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John Stachel’s “Holey” interpretation of the Hole Argument

March 30, 2021

I have been reading through and glancing over sections of this article the past few days and something was bothering me about it, but I couldn’t quite pinpoint it at first.

The issue revolves around Stachel’s claim that Leibniz’ principle of identity of indiscernibles is disobeyed by the points of space-time in general relativity. This is something I have covered in my first book and revolves also around this issue of external relations.

Stachel wrongly claims in an historically revisionist kind of manner that The Leibnizian view had largely held the field in the first half of the 20th century, when it is precisely a failure to appreciate his view that disconnected positivistic science in that era from philosophy, and led to the whole bitter era of dismissing all philosophy as nonsensical metaphysics. They misunderstand Leibniz and do not realise the dangerous implications for a reasonable way of understanding and being in the universe, by postulating arbitrary external relations as preceding any internal relation we have with things. The whole point, and very manifestation of this, is as an absolute, externalised, space-time arena or container, in to which we are “thrown”, to use a Heideggerian term. And the whole purpose of doing it is to disconnect us with being, as a means of organised scientific control through education.

Now, leaving aside some of my more speculative claims there, and getting into the specific details of Stacel’s error, he equivocates between two properties he uses called quiddity and haecceity, and how they are related. Quiddity is an objects general nature, while haecceity is somethings more specific nature to simplify. He argues that because we cannot individuate points of space-time, or certain types of quantum particle, they have quiddity, a general nature, but not haecceity, a specific nature. The argument and error is where he says that a point in space time is defined only in relation to other points and that this means it has no haecceity. On the contrary, I would argue that this begs the question against the Leibnizian view on this point. Leibniz’s principle requires that a thing be individuated based on its properties, and one of his key arguments regarding relationalism of space and time is that some of the properties of a thing are the unique ways it is related to other things in space and time. Those relations are also internal to a thing and give it a specific nature. It would beg the question against Leibniz to say that those properties are external, unless you have some other assumed premise or claim that relationalism is impossible as a view of space and time, but this can’t itself be part of your argument against the relationalist view of space and time, as it would then beg the question.

He may have other arguments, but not in this section of the article, and from what I have read from theoretical physicists such as Julian Barbour, and Lee Smolin in there current work, there is every reason to hope that a relationalist view of space time can be made to fit consistently with our universe and account fully for general relativity and the usual stuff. It also makes me unclear what side of the hole argument he is coming down on. For if, as I had thought and assumed, he believes the hole argument is refuted and general relativity space-time is a consistent patch work with no areas that are ambiguous and unaccountable for, then this would surely show that space-time points do have specific and individualised properties, i.e. they have haecceity as well as quiddity. I can only assume then he is claiming the hole argument is an issue of ambiguity for general relativity as Einstein himself feared for a few years in the 1910’s. But in that case the issue would effect the application of general relativity to reality, not the nature of reality itself, because it would show a limitation to the theory.

In either case, I find myself quite confused and baffled by various things Stachel says in this article that just don’t chime with what I have learned myself and read about relationalist views of space and time, and about internal and external relations and about how to use and apply the Leibnizian principle of the identity of indiscernibles. Perhaps he could clarify some of these points, and I will certainly take a fresh look at the article and other relevant literature to update my own views accordingly if I have made some error here.

But, for now, from the way I see it, the Leibnizian principle stands firm, and as I have said elsewhere and developed the story of in my first book, the implications of denying this principle are quite catastrophic for our attempts to get a genuine understanding of the reality of things.

I will concur with Stachel that when it comes to quantum particles, we do seem to have a genuine case of the identity of indiscernibles breaking down, and of entities with quiddity (a general nature) but not haecceity (a specific/individual nature), but of course in this case they actually behave in ways suggesting they are in some sense literally identical entities when we look at phenomena such as coherent light of a load of Bosons. Thus, they actually tend to become identical by being indiscernible, in line with Leibniz’ principle. Another example being the non local action between two quantum particles, this shows how their identity as entities is overcoming the spatial separation. It shows once more of the secondary and contingent nature of external ways of distinguishing things compared to the internal nature of things., that takes priority both in how things behave and in how we should interpret and discern things with our reason. If we cannot discern the individual quantum particles in certain cases, all the more proof of the standard accepted view of quantum theory that there is an uncertainty of location and identity in space and time of quantum particles.

As for the individuation of space-time points, you are dealing there with something completely different, and you cannot refuse to allow part of the individuation of a space-time point to be its relationship to other space-time points without begging the question against relationalist view, unless you provide some independent grounds for objecting to relationalism.

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