William Large

What is very important concerning the example of the wax in the second meditation is that it follows on from the extension of the cogito. We tend to associate the notion of thinking simply with the reflective or conceptual thought, but for Descartes the cogito includes all aspects of mental activity, such as remembering, wishing, doubting and so on. Most importantly of all, with respect to the example of wax it includes sensory perception. Again we need to remind ourselves of the last quotation:
For even if, as I have supposed, none of the objects of imagination are real, the power of imagination is something which really exists and is part of my thinking. Lastly, it also the same ‘I’ who has sensory perceptions, or is aware of bodily things as it were through the senses. For example, I am now seeing light, hearing a noise, feeling heat. But I am asleep, so all this is false. Yet I certainly seem to see, to hear, and to be warmed. This cannot be false; what is called ‘having a sensory perception’ is strictly just this, and in this restricted sense of the term it is simply thinking [AT VII, 29].
Now what Descartes wants to convince us by the end of the second mediation is that I truly understand things through my mind and not my senses. This, if you like, is a classic rationalist position in philosophy, but it is also difficult for us to understand, for we take it for granted that we grasp the true nature of things through our senses and not through our minds. The strategy, therefore, of the second meditation is to show that knowledge that we think that we gain through the senses is in fact less distinct than that knowledge we gain through our mind. Is therefore to reverse the common sense point of view that seems to make the external world more knowable than the inner world of the mind. By the end of this mediation, Descartes hopes to have convinced us of the reverse: that the mind is much better known than the body. We think that what we know the best are particular things:
Let us consider the things which people commonly think they understand most distinctly of all; that is, the bodies which we touch as see. I do not mean bodies in general – for general perception are apt to be somewhat confused – but one particular body. Let us take for example, this piece of wax [AT VII, 30].
So the first thing that Descartes does it lists the knowledge that we seem to gain from this piece of wax through our five senses:

fragrance of flowers
sweetness of honey
knocks when rapped
hard and cold
white, one inch cube

Now Descartes’ point is that the senses seems to tell us exactly what the wax is and do so in the most clear and distinct way, so why at all should we say that we know things better through our minds, than through our senses, when exactly the opposite seems to be the case:
In short, it has everything which appears necessary to enable a body to be known as distinctly as possible [AT VII, 30].
It should not be a surprise for those who know something about the history of philosophy that Descartes introduces a specific problem to undermine our trust in our senses and that is change. As soon as the wax is placed in the heated room that it undergoes a change. If we take only our senses into consideration is appears to have becomes something entirely different

no fragrance of flowers
no sweetness of honey
no knock when rapped
not hard and cold
not white, not a one-inch cube

Yet even though this wax has changed completely, I am sure, and everyone else is sure, that I am still looking at the same wax. So what is it that remains beyond the change, or despite the change, such that I can be certain that I am still sensing the same wax because of its change through the heat of the room?
But does same wax remain? It must be admitted that it does; no one denies it, no one thinks otherwise. So what was it in the wax that I understood with such distinctness [AT VII, 30]?
My response would be that I still see the wax as wax, even though it has changed. But we have to be careful by what we mean by seeing in this sense, don’t we? For we can’t mean what we see by the senses, for it is precisely all this content that has changed. It must be that I see something else that does not change, that to some extent is beneath the surface changes of the wax, and expresses the wax itself. But what is it that I see? Is it also something that is the seen in the very way that I touch the hardness of the wax, or smell its fragrance? Can I touch the wax itself?

To try and answer this question, Descartes asks to use our imagination. It asks us to strip away all the qualities of the wax that appear to change, its fragrance, sweetness, hardness, and colour, and see what we are left with. If we do this, Descartes argues, we are left only something extendable and flexible:
Let us concentrate, take away everything which does not belong to the wax, and see what is left: merely something extended, flexible and changeable [AT VII, 30-1].
But what is the status of this ‘something’ that is extendable and flexible. Again we might be tempted to think it as some particular physical shape. So we imagine in our minds some particular shape, something round or square and so on. But we know that wax can take on innumerable sizes that it is not possible for to actually imagine. This means that my knowledge of this ‘something extended, flexible and changeable’ extends beyond my imagination, which only presents things in particular shapes and sizes. What Descartes is trying to get us to see is that the idea of a body is precisely that: an idea, and it is not something that we see with our senses, and yet we would see nothing at all without this idea. It is only because I have an idea of wax that remains the same through change that is possible to attribute these changes to the same thing, but this idea of wax itself is dependent on the idea of body in general as ‘something extended, flexible and changeable’:
But what is meant here by ‘flexible’ and ‘changeable’? Is it what I picture in my imagination: that this piece of wax is capable of changing from a round shape to a square shape, or from a square shape to a triangular shape? Not at all; for I can grasp that the wax is capable of countless changes of this kind, yet I am unable to run through this immeasurable number of changes in my imagination, from which it follows that it is not the faculty of imagination that gives me my grasp of the wax as flexible and changeable [AT VII, 31].
What is at stake here for Descartes is that there is a difference between grasping something and imagining it. Thus the reason why I can say that the wax is remains the same though it goes through many changes, is that I can conceive of the idea of extension in my mind which can go through ‘immeasurable number of changes’ whilst staying the same, and that this idea is not the result of senses or the imagination, but is precisely what allows me to sense or imagine a particular body:
But what is this wax which is perceived by the mind alone? It is of course the same wax which I see, which I touch, which I picture in my imagination, in short the same wax which I thought it to be from the start. And yet, and here is the point, the perception I have of it, is a case not of vision or touch or imagination – nor has it even been, despite previous appearances – but of purely mental scrutiny [AT VII, 31].
It follows from this for Descartes that the mind is therefore better at knowing than the body, since it is the idea of wax that determines by sensation or imagination the characteristics of a particular piece of wax, but we shall have to wait to see why this is the case.