
Medieval Theories of Haecceity - benbreen
http://plato.stanford.edu/entries/medieval-haecceity/
======
Animats
Aristotle created some messes in logic that weren't untangled until the 19th
century. This is one of them.

This concept has some practical applications in computing. When are two
objects equal? If they are immutable, and there is no way to distinguish them
via their public interfaces, are they equal? Should they be considered the
same object? If so, copies can be shared, or single objects can be duplicated
without harm.

In logic, this is a statement in the theory of uninterpreted functions:

    
    
       (forall f, x, y  f(x) = f(y)) => x = y
    

Here, if any function f applied to x and y produces the same answer, x=y. x
and y are indistinguishable, and in mathematics, that implies they are
identical. This has applications in constructive mathematics, where all the
functions already in existence can be enumerated and tried. Any new function
must be a composition of existing functions, so if that property holds for the
existing functions, it must hold for all new functions. (I figured this out
ten years after I had a paper rejected by JACM, where I did bulky machine
proofs of the theory of arrays without using set theory. There's a better way
that's fully constructive using the argument above.)

The medievalists apparently didn't pick up on the immutable angle. That led
them into circular reasoning: "Maintaining that an object is singular or
individual because it results from or is endowed with a proper principle of
individuation which is itself singular, amounts to nothing more than
duplicating what should be explained."

~~~
mjburgess
The problem is we're dealing with real objects, conflating real objects and
mathematical objects is begging the question against the person saying we need
haecceity (also called "thisness" \- the property of being "this" thing and
not "that" thing).

If real objects are just like mathematical objects then all they are is
bundles of properties: object A is no more than the set of properties that can
be ascribed to A.

There are a few problems with that, but here's an interesting one. Consider a
world in which there are only two identical iron spheres, say 1 mile wide, 1
mile apart from each other. Now each sphere has exactly the same properties -
are they the same spheres?

Most people would say no. So what individuates them? Well, some property that
makes it the case that one sphere is that sphere and not any other.

To put it in your terminology, for every boolean function f(x) which is true
iff x has property f and false if it doesn't have f (eg. IsIron(x) = True),
then both spheres have exactly the same set of true/false values for all
properties (forall f.). _Unless_ we introduce a haeecity functions: a(x = A) =
True for A, b(x = B) = True for B - ie. properties which are only true when
their arguments pick out the objects which they are about. Then we can
distinguish between objects, because they have different values for haecities
(property functions) a, b.

~~~
anentropic
First time I have read anything about haecceity. The first thing that pops
into my head regarding the two iron spheres is that they must differ in their
position in the universe, so they differ in something other than their
haecceity. If there is no way for two identical real objects to occupy the
same space then maybe this concept never applies to real objects...?

~~~
brudgers
The problem for a Midevalist is that location is an _accidental_
property...transposing their locations does not make one the other and vice
versa. Location as the basis for haecceity is numerical individuation of the
sort Scotus rejects.

~~~
anentropic
Hmm... but in the real world there's no way to transpose their locations
without moving continuously through intermediate positions, so at the end of
the transpositions the two objects will have a different history of location
and their identity can be observed throughout and thus preserved.

If they could be transposed instantaneously they'd be indistinguishable.
Although they would still have a different 'history of locations' property.

Or are we saying the same thing? that there's no need for haecceity in the
real world as there are always real properties that could be used to
distinguish objects?

~~~
brudgers
The real world, so far as I am aware, does not consist entirely of two iron
spheres. Moving the goalposts does not help clarify the reasoning nor refute
the point about haecceity.

That a person cannot tell two things apart is also accidental for the
mediaeval philosopher. God can. Omniscience gets us the Locational history. Of
course this means the universe contains three things: two spheres and God.
That would be a given for any public opinions expressed by Scotus or his
contemporaries.

The obvious move to defeat Haecceity is to postulate a universe with two Gods.
Alas, the medieval philosophy logically precludes this: Two omnipotentencies
is a contradiction and the Council of Nicea dogmaticcally solved that a
millennium before Scotus's time.

If that's what you're saying then yes we are saying the same thing.

------
zem
one of my favourite words!

