Meinongian Logic

MeinongianLogic is a family of logics where there are non-existent objects. Their primary advantage is that they solve a number of problems in fictional discourse, time, etc. in a uniform way. For example, "Luke is Anakin's son.", "My son expects the tooth fairy to visit him tonight.", and "George Washington was the first president of the United States." are all handled similarly. The non-existent Luke, Anakin, and tooth fairy, and the no longer existent George Washington still have the relevant properties.

This does not mean that they don't have their own problems. AlexiusMeinong?''s first theory of objects required that there be an object whose only property was that it was blue. Unfortunately, it also must have the property of only having one property.

DaleJacquette's book Meinongian Logic claims he has come up with a logic that "forestalls" and "neutralizes" not only the semantic paradox of the Liar and similar self-referential paradoxes, but also the classical limitative results of Church and G�del (to the effect that first order logic is undecidable and any theory as strong as Peano Arithmetic is incomplete). Here are some excerpts from the book:

: A uniquely Meinongian solution can be given to forestall formal semantic and set theoretical paradoxes and G�del-Church incompleteness and undecidability results.
: The consequences of forestalling paradox and limiting metatheorems in Meinongian logic are likely to seem liberating or disorienting, depending on one's philosophical and mathematical temperament. The fact that some mathematical propositions are undetermined in truth value in Meinongian logic might be regarded as conceding to G�del, Rosser, and Church the undecidability of the theory. But in trivalent semantics, decidability implies the existence of finite mechanical algorithms or recursive decision procedures for tripartitioning the semantic field, determining of any proposition whether it is true, false, or undetermined. The decidable tripartitioning of the semantic domain is theoretically available to the logic.
: To be complete and decidABLE does not mean to be completED and decidED. Unproven propositions like Goldbach's conjecture are not thought to threaten the decidABILITY of standard first order logic with arithmetic, and can similarly be regarded as posing no deep or special challenge to the decidability of Meinongian logic. If necessary, unproven and undisproven mathematical propositions can decidably be assigned the undetermined value, on modified intuitionist principles. More sophisticated results like G�del's and Cohen's proofs of the consistency and independence of the continuum hypothesis in classical set theory also go by the board in Meinongian logic, because of paradox and limiting metatheorem neutralization.

A few comments from a review of Professor Jacquette's book, published in Studia Logica, where the reviewer only had space to point out what he called "some of its more glaring errors":

"unfortunately its formalization goes seriously wrong"
"the logic contains several horrible mistakes"
"it is in Jacquette's formalization of his logic that the book first goes very seriously wrong"
"it is not completely clear what the rules of Jacquette's system really are. He never states them in general form"
"the soundless and completeness proof go rather badly wrong, partly because the logic is not sound over the model, but also because the inductions are incorrectly carried out"
"clearly a book with so many formal errors should not have been published as it is"

Another review: http://www.looksmarttrends.com/p/articles/mi_m2346/is_n428_v107/ai_21248810

I'll freely admit to only reading the summary above, but limiting your logic in order to prevent the Goedelian results is hardly new, and if the professor thinks it is new or even newsworthy, it does not say good things about his grasp of the subject and its history. Attempts to limit the math in that manner IIRC predate Goedel, whose proof in reaction to these efforts basically showed not that it is impossible to have a decidable math, but that it is impossible to have both a decidable math and a math strong enough to represent itself inside of itself and thus make statements about itself. (As a side-effect, the proof also shows by construction just how little math is necessary to have that result.)

You can, by a sort of executive fiat, ban your math from doing the things that lead to Goedelian paradoxes, but you are left with a fairly boring math.

(Bias note: Were this from a mathematician or something, I would be more inclined to assume that the summary was flawed and the mathematician knew these things. But from someone calling themselves a "philosopher", I consider this sort of hubris perfectly plausible.)

How about this: is there any Wiki lurker with working knowledge of mathematical logic, access to this work and time to spare (possibly waste) able to tell us if this is a crookery, an overblown trivia (the well known scheme downsize math enough, we get rid of Godel), or something for real ? Given that is the work of a philosopher, claims to get over Godell, is called "meinongian", and didn't seem to enjoy much success in math publications, signs are not very good. So in absence of such a clarification why should this page stay here ?

It's a crock. See e.g. final comment on GoedelsIncompletenessTheorem, amongst multiple ways of seeing this. It's here as one of PeterMerel's whimsies ("whimsy" appears to be his middle name :-). If I didn't know that, I'd say delete away, but since it is, I suppose you could check whether he would merely restore it. You might remind him of TheAdjunct in the same breath.

Conceivably similar comments apply to page DaleJacquette. In general it just seems like the usual problem of a philosopher thinking he can do math, when in fact it's not his forte. -- DougMerritt

...able to tell us if this is a crookery?

He's a philosopher, of course it's a crock! More to the point, making a difference between "decidABLE" (a well defined terminus) and "decidED" (pseudoscientific fluff) pretty much invalidates the rest to come as anything but bullshit... err... philosophy... err... Dammit, what was the difference again?

I don't believe in MeinongianLogic. It doesn't exist. --PhlIp

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