Descartes' linchpin

In his second meditation, Descartes makes the claim that if you were to melt and reshape or otherwise significantly alter a piece of wax, one could still know it to be wax, because they know the essence of wax. He claims, ". . . I do not grasp what this wax is through the imagination [the senses]; rather, I perceive it through the mind alone. (Tanner 31)" Here the senses are capable of playing tricks on the mind, due to their lack of perfection, therefore they are to be disregarded in determining what an object is in itself. However, Descartes mentions, if one were to "observe men crossing the square (Tanner 32)", one solely uses judgement to determine that they are men, and that senses just reveal to us qualities of particular men. While I do not disagree with any of these ideas, I believe that Descartes stops just shy of the point he appears to be trying to make. Beginning with the example of the wax–which may not benefit from being called "wax", and might better be represented by the symbol "X"– if one were to take everything that made up what we know as X and completely rearrange it so that it no longer had any of the original qualities of X and instead only had qualities that make Y, we would certainly no longer have X, but Y. However, if we were to take away all but one quality of X, we would not have Y, and X would remain, significantly altered, but still X. While the senses are known to be deceptive, it is not deception to say that X can not exist, therefore neither can our understanding of X, without a single quality of X. It is through the natural sciences that we can come to know a single quality of X, and it is off of this premise that we base our understanding.

How then does it follow that we know a man crossing the square is indeed a man and not something else entirely? Descartes argues we know this by judgement, a faculty only of the mind, but I'm inclined to add on to this idea. If we have seen men cross the square before, anything that closely resembles what we experienced at that first crossing will appear to us as men crossing the square. Every subsequent man crossing the square will only be so because of the first experience we had of a man crossing the square. However that first experience of a man crossing the square had to have made itself known to us without any previous experience, requiring the use of the senses coupled with contemplation, for we can not know man without knowing his qualities just as we can not have X without any of the qualities of X.