Typos fixed, italics added, embedded hyperlinks activated.

Related readings:

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.

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. 


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 

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 

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:


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

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: 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,



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.


Synergetics on the Web
maintained by Kirby Urner