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In the if-you-didn’t-already-know department, Weather Underground is a great way to stick it to the weatherman. Combining a mixture of National Weather Service information and data culled from personal weather stations, WU is a nice alternative to waiting through endless teasers for tomorrow’s weather on the local news. It’s not an ‘all-weather’ replacement: sometimes the NWS forecast requires a little critical analysis, as when they predicted 2-5 inches of snow accumulation for the Portland area one day in December, and information for places outside the US is thinner. But the site is fast and easy to use, and if you want to know just how damn cold it is outside right now there’s no better way.
This just in: David Letterman and Craig Ferguson are returning to CBS with their writers. “Late Show with David Letterman” and “Late Late Show with Craig Ferguson”, both owned by Letterman’s production company Worldwide Pants, cut a deal with the striking Writers Guild of America allowing them to return to the air next week — without following the perfidious example of Carson Daly, Jon Stewart and Stephen Colbert. The former Jennifer Love Hewitt psychopathology and our “liberal heroes” decided to save their loyal non-union staffs from redundancy by returning without writers; Daly asserts he was ordered to do this by NBC executives. Given the current labor climate in the US, it’s surprising that support for the strike has been so strong and the rationales for this strike-breaking so mealy-mouthed: but although the prospect of America saying sayonara to TV the way fans ditched the NHL is intriguing, I think those of us accustomed to doing Stupid Person Tricks can only wish the writers well — for our sake. (In a rare appearance on the contemporary Internet, John Lacny talked up the Letterman negotiations a week ago; I hope he’ll forgive me if I don’t “tip my hat”, as said hat is a petty-bourgeois affectation anyway.)
John Haugeland has made a copy of a recent paper, “Reading Brandom Reading Heidegger“, online. Discussing an essay by his erstwhile colleague Robert Brandom, “Dasein, the Being that Thematizes”, Haugeland offers us a little bit of his contemporary understanding of early Heidegger. It is a short and unsystematic writing, but some of Haugeland’s statements are provocative: however some of those are, I think, fundamentally questionable.
A longstanding assertion of Haugeland’s is that Dasein, as it figures in Being and Time, is a mass noun like “water” rather than a count noun like “person”. In this paper he adduces the evidence that Dasein is not used “with what Quine called the ‘apparatus of divided reference’ (indefinite articles, the plural, and so on)”. But, pace Williamson, this evidence is not quite knowledge: Heidegger writes ein Dasein several times in Being and Time — e.g., “Dass ein Dasein faktisch mit Wissen und Willen der Stimmung Herr werden kann…” (SuZ, p. 136). Daseinen indeed does not appear; so if it makes sense to talk about “a Dasein”, but not “Daseins”, it seems the logical conclusion to draw is that only one Dasein at a time is relevant for the purposes of Daseinsanalytik.
Well, if there’s only one at a time and it’s critically important for “fundamental ontology”, what could Dasein be? Haugeland says Dasein is “neither people nor their being, but rather a way of life shared by the members of some community.” In pre-Heideggerian literary German, Dasein as applied to the human world meant an individual’s mode of life: where they lived, how they spent their days, how they felt about things (“ein glückliches Dasein”). Does Heidegger break with this tradition by insisting on the collective character of Dasein, as someone exposed to the Hegelian concepts of Geist and Sittlichkeit might? Well, as Haugeland notes in this essay, one of the chiefest things that happens to Heidegger’s Dasein in its travails is its “individualization” (Vereinzelung). But Heidegger also talks about Dasein as an expression of an entire culture (“primitive Dasein“), and his work following the Kehre explicitly discusses a collective character for Dasein.
However, although Heidegger’s post hoc interpretations are powerfully suggestive, I think it is more plausible to view them as a reaction against “individualistic” tendencies in Being and Time imported from Kierkegaardian existentialism, rather than Heidegger’s obscure original intent. Dasein, as it appears in Being and Time, is an individual matter; that Heidegger resists its identification with previous concepts of individual life, like “person”, “soul”, etc. has to do with those concepts’ fundamental origin in the activity of looking for “definitory formulae” (logoi) for things, inappropriate where a thing’s essence is derived solely from Existenz. Furthermore, Heidegger’s muted enthusiasm for previous phenomenological descriptions of the person as a locus of “intentional acts” might suggest that he had the later-common thought that a great number of the critically important comportments of the human being toward its world are only inconstantly conscious; an insight, but not one which compels us to abandon the terrain of the individual life for communalities.
Another questionable interpretation of Heidegger’s German occurs when Brandom discusses Gerede, translated by Macquarrie and Robinson as “idle talk”. Haugeland offers a convincing analysis of the English expression, and plausibly links it to Heidegger’s thought in a way critiquing Brandom’s positive assessment of its value. The problem is that “idle talk” is a very free rendering of Gerede, which ordinarily much more nearly has the meaning Brandom isolates, “gossip” (the German Wikipedia page for Gerede calls it “ein anderer Ausdruck für Klatsch, Geschwafel etc”). Perhaps it is fair to say that Heidegger’s use of the expression as a term of art need bear no especially close connection to the colloquial meaning, but going back to the etymological form of Gerede (a common Heideggerian tactic) would suggest no ill omens: in fact, following the function of the prefix Ge- as a device for creating verbal nouns, Robert Denoon Cumming translated Heidegger’s term as “loquacity”.
Haugeland asserts that Brandom’s interpretation of Gerede, as an “ordinary” sort of discourse distinguished from knowledge by lack of explicit justification, is too innocuous: Heidegger’s criticism of Gerede is not derived from rhetorical inadequacies in its discursive make-up, but from the lack of authentic understanding it manifests, “not knowing what you’re talking about”. The Heideggerian tic of insisting that his expression for a phenomenon he clearly takes a dim view of “has no pejorative signification” can be charitably glossed as an unwillingness to tilt at windmills by taking up an “activist” stance against a fundamental feature of human life, but it is true that is not quite to say that Gerede is really part of the apparatus for making knowledge go. This is where the announced topic of Brandom’s essay, which makes a minimal appearance in Haugeland’s response, should come in: “thematization” is precisely what makes knowledge go, by establishing an authentic present which discloses entities in their scientific truth, rather than remaining with the fleeting and illusory present of the Man-selbst.
Still, “really knowing what you’re talking about” is not a very useful evaluative category, and affixing it to Heidegger’s distinctions does him no favors. Gerede and thematization are polar opposites: but celebrating a non-conceptual rapport with being as the upshot of authentic understanding almost makes Gerede the more attractive option.
Having discussed categorial grammar, I can introduce a logical notation employed by Montague which in some respects runs counter to it in intention: the “lambda calculus”. In the early 1930s, the logician Alonzo Church was searching for an alternative to axiomatic set theory for formulating fundamental mathematical principles. Instead of the “functions-as-graphs” concept set theory borrowed from Frege, Church wanted to use the more intuitive conception we have of mathematical functions as methods or rules for deriving an answer by following precise steps. The solution he came up with, the lambda calculus, involves two complementary ideas — a way of specifying the methodical content of a function, and a way of computing that function for a specific value.
The first operation, called “function abstraction”, takes a variable and indicates the procedure the value of the variable is to be substituted into. The variable is written after a lower-case Greek lambda (from whence the name) and before a period separating it from the expression of the procedure: λx.x+2 signifies the function that takes a number and adds two to it. Function abstractions can be nested within other function abstractions: using a procedure developed before Church by Moses Schoenfinkel (but known as “currying”, after Haskell Curry, who developed ideas similar to Church’s contemporaneously) functions of two variables can be represented by iteration of function abstractions using only one variable: λx.λy.(x+y) represents the familiar procedure of adding one variable to another. As originally conceived, lambda abstraction could employ predicates as well: λP.”John is P” would symbolize a function taking any predicate and applying it to John — but although a variant of this predicate abstraction is crucially important for Montague Grammar, it is fraught with peril, as I will explain below.
Like quantifiers, the lambda expression binds the variable in the expression: if it is not the case that all variables are bound or “spoken for” by variables, either directly or by currying, in an expression, then the function is not fully defined. If the function is fully defined, then we can generate a result by the operation of “function application”: written (f)x, it returns the value of the function f for the value x. The application (λx.x+2)3 returns the value 5, for example, since 3 is substituted in the expression x+2 and that expression is evaluated. So far, the lambda calculus might seem superfluous, since we already know how to carry out the operation of defining a function and evaluating it. However, “currying” gives a little taste of the power of defining mathematical concepts this way: and in fact all the mathematical objects used in set theory can be given “functional” definitions using the lambda calculus.
For example, function abstraction doesn’t have to be tied to a “concrete” mathematical procedure: we can put a lambda next to a variable ranging over functions, and define a “function of functions” like composition. Even the natural numbers can be defined using the lambda calculus: in “Church numerals”, the number 0 is represented as λf.λx.x, a function which takes another function and applies it to x 0 times, returning x. In fact, the lambda calculus was so powerful one could easily derive a contradiction similar to Russell’s paradox for naive set theory by abstracting over predicates, as was quickly noticed by the pioneering computer scientist Stephen Kleene. There are two ways around this. One way is to stick with the contradiction-free fragment of lambda calculus abstracting only over functions, the “λI-calculus”; and although this notation is not powerful enough to derive all set-theoretic concepts it is far from useless, as it is expressively equivalent to the formal model of computation devised by Church’s student Alan Turing, the “Turing Machine”.
Consequently, all computer languages employ methods similar to the lambda calculus for specifying subroutines, and the “functional” programming languages directly emulate the lambda calculus’s ability to specify functions of functions (in fact, programs written in them are “desugared” into a version of lambda calculus during compilation). However, the λI-calculus isn’t quite enough for the purposes of Montague Grammar — so I need to say a little bit about the other way around the paradoxes, the typed lambda calculus. The theory of types was introduced by Bertrand Russell to deal with the set-theoretic paradoxes: in all its forms, it amounts to carefully circumscribing the “levels” involved in a mathematical operation, to prevent paradoxical entities like “the set of all sets which are members of themselves”. Using a variant of the theory of types developed by Frank Ramsey, Church introduced a contradiction-free version of the lambda calculus. In the typed lambda calculus, the “type” of the function input and its output are both specified using the notation A→B: the function can only accept inputs of type A and return outputs of type B.
As before, this restriction becomes more intelligible when you consider more complicated formulations: a function which takes a function as argument and returns another function would be typed (A→B)→(A→B); the input must have the type of a function, A→B. Going into how Montague Grammar uses typed lambda expressions would be too much too soon, but it is critically important that the prospective Montague Grammarian develop some facility with them. (If my exposition has left you cold, the paper-puzzle game Alligator Eggs may trick you into “getting” these concepts.)
Ever wonder what it would be like if the guy who can’t stop talking to himself on the street had a blog? Wonder no longer — I’ve added some material from my dark ages under the category “Old”. The stuff was originally posted on Usenet in 2003 and 2004; I would have liked a blog but had exactly $0 to spend on the effort and didn’t care for Blogger. Since the Google Groups archive has become (presumably intentionally) harder to survey, I’ve added it as “archives”. I have suppressed material from that time, mostly for the reason that someone chancing upon it unawares might rationally expect my opinions on a certain topic haven’t changed; the material that is presented has been lightly edited to correct for the paraphasia which was glaringly evident in my speech and writing at that time. Although I wasn’t exactly a sympathetic person, be aware that some of the material is intentionally humorous, and was envisioned as a kind of “serious parody” of cultural studies and “theory” for more demotic circumstances; I was particularly proud of the title “What Color Is Cuauhtemoc Cardenas’ Parachute?”, for instance.
Seen carved into the loading tailgate of a delivery truck in downtown Portland:
There’s never been an inline image on this blog; I don’t own a lot of images, having never had a digital camera, and I’m kind of unclear on the legal protocol for appropriating them from elsewhere. (I did think it would be an amenity for readers if the image header displayed part of a painting by a famous Oregon native, at least until the powers that be complained, but then I changed my mind.) So the blog is going straight to video: a pleasantly surreal clip from the “Onion News Network” about paranoid schizophrenia. I was never all that fond of the Onion, but using real people forces them to work more carefully, and the result is really pretty philosophically interesting — it touches, in a suitably unhinged way, on the interest-relative character of the assessment of delusion. Enjoy.
I’ll start off the series on Montague Grammar today. The exposition will follow Montague’s paper “The Proper Treatment of Quantification in Ordinary English”, since that has historically been the most influential of Montague’s semantic writings: I guess I might say something about “Universal Grammar” at the end, although I expect the reader will find mastering the ideas of “PTQ” to be more than enough. As for acquiring your own copy, “PTQ” was published after Montague’s untimely death in a Synthese volume, then reprinted in Formal Philosophy, Montague’s collected papers. Most large university libraries will have Formal Philosophy and the paper is (rather unhappily) short and suitable for photocopying: however, it was also recently made available again in the anthology Formal Semantics, co-edited by Barbara Partee (a linguist who is responsible for Montague’s posthumous influence in that discipline).
The paper has four sections: the first is devoted to syntactic rules for a fragment of English — which is small, but includes a number of “intensional” verbs that make trouble for less complicated semantic approaches. These syntactic rules make use of categorial grammar, the topic of this post. I think explaining categorial grammar in sufficient generality, for people who might have no more “mathematical sophistication” than I had when I started out reading this stuff, will require going pretty far back: back, in fact, to Dirichlet’s definition of a mathematical function. When we are using them naively, to calculate results, mathematical functions seem to be “rules” which we follow to arrive at a certain result. But this approach is fraught with unclarity, and a major advance in the foundations of mathematics occurred when Gustav Lejeune Dirichlet defined a mathematical function as a collection of ordered pairs, one element of a pair being from the domain and another from the range; such a structure is known as a “graph”.
Now, if you took high school algebra after the introduction of “New Math” (i.e., are not seventy years old) someone once tried to teach you this definition; maybe it even took. But the real power of Dirichlet’s definition comes when you consider “higher-order” functions like composition, where you feed the results of one function into another function. Getting the composition of “functions-as-rules” straight in your head is very tricky, but the definition in terms of graphs is simple; just as one function can be represented by the ordered pairs <d, r>, composition can be represented by an ordered pair containing an ordered pair of the two functions being composed, and the composed function with the first function’s domain and (a subset of) the second function’s range: <<<a, b>,<c,d>>,<a,d>>. In this way, you can explain the functional articulation of mathematical concepts with ease.
What does all this have to do with the semantics of natural language? Well, enter Gottlob Frege. Frege’s attempt to formalize the language of mathematics required an analysis of language which divided up parts of speech in a really novel way, inventing the quantifiers we are familiar with today: functions-as-graphs are at the heart of his method. For example, Frege analyzed predicates (“x is red”) as functions from objects to truth-values: if an object possesses the property described by a predicate, the function maps it onto the truth-value “true”, and if not onto “false”. That might seem obvious, but other parts of speech can be given more complex but illuminating glosses in this manner: the Polish logician Kazimierz Adjukiewicz consequently took Frege’s syntactic analysis and formalized it as categorial grammar.
The building-blocks of categorial grammar are noun phrases (often written “N”), sentences (“S”), and functional relationships between them (symbolized by a slash): the predicate example given above would be written “N/S”, since it takes a noun and returns a sentence. An adverb, which takes a predicate and returns another predicate, would be written (N/S)/(N/S). Now, Montague added one further twist to the categorial-grammar framework; he noticed that some expressions of English were categorially equivalent, yet commonly identified as different parts of speech. For example, some verb phrases modifying another verb phrase (“try to”) would have the same analysis as the adverbs above. To “save the appearances”, he used a double slash, e.g. “N//S”, to keep one set of expressions distinct from the others.
I suppose I’m not, in point of fact, much of a revolutionary. The federal government has been better to me financially than private employers (paying for all of my childhood and some of my adulthood, although the former support was more generous than the latter); and Americans that talk about who should be “up against the wall when the Revolution comes” usually seem to me to be junior members of the Establishment hedging their bets in a gruesome and crypto-reactionary manner. But I suspect I’m enough of a revolutionary to have a potential problem in the form of the “Violent Radicalization and Homegrown Terrorism Act” — and you might be too, even if your people have been growing in this particular home since decidedly pre-Revolutionary times. Lindsay Beyerstein wrote a useful summary of the Act for In These Times, including an interview with the Act’s author, California Democrat Jane Harman; Democracy Now! had another journalist and a member of the Black Lawyers Guild on to explain exactly why someone involved with the activist left should have a problem with its attempt to combat “violent extremism” at a level prior to conspiracy to commit terrorist acts.