Tag Archives: Abstract Objects

Paul Vincent Spade On Motivating The Mediaeval Problem Of Universals

“It is well known that the problem of universals was widely discussed in mediaeval philosophy — indeed, some would say it was discussed then with a level of insight and rigor it has never enjoyed since.” What follows is an extremely good motivation of the medieval problem of universals, offered by Paul Vincent Spade in the introduction to FIVE TEXTS ON THE MEDIAEVAL PROBLEM OF UNIVERSALS.

“It is easy to motivate the problem of universals. Consider these two capital letters: A A. Ignore everything else about them and for now observe only that they are of the same color: they are both black.

As you look at the two letters, how many colors do you see?  Two different answers are plausible.  You may want to say  you see only one color here, blackness.  You see it twice, once in each of the two capitals, but it is the same color in both cases.  After all, did I not just say the two letters were “of the same color“?  Isn’t that obvious by just looking at them?  This single blackness is the kind of entity that is repeatable, found intact in both letters at the same time; it is what philosophers call a “universal.”  If this is your answer, then you believe in the reality of at least one universal, and are in that sense a “realist” on the question.

But now reset your mental apparatus and look at the two letters again.  On second glance, isn’t it obvious that you see two colors here, two blacknesses:  the blackness of the first A, this blackness, and then the blackness of the second A, that blackness?  The two colors look exactly alike, yes, but aren’t they visually as distinct as the two letters themselves?  If this is your answer, then you do not believe in the reality of universals (at least not in this case) and are a “nominalist” on the question.  The problem of universals is in effect the problem of deciding between these answers. ”

Of course, my eros for the mediaeval problem of universals is just a stepping stone on the path to eros for the platonic form BEAUTY.  And the stepping stone previous to eros for the mediaeval problem of universals is, in the grand tradition of platonic philosophy, eros for gorgeous young men such as this one, who is today’s homage to Plato’s SYMPOSIUM.

most_beautiful_men_04

If Plato can include a bad boy like Alkibiades in his SYMPOSIUM, I can include a bad boy like Josh in my post.

Advertisements

Some Clean-Up Work: Why A Name Needs A Selector If One Is To Be Fully Explicit

Let me unpack a bit the NAME() selectors I have been using.  A selector such as NAME(‘Tom’) takes as an argument the string ‘Tom’ and returns the name Tom.(Tom is being mentioned here, not used.  The arguments surely have to be syntactic arguments.)  A string comprises 0 or more written characters (henceforth  just ‘characters’).  A character is an abstract object:  the character ‘e’, for example, can be instantiated by a blob of ink, a pencil mark, a set of pixels….  So a string is an abstract object comprising other abstract objects, and exists at one level-of-abstraction higher than they.

A string of characters is not itself a name, since a name can also be instantiated by a zero or more sounds.  I say “0 or more” because I can imagine a language that uses the glottal stop as a name, whatever the merely practical difficulties might be in doing so.  (A name that could never be pronounced by itself, but only within a stream of other sounds?)

(Perhaps — to jump back to characters for a moment — this language could write the name as ”.  So a name could be instantiated by strings comprising 0 or more characters. )

(Perhaps — to jump back to sounds for a moment — if I tried hard enough I could turn a sound into an abstract object (perhaps one sound can be instantiated by any number of configurations of sound waves?), but I will not try this at the moment. )

Instantiated, as I was saying, by either strings or sounds, a name is an abstract object, one existing at one level of abstraction higher than the abstract object STRING, which itself is one level of abstraction higher than the abstract object CHARACTER.   Not identical with either a sound or a string, a name is best represented not by, for example, ‘Tom’ or <<some sound>>, but by NAME(‘Tom’) or NAME(<<some representation of a string of sounds>>).

This, then, is why, when I am trying to be fully explicit, I refer to a name not as, e.g., ‘Tom’, but as NAME(‘Tom’).

Today’s homage to Plato’s SYMPOSIUM is Ashton Kutcher:

Ashton_Kutcher

There is too much beauty in the world.  How can one concentrate on anything at all with gods like this walking the earth?