Critique of Wittgenstein's Tractatus Logico-Philosophicus

It may be asked whether impudent perversity or idle vanity impelled me to write, let alone submit, the following article. I can only attest to what my powers of insight tell me, that this work sprung not from a sense of my strengths, but rather my limitations. For it occurred to me that I am good for nothing but the strange activity to which I toil for proficiency in the following pages. It would not in the least surprise me if my philosophical gifts turned out to be as moderate as all my others.

A knotty fallacy has survived over fifty years of philosophical debate: namely, that Wittgenstein advocated a logical atomism something like that of the Vienna Circle. He didn't, something which becomes clear in the opening lines of the Tractatus:

1.1 The world is made up of facts, not things

Right from the off Wittgenstein makes a distinction between ‘facts' or ‘states of affairs' and ‘things' or ‘objects'. It is my thesis (or, rather, restatement of Wittgenstein's thesis) that this sets up an ontology where logical space is divided up both continuously (‘facts') and discretely (‘things'). I have borrowed unabashedly from natural science here, and my point can be illustrated simply enough. To see a state of affairs is to be able to divide up logical space infinitely â€' how it is divided is determined by the frame of reference. The sciences attain objectivity and agreement by operating in a shared frame of reference. ‘Things', however, “subsist independently of what is the case”: that is, they are the same no matter what the frame of reference. Objects are “simple” â€' they are atoms which make up the possibility of the world.
So we see that, though Wittgenstein favours a logical atomism of sorts, it is an unexpected variety. The question arises: why, if he says the world is made up of facts and not things, does he feel the need to define things at all? Because he was setting up a realm of facts circumscribed by their possibility been limited to configurations of objects. He was, I think, trying to account for what Jacques Lacan was later to call the “real” those grey areas in human knowledge which systematically shape our actual knowledge, the “hole in the donut” as Zizek called it. Wittgenstein said that the Tractatus should be divided into two parts, that which was written and that which was unwritten: and the second part, the unsayable, the mystical, was precisely the part that was most important. The main thesis thus emerges as this: the world must mirror the logical structure of language for us to be able to say anything with sense (Frege's bedeutung) â€' but there is much more to the world than this. Hence, a thoroughgoing anti-realism props up the frame of the Tractatus.
More to follow.

Question:can 'facts' be combined - in other words, are there gradations of facts? In a word, can they be defined such that pUq=u where u is the universal set and p, q and u are facts? Certainly so - from the sentence "there is a tree" there can be ascertained the consequent "there are leaves". One might say: "here is atree without leaves". But a rejoinder is easily fashioned, namely, that the tree's not having leaves must be included in the universal set for p and q to be composite.

Question: can the world be the universal set?; that is, can the totality of facts be considered itself a fact? Recall that facts attain objectivity only insofar as we impute to them a shared frame of reference. Facts divide up logical space with infinite potentialities. In short, we define facts by way of divisons, and preceisely for this reason they are what I call inertial: they are defined by the relations between the parts, rather than the parts themselves. So when we ask if the world is itself a fact, we mean the totality of relationships - and we are asking if this itself can be a set. It is my assertion that is a problem that cannot be resolved. For the set of all relationships is surely biggger than the set of all sets. Wiitgenstein thus fell into the trap of what Rusell called the Reflexive Fallacy, which Godel was to identify as the problem of one set of transformations relying for verification on another, anterior, set of transformations.