The essence of material things, and the existence of God considered a second time

 

V. FIFTH MEDITATION: The essence of material things, and the existence of God considered a second time 

A. The ideas of corporeal things are not chimerical 

Thesis: Whereas the act of thinking of corporeal things is subject to my will (I can attend to them or not as I please), certain of the contents of our thought of them (i.e. their nature, essence) are not: “they are not my invention but have their own true and immutable natures." 

Proof: The ability to demonstrate mathematically that certain determinations hold of necessity with reference to general ideas of spatial extension, e.g. the properties of a triangle, proves that I cannot have invented these ideas. For if these ideas were my inventions, it would be in my power to add or subtract determinations from them at will, e.g., I could, at a whim, change things so that the sum of the angles of a triangle equals three right angles instead of two. However, once mathematical methods enable me to perceive clearly and distinctly that certain properties belong to ideas of extension of necessity (e.g. the necessary equality between the sum of the angles of any triangle and two right angles), I clearly and distinctly perceive that it is not in my power to take away or alter this determination at will. For the same reason, I also clearly and distinctly perceive that I could not have put it in there in the first place; for whatever is in the power of my will to add to an idea must also be in my power to take away from it. Thus, "whether I want [these determinations in the ideal or not, even if I never thought of them at all when I previously imagined the triangle," they necessarily belong to it; and this, according to Descartes, proves beyond any possibility of doubt that these properties "cannot have been invented by me," but instead pertain to the nature of triangles as such. From this it follows that the idea of a triangle – the thing to which these uninvented properties belong - also cannot have been invented by me and therefore (is not a chimera but) has objective reality: a determinate nature, or essence, or form of the triangle which is immutable and eternal, and not invented by me or dependent on my mind." And the same holds true for all extended beings in which we clearly and distinctly perceive properties that belong to them of necessity which the imagination can neither have added to them originally nor subtract from them afterwards. 

Having established that ideas of extended beings are not chimerical and so may possibly exist, the task awaiting Descartes in the Sixth Meditation is to prove that such things actually exist. 

NB. For Descartes, corporeal reality is res extensa (extended being). This means that there is no real distinction between body and space, i.e. the notion of 

empty space is a contradiction (a chimera): "There is no real difference between space and corporeal substance. It is easy for us to recognize that the extension constituting the nature of a body is exactly the same as that constituting the nature of a space. There is no more difference between them than there is between the nature of a genus or species and the nature of an individual. Suppose we attend to the idea we have of some body, for example a stone, and leave out everything we know to be non-essential to the nature of body: we will first of all exclude hardness, since if the stone is melted or pulverized it will lose its hardness without thereby ceasing to be a body; next we will exclude color, since we have often seen stones so transparent as to lack color; next we will exclude heaviness, since although fire is extremely light it is still thought of as being corporeal; and finally we will exclude cold and heat and all other such qualities, either because they are not thought of as being in the stone, or because if they change, the stone is not on that account reckoned to have lost its bodily nature. After all this, we will see that nothing remains in the idea of the stone except that it is something extended in length, breadth and depth. Yet this is just what is comprised in the idea of a space - not merely a space which is full of bodies, but even a space which is called 'empty' (vacuum)." (Principles II,11) 

Gloss. To understand this, you must not confuse the insensibility of certain kinds of matter with an idea of empty space. E.g. to see only blackness in a region of space (e.g. through a telescope) is not to see empty space; it simply means that our eyes are not sufficiently sensitive to see whatever corporeal being may be present in that region. Indeed, empty space is, by definition, not an object of a possible sense perception: perception requires that there be something capable of affecting our sense organs; since such affection is only possible by means of corporeal causes acting on our (equally corporeal) organs of sensation, it follows that empty space can have no causal interaction with our senses, or, indeed, with any body whatsoever. Accordingly, the possibility of empty space cannot be established empirically but only by rational (purely conceptual) considerations alone, if at all. In the text cited above, Descartes makes the conceptual point that it is impossible to abstract out everything essential to body without also abstracting everything that is essential to space. The implication is that there is no conception we can form to give the words "empty space'a meaning (e.g. the very question itself as to whether a vacuum exists, or is possible, is empty, devoid of meaning, nonsensical). 

B. Descartes's ontological proof for the existence of God (1) I find in me the idea of God, a supremely perfect being. (2) I perceive in this idea that actual and eternal existence belongs to the nature of God of necessity. 

(3) Since actual, eternal existence belongs to the idea of God of necessity, it is impossible for me to think the nature of God without also thinking that actual existence pertains to God. (4) Since a property I cannot remove from the nature of thing I also cannot have originally added to it, actual existence belongs to the nature of God in precisely the same way "I prove of any shape or number that some property belongs to its nature." (5) I thus know that God actually exists with "at least the same level of certainty as I have hitherto attributed to the truths of mathematics, which concern only figures and numbers." That is, the assertion that God exists can be known with certainty to satisfy the Fourth Meditation truth criterion. (6) Therefore, God exists.