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In the interests of having new material for people to read without having to, y’know, write it, I’ve added some longer things I wrote about four years ago under a new “Essays” page on the bar. These were part of a series of things I wrote under the title “Logic and Politics” in 2003: insofar as they are a coherent anything, they amount to an attempt to formalize Gramscian and Frankfurter social theory. (I’ve only included the ones which were halfway successful: if you want to see what I had to say about Althusser and Turing Machines, or glasnost and Gentzen’s consistency proof for arithmetic, or a reading of Nietzsche via Talcott Parsons, you’ll have to do some digging in the Google Groups archives.)
Topics addressed include:
- Sequent calculi (esp. the “cut” and “mix” rules)
- The logic of political “left” and “right”
- Schmitt’s friend-enemy distinction
- The master-slave dialectic
- The Lacanian character of the United States
- De re vs. de dicto
- Arrow’s Impossibility Theorem
- The dictatorship of the proletariat
- Lindström’s Theorem
- Gricean pragmatics
- The “cultural state”
- “The temperature is ninety and rising”
The formal logic used is real, if inexpertly wielded, and the political sentiments are heartfelt. I wanted to forget them for a long time, since they brought me nothing but grief, but this seems like a genuinely more open time in intellectual life and the writing does not displease me. They are edited for spelling and grammar, and errors of fact (as opposed to lapses of reason) have been corrected; but even if you’re sympathetic to this particular “hermeneutics of suspicion” you’d probably do well not to take them too seriously. (One of these days I’ll get around to long-form explanations of every little thing again, but as they say I have “other fish to fry” at the moment.)
I just finished Simon Critchley’s Infinitely Demanding. For starters, the book is inaptly named: two days’ worth of bus travel was enough to cover its 150 pages. That’s okay, but I really wish Critchley’s editors and Verso’s fact-checkers had been more demanding of him — the prose is an awkward mishmash of hip mannerisms that might be charmingly low-key at a party, but fail basic tests of expository soundness. Several times Critchley uses “to coin a phrase” ironically, to indicate how hackneyed the term he is about to use is; but for less-educated people one would hope would be at least some of the audience for such a book, this would be confusing (precisely because the inherent lameness of the rhetorical figure fails to provide a formally adequate clue to the nature of the phrase). When Critchley does break down and make straightforward assertions, the statements are often none too warranted: he tells us that Judaism has never been a proselytizing religion, which those with a modicum of knowledge about antiquity know not to be the case, and makes the claim that Spanish has hegemony over English in the US — Gramsci would not be amused.
As for the philosophical and political content, it’s almost innovative. Critchley often gestures at contemporary analytic ethicists, but fails to provide adequate motivation for taking his invocations seriously. He is obviously more comfortable with the “continental” writers (I guess he is a Levinas expert, although I’ve never read his other books), but can’t quite decide what use he wants to make of them, what he is talking about to whom. All these figures are laminated together in the praise of the tactics and worldview of contemporary anarchists, who are “political” at a “distance” from the state. I agree there is a lot to like about anarchists, but perhaps their stances seem more attractive than they really are to a professoriat socially blocked from taking up “vanguardist” leftism (Critchley equates Al-Qaeda with Leninism, managing the heretofore unimaginable feat of insulting both).
Ultimately, contemporary politics is not a matter of creating a homogenous strike force for the proletariat: but for those without bourgeois options it is really too ugly a fight to engender the “irrepressible joy of being communist” urged by Negri and Hardt, and co-signed on here by Critchley — and I suspect a only a thoroughgoing political “finitism” would accurately reflect the attitudes and abilities of serious leftists suffering from both Bush- and liberal-fatigue.
I said I’d never dissect search terms that led people to this blog, but one such search led me to this extremely cool piece of real-live agit-prop (from Salvadorean reggaeton artists also calling themselves “Trick Daddy”). The song is an ode to the FMLN, deftly adapting the US ghetto’s political imagination to promise an electoral beat-down for corrupt rightists; if you ever needed proof that the left is capable of rolling with historical novelty, here it is.
It’s time for the world’s shortest and most simple-minded introduction to the model theory of modal logic. Since “model theory” generally employs some fairly exotic concepts, I suppose it’d be best to begin by trying to concretize the idea of a model of a sentence. A model of a logical sentence establishes a systematic correspondence between the parts of that sentence and mathematical entities possessing the same formal properties. Since these sentences, like sentences in a natural language, can be indefinitely complicated by operations for building new sentences out of old ones (like joining two sentences by “and”), establishing this correspondence for all sentences requires a way of “disassembling” an arbitrary sentence: as I’ve remarked before, in model theory this takes the form of a recursive definition, where the meaning of a longer sentence is defined in terms of its subsentences until we reach semantic primitives, which are “satisfied” (represented) by arbitrarily chosen mathematical entities. For example, the recursive definition for a logic involving disjunction (“inclusive or”) would feature a clause stating this:
“X v Y” is satisfied if either X is satisfied or Y is satisfied.
All the regular “extensional” connectives have relatively simple clauses like this: when we get to the quantifiers things get a little more complicated, but by making the mathematical entities satisfying quantified sentences infinite sequences and assigning quantified variables to specific positions in those sequences (“for all x” being satisfied by all sequences varying in at most the xth position, “there is some x” satisfied by at least one sequence varying in at most the xth position) Tarski solved that problem in the ’30s. He used this complete recursive definition of logical sentences to define a logical truth as a sentence which cannot fail to be satisfied. What took a longer time was figuring out how to model-theoretically represent modal or “intensional” operators, which cause the meaning of a sentence to not be a straightforward truth-functional consequence of the meaning of its component parts; Kripke solved this problem by developing a model theory using “possible worlds”. A model of an ordinary first-order language consists of an ordered pair, the sentences of the language and a satisfaction relation: a model of a modal language consists of an ordered triple, written <W,R,V>. Let me explain each element.
W is the set of possible worlds; V is the set of the sets of the propositions which are true in particular possible worlds, and R is the “accessibility relation”, which determines how relevant truth in one possible world is to truth in another. If a statement is true in an accessible world, the statement is possibly true in the world under consideration (symbolized ◊x): if a statement is true in all accessible worlds, the statement is necessarily true in the world under consideration (□x). Varying the accessibility relation is very important for comparative study of modal logics: a different accessibility relation gives you a model of a different modal logic. Conveniently for us, Montague uses the most intuitive accessibility relation, an equivalence relation: it is reflexive (world x is accessible from itself), transitive (if x is accessible from y and y is accessible from z, x is accessible from z), and symmetric (if x is accessible from y, y is accessible from x). This means that all worlds are accessible from each other, such that a statement which is true in some possible world is possibly true in all worlds, or is necessarily possible: this is the model-theoretic equivalent of an axiom of the modal logic S5, ◊x→□◊x, and S5 is the language defined by the accessibility relation of equivalence.
But the language of metaphysical possibility and necessity, or “alethic” modality, is not the only intensional logic possible. One other such logic is tense logic, which has historical roots in the ancient and medieval philosophy of time but erupted into the modern philosophical consciousness through the work of Arthur Prior. Ordinary tense logic is “multi-modal”, featuring two primitive modalities Gx (x is going to be the case) and Hx (x has been the case). These can be combined to express many of the statements about time, such as Gx → GHx (if it is going to be the case that x, after that point it is going to be the case that x has been the case). Ordinary tense logic requires an accessibility relation modeling the order of instants of time before and after other instants, and Montague chooses a linear order like “less than or equal to”, which is reflexive, transitive, and antisymmetric (if a is accessible from b, and b is accessible from a, then a must be b). Gx is true if x is true at some instant of time following (accessible from) the instant of time under consideration, and Hx is true if x was true at some instant of time which the instant of time under consideration is accessible from.
There is one further application of modality in Montague Grammar: intensions. The arbitrary mathematical entities representing things and truth-values in Montague Grammar are called “e” and “t”: Montague says we can think of them as the numbers 0 and 1, if we like (i.e. it’s not important what they actually are). He adds to this a third entity, “s”, representing “senses” or intensions: these three categories combine type-theoretically, as in <s,t>, a function from senses to truth values. Generally speaking an intension is a function from possible worlds to “extensions”, either things or truth-values: the intension of “blue” would be an ordered pair of possible worlds and a set of the sets of things which are blue in each possible world. Carnap developed intensions as a way of modeling Frege’s idea of the Sinn or “cognitive significance” of a word, not just what it happened to refer to but what it would refer to if the world were different (or, as the case might very well be, we believed it was different): the adequacy of this as an interpretation of Frege has been hotly contested for decades, but a highly ramified use of intensions is critical for Montague’s analysis of the meaning of words, even common nouns like “ball”.
I promised people “anti-election” political posts. Here’s a topic dear to my heart: in response to a perceived uptick in crimes aboard TriMet (the public bus and light rail service in the Portland area), director Fred Hansen has proposed that the “Fareless Square” program be limited in time from 7 am to 7 pm. Fareless Square is an area of the central city — originally confined to Portland’s westside downtown but recently expanded to cover the eastside Lloyd Center district — where all bus, light rail, and streetcar trips are free. A legacy of Portland’s late-’70s urban planning push, Fareless Square was intended to limit car trips in Portland’s then-smoggy downtown: but since an elderly man was severely beaten at a light rail station (in suburban Gresham) the interaction between the program and Portland’s homeless population has drawn ire.
I think the issue of violence aboard TriMet is overblown, and I say this after having someone try to beat me to death at another suburban Transit Center a couple years ago. (He told me I was going to die, but he only got a few medium-good licks in before the police showed up; I continued on to the liquor store, my nose bloodied but my excellent sense of priorities obviously unaffected.) The people who are most nonplussed are in my estimation whiners who showed up in Portland during the repressive times earlier this decade, and who consequently are used to thinking their money and snobbery are worth more respect than the traditionally freewheeling lower classes here would normally be inclined to give them.
As a pass holder, Fareless Square is not of great use to me personally (and I have recently noticed an increase in paid petitioners and enterprising bums riding the downtown stretch of light rail), but I think it would be a shame if its real value for ferrying people between events at the Convention Center and downtown, or from dinner to a movie or bar — which would be swiftly disposed of by charging visitors and residents the now-princely regular fares during nighttime — got drowned out by this manufactured panic.
Every so often, I crack a book by Foucault: not to advance my fortunes as an amateur social scientist, but to try to bridge some discursive gaps between my idiosyncratic social theories and the views of “the regular guys”. I suppose you might think that there is surely some easier and more effective way to “get across”, like reading the Bible or taking up yoga or campaigning for Mitt Romney. But Foucault books are readily available, readable enough, and actually not without their parallels in the more “pragmatic” realms of human activity. For example, the epistemological statuses of Foucault’s theories are almost as questionable as the epistemological statuses of the disciplines and subdisciplines he classifies, to the point where he himself described his work as an “antiscience”; if it seems that this makes his writing totally useless when confronted with the rigor of “harder” disciplines, I’d like to advert to a precinct of one of those disciplines, “design patterns” in computer science, as an example of how a discourse orthogonal to “scientificity” serves a useful cognitive purpose. I hope you’ll find, as I have, that the parallels to Foucault are significant and striking enough to justify this rather outre comparison.
Design patterns are an idea originating in the study of architecture. The architectural theorist Christopher Alexander thought to systematically work through the successful elements of various architectural designs and develop a “pattern language”, a set of meta-blueprints that could be tweaked such that new architectural designs might build on old strengths. Although Alexander himself later decided the architecture designed using this method was rather sterile, design patterns were “in the air” long enough to percolate down to computer researchers trying to decide how best to make use of the new “object-oriented” computer languages, which were originally designed to model real-world situations using an “object” to represent each element of that situation. It was decided that objects offered fertile ground for implementing something very much like Alexander’s pattern language: a successful object would share very many features with other objects designed for similar tasks, so why not cook up patterns for such scenarios?
The computer world is, of course, full of fads that become buzzwords for ambitious managers: however, design patterns were one trend which had legs, since they operate at the interface between human ingenuity and necessary structure and help to make programs easy to develop and intelligible. In fact, quite a lot of other phenomena operate at a similar level: the interaction between the increase of scientific knowledge and “technological” exigency creates orders which are neither “nomological” instances of exceptionless laws nor matters of arbitrary choice — and this is precisely where Foucault situates his works. I don’t think it’s beyond reason to say that he provides us with “design patterns” for organizing knowledge; in fact, I think it captures very well his insistence that the fundamental structuring of disciplines is not a matter of veridicality per se, but instead a place where the complex forces of history channel and multiply their energies through the interaction of knowledge and Foucault’s version of power. (And who knows, it might even be some comfort to the Panoptically-monitored programmer to conceive of the great intellectual considering relatively abstract factories and their effects on flyweights).