Friday, 25 September 2015

Ladyman and Ross's Philosophy of Physics: Platonism (2)

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 

"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 

  • “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 

“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.


(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.


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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