This question is about the Tractatus, and the role of different logics.
The answer I gave is explaining the fact that the logic you use is largely conventional, in that any alternate logic, once precisely defined, can be embedded in an axiom system on top of first order logic, and if the other logic is complete in the sense of Godel, that it can in some sense produce all first order consequences of a set of axioms, then you can embed first order logic back. These results are entirely analogous to the mutual equivalence of any two Turing complete computers, and this stuff confuses non-computer people endlessly.
I see no justification for deletion.
The existence of different logics is interesting, but not particularly relevant, because of Godel/Turing universality. If you have a statement about possibilities, a statement in modal logic, you can encode it in a semantics about possible worlds, in a first order logical form about an expanded universe of discourse (see Kripke semantics). Further, if you have a "fuzzy logic", you can speak about it in an appropriate axiomatic mathematical system which includes real numbers, and makes a map between propositions and fuzzy values.
There are also Baysian probability calculi which can be thought of as a different logic, some people regard quantum amplitudes as a logic, while other schemes regard permission as in the logic. What you put in the logic and what you put in the axioms is largely up to you.
But the main point is that the ordinary first order logic is complete, it will produce any logical consequence of any axioms, and this was proved by Godel. This means that if you have a mathematically precise description of some other logic, you can always talk about this logic in terms of first order logic, and consider the other logic as axioms on top of first order logic. This is not a natural point of view, but it is a possible point of view.
The universality of first order logic is the logical analog of Turing universality--- that a finite complexity computer with unbounded memory can simulate any other computer with suitable programming. The formalism of logic is like the instruction set, the axioms are like the instructions of the program, and the deductions are the running of the program. A Turing machine can do Godel deduction (you can program a computer to deduce in first order logic) and Godel deduction can describe a computer, so the two results are essentially equivalent, and anything that can be stated in any coherent logical system is something that is meaningful for a computer to analyze and interpret.
So there really is only one type of logic, and Wittgenstein is mostly right. Althogh it is a mistake to attribute this to Wittgenstein, who was not as mathematically or logically precise at the mathematicians and logicians of the early 20th century in whose footsteps he followed, not as precise, nor as iconaclastic, as Russell, and did not contribute commensurately to the formal developments as Russel did. Further, one may say that Wittgenstein's ideas have a sonority and a lack of mathematical precision that leads those in techical fields to perhaps use the phrase "running one's mouth". The proper attribution of first order logic, the recognition of its importance in philosophy, and the associated logical postivism, better belongs to Hilbert, Frege, Boole, Quine, Godel, Turing, Russel, Whitehead and others who come before. It continued with those who built the Vienna school, including Carnap, which made logical positivism the ascendent philosophy until the 1970s.
The use of predicate language to remove ambiguity, and the thesis that all statements should be formulated in some predicate language about precise observable criteria, is the central tenet of logical positivism, which flourished in the mid-20th century, but took a beating in the 1970-90s. This coincided with the popularity of the illicit drug cannabis, and once the influence of the cannabis smokers wanes, it should be rehabilitated.