Things between Relations

This post will be concerned with Structural Realism. More precisely, with an article by John Stachel, one of the fathers of the modern version of the Hole Argument, which was first considered by Einstein. For an introduction to the Hole Argument read the Stanford Encyclopedia entry here:
http://plato.stanford.edu/entries/spacetime-holearg/

In "The Relations between Things" versus "The Things between Relations": The Deeper Meaning of the Hole Argument (published in Reading Natural Philosophy, edited by D. B. Malament) Stachel considers a generalization of the argument which not only covers diffeomorphisms on manifolds, but permutations in general, including those arising in quantum mechanics due to the indiscernability of elementary particles. His ideas are highly controversial, but I am quite sympathetic about his views. This article also gave me the occasion to deal with the theory of reference of Hilary Putnam, which I will discuss in a separate post.

Let me briefly outline the general setting first: the so-called manifold-substantialist, who believes that space-time points are individuated separately from the fields that they "carry", is considered not to escape the hole argument. He is oblieged to the view that a hole diffeomorphism yields a physically distinct solution to the field equations. But since the fields outside the hole (where the diffeomorphism reduces to the identity) do not determine the solution within the hole uniquely, indeterminism arises. In contrast, the relationalist is not commited to such a view, he does not run into the hole argument since he does not think of space-time points as independently individuated entities. To him, all the solutions yielded by diffeomorphisms are the same, and no indeterminism arises.

Note that the indeterminism is destructive because the indeterminism is not a matter open to empiricical evidence, it is a priori implemented in the theory. But this is considered to be highly implausible. Of course, this kind of indeterminism has no observational consequences, and hence this conclusion was challenged (e. g. Liu, 1997).
However, for the sake of the argument made by Stachel, let us consider his view to be largely correct. Is it now possible to extend the hole argument in a way to apply to quantum physics as well? Is there a common feature concerning the underdetermination theories which will
And if so, can the structural content be isolated? These suggestions are absolutely mind-thrilling to me, and if the arguments made by Stachel turned out to be correct, it should have some impact on physical science as well, for certain aspects on the individuality of particles are still not well understood.

Stachel proposes to forget about the differentiable properties and consider just o set of points, then covariance of the field equations becomes permutablility (invariance under symmetric group)

Usually, one first introduces a set S of entities and then defines the relations R=(R1..R_M) on top, which form a relational structure (S,R). Stachel now also considers reflexive definitions of relations. More precisely, he offers the two alternatives:
(1) relations between things: things are independently
(2) things between relations: things are reflexively defined
Consider as an example for the second type simply the notion of king and subject: of course, there need to be people who can bear these roles, but this is not essential for this relation. There is no subject without a king, and no king without subjects: the relation is established at once, the people become subjects in the moment the king is crowned. Of course, the person who (accidentely) happens to be the king can be individuated otherwise, since he (the person) is an independent being.

Stachel then argues that in in a generally covariant theory, the points of space-time are defined reflexively. He then introduces the notion of general permutability, which simpliy means that any permutation of the entities in S yields the same possible world, i.e. all relations are defined reflexively (the "things" have no individuality, and its individuation depends entirely on the place it occupies in the relational structure). In this picture, the relationalist holds that space-time points are reflexively defined (spacetime-points are indistinguisable like electrons in an atom), whereas the manifold substantialist holdsthe view that space-time-points are independently defined (like cards in a card house), and hence the generalized hole argument arises: we can permute the entities which are not fixed by the relations, yielding a physically distinct wolrd but same observational consequences.

Pooley has challenged this analogy, and he .. haeccist and anti-haeccist....
[to be continued...]

S. Weinberg on "a piece of chalk"

In this second post on "Hegel's Paradox", as I called it, I will quote and discuss a set of interesting passages from "Dreams of a Final Theory", a highly recommendable book by the prominent physicist Steven Weinberg (published at Pantheon Books, 1992).

The issue which I am interested in concerns his characterization of physics (and chemistry) as sciences which want to establish eternal, universal laws of nature, as opposed to biology, geology, astronomy, which contain arbitrary elements as well which can only be explained by historical means. The way evolution took place, the way the earth devolped, the way our solar system or the milky way developed, all this was not determined by natural laws only. Explanations in these subject cannot be reduced to physical laws only, but also depend on certain conditions which have no explanations. Explaining the theory of evolution in terms of genetics, genetics in terms of chemistry, and chemistry in terms of physics will not explain why there are humans, or even why there are animals at all.

However, Weinberg even admitts that there might be historical factors in physical theory as well. He writes:

"It is not clear whether universal and the historical elements in our science will remain forever distinct." (p. 34)

This is an interesting twist: maybe, not only the fact that all planets go around the sun in the same direction is also a matter of history, but also the values of certain parameters in the standard model:

“Not only is it possible that what we now regard as arbitrary initial conditions may ultimately be deduced from universal laws – it is also conversely possible that principles that we now regard as universal laws will eventually turn out to represent historical accidents.” (p. 38)

He continues illustrating the idea of multiverses and subuniverses, which I will touch at another occasion. Nevertheless, he claims, this will not detain us being able one day to find a final theory:

“The most extreme hope for science is that we will be able to trace the explanations of all natural phenomena to final laws and historical accidents.” (p. 37)

After having read this chapter "on a piece of chalk", I again felt reminded strongly on the idea that there might somehow be no difference between physical laws and historical accidents. There might be a viewpoint from which all laws are accidential, and another viewpoint from which nothing is accidential and everything lawlike. What goes wrong here is maybe that it is notoriously difficult to exemplify the notion of regularity, which underlies the notion of a natural law. We con only observe the former, never the latter. What I actually want to get into is not the problem of induction itself, but what it has to do with the dichotomy between theory and observation. But more on this problem next time.

Hegel's Paradox

There is a remarkable part in Hegel's "Phänomenologogie des Geistes" which makes me think since years. It is Hegel's notion of the "verkehrte welt", which has two connotations in english, namely "inverted world" and "wrong world". I am no expert in the exegesis of Hegel, so I cannot give this notion a definite meaning, but I at least want to explain why his ideas did puzzle me so much, in the light of theory of science.

Before I will discuss the original text, I will motivate the problem Hegel was concerned with by a number of rather different, most contemporary texts in the philosophy of science and physics.
For now, it will suffice to explain what I mean by "Hegel's Paradox" and what is at stake in the upcoming blog entries on this topic.

In short, in the course of the development of our understanding what the world is about, we eventually will reach the stage that the world is composed of items ("Gegenstände", "Dinge") such as apples and the like. However, by investigating what is specific to these items , by differentiating them into their properties (being white, tasting salty, having a peculiar shape and texture), we might adopt the view that these items are vastly arbitrary combinations of its properties: the item decays into its properties, it is no longer considered to be a unified, monolithical object of our experience.
Instead, after a course of dialectic movementes, one might adopt the scientists attitude not to regard objects, but natural laws as the constituents of nature. Instead of items or its properties it is now the play of forces ("Spiel der Kräfte") which govern reality.
However, to regard the laws to be the "Absolute" is what will turn out to "reverse" the world as it is. Taking theories "at face value" (in modern terminology) leaves us with an inverted world, in which actual sensations and conscous experience is in no means explained - it is an empty world.
Maybe, Hegel also had in mind what Kant said in the Critique of Pure Reason:"Thoughts without content are empty, intuitions without concepts are blind" ("Gedanken ohne Inhalt sind leer, Anschauungen ohne Begriffe sind blind) (A 51)

The interesting aspect in Hegel's exposition of the inverted world (and which is not transferable to what Kant said) is that it is not clear at all if there is a distinction between natural laws, formulated as a theory, and what the theory actually speaks about, "the content", which enters the theory as initial conditions or boundary conditions. After all, in Hegel's exposition it is again a dialectic movement, which brings the world back on its feet. Hence the world in terms of concrete objects is wrong, and a world of natural laws. The position Hegel develops next (but which is also only a intermediate position about the "Absolute") thus overcomes both views.

In the entries devoted that topic I will suggest that there are interesting parallels some of the discussions going on in the philosophy of science. Hegel is still up to date: his view might be relevant both for ontology and methodology, and his thoughts are certainly a promising subject for philosophical investigation. I hope, you, the reader, will enjoy this topic as well.