Editing Tractatus Logico-Philosophicus (section)

===Proposition 6.''N''===
At the beginning of Proposition 6, Wittgenstein postulates the essential form of all sentences. He uses the notation <math>[\bar p,\bar\xi, N(\bar\xi)]</math>, where
* <math>\bar p</math> stands for all atomic propositions,
* <math>\bar\xi</math> stands for any subset of propositions, and
* <math>N(\bar\xi)</math> stands for the negation of all propositions making up <math>\bar\xi</math>.

Proposition 6 says that any logical sentence can be derived from a series of [[Logical NOR|NOR]] operations on the totality of atomic propositions. Wittgenstein drew from [[Henry M. Sheffer]]'s logical [[theorem]] making that statement in the context of the [[propositional calculus]].  Wittgenstein's N-operator is a broader [[infinitary]] analogue of the [[Sheffer stroke]], which applied to a set of propositions produces a proposition that is equivalent to the denial of every member of that set.  Wittgenstein shows that this operator can cope with the whole of predicate logic with identity, defining the quantifiers at 5.52, and showing how identity would then be handled at 5.53–5.532.

The subsidiaries of 6. contain more philosophical reflections on logic, connecting to ideas of knowledge, thought, and the ''[[A priori and a posteriori|a priori]]'' and [[transcendence (philosophy)|transcendental]]. The final passages argue that logic and mathematics express only tautologies and are transcendental, i.e. they lie outside of the metaphysical subject's world. In turn, a logically "ideal" language cannot supply [[Meaning (philosophy of language)|meaning]], it can only reflect the world, and so, sentences in a logical language cannot remain meaningful if they are not merely reflections of the facts.

From Propositions 6.4–6.54, the Tractatus shifts its focus from primarily logical considerations to what may be considered more traditionally philosophical foci (God, ethics, meta-ethics, death, the will) and, less traditionally along with these, the mystical. The philosophy of language presented in the Tractatus attempts to demonstrate just what the limits of language are – to delineate precisely what can and cannot be sensically said. Among the sensibly sayable for Wittgenstein are the propositions of natural science, and to the nonsensical, or unsayable, those subjects associated with philosophy traditionally – ethics and metaphysics, for instance.<ref>TLP 6.53</ref>  Curiously, on this score, the penultimate proposition of the Tractatus, proposition 6.54, states that once one understands the propositions of the Tractatus, he will recognize that they are senseless, and that they must be thrown away. Proposition 6.54, then, presents a difficult interpretative problem. If the so-called 'picture theory' of meaning is correct, and it is impossible to represent logical form, then the theory, by trying to say something about how language and the world must be for there to be meaning, is self-undermining. This is to say that the 'picture theory' of meaning itself requires that something be said about the logical form sentences must share with reality for meaning to be possible.<ref name=":0">{{Cite journal|last1=Morris|first1=Michael|last2=Dodd|first2=Julian|date=2009-06-01|title=Mysticism and Nonsense in the Tractatus|journal=European Journal of Philosophy|language=en|volume=17|issue=2|pages=247–276|doi=10.1111/j.1468-0378.2007.00268.x|issn=1468-0378}}</ref> This requires doing precisely what the 'picture theory' of meaning precludes. It would appear, then, that the metaphysics and the philosophy of language endorsed by the Tractatus give rise to a paradox: for the Tractatus to be true, it will necessarily have to be nonsense by self-application; but for this self-application to render the propositions of the Tractatus nonsense (in the Tractarian sense), then the Tractatus must be true.<ref name=":1">{{Cite book|title=Routledge Philosophy Guidebook to Wittgenstein and the Tractatus Logico-Philosophicus|last=Morris|first=Michael|date=2008|publisher=Routledge|isbn=9780203003091|pages=338–354|oclc=289386356}}</ref>

There are three primarily [[dialectical]] approaches to solving this paradox<ref name=":0" /> 1) the traditionalist, or Ineffable-Truths View;<ref name=":1" /> 2) the resolute, 'new Wittgenstein', or Not-All-Nonsense View;<ref name=":1" /> 3) the No-Truths-At-All View.<ref name=":1" /> The traditionalist approach to resolving this paradox is to hold that Wittgenstein accepted that philosophical statements could not be made, but that nevertheless, by appealing to the distinction between saying and showing, that these truths can be communicated by showing.<ref name=":1" /> On the resolute reading, some of the propositions of the Tractatus are withheld from self-application, they are not themselves nonsense, but point out the nonsensical nature of the Tractatus. This view often appeals to the so-called 'frame' of the Tractatus, comprising the preface and propositions 6.54.<ref name=":0" /> The No-Truths-At-All View states that Wittgenstein held the propositions of the Tractatus to be ambiguously both true and nonsensical, at once. While the propositions could not be, by self-application of the attendant philosophy of the Tractatus, true (or even sensical), it was only the philosophy of the Tractatus itself that could render them so. This is presumably what made Wittgenstein compelled to accept the philosophy of the Tractatus as specially having solved the problems of philosophy. It is the philosophy of the Tractatus, alone, that can solve the problems. Indeed, the philosophy of the Tractatus is for Wittgenstein, on this view, problematic only when applied to itself.<ref name=":1" />

At the end of the text Wittgenstein uses an analogy from [[Arthur Schopenhauer]] and compares the book to a ladder that must be thrown away after it has been climbed.