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As part of reconceptualizing the blog, I’m going to leave poor Nate Charlow alone on the weekends and feature a piece of “high art”. This week, I have for you the YouTube copy of French director Chris Marker’s famous short film La Jetee. Shot in a “filmstrip” style, the film (lasting half an hour) tells the story of a nuclear holocaust survivor who is conscripted to travel through time. Although this is Serious Stuff, anyone who enjoys science fiction will find it interesting — I had never seen it before, and I think it’s great that it’s available on the Internet for all to watch. (I should probably mention to my more cosmically inclined readers that this is not your life. Or maybe it is, a little bit.)
The Famous Philosopher Colin McGinn seems to spend most of his time at his blog “rubbishing” democracy, which doesn’t make me feel too bad about thinking Godwin’s Law should be repealed. Today it was popular sovereignty: he quotes Tocqueville on American government (usually a bad sign when it is done approvingly), then goes on to say the obvious inequality among persons makes the project of self-government a delusional one. What to say about this? Well, my recent thoughts on the topic are bound up with the blog Pandagon: it seems to me that Amanda Marcotte and company are exemplary of what popular sovereignty is. Unlike many blogs, they’re not leveraging some organizational position: like most people they have jobs, but the jobs are not why they are interesting and do not determine what they have to say to their readership (a somewhat old-fashioned approach to cultural journalism).
Instead, the feminists and friends there are talking about politics and society as individuals — and they are models of popular sovereignty because they are good enough to be themselves, instead of taking over (or being forced to take over) self-understandings from “enlightened” authorities and capitalist “hype men”. I think their project is fantastically politically significant, and that an index of this is the flak the acerbic Ms. Marcotte catches from people who are unhappy with others not going with the corporate-choad flow (including the famous, and seemingly rather proprietary, interest taken in her by Catholic ideological shock troops). Efforts like this help defuse the interest of “wise men” in controlling social and political processes that materially considered do not militate for “winners” and “losers” in anything like the way McGinn thinks; I wish there were ten blogs somewhat like Pandagon, to generalize popular control over public discourse.
Another forty-year anniversary: the slogan “Nixon’s the One” from the 1968 Presidential campaign, which I used to find amusing for philosophical reasons. One of Heidegger’s main concepts in Being and Time is that of das Man, the inauthentic self of fallen existence in which we take our understanding of life over from what is “proximally and for the most part” intelligible. Das Man was translated by Macquarrie and Robinson as “the they”, and by more recent Heidegger aficionados as “the anyone”, but it always seemed to me that the correct rendering of it in English was a no-brainer: man in German is the exact grammatical equivalent of “one” in English expressions like “one ought to do this”, and expressions like man sagt… are clearly exactly what Heidegger had in mind in coining the substantive.
Although it’s hard to tell whether it would have pleased Heidegger to hear it, I used to find the idea that Nixon really was “the one”, an exemplar of phony normativity, enlightening. (Alternatively, you can find a critique of this sort of Heideggerianism in Nixon pal James Brown’s dictum “Funk is on the one”.)
You could also do a Heideggerian work-up of Nixon’s 1972 campaign slogan:
but I wouldn’t recommend it.
UPDATE: Do you suppose this was a “one-off device”?
The month of May is drawing to a close, and with it the 40-year anniversary of Mai ’68. As someone aged twenty-eight, as someone who’s never been to Europe, and as a socialist with a definite conservative streak I suppose I don’t really have much to do with that period of revolutionary ferment: but I have always appreciated the posters produced by the People’s Atelier in Paris during that time, as art and as indices of social hope. Unfortunately the complete collection of scanned posters once hosted by UCSD is no longer available, but partial selections are available at these sites:
While we’re on the topic of the second-order, I’d like to mention that legitimate electronic copies of Jean-Yves Girard’s Proofs and Types are available from its translator Paul Taylor here. The Cambridge Tracts in Theoretical Computer Science are generally very good, technically rich but accessible, and this early installment is a friendly introduction to proof theory for the computationally minded. Standard topics like the Curry-Howard isomorphism and normalization are clearly explained, but there are also very good sections on two important logical formalisms Girard invented: System F, the second-order lambda calculus that languages like OCaml use to handle parametric polymorphism, and linear logic (a “substructural” logic that treats statements as informational resources). There’s no excuse not to check it out.
“History continually effects totalisations of totalisations” — Sartre, Critique of Dialectical Reason
One of the blogs I’m currently very interested in is Metalogic is Ethics, run by a graduate student in Philadelphia. John and I agree about the importance of formal concerns to “Continental” issues, and we are both thankful for the liberalizing influence of Badiouianism on that interface without quite having the grateful consciousness of disciples. Something we’ve discussed is the significance of second-order logic for considering dialectics: although I doubt anyone ever completely agrees with what I say, hopefully this work-up of my position on that topic will mark out an area broad enough to be occupied by a group larger than a party of one.
To put it mildly, formal logicians are not Hegel fans; going back to Russell’s turn away from British Idealism, formal logic has been informally defined as everything Hegel’s “logic” was not. The closest any formal thinkers have gotten to appropriating Hegelian themes is “dialetheism”, the Australasian philosophical movement which holds that paraconsistent logics (which have rules for reasoning with contradictions that are more sophisticated than the traditional “principle of explosion”) demonstrate that it’s coherent to believe there are real contradictions, “contradictions in the object” as a traditional dialectician might say. People like Graham Priest have mentioned Hegel in connection with this project, as well they might; but I think the real story of Hegel and logic is a little bit more complicated than simply accepting dialetheism. The story begins, as well it might, with Plato.
I’m no Plato scholar, but I imagine it’d be an uncontroversial observation that Platonic dialogues operate in this fashion: Socrates gets one of his interlocutors to produce a description of an Idea, and then they collectively reason about the consequences of that Idea for reasoning with Ideas generally, and the consequences of reasoning with Ideas generally for the employment of that Idea. This is clearly a “second-order” process of reasoning, but those less familiar with formal logic may not know there’s no need to leave “second-order” as an inexact descriptor: there is “second-order” logic. First-order logic allows the reasoner to quantify over objects in the universe of discourse, which produces universal and existential statements about the application of predicates to those objects: second-order logic allows one to quantify over those predicates, producing universal and existential statements about predication in general.
Sounds great, huh? In fact, using second-order logic one can describe all mathematical concepts without resorting to set-theoretic axioms, as Frege did with his second-order logic, his “laws of the laws of nature”. Or at least you could, if that didn’t produce paradoxes like Russell’s “set of all barbers that shave themselves”. Some people have recently tried to salvage Frege’s logicism from the paradoxes (by restricting his Basic Law V), but that’s not quite what I want to talk about here — although his mathematical “platonism” may shed some light on the original article, he was certainly no dialectician. No, what I aim to talk about is the relationship between Platonic and Hegelian dialectics in light of second-order considerations.
Between Plato and Hegel, we have Kant’s “Transcendental Dialectic”, his logic of metaphysical illusion. Unlike the understanding, which operates by subsuming intuitions under concepts (much as constants are included in the extension of predicates), Kant’s Reason works with Ideas (concepts involving totality, the unconditioned, and the perfect) and gets entangled in antinomies and contradictions on account of their character. I guess you could anachronistically characterize Kant as a Quinean of sorts, interested in restricting theoretical cognition to “first-order” concepts of the understanding, and I think that would not be an unreasonable way to gloss the influence of modern science on modern philosophy which culminated in his work.
Hegel accepts the results of Newtonian physics, and the constraints of experimental method on philosophy of nature: but unlike Kant he held no truck with skepticism, and wanted a modern version of Plato’s productive dialectic. Consequently, Hegel returned to the second-order, and his dialectic is much more nearly a process of moving back and forth between orders of abstraction than cookie-cutter application of a “thesis-antithesis-synthesis” schema. That contradictions seem to occur in this process is perhaps an indication of the fact that this second-order reasoning falls prey to the affliction of any formal system powerful enough to generate the principles of mathematics, incompleteness: the interrelation between dialectically demonstrated truths cannot be systematized axiomatically.
Maybe that’s tendentious — but there’s an interesting feature of second-order logic which I think is quite illuminating for considering Hegel and Hegelianism. “Standard semantics” for second-order logic is incomplete, but the logician Leon Henkin (who developed the proof of first-order completeness which is commonly taught today) devised a “Henkin semantics” for second-order logic which is complete. Henkin semantics only allows second-order statements over defined first-order totalities: this is similar to the restriction in the Zermelo-Frankel “axiom of comprehension” which replaced Frege’s unrestricted law of comprehension. If we consider Hegel as second-order, perhaps Henkin semantics is a good “model” of Left Hegelianism (where dialectic reasoning is preserved but only in reference to “real abstractions”, concepts that are incarnated by material realities); Right Hegelianism preserves the full expressive power of second-order dialectic (Henkin second-order logic is no more expressive than first-order logic), but at the cost of rational cogency and lack of “mystification”.
I’m definitely floating with the universe by the end of this line of thought, but there is a more recent “dialectical” concept that reminds me very much of another thought I independently had about two approaches to logic and geo-linguistic correspondences to them. One of Sartre’s major concepts in his Critique of Dialectical Reason is the “practico-inert”, elements of social organization which are resistant to the subjective projects of praxis and form the ground of social struggle. Now, in 1970s logic a distinction was made between “Western model theory” and “Eastern model theory”; the former being exemplified by the work of Alfred Tarski and his students at Berkeley, the latter being exemplified by the work of Abraham Robinson and his students at Yale.
In pure logic there’s not much heavy weather to be made over this distinction; both Tarski and Robinson were from Central Europe (by way of Palestine and Britain in Robinson’s case), and Robinson had quite happily taught at UCLA. However, I think the distinction is not without its geographical aptness. Western model theory was more heavily “logical”, and focused on the significance of models for definitions of logical consequence and other “abstract” features of logic. Eastern model theory was more heavily “mathematical”, and focused on the significance of models for proving things about mathematical theories and other “concrete” formal phenomena. This parallels a distinction in discursive styles between the western and eastern US. In the West, people have traditionally been quite fond of solecism and sophistry as devices for getting points across indirectly, whereas in the East there’s more of a focus on ineliminable realities bound up with noble sentiment: a Western raconteur might be “temporarily disabled” by a stunning woman, whereas an Easterner might be discomfited by the plight of personally aggressive people with “disabilities”.
It seems to me that this “Eastern model theory” seems to capture the presence in language of the practico-inert which Sartre touches on at one point, the crude and tasteless plays on words you just can’t get away from, low “interpretations” of signifiers which distract us from drawing the appropriate conclusions. But lest this seem to be mere provincial boastfulness, I will mention that the reason people don’t use this distinction in logic anymore is that all new work in model theory today is “Eastern” model theory, leading to Wilfrid Hodges’ redefinition of the subject as “universal algebra minus fields” rather than Chang and Keisler’s “universal algebra plus logic”. And, like Sartre says, as undesirable as many aspects of the practico-inert are from the standpoint of revolutionary subjectivity it’s a fundamental existentiale of sociality which you can’t get away from.
I’ve gotten a new crop of people blogrolling me, so I’ve doubled the size of my blogroll. Not all of these people are my friends, or even my imaginary friends: as a former print person, the drive towards symmetricality associated with this medium confuses me a little. They’re blogs I read and recommend you read. Additionally, I’ve replaced the “Rubardiana” category with a more extensive list of egocentric particulars for people who are having a hard time placing me in geographical and social space. Beyond that, I think a certain presentation of self associated with the blog has run its course; I want to turn my attention away from salvaging intellectual and other elements of my biography. I’m still watching Redbone videos on YouTube, and remembering people I used to know, and I don’t feel too bad about that — but maybe it’s time to focus on things that might be a little more relevant for people who don’t have “lost years” to account for. Stay tuned for some attempts to Get With The Youth.
In what is surely a sign of the times I am ill-prepared to deal with, they shut down the Portland hip-hop station and replaced it with sports talk radio. As a consequence (and perhaps another ill omen, as those old enough to remember the concept of “left of the radio” may recognize) I’ve moved to the top of the band, where two oldies stations a fraction of a megahertz away from each other battle it out. The formats have changed since the heyday of that sort of thing; lots of stuff from the ’70s I don’t recognize, and hourly “programs” that last all of three songs, and even more repetition than before — although it certainly has not-inconsiderable retro-hip value, it is indeed possible to hear “Suspicious Minds” too many times.
All this is by way of introducing something I’ve planned to write a “squib” on for a very long time, my appreciation of a band which has almost-infinitesimal retro-hip value yet which managed to produce AM warhorses that everyone secretly still enjoys: Tommy James and the Shondells. The mature face of the “bubblegum” movement, these Pittsburgh studio rats (and godding knows how many record-label minders) took the trebly trifles of that genre and Made Them Great. The music is the soundtrack of one’s maximally inauthentic moments, of which there are of course many, and considering the omnipresence of tracks like “Crimson and Clover” and “Crystal Blue Persuasion” in the radio landscape of the last forty years it should hardly be surprising that their invocation through sampling occurs fairly regularly.
Obviously there’s a lot to hate about radio, and access to a more diverse range of music through blog aggregators and music services will inaugurate a new era of something or other, but I don’t regret my moments spent with general-issue material like the Shondells. “Leveling” can be a beautiful thing.
Riddle me this, algebraic logicians and model theorists: a filter defines a set D over a “base” set I where the “meet” (intersection) of two set elements is a member of the set and set inclusion is transitive (a set included in a subset of D is also a member of D). If you are modeling propositional logic with a Boolean algebra or first-order logic with a cylindric algebra, a filter on the algebra defines a theory: the representation of a conjunctive statement is only included in the filter if the two conjuncts both are, preserving truth in the fashion of regular model theory.
Now, Rasiowa and Sikorski told us a long time ago that a proper filter (one which does not include the empty set) defines a consistent theory (one which does not include falsum as one of its consequences), and a maximal proper filter (one not included in any other filter) defines a complete theory (one where either a statement or its negation is true). Now, in model theory maximal proper filters are called ultrafilters, and the equivalence class of functional values for functions with range I and domain in D is called an ultraproduct, or an ultrapower when the filter is an ultrafilter.
Question: given the basic algebraic logic above, isn’t an ultrapower equivalent to the set of logical consequences of the “axioms” I, i.e. all the theorems of a theory? It seems it must be, and although ultrapowers are not introduced in this way, if it’s so it’s illuminating.
Without going outside, you may know the whole world.
Without looking through the window, you may see the ways of heaven.
The farther you go, the less you know.
Thus the sage knows without travelling;
He sees without looking;
He works without doing.
Tao Te Ching, Chapter 47
Reading the Maps, an essential source for information about Antipodean leftism, has an incredible essay on the politics of New Zealand’s travel industry and “anti-travel writing”. I’ve personally never traveled anywhere a relative didn’t live, outside of college (and Pittsburgh isn’t conveniently located for travel to other cities); the Deadhead saying “wherever you go, there you are” has a flipside that stays on my mind. But I also think that any socialist transformation of society worth its salt would result in a great reduction in air travel, and even without such an occurrence coming to pass that the future belongs (for demographic and electronic reasons) to people staying put in mid-size conurbations across the world without losing touch with what’s happening other places. Let’s not go and listen to people who did.