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.

I see that you edited it within the last hour or so. I appreciate your attempt to tone down your self-admittedly improper writing habits.

I took the liberty of editing it as well. You'll notice that I corrected a number of spellings (and because I only recently learned how to do this quickly, I used Gödel instead of Godel). I also removed your last sentence, relating to pot-smokers.

I have restored the answer, largely due to the lack of tangential offensive comments. However, I think that both commentators on the question have valid criticisms of your answer.

To that end, this is sort of an experiment. If many downvotes or flags get raised against your answer, saying it's off topic or something, than perhaps I'll regret restoring it. But that's in the community's hands, and not mine.

• I support this action. The last sentence about pot-smoking does not belong there (if only because there's absolutely no credible evidence presented as to its validity), but once that's edited out, the answer looks OK to me in form. Obviously there are still some content disputes, but those should be hashed out by the community with votes, not by unilateral deletion of the answer. Apr 17 '12 at 6:41
• I was basing this on my assumption that Derrida and the French continental school was a collection of pot smokers. I based this on being offered Marijuana by a Derridian professor, and on Derrida's popularity with the Paris '68 crowd. The death of positivism was associated with the rise of new-age thinking and magical ideas which are clearly linked to cannabis, although I have been assured by a philosopher that in the Anglo-American tradition death of positivism wasn't about pot-smoking, but about restoring the idea of an objective observer-independent reality (as if positivism denied this). Apr 17 '12 at 7:22
• Thanks, mixedmath. Apr 17 '12 at 7:26
• @mixedmath: I do not admit that anything I wrote is improper--- rather when you try to tell the truth honestly, there is always a political order that opposes you, with people either consciously or not, attempting to suppress honest speech. This is not the fault of individuals, it is a collective effect. Apr 17 '12 at 18:31
• Saying that "Derrida and the French continental school was a collection of pot smokers" goes far beyond "trying to tell the truth honestly," and it seems disingenuous to pretend otherwise. This is not a debate site, and a polemical tone is rarely (if ever) appropriate here. We're here to convince others of the rightness of our views-- rather, we are here to provide informed, fact and analysis based answers to specific, posed technical questions relating to the philosophical tradition. One should resist the temptation to use the question as a coat-rack upon which to hang one's own opinions. Apr 18 '12 at 7:29
• @MichaelDorfman: But weren't they? I always suspected so, but this doesn't get into history books or biographies very easily. It isn't necessarily an insult--- lots of people enjoy smoking pot (although I hate it personally). In this case, I was trying to tell a possible truth I was massively unsure of--- but it might still be true--- usually people correct you when you say something outrageous and false. Apr 19 '12 at 3:19
• .. A quick google search revealed this and quoting: ... reportedly, this reconciliation was due in part to Foucault's defense of Derrida after the latter was alleged to have been caught with marijuana in Prague ... . Here is another site: Jacques Derrida clarifies the slippery status of many drugs with his deconstruction of faulty terms such as “natural” that get called into play on both sides of the debate over drug use ... . Apr 19 '12 at 3:23
• On the other hand this book suggests that the 1980 charges against Derrida were trumped up, as does this book Apr 19 '12 at 3:34
• The drug charges against Derrida were infamously trumped up; but that's not the point. The point is that it has no place in a question concerning the use of alternate logics in the Tractatus. Our aim should be to answer the OP's question, not to use the question as a catalyst to trot out our own hobby-horses. Apr 19 '12 at 6:34