Ladyman and Ross's Philosophy of Physics: Structuralism (3)

 

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.

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It's not as if Ladyman & Ross (L & R) are unaware of the obvious ripostes to their position of ontic structural realism.

For example, they quote Anjan Chakravartty (1999) saying

“‘one cannot intelligibly subscribe to the reality of relations unless one is also committed to the fact that some things are related’”.

L & R elaborate on Chakravartty's position by saying:

“... the question is, how can you have structure without (non-structural) objects, or, in particular, how can we talk about a group without talking about the elements of a group?”

And then to seal the position, L & R write (about themselves):

“Even many of those sympathetic to the OSR of French and Ladyman have objected that they cannot make sense of the idea of relations without relata...”

Mathematical Structuralism

Strangely enough (at least to me), the position of ontic structural realism is expressed at its purest and simplest when L & R discuss Bertrand Russell's philosophy of mathematics.

L & R express Russell's position on mathematical structuralism in the following manner:

“... many philosophers have followed Russell in arguing that it is incoherent to suppose there could be individuals which don’t possess any intrinsic properties, but whose individuality is conferred by their relations to other individuals.”

Indeed that passage can be rewritten to make it more germane to L & R's ontic structural realism. Thus:

It is incoherent to suppose there could be individuals (e.g., particles, etc.) which don’t possess any intrinsic properties, but whose individuality is conferred by their relations to other individuals, structures, fields, states, etc.

Thus we can ask the following question:

Does a number gain its identity from its place in a structure or does it have its place in a structure because of its (prior) identity?

Similarly we can ask:

Does an object/entity (e.g. a particle) gain its identity from its place in a structure or does it have its place in a structure because of its (prior) identity?

Indeed L & R state that Paul Benacerraf believed that

“an object with only a structural character could be identified with any object in the appropriate place in any exemplary structure and could not therefore be an individual”.

In other words, Benacerraf seems to have taken the position cited earlier. Namely, an object/individual has its place in a structure because of its (prior) identity. That is, an object/individual doesn't gain its (entire) identity from its place in a structure.

To elaborate on Benacerraf's position. It can be said that if structure is everything (or, at the least, if an object gains its identity from its place in a structure), then any object can take a place in a structure. Indeed any object can take specific place X in a given structure if the individuality or identity of an object is passed onto it (as it were) by the structure it's a part of.

The problem with this (or perhaps any) form of structuralism, however, is summed up by L & R who state that “individuals are nothing over and above the nexus of relations in which they stand”. However, L & R do preface that by saying that it – only!? - applies to “individuals in the context of quantum mechanics”.

Ladyman continues by saying that “the identity or difference of places in a structure is not to be accounted for by anything other than the structure itself”. Not only that: the mathematical structuralism just discussed “provides evidence for this view”.

Things are Structures

Despite everything, L & R often state that they don't deny the existence of entities or individuals per se. Nonetheless, it's hard to make sense of L & R's claim that “there are objects in our metaphysics” and then go on to state that

“but they have been purged of their intrinsic natures, identity, and individuality, and they are not metaphysically fundamental”.

In other words, if you take away “intrinsic natures, identity, and individuality” what's left of objects after all that's been taken away? Structure or relations? But what does that mean?

In any case, L & R see individuals as “abstractions from modal structure”. By “modal structure” L & R mean

“the relationships among phenomena events, and processes) that pertain to necessity, possibility, potentiality, and probability”.

… Yes, you've pre-empted me. It can too easily be said that structures involve individuals and relations involve relata. At a prima facie level we can also ask: In what way do “abstractions” involve themselves in modal realities? Well, mathematics itself involves necessity, possibility and probability. And if structures are inherently mathematical, then structures have modal properties. All that may be true. Though what about modality as applied to the concrete world of objects, events, conditions, etc.? What about metaphysical modality as understood by philosophers like Saul Kripke, David Lewis, D.M. Armstrong and so on?

L & R quote John Stachel saying that entities “'inherit [individuality] from the structure of relations in which they are enmeshed'”. However, saying that is a long way from saying that individuals don't exist. Even the very use of the word “inherit” means that things are doing the inheriting.

Now is it that L & R reject this position and simply deny ontological status to individuals: full stop? Or is the position that entities inherit their individuality from the “structure of relations in which they are enmeshed” as far as they need to go? Thus it's not that L & R are elimitivists about objects. It's simply that they have a radical take on objects. A take which claims that entities gain their individuality from structure. That is, before individuals are “enmeshed” in structures, they have no intrinsic natures.

Can we go so far as to say that before objects are enmeshed in structures, they don't exist? Thus it's not just the nature of entities we're talking about: it's also their existence. Do entities spring into being only when they're enmeshed in structures? This position would go against the claim, for example, of David Lewis that objects have intrinsic natures regardless of the rest of the world.

So now we still have the following positions:

i) Objects gain their natures from the structures they belong to.

ii) Objects come into existence in structures.

How is i) different from saying that entities are structures? In other words, the temporal and grammatical construction of i) may seem to imply that we have an entity at time t₁ and at t₂ it gains its nature from the structure it's embedded in. However, if ii) is correct, than that entity comes into existence in the structure. It doesn't only gain its nature from a structure – it comes into existence in the structure in which it's embedded.

Such abstract metaphysics is made concrete when L & R take the example of fermions. They cite the position that

“that fermions are not self-subsistent because they are the individuals that they are only given the relations that obtain among them”.

What's more, “[t]here is nothing to ground their individuality other than the relations into which they enter”. And, according to L & R, even Albert Einstein once claimed that particles don't have their own “being thus”.

Reference

Ladyman, James, Ross, Don. (2007) Every Thing Must Go: Metaphysics Naturalised.