Parts, Wholes, and A Thing Greater Than Any That Can Be Conceived

There has crept into my mind a certain skepticism that now takes up the greater part of my thought. I am not unsure that this is a worry I am merely restating and which has been brought up on numerous occasions in many discussions, but given its effect on me, I will share it nevertheless.

There are parts which make wholes. But it appears to me now that this may not be the case. I will waste little time in explaining my worry, for I think it straightforward.

If it is the case that it is the parts that make wholes, then statements of the form ‘1+4=5’ must be of the nature that nothing can be learned from them, but it is the case that knowing that ‘1+4=5’ is more than knowing ‘1’ or ‘4’ alone, so it must be the case that something new is added when a ‘truth’ of this kind is learned, it must of course be learned.

The ‘union’ of particulars then is greater than the particulars themselves, and though it is the particulars that comprise the object, their synthesis results in something greater than their mere union, its is not the case that the summation of ‘1’ and ‘4’ results in simply x = {1,4}, but it is instead something else than contained in x, which seems to go against all intuition.

So far, I have said little that is of surprise. It is here that I am conflicted, a natural question arises of the limits of this notion of wholes being greater than their parts, and I must inquire as to how far it applies.

In an attempt to explore what this comprises, I thought it ‘wise’ to approach it negatively, to explore where the notion is not contained. A natural place to start would be one where a statement is made that contains its own self, an analytic judgement. Of course this is entirely unhelpful (even if we were to ignore the problems with the category of judgments on a whole) since analytic judgments do not contain parts and wholes, since they are by their own definition contained in themselves, applying this line of thinking could not yield anything of benefit.

Since I can conceive of no manner of judgement (thought) wherein it is meaningful to say then that the whole is equal to its parts, I am forced to conclude at this time that this universally applies.

What occurs now to me is the Cartesian assertion of the third meditation, where it is claimed that an effect must have at least as much formal reality as does the cause, but this cannot hold, since if parts make wholes, and it is the case that the wholes are the effects of their parts, then it is necessarily always the case that every effect is greater than its cause.

And yet, ironically enough, though I have directed this towards the third meditation, it in effect provides a similar assertion, insofar as it is the conclusion of the extension of this line of thinking is concerned. If it is the case that everything may be conceived of as a part of something, for it cannot be the case that any object we know of can be but a part of something greater, then it must be the case that there is a whole containing every object that is a part of its, and the unity of every part is a synthesis which must be greater than everything conceivable, for it cannot be conceived, we are returned in this inversion to our original assertion.

HEHE