Wednesday, February 23, 2011

A Taxonomy of Nominalism

Among my favorite books in the field of logic is Susan Haack, Philosophy of Logics (1978).  The plural in the title might be surprising -- isn’t Logic simply the formalization of the way things are?  -- but it is by no means a typo.  She distinguishes no fewer than five families of logics:  traditional logic (i.e., the Aristotelian syllogistic), classical logic (what you were  taught in college, unless you spent all your time on panty raids), extended logics, deviant logics (no no, it’s not what you imagine), and inductive logics.  These each come in various flavors:  thus, under “extended logics”, we understand:

            modal logics
            tense logics
            deontic logics
            epistemic logics
            preference logics
            imperative logics
            erotetic logics  (no, that’s not what you imagine either)

Note the plurals:  These each have subflavors too.

Are we having fun yet?  We should be.  William James remarks (The Principles of Psychology (1890), vol. II)  that humanity seems to have a kind of taxonomic instinct, reveling in setting up systems of pigeon-holes:  rather like the sex instinct but even better because you don’t get AIDS.  Surely you remember the delight you felt as a ten-year-old, putting your return address on the envelope of a letter to a friend (well, that was before e-mail;  you’ll remember if you are over about eighty years old):

Timmy Thompson
322 Mulberry Street
The Midwest
The Western Hemisphere
The Planet Earth
The Solar System
The Milky Way …

Nowadays it’s even better, since you can keep going all the way up to the Multiverse.  (Only, no-one writes letters anymore, and there are no more ten-year-olds.)

In her later work, Evidence and Inquiry (1993), in the course of arriving at her new style of epistemology --- “double-aspect foundherentism”, no less -- Susan Haack coins or refines nomenclature for a great many epistemological schools and subschools, and even for individual varieties of ideas, labeling these with such tags as 
            FD1 superscript-E subscript-EXT
            FD2 superscript-P

rather reminiscent of the old joke about the comedy club, for whom the jokes were so familiar they all had numbers.  (Punchline:  “933.”  Nobody laughs.  Why not? “He didn’t tell it right.”)

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In this spirit, we shall here embark upon an ambitious project of anatomizing Nominalism.  (Funded by USAF grant #586-77-E8-99999.)

(1)  On Nominalism

There are a great many individual theories beneath the big tent of Nominalism.  Since, however, they all suck, these need not detain us.

Much more rewarding is the following.

(2)  On Anti-Nominalism

There are several venerable schools in this vein.  Most familiar is Classical Anti-Nominalism, also known as Anti-Nominalism simpliciter, whose central thesis reads as follows:

(C.A-N.)  Nominalists just suck.  End of story.

Then there is Aetiological Anti-Nominalism, characterized by the following insight:

(Ae. A-N.) Nominalists were all dropped on their heads as infants;  a fact that explains, while it does not excuse, their behavior.

And lastly Pediculotic Anti-Nominalism, which maintains:

(P. A-N.)  Nominalists can best be understood as a form of body lice.

This popular view breaks into three schools, according as the insects in question be specifically head lice (Pediculosis capitis), lice infesting the armpit hair, or some even naughtier lice of which decorum forbids mention.

(This will all be on your mid-term.)

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[update October 2011]
I just stumbled upon this spicily-titled item:
Scientific Realism and Mathematical Nominalism:  A Marriage Made in Hell

Here we learn that “Nominalists hold that there are no numbers”;  this involves them in certain epistemological difficulties.   But en revanche (ô doulce revanche), numbers hold that there are no nominalists.  This  involves them in no difficulties at all.

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Nevertheless, in that broad spirit of tolerance so characteristic of Realists, we here list those instances in which a Nominalist did (against all odds) manage to come up with something witty or interesting.  We believe this list to be complete.

Unum, verum, bonum -- the old favorites deserve their celebrity.  There is something odd about each of them.    Theoretical theology is a form of onomatolatry.
-- J. L. Austin, “Truth” (1950)

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[Update 2016]   Well okay -- one synonym from a linguistically-inclined Nominalist in his treatise about ambiguity and vagueness:

Applied to semantical topics, the nominalistic attitude here outlined  may be lbeled  inscriptionalism.  The label implies no theoretical contrast with nominalism;  it simply calls attention to the favored status of tokens, and the exclusion of types, classes, meanings, forms, and attributes  from our semantic apparatus.
-- Israel Scheffler, Beyond the Letter (1979), p. 8

Cf. Realism, in a math context, being called Platonism.


  1. Nominalists arguably play one important role, and that is passively to receive the mud which some sling at them. Every Hatfield needs mis McCoy, I suppose, even if it means propping up McCoy's mummified remains in front of the cabin the better to absorb those Springfield rounds.

    Well, but what of this? If we divide the number line into units shorter than any possible meaningful particle or sub-particle, we have an ideal that corresponds to no real object. If, on the other side, we posit the existence of an ideal circle which is minutely skewed or eccentric, somewhat in the manner of certain anti-nominalists, so that its deformity passes unnoticed in all our quotidian approximations, we have an ideal whose real nature eludes our naive generalizations. If the world is filled with ideals that do not correspond to our reality, or belie our versions of it, the nominalist may have the stronger view, unless we are speaking only of *comfort.*

    Oliver Sacks' discussion of color is well-known in this regard. Is my "green" your green? Where's the ideal?

  2. Thank you for your comments.
    I heartily agree with your observation, "Nominalists arguably play one important role, and that is passively to receive...", though I might end the sentence somewhat differently.