Do abstract objects exist?

hello YouTube so do abstract objects

exist what I want to do in this video is

just outline my take on this question

um so now a first problem we have to

deal with when asking this question is

what exactly is an abstract object

um it turns out that defining the

distinction between abstract objects and

concrete objects is actually really

difficult and I'm not going to go into

the debate about that I'm just hoping

that anybody watching this video has

some intuitive sense of what that

distinction is supposed to be but

briefly uh the way that philosophers

usually talk about this abstract objects

are supposed to be

non-causal they have no causal Powers

um they're non-spatio temporal so they

don't exist in space and time the

standard examples of abstract objects

are things like numbers sets and other

mathematical objects

um and so uh whereas you know and this

contrasts with with concrete objects

like hands and tables and chairs and uh

protons and neutrons and so on

um so yeah you know the objects that are

are sort of found in your everyday

perceptions

um our concrete objects

um but then in mathematics for instance

we seem to talk about objects like the

number five and you know the number five

uh that's not something you see and it

doesn't seem to you know it doesn't sort

of seem to exist in the world at least

not in space and time and so on so

um that's that's the basic distinction

and then the question is well are there

abstract objects

um you know does the number five for

instance really exist

um so okay what's my take on this well I

think that the first thing to note is

that the standard way of framing this

question about whether or not there are

abstract objects when in the standard

ways of framing this concrete objects

tend to be kind of taken for granted so

we sort of take it for granted that

there are hands and trees and Fields and

cars and planets and protons and

neutrons and so on

um and so we have a sort of you know

world view where uh uh we have space and

time and it's populated with all of

these concrete objects and then and then

there's this problem of well how do we

fit abstract objects into this world

view

um so uh and then and then the issue is

well if we think of abstract objects as

being by definition you know

non-spatio-temporal or non-causal then

we run into a whole load of

um of sort of difficulties uh accounting

for things like how we're supposed to

know about them so in the case of

concrete objects

um accounting for our knowledge of

concrete objects is fairly

straightforward uh so take my hand right

well my hand uh exists out there in the

world

um I believe that I have a hand how did

I come to have knowledge of my hand well

there's there's this object out there

light hits the object it bounces off the

object interacts with my eyes you know

and and so on and then and then whatever

there's some sort of brain process that

occurs but but the point is is that I

can like enter into these causal

relationships with this object out there

and you know that gives us a very

straightforward account of how I can

have knowledge of this object whereas

with abstract objects given that they

are non-spatio-temporal but they have no

causal Powers

it's not at all clear how I could have

knowledge of them you know I mean so the

number five right well the number five

doesn't sort of it doesn't exist any it

doesn't exist in the world it's not

something I can perceive or interact

with in any way

um so

you know like how do how do I get

knowledge of this stuff

okay that's a problem

um all right so

that's the sort of usual way the debate

is framed right we are kind of taking a

world view for granted where we have

concrete objects and then there is this

problem of abstract objects

now I think what I want to say is well

I'm a constructivist about all objects

so I would say that hands tables chairs

planets and so on

these objects exist only relative to

particular perspectives and they exist

in virtue of uh

the fact that we are kind of arbitrarily

drawing lines and drawing boundaries in

particular ways we make concrete objects

up

um and you know the the

and how this applies to abstract

objectives well I would say just as we

can construct concrete objects we can

similarly construct abstract objects so

okay to explain this in a bit more

detail the first thing to say is that

concrete objects are really weird

they're really bizarre there's all sorts

of philosophical problems that um that

can be pushed against the existence of

concrete objects so for example there

are problems of vagueness so if I take a

hand well you know the hand has certain

boundaries and then I can say like you

know this this is you know there's like

an atom here that is part of the hand

and then there's an atom here that's

part of the arm not part of the hand but

then where exactly is the line between

hand and arm uh you know there's going

to be some some sort of Point as you as

you kind of move up

um where it's just not at all clear uh

whether or not something whether or not

there's an atom counts as being part of

the hand

um similarly you can consider at what

point if you were to make changes to a

hand

you know we can imagine like altering a

hand atom by atom

um imagine like a series of objects

where you start with this hand and then

you alter it atom by atom until you end

up with a scrambled egg and then the

question is well like again Where's the

Line like when does it stop being a hand

where in that sort of series of changes

do we go from you know this is a hand to

this is not a hand so this is problem of

vagueness

um another problem is the problem of the

many so the problem with the many is

um if you take my hand

and we say that you know if we say that

there's a hand here then there's going

to be some set of atoms that is

identical with that hand you know I mean

presumably like the the reason why

there's a hand here is because there's a

set of atoms or you know I don't know

other parts or whatever that that make

up this hand

um but there's going to be trillions of

other sets of atoms that differ minutely

from that initial set of atoms and those

trillions of other sets of atoms seem to

have like perfectly equal legitimate

claims to being hands so if you take the

set of atoms that constitute this hand

and then you you know take one atom away

well what you end up with is a set of

atoms that has a totally legitimate

claim to being a hand and I mean that

set of atoms is is there right so

there's basically trillions of sets of

atoms that all have perfectly legitimate

claim to being a hand

um and so we seem to end up with this

conclusion that if there's a hand here

then there's actually trillion of hands

here

um so that's that's a bit strange

um there are philosophical problems

about uh under what circumstances

um two objects compose a further object

you know like do the objects need to be

in contact are they actually need to

have physical contact with each other is

it enough for there to be some sort of

you know other type of influence or

maybe you know there's some sort of

functional role that the two parts play

and that's what makes them a further

object

um there's actually even even a causal

problem with concrete objects because a

lot of the ordinary objects of

perception like hands you might argue

are causally redundant

um because

whatever so like if I say well I'm

perceiving a hand and then I give some

sort of causal model for this well it's

not quite true to say that you know

light hits the hand and then bounces off

the hand and hits my eyes right I mean

what's happening strictly speaking uh at

least on the standard physicalist model

is you know you have photons that are

interacting with atoms just on the

surface of the hand

um and then that's bouncing off in it so

the point is is that any kind of

anything that you claim any kind of

causal claim that's made about what this

hand is doing

um it seems that that's preempted by

um the causal powers of the atoms uh

that compose the hand so actually the

hand itself just doesn't have any causal

role it's causally redundant

um

so okay these are just some of the

philosophical problems that uh that

arise when we start thinking about

concrete objects now the sort of view

that I have is that

is that all all of the concrete objects

of our perception are actually just I

mean we we just make them up basically

they're just made up right

um so I mean you could if you want say I

I suppose that there just are no

concrete objects um that

um at least no ordinary objects you

could if you want to say that well maybe

there just are no hands on this sort of

view what I prefer to say is no there

are hands but hands are constructed

um like you know we we make things up so

that there are hands and actually I mean

if you say that there are no hands so

one sort of view for instance is

mirological nihilism

um a standard neurological nihilist will

say that there are no composite objects

um and there are only simple simple

Parts

um sorry not Parts there are just

simples and these symbols never compose

a further object so we might think of

these as being like fundamental

particles right there are just

fundamental particles Vehicles arranged

hand wise but there are no hands

um you know a neurological nihilist will

say that my view actually is that

um

neurological nihilism is one perfectly

legitimate way of constructing objects

but I don't take it to you know have any

you know it's I don't take that to be

you know in any way like more accurate

or more true or more legitimate than the

common sense way that we construct

objects so you know in the common sense

way that we construct objects we you

know we draw uh all sorts of boundaries

around composite macroscopic objects we

kind of project composite macroscopic

objects onto the world and we say you

know I have hands

um so uh I I endorse a pretty kind of

global constructivism about objects and

okay that's concrete objects

so

from that point of view then

um it's perfectly fine to say that you

know hands exist and tables and chairs

and so on exist but they exist from

you know certain perspectives right

there are certain kind of object

Frameworks as it were that we have

constructed and

um and it's you know within those

Frameworks we say that these objects

exist

um but that's you know that's as far as

it goes

um

now if we then turn to the question of

abstract objects

well

I mean the way I would say this is that

in just the same way that we construct

concrete objects you can construct

abstract objects in fact mental

abstraction seems like a very

straightforward process to me so

we can take an object of a particular

shape and say oh this object is square

right you know I mean I'm looking at my

computer right now and

um well I guess it's you know it's

rectangular right so I I say okay the

screen is rectangular

um now of course

um you know the screen is not perfectly

rectangular if I was to sort of zoom in

I would find actually there's all sorts

of

deviations from a Kind of Perfect

rectangle but what's happening here I

think is that you know I'm looking at

this object and then uh I'm I'm

abstracting right from from what I see

I'm simplifying so you know I can take

it that the computer

obviously it doesn't actually

instantiate a perfectly straight line

but I can imagine that there is a

perfectly straight line there and then I

can kind of construct this kind of Ideal

rectangle

um and one thing I could say is that I

mean I could actually just say well

you know the computer just instantiates

rectangular rectangularity

um and that's sort of true enough

um given the sort of context in which

I'm speaking like in an everyday context

it's true enough to say that the

computer is just the shape of the

computer's screen is just rectangular

um and then I just take it as as if it

instantiated a perfectly straight line

um and it was a perfect ideal rectangle

um so okay what's happening is I'm

looking at this object I'm kind of

abstracting and sort of treating it as

though it was composed of these very

simple perfectly straight lines and then

I can engage in this other Pro in this

other type of abstraction and consider

rectangularity in general

um I can think of like other things that

instantiate rectangularity

um and then I can investigate the

properties of rectangularity in general

just like just rectangle angularity

um so I I mean there's no I it doesn't

seem to me like there's really any kind

of there's there's really any

philosophical problem here right like

this is just clearly something that

um human beings have the cognitive

capacity to do is

um in in the same way I would say that

we can you know sort of draw boundaries

in such a way that we create the

computer

um and when I say create the computer I

mean uh you know we create it via the

sort of boundary drawing

um obviously we also create it in the

sense that we've put the parts together

physically but you know I mean uh I mean

like I can like walk into a room and

then I'm you know I'm kind of

classifying and drawing boundaries in

such a way that I you know I'm

conceptualizing this thing is there's a

computer where in the same way that we

do that

um we can construct uh

rectangularity or with you know numbers

right I can uh I can say like oh that's

a computer that's a phone that's a cup

and so I now have this thing this

freeness right and then I can

investigate the properties of threeness

um and this is just a product of

construction

um but it's not fundamentally different

to uh the way in which concrete objects

are constructed

um and in fact I would say you know from

this sort of point of view there really

isn't actually a fundamental difference

between concrete objects and Abstract

objects

um because when you think about these

problems

you know the problem of vague boundaries

the problem of the many all of this one

way to interpret what is going on uh

when we say that you know there is a

hand despite You know despite the fact

that we have this problem of vague

boundaries that we have this problem of

the many and all that stuff one way to

interpret what's going on is that we're

abstracting

um so like I can say like you know here

is a hand here is one hand

um but I mean actually okay

um we have this situation where we could

just as well say that there are

trillions of hands

um

for pragmatic purposes we kind of

project a single hand where we could say

that there are trillions and trillions

of hands

um or maybe another example of this is

to think about the sorts of properties

that we assign to objects so

um consider something like the length of

a coastline

well the coastline is a concrete object

um but I mean what exactly is the

coastline well

if you try to

um sort of if you try to say like what

the length of a coastline is

um

the the smaller your unit of measurement

the longer the length the coastline will

be

um or maybe actually another way to put

this is like the smaller your unit of

measurement

you're just going to get a different as

you change the units of measurement

you're going to get different coastlines

so you know if you take an island and

you have

different units of measurement you can

generate different coastlines for that

Island

um I mean strictly speaking I would say

you know it seems perfectly reasonable

to say that there's not really any such

thing as the length of the coastline and

there's not really any such thing as the

coastline

um but you know we adopt a particular

unit of measurement and then we kind of

apply that and then sort of you apply

that unit of measurement and construct

this thing the coastline

um uh or think about something like a

person's height so I can say for

instance Verity's height is five foot

six

um now in fact

Verity's height first of all is going to

change throughout the day

um uh you know like As She lays down

she'll get a bit taller

um you know in in sort of different

environments the height will change very

slightly and of course even if you take

Verity at One Moment In Time if you zoom

in Far Enough

um there's not going to be any like

determinate boundary between Verity and

you know the rest of the environment

because

um like any sort of particle is

I mean first of all you won't be able to

specify exactly which particles count as

part of verity and even if you could

specify which particles count as part of

verity particles are more like clouds of

probability that like smeared out over

space so so strictly speaking there

isn't any such thing as Verity's height

right so like

Verity's height I mean even if you were

to say something like um you know even

if you were to make a claim where you

you make a sort of interval claim where

you say well you know Verity's height is

between five foot five and five foot

seven

um no there's still an abstraction going

on there because the point is is that

when you say like verities height is

between five foot five and five foot

seven you're still presupposing that

there is this there is this property of

Verity's height you know that Verity has

some determinant height that is that is

lying between in that interval and

actually no that's not strictly speaking

what's going on

um or perhaps I should say you know you

can very easily adopt perspectives from

which it just doesn't even make sense to

talk about things like Verity's height

right Verity's height is something that

manifests once we

you know propose a particular

classification scheme

um once we have particular types of

instrumentation

um for you know measurement and so on

um like it's within that perspective

that you get Verity's height

um but that's something which you know

it that's not something that is

like a a property of a concrete object

at least as concrete objects have been

traditionally conceived

um so what I want to say is that even

when we're talking about concrete

objects

there's actually a kind of abstraction

going on so the abstract and the

concrete are already kind of intertwined

uh in a very deep way

um

so what does what's what's the point of

all of this

um well

um I I suppose then you know do abstract

objects exist well I want to say yeah

actually I'm happy to say that abstract

objects exist

um abstract objects exist in they they

have a sort of equal claim to existence

as concrete objects do they are both

concrete objects and Abstract objects

are perfectly legitimate objects of

construction

um so you know I would say that yeah I

mean insofar as hands and tables and

chairs and so on exist I'm happy to say

that numbers and sets and you know other

mathematical objects for instance exist

um or that you know I don't know like

triangularity or squareness in the

abstract right like that exists that's

fine

um

so I suppose that I would you know in

some sense like I mean I'm certainly not

a platonist right like I don't think

that there are objective mind

independent or stance independent

abstract objects but then I don't think

there are objective mind Independence

stance independent concrete objects

either so

um you know that's

that's my view that's my take on the

abstract concrete distinction and uh you

know that is um that is all I have to

say I think for this video yep I think

that's long enough I will uh I will

leave that there

thanks for watching