Jon Cogburn's Blog

more awfulness from Noam Chomsky and friends

[Update: Newapps thread on this HERE. I said my piece in the comment section and fully expect the Chomskyans to come out in force. So it should be interesting reading. My policy now with respect to that kind of debate is to say my piece and then get out, not bother responding myself to criticisms engendered.]

Great story about the Piraha brouhaha HERE.

Anyone who has read Harris' The Linguistics Wars, or Houck's Ideology and Linguistic Theory, or Geoffrey Pullum's work, or debates engendered by computational syntacticians and semanticists completely giving up on approaches stemming from "universal grammar" will find nothing surprising in how the Chomskyans are responding the issue of whether the Piraha language involves recursion.

Three maneuvers you always see, from the Katz-Postal-Fodor hypothesis to defenses of the Khmer Rouge etc. etc. etc. to the the issue of whether generativity equals recursivity to the current issue involving recursivity and universal grammar : (1) Use institutional power to eviscerate the anti-Chomskyan scholar unprofessionally, in this case outrageously accusing the linguist in question of racism so as to get the Brazilian government to no longer grant him access to the Piraha (compare with the shameful treatment of Haj Ross during the generative semantics brouhaha), (2) alter the claim minutely and pretend never to have said what you said in print dozens of times, (3) in the process of such alterations making ones own claims unfalsifiable, and so slippery that empirical content bleeds out. Decade after decade of this third step is why almost nobody (I know of one exception) in computational linguistics uses Chomsky's theories any more.

The article is very good, especially by letting Ray Jackendoff have the last word and showing the relevance of Harris' book.

One potentially confusing thing is that when Pullum and others correctly note that Universal Grammar is dead, they in no way mean to be attacking generative linguistics. The author comes too close to opposing Universal Grammar and corpus based linguistics. But theories like HPSG are generative in the original 1972 sense and not corpus based (though unlike Chomsky, HPSGers are not a priori hostile to corpus based work) but also not transformational in Chomsky's sense.

In this respect, the only thing wrong with the article is that it is not clear that non-trasformational generative frameworks that have no truck with "universal grammar" or bizarre ways that supposed innateness is supposed to constrain syntax, but rather just try to get the distributional data correct, are far more successful at actually formalizing robust fragments of natural language than Chomsky's Minimalism or Government and Binding before that. This in spite of the fact that most academic syntactitians still follow Chomsky on these things.

For example, your grammar checker on MS Word (which, properly understood, represents a huge victory for generative linguistics) does not use Chomskyan syntax. Though it's proprietary, I do know some of the people who went on to work on it, and they all used Head Driven Phrase Structure Grammar and related frameworks such as Categorial Grammar and Lexical Functional Grammar. Minimalist syntax would not be able to succeed here. It's really quite stunning. If you travelled back twenty five years ago and showed linguistis the Microsoft grammar checker you would have been nominated for a Nobel Prize (this is not an exaggeration). But people are so wound up in the weird nativism now that they don't recognize this huge victory.

Anyhow, once we clearly differentiate "Universal Grammar," where nativist doctrines are taken to a priori constrain the mechanisms of the syntax, from proper generative syntax not so driven, the following is I think pretty obvious:

As for Universal Grammar, some are already writing its obituary. Michael Tomasello, co-director of the Max Planck Institute for Evolutionary Anthropology, has stated flatly that "Universal Grammar is dead." Two linguists, Nicholas Evans and Stephen Levinson, published a paper in 2009 titled "The Myth of Language Universals," arguing that the "claims of Universal Grammar ... are either empirically false, unfalsifiable, or misleading in that they refer to tendencies rather than strict universals." Pullum has a similar take: "There is no Universal Grammar now, not if you take Chomsky seriously about the things he says."

Gibson puts it even more harshly. Just as Chomsky doesn't think corpus linguistics is science, Gibson doesn't think Universal Grammar is worthwhile. "The question is, 'What is it?' How much is built-in and what does it do? There are no details," he says. "It's crazy to say it's dead. It was never alive."

letter to the NY Times about Ruth Barcan Marcus

Via Leiter Reports HERE, a very nice letter from Michael Della Rocca, Don Garrett, and Diana Raffman to the people in charge of obituaries in the New York Times.

Dear Mr. McDonald and Mr. Kadden,

Because time is crucial in this matter, we will be brief, direct, and blunt.

Ruth Barcan Marcus -- who died, as we believe you know, on Sunday, February 19th -- was one of the central figures in philosophy over the last 65 years.   Her work advanced in multifarious ways our understanding of logic, metaphysics, philosophy of language, and moral philosophy.  Her results in logic in the 1940's alone -- work whose significance is still being plumbed -- is sufficient for her to have a permanent place in the pantheon of logicians.  Her discovery of the Barcan formula forever changed the way in which we must reason about necessity, possibility, and identity.  The seminal essays in which she introduced the formula quite simply created a new field of logic -- quantified modal logic -- a field which continues to thrive.    Her subsequent development of this work changed our understanding of the reference of words and proper names and made possible much of the most important work in the philosophy of language down to the present day.  Her pursuits in moral philosophy -- embodied in what is perhaps her most widely-cited paper, "Moral Dilemmas" -- changed the way philosophers approach the topic of moral obligation.  (This paper was a focus of the recent obituary in the _Economist_.)  All of this is enough to be worthy of recognition in the Times.

But this brief summary of Marcus' scholarly contributions does not even begin to touch on her powerful role in philosophy and in academia general.  She was one of the few women in philosophy and especially in logic at a time was sexism was rampant in the field.  She persevered and succeeded not only in establishing herself in the field but in helping to bring about changes in hiring practices so that appointments in philosophy were no longer governed by the "old boys network".  For this and other roles she played, the American Philosophical Association recently awarded her the Quinn Prize for service to the profession

I know that you have already received much information about Marcus' accomplishments and accolades.  So we will not say more about them here.  But we feel obliged to point out that the fact that an obituary has not yet appeared in the Times indicates that you have not yet decided whether to publish such an obituary or that -- absurdly -- you have already decided not to do so.  This is, in our opinion, outrageous.  The Times has, we are happy to note, provided timely recognition of many prominent philosophers in its obituary section in recent years.  (A list of several such obituaries was sent to you by Michael Della Rocca through Yale.)  None of these other philosophers has been more significant both to philosophy and to the profession of philosophy than Marcus.  And many of those who were recognized by the Times were, we must say, figures who were not nearly as significant in these respects as Marcus was.  If the Times were to fail to recognize Marcus, this would be not only an embarrassment for the Times, but it would reveal that the Times is woefully out of touch with what are the most significant developments within philosophy over the last half-century or more.  We do not expect the Times' authors and editors to be philosophers themselves, but we -- as well as the cultural and intellectual community at large -- do expect the Times to be aware of the most basic accomplishments in central academic fields, including developments in philosophy, the oldest and most fundamental field of intellectual inquiry.

We hope that the Times has not failed in its responsibilities.  There is still time to rectify this scandalous omission.  We urge you to do so.

Sincerely,

Michael Della Rocca
Andrew Downey Orrick Professor
Yale University

Don Garrett
Professor and Chair
Department of Philosophy
NYU

Diana Raffman
Professor
Department of Philosophy
University of Toronto

I don't know how big a deal a NY Times obituary is. But I understand the letter writers' angst.

The thing is, Marcus just got crap from all sides. And  sadly, I suspect that any woman or her overwhelming genius from that era got an equivalent amount of crap.

If you read the transcript of the classic meeting where she presented her refutation of Quine on quantified modal logic, then Kripke and Quine's pathological inability to take her seriously really do read like something out of one of the very most uncomfortable episodes of Mad Men (this is just an unbiased reading of the transcripts, maybe it was less foul in person). And she was right! I'm not claiming that Kripke plagiarized her. But the disconnect between how he and Quine treated her in the transcripts with the fact that his later work entails that she is right remains incredibly jarring.

On the other hand, there's a narrative from continental philosophers blaming her for every single aspect of the massive dysfunction of the Yale Philosophy Department during the period that led to them being put under receivership. But, again, these stories are way too convenient. In real life there's always blame to spread around for such institutional failures. The only analogue I can come up with is Roman historians (esp. Seutonisus) blaming Livia and Messalina for everything that went wrong during the reigns of Augustus and Claudius. This kind of thing was no more plausible then than it is now.

In both cases I can't help but seeing the typical sexist Catch 22 that talented women still face, how ever many decades after the Barcan/Quine/Kripke meeting. If you exhibit any greatness at all and you are female, people are so invested in you being out of line that they will treat you horribly and tell the most fantastical tales about you.

Well, Ruth Barcan Marcus was great. She has a formula, and an inverse formula, rightfully named after her. These formulae are so fundamental that one could do far worse than spending the rest of one's life thinking about the them.

Werner Herzog on one form of the liar paradox (from Kaspar Hauser)

"Are you a tree frog?" Fantastic.

illness inspired question about three valued logic

I've got a cold and am running a fever. Posting on the interwebs is contra-indicated by such a condition. Nonetheless, in my addled state I'm  haunted by the following.

Assuming Trivalence (that every meaningful assertion is determinately either true, false, or neither), how does neither iterate?

To say that "P is true" is neither true nor false (NTP) is equivalent to saying that P is neither true nor false (NP).

To say that "P is false" is neither true nor false (NFP) is also equivalent to saying that P is neither true nor false (if  P were false, then "P is false" would be true; if P were true, then "P is false" would be false; so P must be neither).

But what does it say about P to say that "P is neither true nor false" is neither true nor false (NNP)? I can't make sense of this, and I'm sure I'm goofing something up. Here's an argument that the notion of NNP is incoherent.

Assume that P is such that NNP holds. By trivalence P is true, false, or neither. Assume P is neither (NP). Then it is true that P is neither (TNP), but this contradicts NNP. So our assumption is wrong, and we know that from NNP it follows that P is not neither, which  by trivalence entails that P is either true or false.

But if P is either true or false then we know that P is not neither true nor false which contradicts the claim that NNP.

I'm pretty sure that here last step is probably wrong, because asserting that something is not the case is the assertion that it is not true, which is consistent with it being neither.

But this still doesn't help me make sense of what is being affirmed about a sentence when we assert that the claim that it is neither true nor false is itself neither true nor false. Is it just to assert that P is either true or false?

I realize the above could be the fever. I won't be embarrassed if someone points out an obvious flaw in the above reasoning. I would be relieved. Especially if the pointing out also explained just what is going on with NNP (in particular, what this tells us about P in three valued logics).

natural deduction formulations of Priest's take on paradox

I've got two natural deduction versions of Priest's take on Russell's paradox in a doc file HERE. The first one uses the restricted Inclosure Schema and the second uses the full Inclosure Schema (so that one can craft derivations of the semantic paradoxes with structurally analogous proofs). I've also got a proof of Berry's paradox. 

I'm going to run through all the paradoxes of Priest's great 1994 Mind paper ("The Structure of the Paradoxes of Self Reference") and then use that as a resource to really closely read Beyond the Limits of Thought.

Better logicians than me (and all logicians proper are better logicians than me) almost always think it's silly to model arguments to this level of hyperspecification, but it serves me well. Sometimes you learn interesting things that everybody else has missed, and it also makes it easier for non-logicians (like myself) to follow what is going on. A couple of minor interesting points (concerning Emil Badici's criticism and also the slingshot argument) have already arisen which are noted in the document.

question about applying Priest's schema to God arguments

I just ordered another copy of Graham Priest's Beyond the Limits of Thought. He's got a couple of pages on the ontological proof and the conceivability of God. I don't remember what he says though.

His Inclosure Schema clearly works to model the argument for the paradox of the stone. It should work for the ontological proof I think if you start by assuming there exists a (possibly empty) set of entities that are such that no entity is greater than those entities. Of course if you model it that way the conclusion might be not that such an entity exists but that we were wrong to think we could form a set of that sort! That is, we don't have a concept of that which no greater can be conceived after all. For all I know, this is what Priest concludes. I read his book way too hastily years ago. I'm going to read it really carefully this time around.

Neil Tennant in conversation once showed that if the ontological proof is valid then you can in parallel fashion prove that the empty set ("that than which no lesser can be conceived") does not exist. I don't think he published this though.

I'll do a post on it this week which actually explains how the Inclosure Schema models so many different paradoxes on Russell's paradox and which at least models the proof for the paradox of the stone, but if anyone knows of anyone who (pre-Priest) has connected up Russell's Paradox to either the paradox of the stone or the ontological argument, or who has (post-Priest) either explicitly applied Priest's scheme to them or (assuming Priest does this in the book) tries to refute him, please let me know.

another possibly hopeless idea (this one involving dialetheism) that may have been explored by others

This may be catastrophically simple-minded and lazy to boot, but I'm just not sure that dialetheism (the view that there are true contradictions) should be thought of as leading to logical revision. [Before reading any more, I realize that I'm way out of date on all of this, and that there is an extant literature surrounding "classical recapture" that is relevant and that I haven't addressed in what follows.]

The argument that dialetheism entails revising classical inference simply notes that in normal classical logic a contradiction entails everything (ex falso quodlibet, P, ~P |- Q). This is actually a really hard principle to give up because any logic that entails disjunctive syllogism entails ex falso quodlibet [Assume you've got a contradiction P and ~P. From P by disjunction introduction you've got (P v Q) and ~P. But then by disjunctive syllogism you can conclude Q. So from any P and ~P, any Q follows.] So if I want to say with Graham Priest that paradoxical sentences such as "I am not true" are both true and false, and I don't want to be committed to the truth of everything, I better adopt a paraconsistent logic that does not license ex falso quodlibet.

But couldn't a true contradiction work as a logical/pragmatic stop-sign? The thought would be that if you derive a contradiction within something assumed for further discharge such as negation introduction or disjunction elimination you go about your business and continue to use classical logic, but if you derive it outside of these contexts it tells you to stop using the logic.

This works really well for true contradictions that are generated outside of paradoxes involving self-reference (I don't know any other philosophers besides me, in my essay in The Law of Non-Contradiction, who have argued for such). Say that our only notion of ethical truth is truth-relative-to-a-moral-tradition such as in MacIntyre's historicist days (and that the T-Schema is valid for each relativized truth predicate). These traditions will each be independently plausible, but inconsistent with one another. Given the T schema you can generate contradictions from the traditions' joint inconsistency.

And people are pretty good at bouncing back and forth between different moral theories, combining them when it's safe. But sometimes we mess up and apply both in situations where they contradict one another (maybe think of Kantian and Millian ethics on whether a given lie is morally permissible). If the best we can do at the limit of reflective equilibrium is getting a set of good mutually inconsistent (but each internally consistent) theories (something I think holds for ethical, philosophical, and aesthetic theories generally), then a true contradiction is just a place where two of the theories at the limit of reflective equilibrium disagree.

But at least that kind of true contradiction should not lead you to abandon classical logic. In subvaluational "glut semantics" a sentence is supertrue in a model if there is at least one valuation in that model that makes it true. True contradictions happen when a sentence is made true on one valuation and false on another.

On the account of entailment where you say gamma entails alpha if and only if alpha is subtrue when all of gamma are you get a horrifically messy non-classical entailment relation (in Williamson's book on vagueness this is called "wide entailment," albeit there in respect to gap supervaluational semantics for vagueness, where a sentence is true in a model if it is true at *all* relevant interpretations). But such semantics also give you the option of just keeping classical entailment, gamma entails alpha if and only if there is no valuation (remember that models are sets of such valuations) that makes all of gamma true and alpha false. Williamson argues that this form of narrow entailment should not the relevant one for vagueness for the supervaluationist, but I remember finding his arguments here less than persuasive. One would need to examine them in this context.

But the model is compelling. Each one of the interpretations making up the glut semantics model is analogous to a correct theory in the limit of investigation after reflective equilibrium is considered. And narrow entailment can be understood as legitimizing classical logic as long as we in some sense stay within one of the correct theories in the limit of investigation after reflective equilibrium is considered. Since we're in the limit of investigation all a true contradiction tells you is that your bringing together of two of the theories into the same context has run into trouble. It just tells you not to do that in this context.

The big if is whether such a view can be argued to apply to self referential paradoxes. I'm not at all sure that it can. Consider the paradox of the stone. What would the analog to the two interpretations be? I'm going to look at Priest's brilliant 1994 Mind paper "The Structure of the Paradoxes of Self-Reference" (still brilliant even if one agrees with the conclusion of Badici's "The Liar Paradox and the Inclosure Schema," Australasian, 86, 2008) really carefully over the next two weeks and see if there is any hope at all for the idea true contradictions generated from paradoxes can be argued to be consistent with classical logic.

I'm not  that optimistic, because you'd have to say something like a new subvaluational interpretation is generated every time Priest's Transcendence is applied. To the extent that it might work, one could probably piggy back on extant attempted solutions to the paradoxes that involve indexing in various ways. But that literature is a mess and one of the primary benefits of dialetheism is that you were supposed to be able to circumvent it (albeit at the cost of a messy logic).