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Date: Tue, 05 Oct 1999 13:20:30 -0700 To: edapple@aol.com From: Kirby Urner <pdx4d@teleport.com> Subject: Re: Philosophy of mathematics, Nominalism, LW and RBF Howdy Ed -- Was at the local Powell's on Hawthorne last night, and picked out James Robert Brown's new book Philosophy of Mathematics: an introduction to the world of proofs and pictures (Routledge, 1999). I also got a new (used) copy of Critical Path as mine has disintegrated (have another copy on disk) -- plus a couple Octavia Butler scifi novels for airplane reading. A number of things I like about this philosophy book. However, I also want to circle a potential source of confusion when it comes to discussing Wittgenstein's stuff -- which this book does, at some length. The confusion centers around this word 'Nominalism', which gets its initial trajectory in Medieval Times. It's usually cast against both Platonism and/or Realism (also potentially confusing, as nominalism may sound more "realistic" vis-a-vis an insistence on the "reality" of Platonic universals). Whereas the Platonist thinks meanings of words may stem from their pointing to metaphysical universals, the nominalist considers these same words to be linked only to particulars, as universals do not exist. That sounds like a sentence you'd typically find in a philosophy book. Quoting from Encarta: Nominalism, doctrine in the medieval philosophy of Scholasticism, stating that abstractions, known as universals, are without essential or substantive reality, and that only individual objects have real existence. The nominalistic doctrine is opposed to the philosophical theory called extreme realism, according to which universals have a real and independent existence prior to and apart from particular objects. Nominalism evolved from the thesis of Greek philosopher Aristotle that all reality consists of individual things; extreme realism was first enunciated by Greek philosopher Plato in his doctrine of universal ideas. [http://encarta.msn.com/index/conciseindex/06/0067F000.htm] However, what both Platonism and Nominalism seem to share, is a model whereby "meaning" or "sense" is primarily owing to the fact that signs or symbols have referents. What's at issue is the nature of those referents: are they "particulars" or are they "universals"? Both schools of thought share a name->thing model of meaning. As the Catholic Encyclopedia puts it: What are called general ideas are only names, mere verbal designations, serving as labels for a collection of things or a series of particular events. Hence the term Nominalism. Neither Exaggerated Realism nor Nominalism finds any difficulty in establishing a correspondance between the thing in thought and the thing existing in nature, since in different ways, they both postulate perfect harmony between the two. [http://www.knight.org/advent/cathen/11090c.htm] I might rewrite this last sentence to say "since in different ways, both postulate a one-to-one correspondence between signifiers on the one hand, and objects (of whatever ilk) as the 'meanings' and/or 'referents' of those signifiers". It's this "meanings as referents" doctrine which Wittgenstein takes issue with. This is why he starts Philosophical Investigations with that quote from St. Augustine (in Latin) -- he considers it a clear statement of this "meaning through naming" picture, and he wants his introductory paragraphs to get us moving in a different direction i.e. he's using Augustine's view for contrast. And it's this model of meaning which we might also call "Nominalist" (because it centers around "naming"). But in so using this term, we're setting "nominalism" on a trajectory such that Brown's kind of Platonism (as described above) is likewise a kind of nominalism (because also holding to the name->object view). So you see the potential for confusion here. Here's a quote from Philosophy of Mathematics wherein Brown is sounding like a nominalist (in the sense I mean above, i.e. like an Augustinian): Platonism and standard semantics (as it is often called) go hand-in-hand. Standard semantics is just what you think it is. Let us suppose the sentence 'Mary loves ice cream' is true. What makes it so? In answering such a question, we'd say 'Mary' refers to the person Mary, 'ice cream' to the substance, and 'love' refers to a particular relation which holds between Mary and ice cream. It follows rather trivially from this that Mary exists. If she didn't, the 'Mary loves ice cream' couldn't be true, any more than 'Phlogiston is released on burning' could be true when phlogiston does not exist. [JRB, Philosophy of Mathematics, pg. 12] He seems to inherit his nominalism (aka "standard semantics") from Frege and works from this "given" back to the Platonist position (cite pg. 147). When he discusses LW's work, he never effectively contrasts it against "standard semantics", perhaps because he doesn't appreciate the depth (and consistency) of LW's critique? Rather, he falls back on Frege, while taking LW's use of pictures and diagrams as grist for his mill, as examples of how we might elevate at least some such pictures to the level of "formal, mathematical proof", thereby making them "windows to Plato's heaven" (pg.39). Here's how Brown actually writes about "nominalism" (which, as a Platonist, he considers an alien "ism"): Of course, there are red things, but is there _redness_ itself? Some people are wise, but does _wisdom_ exist in its own right? Many think the answer to these questions obvious: No, such queer entities do not exist. Those who dismiss them are the nominalists at heart. Abstract terms, according to nominalists, are not the names of abstract objects. Redness and wisdom are just words and nothing more -- hence 'nominalism'. As for mathematics, the instinctive nominalist holds that there are no numbers, only numerals. Platonists think that the numeral '2' is the name of the number two, just as 'Jim' names me. But, for the nominalist, there are no numbers; the real subject matter of mathematics is numerals, symbols, and words, all of them strictly meaningless -- not in the sense of gibberish, but in the sense that there is nothing that they mean, or name, or to which they refer. (pg 63). Reading the above, you actually get close to the Wittgensteinian view in some respects, and indeed, Brown considers Wittgenstein a "radical conventionalist" with views "akin" to the nominalist's. (pg. 63) In the above passage, Brown seems to stray from the Medieval meaning (he's free to do so of course), depriving the nominalist of any objects at all, rather than leaving referents in the picture, but having them be particulars, versus Platonic universals. That's partly why his characterization sounds somewhat Wittgensteinian I think. So, for Brown, Wittgenstein is a quasi-nominalist, whereas for me, LW's an anti-nominalist operationalist. Plus I see Brown himself as a nominalist of sorts, despite his self-professed Platonism. I suppose I could make this whole business simpler and just say I'm the only one who's seriously confused about "nominalism", and hence forth abandon my current usage. On the other hand, given both the Platonist and the Nominalist share this propensity to accept the name->object "standard semantic" model, and given the word "nominalist" connotes "one fixated on names and naming" (more so than does the word "Platonist"), I'd like to keep "nominalism" with the meaning I'm giving it. I choose to keep "nominalist" on the trajectory I've supplied -- even if this is divergent from Brown's more standard usage pattern. I circle the potential for confusion here not just anticipatorily, but with hindsight, given last year's fracas in the newsgroups. There, as here, I went to some lengths to give definition to nominalism as that which LW takes issue with in the Investigations. You can find such posts at: http://www.deja.com/getdoc.xp?AN=392232336&fmt=text http://www.deja.com/getdoc.xp?AN=392458776&fmt=text Quoting from the 2nd (above), you can see how I'm addressing this very confusion, and how my sparring partner is highly suspicious of my reasoning, wondering if I'm making any sense at all, or just indulging in "squink" (purposely obscurantist lingo used with an eye towards escaping capture and exposure). Note also that I classify RBF as an "operationalist" (with the later LW) -- not that any of this is news to you of course. ======= >I pointed out that these views fall on the >realist side of any reasonable realist/nominalist divide, and now you >come back with evidence that his *later* views can be called >nominalist. No, you're confused. My evidence was to the point that he [Wittgenstein -- KU] was targeting a kind of "nominalism" or "essentialism" (Feyerabend, Popper), _including his own_, in his later philosophy. Hence my quotes from Finch, in which "the nominalist" is the one most frustrated (most countered) by the PI approach. In other words, I was consistently advancing "nominalism" as a useful label for those philosophies, whether realist or idealist, which incorporate a name->object model as basic to their language->world picture. Specifically, I was using nominalist to identify (quoting myself): (a) the philosophy of the TLP and (b) a more generic model of meaning as embodied in the opening quote from St. Augustine, used by LW in his PI to set the stage for his following critique and (c) my own use of name->thing notation (under which I file numeral->number as a subclass) In my previous post, I was establishing: (a) how this use of "nominalist" makes sense, independently of any realist versus idealist polarity and (b) that at least one other authority on LW's philosophy uses "nominalist" in the same sense I do (i.e. Finch) >Since those later views (as you yourself note) run >counter to the earlier ones, this is (for you) at best irrelevant and >at worst support for *my* assertion. > No, you have gotten yourself in a muddle. Bringing "realism" into the picture to counter "nominalism" is likely to establish a useful polarity in some contexts, but in this one it hasn't served you well. To further clarify: Nominalist Operationalist TLP PI early LW later LW St. Augustine R. Buckminster Fuller Numeral->Number symbol-use activities >You're a dishonest fool. > [From: From: urner@alumni.princeton.edu (Kirby Urner) Subject: Re: Lightbulbs. Was: Mean value theorem, ... Date: 18 Sep 1998 00:00:00 GMT Message-ID: <3602830f.310886@news.teleport.com> Newsgroups: sci.math,misc.education,sci.philosophy.meta, alt.philosophy.debate ] ======= I consider RBF an operationalist in the sense that he's explicit about there being a precessional relationship between the generalized principles and our universe of human-to-human communications -- and not a literal, 180 degree, simple name->object "pointing" relationship (e.g. meaning involves "doing truth", not just "seeing truth"). There's a specific card-entry in your Dictionary about this (encodings of principles as precessional to the principles themselves) that I'm recalling, but I couldn't find it to quote for this letter (perhaps I will later). Wittgenstein's philosophy is useful in clarifying how a language as remote as the one in Synergetics might nevertheless be meaningful (operational). None of this is about closing the door between Fuller and Plato by the way. There's much to synchronize in their respective spheres, even if we drop the nominalist's rope bridge between the two. Kirby |
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