Dear Jochen,

thanks for your reply. The time you take for this is highly appreciated!

Before going into details of what you write, I think that the answer to many of your comments is: it depends on what we mean by "structure". In my essay, I'm not really defining it properly (in particular in the section on the physical world). Any serious philosophical approach that tries what I've...

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Dear Jochen,

thanks for your reply. The time you take for this is highly appreciated!

Before going into details of what you write, I think that the answer to many of your comments is: it depends on what we mean by "structure". In my essay, I'm not really defining it properly (in particular in the section on the physical world). Any serious philosophical approach that tries what I've sketched will have to give a clear(er) definition. Also OSR has to do that (and I suspect that it does, but they mean something slightly different from what I mean).

Regarding your example of the Maxwell's equations and String Theory, I think that what this tells us is that we should define "structure" in terms of "big enough equivalence classes", or admit "coarse enough isomorphisms" when we define it. In particular, there may be two theories T and T' that talk about the same structure S. I would say that your example of Electromagnetism (i) and String Theory (ii) is of that kind: two theories that give the *same* structure.

Being a structural realist in *that* sense, I'd say that there is no ontological difference between the statements that "(i) is true" and that "(ii) is true". But I admit that this does not really come across in my essay, because I'm not giving a clear-enough definition of "structure". And there are many questions that such a view leaves open.

You are right that it would be nice to talk more to Karl Svozil; I've only met and chatted with him once, and he seems to have many clever ideas and insights that touch these topics.

But I'd also find it nice to meet you in person at some point in the near future. Perhaps I can invite you to visit IQOQI when the Corona crisis is over? It would be a lot of fun to chat in person! Also, we have a regular Physics-Philosophy-Meeting here that you might enjoy.

Now, regarding your second email and quantum mechanics:

Again, I was clearly not detailed enough to say what I mean by structure or differentiation in this context. That is certainly a drawback of my essay (also due to space limits, of course, but also I don't really know how to do the definitions properly -- it's more an idea than something fully worked out.)

Here's what I do *not* mean. I don't mean to say that the world now is structure S, and once we learn an additional measurement outcome, it evolves into a more differentiated structure S'.

Instead, consider the quantum world on all of spacetime. There are certain "real patterns" in accordance with quantum physics: for example, certain events that happen earlier on (perhaps "preparations") are in correspondence with frequencies of certain types of events later on (correlations with "measurement outcomes"). This would be structure S.

A more differentiated structure S' would be the world according to de Broglie-Bohm theory: additional (unobservable) events earlier on that are deterministically correlated with outcomes later on. The corresponding theory T' makes more claims than T, and so S' would be more differentiated than S.

In other words: I'm just saying that views in which quantum probabilities are not "knowledge *about* the world" are in some structural sense less differentiated than view in which they are. So a structural view may increase one's confidence to accept views of the former kind.

I'm really curious to find out about your "middle way", but I'll postpone commenting on it until I have read your essay. I'm having a busy time with some deadlines next week, but I'm eager to read your essay directly after that.

Best,

Markus

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Dear Marcus,

I have you to thank for engaging with my comments in such an open way! These contests are always at their best when they stimulate frank exchanges on views that may go slightly beyond what one would normally put into a journal article or the like.

And I'd very much like to come for a visit to Vienna---although thinking about traveling plans seems almost frivolous these...

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Dear Marcus,

I have you to thank for engaging with my comments in such an open way! These contests are always at their best when they stimulate frank exchanges on views that may go slightly beyond what one would normally put into a journal article or the like.

And I'd very much like to come for a visit to Vienna---although thinking about traveling plans seems almost frivolous these days. Perhaps one lesson we could take away from the present situation is that we should try to create more and better avenues for online exchange of views---something like virtual research/discussion groups, where people interested in some topic can congregate, discuss with either live-sessions or in a chat/forum based manner, exchange drafts for articles/request comments and the like. Could be as simple as a Teams channel, or something like that.

But back to the things themselves, as Husserl said---or to their absence, as it were. Regarding the 'modding out' of equivalences between structures, I'm afraid that this might leave us with altogether too little in the way of substance to account for the world and out experience within it---if we agree that in my example, electromagnetism and string theory yield in some sense the same structure, then one could also draw in all manner of 'different' systems---say, for example, the three body problem is at least conjectured to be computationally universal, so you could encode the requisite data into its initial configuration, and then just let Newton's laws do the rest. Or, of course, any other theory that allows for universal computation.

So fine, one might try to say that then, most of the structure is in the initial condition---the program, so to speak. But this, too, is far from unique: you can instantiate the three body problem with all manner of initial states, implementing different Turing machines that then instantiate the requisite computation from different initial conditions. In each case, that would add some constant number of bits to the length of the initial program, corresponding to the specification of a Turing machine to be simulated.

So suppose that you have an initial condition for the three body problem that can be specified using n bits, such that the resulting system implements the 'structure of the world' in some sense, by essentially implementing some Turing machine T executing the n bit program. Then, it seems to me you could find a TM T' such that it takes at most n + O(1) bits input to implement the same program, with the O(1) factor corresponding to T' simulating T. But then, have you really said more about the world other than 'it contains at least n bit of information' if you specify its structure in this way?

I think this is essentially the Newman problem again. In some sense, all 'universal' structures---structures corresponding to theories allowing for universal computation---are equivalent: whatever you can describe using one, you can describe using another, with at most some constant overhead.

Maybe one could try to argue for parsimony, and single out that structure which yields the most compact specification---which has the problem that the question which one this is will be undecidable, due to the uncomputability of Kolmogorov complexity. Or, one could try to adapt the various attempts at solving the threat of trivializing computationalism---because that's essentially the same problem, again: virtually every system can, naively, be viewed as instantiating virtually every computation. There are, I think, certain avenues regarding dispositional/counterfactual/causal accounts of computation that one could pursue, in order to arrive at a notion of isomorphism between structures that's coarse-grained enough to allow for the identification of 'obviously identical' structures, without being so coarse-grained as to trivially identify virtually all structures with one another. I'm not sure if that'll work, but, with a more careful fleshing out of the notion of structure, I think there's at least a few avenues to explore here.

Regarding the concrete application towards quantum mechanics, I think I understand your proposal somewhat better now; but if the structure, as such, only accounts for the correlations in measured data, then how are concrete measurement outcomes accounted for? Pre-measurement, only a certain probability distribution over outcomes exists, but post-measurement, we at least seem to have observed one definite outcome.

Now, I suppose one way to account for this without appealing to some sort of coming-into-being of a more differentiated structure is to appeal to a sort of facts-as-relations account: before the measurement, relative to the '|ready>' state of the detector, the (say) qubit is in an equal superposition; after the measurement, relative to the '|detected 1>'-state of the detector, the qubit is in the state |1>, and relative to the '|detected 0>' state of the detector, it's in the state |0>. We think about this as moving from a superposition to a definite state, but this is really thinking as if we could hold the state of the detector fixed---but thinking about this as a relation between the detector and the qubit, the three propositions 'relative to |ready>, the qubit is |0> + |1>', 'relative to |detected 1>, the qubit is |1>', and 'relative to |detected 0>, the qubit is |0>'---which are not actually in conflict at all, and hence, can well be part of a consistent structure.

As for my 'middle way' between the naive box-of-things view of the world, and the---to my way of thinking---somewhat too rarefied view of relata-less relations, I don't really go into that in the present essay, but the germ of the idea---which is still pretty much all I've got---is in my entry into last year's contest, where I essentially propose that there are fundamental facts only relative to a certain perspective on the world, or a certain way to split the world into distinct subsets, or sub-objects, or perhaps, subject and object. It's a bit of a tightrope walk, and I'm far from certain something like that can be made to work at all, but not really liking to drop to either side, it's kinda all I got.

I hope you manage to meet all your deadlines!

Cheers

Jochen

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