These
pieces are primarily commentaries on the 'Ontic Structural Realism
and the Philosophy of Physics' chapter of James Ladyman and Don
Ross's book

*Every Thing Must Go*. There are also a handful of references to – and quotes from – other parts of that book.***********************************************

James
Ladyman and Don Ross (L & R) have been classed - variously - as
“neo-Pythagoreans” and “neo-Platonists”.

If
one were a neo-Pythagorean (rather than a straight Pythagorean), one
may think that

At least this position “suggest[s] a kind of Pythagoreanism” to L & R. However, the fusing of mathematical entities with the physical world doesn't seem altogether Platonic - even if it is Pythagorean; though it may express L & R's position very well. (It's not Platonic because Plato's prime concern was the abstract and atemporal realm of mathematics; not numbers or maths as they are instantiated in the physical world.)

"mathematical entities such as sets and other structures are part of the physical world and not therefore mysterious abstract objects”.

At least this position “suggest[s] a kind of Pythagoreanism” to L & R. However, the fusing of mathematical entities with the physical world doesn't seem altogether Platonic - even if it is Pythagorean; though it may express L & R's position very well. (It's not Platonic because Plato's prime concern was the abstract and atemporal realm of mathematics; not numbers or maths as they are instantiated in the physical world.)

What
does sound very much like L & R's position (as well as being
partially Pythagorean) is

L & R go on to say that such “abstract structures employed in models” are the “objects of physics” if such a distinction is indeed abandoned. In L & R's case, we can say that abstract structures are the

- “abandoning the distinction between the abstract structures employed in models and the concrete structures that are the objects of physics”.

L & R go on to say that such “abstract structures employed in models” are the “objects of physics” if such a distinction is indeed abandoned. In L & R's case, we can say that abstract structures are the

*things*or individuals of physics. In other words, if we erase abstract structures from the picture of physics - we have*nothing*. Though does it follow that abstract structures are*everything*?
In
any case, L & R quote Bas
van Fraassen saying that

L & R then express a position which one would imagine many people have aimed at L & R themselves. They say that

“it is often not at all obvious whether a theoretical term refers to a concrete entity or a mathematical entity”.

L & R then express a position which one would imagine many people have aimed at L & R themselves. They say that

“the
fact that we only know the entities of physics in mathematical terms
need not mean that they are actually mathematical entities”.

Now
are L & R endorsing that position or simply saying that, as a
matter of logic, the following statement is invalid? -

i)
If we only know the entities of physics in mathematical terms

ii)
then the entities of physics *are*mathematical entities.

L
& R go on to explain this position in terms of rejecting what
they call the “abstract/concrete distinction”. They say that

“the
dependence of physics on ideal entities (such as point masses and
frictionless planes) and models also offers another argument against
attaching any significance to the abstract/concrete distinction”.

We
still have the precise question of whether or not (in L & R's
words) “the fact that we only know the entities of physics in
mathematical terms need not mean that they are actually mathematical
entities”. Yes, it

*needn't*mean that; though, to L & R,*does*it mean that?
If
there were only mathematical models or structures, we couldn't call
them “models” or “structures” in the first place. Such words exist
precisely because of the abstract/concrete distinction. This isn't
necessarily to say that we should attach too much significance to
that distinction (though we'd need to know what “too much” means); or even that we can know physical entities without abstract mathematical
entities and models – we can't. Nonetheless, none of this (in
itself) is a reason to reject the abstract/concrete distinction or
even (in L & R's words) to refuse to “attach any significance
to” it.

A
realist about entities (not structures) can happily accept that
mathematical structures are

“used
for the representation of physical structure and relations, and this
kind of representation is ineliminable and irreducible in science”

and
still be a realist about entities/events/conditions/etc. However,
it's precisely because of the ineliminable nature of mathematical
structures in physics that has led ontic structural realists to
become eliminativists about entities (though they see entities as
structures too); just as it led Plato and Pythagoras to similar
conclusions.

Indeed
we can even accept that it's a hugely important fact that (as mathematical structuralists put it) the “world instantiat[es]
mathematical structure” and still think the abstract/concrete
distinction is important. The coffee cup and carrot in front of me
instantiate mathematical structures; though they also exists

*qua*coffee cup and*qua*carrot. There's also the fact that all objects, events – all things! - exhibit (or instantiate) mathematical structure. That, however, is (in a sense) a banal fact because all it amounts to is the fact that every*thing*can be given a mathematical description and also be mathematically – or otherwise – modelled (even a coffee cup or a carrot).**Platonism: Relations and Relata**

L
& R provides a useful set of four positions which focus on the
nature of relations and “things”. Thus:

(i) There are only relations and no relata. (ii) There are relations in which things are primary, and their relations are secondary. (iii) There are relations in which relations are primary, while things are secondary. (iv) There are things such that any relation between them is only apparent.

At
first glance one would take ontic structural realism to endorse (i)
or (iii). However, since

*things*are themselves structures (according to L & R), then we must settle for (i) above: “There are only relations and no relata.”
Looking
at (i) to (iv) again, couldn't it be said that (ii) and (iii) amount
to the same thing? In other words, how can we distinguish

(ii)
There are relations in which the things are primary, and their
relations are secondary.

from

(iii)
There are relations in which relations are primary, while things are
secondary.

Isn't
this a difference which doesn't make a difference? One can still ask
- in the metaphysical pictures of (ii) and (iii) - the following
question:

Can
things exist without relations and can relations exist without
things?

That's
a question of existence. Now what about natures?

One
can now ask:

Can
things have their natures without relations and can relations have
their natures without things?

As
I've said, L & R adopt option (i) above:

*There are only relations and no relata.*
L
& R give a very interesting platonic reason for why they adopt
(i).

They
cite the example of the assertion that “The Earth is bigger than
the moon”. In terms of relata, it's certainly true that the Earth
and the moon exist. It's also true that the Earth

*is bigger than*the moon. Thus, in this instance, the relata exist.
What
about the relation “is bigger than”?

Here
(just as in Bertrand Russell's 'The
World of Universals') universals come to the rescue. L & R
say that the

“best sense that can be made of the idea of a relation without relata is the idea of a universal”.

Thus
the relation

*is bigger than*is a universal. L & R also see it as being “formal”. That is,
“when
we refer to the relation referred to by ‘larger than’, it is
because we have an interest in its formal properties that are
independent of the contingencies of their instantiation”.

In
other words, the universal IS BIGGER THAN (or BIGGER THAN) doesn't
need the moon, Earth or anything else concrete to have

*being*. Indeed the universal IS BIGGER THAN need never be instantiated in concrete objects. This is the classic position of Plato. Aristotle, on the other hand, believed that universals must be instantiated.
L
& R round this off by making their Platonism explicit. They
write:

“To
say that all that there is are relations and no relata, is therefore
to follow Plato and say that the world of appearances is illusory.”

Let's
be explicit here. That “world of appearances” may well include
carrots, cups and even other human beings. More emphatically, it
certainly

*doesn't*include subatomic particles. Thus, in order to get to the platonic truth, we must cut through appearances (which are “illusory”) and get to the mathematical structures of what it is we're examining. Or, in this case, discover the universals and mathematical structures which underpin appearances.**References**

Ladyman, James, Ross, Don. (2007)

*Every Thing Must Go: Metaphysics Naturalised*.

Plato.

*Meno*

Russell, Bertrand. (1912)

*The Problems of Philosophy (see*the 'The World of Universals' chapter).

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