infinite, we couldn’t conceive of any boundaries to it; and as we can’t conceive of any boundaries to it, without conceiving of something beyond it which is a constant marker of its extent, this is a clear proof that there are no boundaries in extension, and consequently, that it is infinite. Equally, when we think of the duration of time, our idea of its duration cannot be erased from our mind, we can’t conceive that there is no time, just as we can’t conceive that there is no extension, this idea alone is therefore a clear proof that time is and not only that it is, but also that it has necessarily always been, and that it always will be, and consequently that it is infinite in duration, and that is actually how we conceive of it.
From the knowledge we naturally acquire of these two kinds of infinites, we pass along naturally to the knowledge of another kind of infinity: infinity in number and multitude, which is necessarily included in the totality of these two infinities that I’ve just spoken of. For, in the totality of extension, which is infinite, as I’ve shown, we necessarily find there, and we clearly see there the wherewithal to make an infinite number of particular portions of extension, as, for example, to observe an infinite number of feet, an infinite number of yards, and an infinite number of leagues; for it’s quite obvious that no finite number of leagues, or any other particular kind of extension can be equal to an infinite extension, and consequently an infinite number of leagues would be necessary to equal an infinite extension. Similarly, in the totality of the infinite and successive duration and of time, we necessarily find there, and also observe there the materials to form, not only an infinite number of days, but also an infinite number of years and centuries, for we also clearly observe that a finite number of years or centuries can’t equal the infinite duration of time, and consequently, that nothing less than an infinite number of years and centuries are necessary to equal this, i.e., to equal the infinite duration of time.
There would be no purpose in saying here that, in an infinite extension, there would always necessarily be a greater number of feet than of yards and a greater number of yards than of leagues. Equally, in that in the infinite duration of time, there would also necessarily be a greater number of days than years, and a greater number of years than centuries, and therefore, according to this doctrine, there would be infinities larger than infinity itself, i.e., there would be in extension an infinite number of yards that is larger than the infinite number of yards; and that the infinite number of yards would be larger than the infinite number of leagues in the same extension. If there were in the successive duration of time an infinite number of days, which would be larger than the infinite number of centuries that would be there, which is completely repugnant to reason, it will be said, since nothing can be larger than infinity. To that I respond that, in an infinite extension, there would still be more feet than yards, and more yards than leagues. Equally, that in the successive duration of time, there would truly be more days than years, and more years than centuries; but since, in the totality of extension, there would necessarily be an infinite extension to cover and in the totality of the duration of time there would be an infinite duration to cover, there would always be, in extension, endless leagues and yards, and there would be no more of an end to these than for the others, they wouldn’t, therefore, be more finite or more infinite than each other. Similarly, in the successive duration of time, there would always be nonstop years and centuries to count, as well as to count the days and hours; and since there is no end to the tally of either things, they wouldn’t, therefore, be any more finite or more infinite than each other, and still, my arguments retain all their force.
It might be said, again, with Mr. de Cambrai, that no extension or composite can be infinite, since the whole of extension and all composites are nothing but heaps of many bounded and finite units, which all together can never compose an infinity, since nothing that is limited and finite can form an infinity. Here is his argument[826];
My conclusion is that any composite can never be infinite. All its real parts, which are limited and measurable, can only compose something finite. No collective or successive number can ever be infinite. Number means a cluster of units, which are really distinct and reciprocally independent of each other, to exist and not exist. A cluster of units that are reciprocally independent of each other means a whole that can be diminished, and which is, therefore, not infinite[827]. When a whole is lessened, it is not infinite. That which is less is limited, for that which is beneath infinity is not infinite. If this whole is lessened, it is limited. Since it is only lessened by the removal of a single known unit, it clearly follows that it wasn’t infinite, even before this unit was taken from it; for you can never make an infinity from a finite composite, by adding a single finite unit to it[828]. It’s certain that the same number was larger before the removal of a unit, than it is after it’s removed. After the removal of this limited unit, the whole is no longer infinite; thus, it wasn’t infinite before this removal, either.
This whole argument can, I think, be boiled down to two main points, the first in knowing whether a number or a multitude as it may be of limited, finite, and mutually independent units, can or cannot ever compose an infinite whole. The second is that if a number of a totality, which would be composed of an infinite multitude of limited unities which a
re mutually independent, ceased to be infinite by the removal of certain limited units, or it wouldn’t cease to be infinite; for this, it seems, is where the greatest difficulty lies in the objection proposed above. To that I reply: 1). That a number, or an infinite number of bounded and mutually independent units, when joined together, would necessarily form a whole, which would be of an infinite extent. Of which here’s the clear proof: each unit in this infinite multitude of limited units, which would already have its extension in itself, independently of the extension of any other unit, which would also have its extension independently of all the rest, would necessarily make the extension larger, and the more similar units were added to these first two, all the more also would the extension increase, and it would necessarily increase in proportion to the amount of units added. Now, there would be an infinite multitude of limited units joined together in a totality, which would be composed of all these units; thus, it would be truly and actually of an infinite extension, and consequently, it is evident that an infinity can be made of an infinite multitude of limited and finite unities; this is something we conceive quite clearly, and not only do we clearly conceive that infinity can be composed of an infinite multitude of limited unities, but we also clearly conceive that it can be composed and that presently there is, in the totality of the numbers of the infinities of infinites, all composed of an infinite multitude of limited and finite units.
82. CONSEQUENTLY, THEY SHOULD ALSO RECOGNIZE THAT MATTER RECEIVED ITS MOTION FROM ITSELF, WHICH IS, HOWEVER, CONTRARY TO THEIR VIEWS.
Here is the clear proof of this. It is obvious that there is, in the totality of extension, whether we think about it or not, an infinity of lines, or at least the wherewithal to make an infinity of lines, which would all be infinite, since they would all be as extensive in length as the very totality of extension, which is infinite in all its dimensions. Now, it is clear that for each of these lines to be infinite in length, it must necessarily be composed of a number or an infinite multitude of subordinate parts, such as, for example, a number or an infinite multitude of atoms, which are all independent of each other, for if these parts or atoms were not infinite in number, they could clearly not form an infinite line. Since, then, this line is necessarily infinite, it must also be composed of a number or an infinite multitude of limited parts, and thus, clearly, in each line there is also a number or an infinite multitude of atoms and limited parts, all independent of each other. But there obviously is, in the totality of extension, the wherewithal to make infinities of lines, equal to those I’ve just mentioned, which are all infinite and which are all composed of a number or an infinite multitude of atoms and limited parts; thus, there is obviously, as I said, an infinity of infinities in the totality of extension and in the totality of numbers. There is no reason to be surprised when I say that there are infinities of infinites in extension and in numbers, since all those who accept the divisibility of matter to infinity must also recognize an infinity of parts in each part of matter, otherwise it couldn’t be infinitely divisible; and if each part of matter contains an infinite number of parts, then there must also be infinities of infinite numbers of parts in matter.
Far, then, from saying, like Mr. de Cambrai, that any composite can never be infinite and that everything which has limited and measurable parts can only compose something which is finite and that all number, whether collective or successive, can never be infinite, it must instead, by following the clearest light of reason, say that a simple and single unit, which would have no parts, can never be infinite, since a single and simple unit which would have no parts would have no extension, and, without any extension, or having only quite little thereof, it is clear that it could never be infinite, which is necessarily and essentially infinitely extended.. And if a single and simple unity, which would have no parts, can never be infinite, then infinity in extension or number must necessarily be composed of a number, or an infinite multitude of units, or parts that are joined together. This entire argument is clearly evident. But Mr. de Cambrai had formed the imaginary and chimerical idea of an all-powerful God, who is infinitely perfect in all sorts of perfections, and so he must also have formed the idea of an imaginary and chimerical infinity, since he couldn’t find in the idea of any true infinite the imaginary perfections he wished to attribute to His God. 2).
As for what he adds, that, by removing from any composite, even a single unit, this compound would necessarily be lessened and diminished, and that, consequently, it wasn’t infinite prior to the removal of this unit, since an infinity can never be made of a finite composite, by adding a single finite unit to it, and consequently, again, that no composite can be infinite, to this I respond that nothing can truly and really be added to something that is truly infinite, as to its infinite aspect, and that similarly nothing real can be removed from it, since nothing can be annihilated; and thus, since the hypothesis of this removal of a single unit from an infinite composite is impossible, the argument proves nothing; especially since an impossible hypothesis can only produce absurdities. But, since this removal of some unity from an infinite composite can be done at least in thought, and we can conceive of some of these unities as removed from the others, or as if annihilated, I say in second place that, even in this hypothesis, as impossible as it may be, the composite wouldn’t fail to always be infinite, at least on the side in which nothing was removed from it; it would indeed be lessened and diminished where the unit was removed from it, but otherwise it would necessarily always remain infinite. I even say that no particular removal of its parts, as large as it may be, would keep it from being infinite: as no removal of parts can exhaust infinity, and infinity can’t be exhausted by any removal of its parts: it clearly follows that no removal of its parts can keep it from being always infinite, at least, as I’ve said, where nothing was removed. It is clear and obvious that the thing would go thus and that it couldn’t even go otherwise in this hypothesis. All that is conceived by clear and distinct ideas, which clearly show the truth of things.
83. IT’S AN ERROR AND AN ILLUSION TO CONFUSE THE INFINITE BEING WHICH DOES EXIST WITH A SUPPOSEDLY INFINITELY PERFECT BEING WHICH DOES NOT EXIST, AND AN ILLUSION TO CONCLUDE THAT SINCE THE FIRST EXISTS THEN THE SECOND ONE DOES TOO.
But who can conceive in this way, with clear and distinct ideas, the imaginary and chimerical infinite that Mr. de Cambrai and all our God-cultists propose for worship as an all-powerful and an infinitely perfect being in all manner of perfections, even though it has no visible and perceptible perfection, and has neither form nor shape, or even any part, or any extension? Certainly, nobody can form any true idea of such an infinite. Even the most spiritual among our Christ-cultists can’t form any true idea of it, and so I conclude again, evidently, against them, with this other truth, which is that the idea they form of their God, does nothing to prove His existence; and it is surprising to see intelligent people claiming to prove His existence in this way. Let us examine this more closely.
Here is their reasoning and their argument, which they think are conclusive. We must, they say[829], attribute the existence of God to something that is clearly conceived as contained in the idea which represents it. This is the general principle of all the sciences; and present and necessary existence is clearly contained in the idea of God, i.e., in the idea of an infinitely perfect being; thus, God, or the infinitely perfect being, exists. Our new Cartesian God-cultists think and believe they’ve been successful in conclusively proving, with this argument, the existence of their God. But it’s obviously nothing but an illusion to imagine that; for it’s clear and evident that this argument doesn’t conclude in favor of the existence of a God or an infinitely perfect being, except that it supposes that this being, which is conceived of as infinitely perfect, is truly something real and not only something imaginary; for if it didn’t suppose that it truly was something real, it would be ridiculous to conclude in favor of His existence from the mere fact that one has an idea thereof. But it’s not a case here of si
mply supposing that the supposed being which is conceived of as infinitely perfect, truly is something real; one must prove it, since it's being denied, and since the above argument doesn’t prove that the supposed being who is conceived of as infinitely perfect truly is something real, but it only assumes this, instead of proving it, it is clear that the above argument is sheer sophistry, which proves nothing; and the clear mark of that is that if it proved anything, it would be as easy to prove by the same argument that an infinitely perfect man existed, that an infinitely perfect horse existed, that an infinitely perfect bird existed, or all other such things existed, because it’s just as easy to imagine an infinitely perfect man, an infinitely perfect horse, and an infinitely perfect bird, as to imagine any other infinitely perfect being, and it would be as easy to prove by this argument that an infinitely perfect man existed, than an infinitely perfect horse or an infinitely perfect bird existed, than to prove than another infinitely perfect being existed, because it’s obvious that it would be as easy to apply the argument in either case, and it would be as easy to say it in favor of either thing. We must attribute to a thing that which is clearly conceived of as contained in the idea which represents it; this is the general principle of all the sciences; now, necessary existence is clearly contained in the idea of an infinitely perfect man, in the idea of an infinitely perfect horse, and in the idea of an infinitely perfect bird, therefore, the infinitely perfect man exists, therefore, the infinitely perfect horse exists, therefore, finally, the infinitely perfect bird exists. All these conclusions are equally derived from the same principle and the same reasoning to which our God-cultists appeal to demonstrate the existence of their God. But would it not be ridiculous to demonstrate, or to claim to demonstrate, with this fine piece of argumentation, the actual existence of an infinitely perfect man, an infinitely perfect horse, or an infinitely perfect bird? Yes, certainly, this supposed demonstration would be ridiculous, and our God-cultists would also jeer at anyone who offered them such a demonstration; how, then, can they claim to use it to demonstrate the existence of their God, since this supposed demonstration is no less ridiculous in either case; and it is shocking, as I’ve said, to see intelligent people daring to even propose such an argument.