---
breaks: False
tags: vsu, philosophy, epistemology
---
Voronezh SU, Philosophy, 01-abstract-objects
====

**Sergey K**, year 4, group 6.

## Statement

0. Read https://plato.stanford.edu/entries/abstract-objects
1. Describe the difference between abstract and concrete objects
in everyday life?
2. How these distinctions are insufficient
for the purposes of philosophy and science?
3. How did philosophers of the ancient and the modern age
approach this question?
4. Comment on Frege's definition of abstract objects.
5. Is an artifact an abstract object?
6. Is the sole presence of an object in space
a sufficient criterion for it to be called *concrete*?
What's a space then?

## 1. A commoner's distinction
1. Concrete things are the tangible ones
(doesn't work for elementary particles, EM-fields, gravity)
2. Concrete objects have spatial location,
whereas abstracta exist nowhere in space-time
(did the game of chess exist 'fore it was invented
and would it cease to exist if the mankind was to extinct?)
3.

## 2. Insufficiency of commoners approach

## 3. Ancient v. contemporary

> ...the distinction between abstract and concrete...
> played no significant role in philosophy before 20'th century

0. Plato.
1. Locke:
> "abstract ideas are formed from concrete ones
> by omission of distinguishing detail".
2. Distinction btw mental and material

Asbtracta --- the Frege's "third realm",
things neither concrete nor mental.

E.g. numbers exist independently of one's consciousness
and they sure are not material: they're *abstract objects*.
3. Existence of abstracta:
platonists (there is at least one abstract object)
vs nominalists (there is none).
4. Non-spatiality and inefficacy criterion
> An object is abstract IFF it's non-spatial
> and causally inefficacious
5. The way of example:
just list paradigmatic abstracta and concreta
6. The way of conflation.
7. The way of abstraction.

## 4. Frege

Asbtracta are the Frege's "third realm",
things neither concrete (belonging to the sensible external world)
nor mental (belonging to the internal world of consciousness).
Lewis calls such an approach the "Way of Negation":
abstract objects are defined to be those
which lack certain features distinguishing to concrete objects.

> An object is abstract IFF
> it is both non-mental and non-sensible.

The rest of the article that describes the neo-Fregian approach...
Well it doesn't really make sense
and consists of trivial criterions like
"$x$ is a value of $f$ if $x$ is a value of $f$".

> "$f$ is an abstraction function... iff for some equivalence relation $R$
> ... $f(x){=}f(y)$ IFF $xRy$."

The thing is this expression together with the function $f$
already defines such a relation $R$.
Given that the "function" is a function
and "sets" are sets
in mathematical sense, of course.
Which doesn't seem to be the case.

## 5. Artifacts
There are *abstract artifacts*
which owe their creation to the consciousness
but exist independent of it.

> If the world took a brief collective nap,
> Pride and Prejudice would not pop out of existence

Such artifacts may be considered abstract objects
in the sense that they're mind-independent
yet not physical.

## 6. Non-spatiality

> An object is abstract IFF it's non-spatial
> and causally inefficacious.

Alt:

> An object is abstract (if and) only if it
> fails to occupy anything like a determinate region
> of spacetime.

Caveats:
ambiguity in the case of impure sets &c.

## A bunch of excerpts

> There's no "correct" way to draw the line between abstract and concrete objects.
>
> ...what we seek is ..., rather a proposal for how the term
> might fruitfully be used in the future.

By intuition (though not *really* intuitive in most of the cases):
| Abstracta | Concrete |
| --------- | -------- |
| Letter 'A' | Letter 'A' spelled on a blackboard |
| Whiteness | White (n) |
| Whiteness | White chalk (a) |