A Few Stray Thoughts

Greetings to everyone. I hope you’re all settling into this strange new decade we’ve found ourselves in. Since I last posted I’ve had a small personal crisis that’s stopped me from getting any blogging done. Long story short, I’m now back living in the north-east of England (anyone in the area, feel free to drop me a line), and spending my days at Newcastle university library trying to get my thesis done (it’s going well at the moment…). Given this, I don’t really have the time to dedicate to one of my usual comprehensive blog posts, so I’m going to try out something a bit unusual (or perhaps more usual for other people) and just write up a few ideas with minimal context, for those of you who’ve been following my work here on the blog.

1. ETMG

I’ve finally gotten around to reading Ladyman and Ross’ Every Thing Must Go, and though my reading has been stalled somewhat by the move, I’ve really been enjoying it. Here’s a quick list of positives and negatives so far. Positives:-

a) Their criticisms of analytic metaphysics are pretty much spot on, particularly their criticisms of the idea that ‘intuitions’ can be used as evidence. I have a bit of a soft spot for David Lewis (he’s actually a very enjoyable read for all his crazy ideas), but they really do nail him hard.

b) Their discussions of the literature in the philosophy of science are in fairly in depth and helpful. They are a little intimidating at times as they cite massive amounts of literature that they only partially summarise, but it does make me want to seek some of it out and get better acquainted with the debates, which is a good sign.

c) Their summaries of scientific theories and the metaphysical problems they pose are masterful and have made me think long and hard about a number of issues. I’ve been putting off thinking about the implications of quantum theory (and particularly Bell’s Inequality) for a while, and they’ve convinced me that I’m going to have to do some serious work on that stuff at some point.

Negatives:-

a) Their definition of metaphysics seems needlessly deflationary. They admit that they’ve been quite heavily influenced by Bas Van Fraasen’s constructive empiricism, and even though they argue against it in favour of metaphysics, the picture of metaphysics they argue for is very weak indeed. Moreover, it creates too much of a discontinuity between the problems of contemporary metaphysics and those of the tradition. There’s still some life in Spinoza and Leibniz yet.

b) They take their criticisms of ‘intuition’ too far, resulting in an overt hostility to anything remotely a priori or transcendental. As I’ve argued before (here), a priori knowledge does not involve a special form of intuition, but simply a special form of argument in which no observation claims are deployed at all. This results in them making some very probative claims based on empirical descriptions of the norms governing actual scientific practice where they could make much stronger claims based on transcendental norms of ideal scientific practice. There’s still some life in Kant yet.

c) They blur the line between metaphysics and epistemology a bit much for my tastes. This seems to be what happens in their defence of ontic structural realism. They at one and the same time want to say that scientists describe reality, but that their theories about it cannot be literally true due to the pessimistic meta-induction. They thus opt for a position in which scientific theories represent real mathematical structures present in the world, rather than the entities and properties they explicitly refer to. Science gets to explain reality as long as nothing it says is understood literally. For my part, I don’t see why we couldn’t take metaphysics to be in exactly the same fallibilist position as science, and thus base it upon our best literal understanding of the world at all times. This would mean that revisions to our best scientific understanding potentially force revisions to our best metaphysical understanding. It seems that for Ladyman and Ross metaphysics is supposed to underwrite the epistemology of science, whereas I think that the epistemology of science is supposed to provide the constraints within which metaphysics can takes place.

d) Their refusal to explain the difference between physical and mathematical structure is a genuine howler. This isn’t to say that they have nothing to say about structure, they do, but this doesn’t excuse ignoring the metaphysical elephant in the room. The issue of the mathematisability of reality and how to understand it is increasingly becoming a hot button issue for metaphysics (especially with Badiou and Meillassoux becoming increasingly popular). I’ve got a basic framework within which to deal with this issue, and I’ll say a little more about this below.

2. Essay on Transcendental Realism Addendums

I’ll keep these brief:-

i) I’m increasingly convinced that causality is a category in the sense I defined in the TR Essay. The corollary to this is that it means that time must be a category too. The question is whether it implies that space is a category. The other option is that it implies some single unified category of location, and that the notions of space and time are metaphysical interpretations of this notion.

ii) The account of conceptual content presented in the Essay requires a serious overhall. The most glaring problem is the notion of an individual concept that I defined there, which needs to be totally revised. However, I have been developing some of the additional resources necessary to describe the secondary dimension of conceptual content and the various kinds of conceptual content posited in the essay, so it’s not all bad.

iii) The argument for transcendental realism outlined in the Essay is obviously insufficient, and its going to take quite a bit of work before its plausible. However, given the relation between mathematical and empirical content sketched there, we can prove that if there is an objective world, then it must be mathematisable, insofar as empirical concepts can have mathematical content. This is a transcendental argument for the mathematisability of nature, and provides the leaping off point for a more in depth metaphysics of mathematical structure.

iv) However, the account of the relation between mathematics and logic needs further development. I’m increasingly coming to the conclusion that mathematics is effectively a pragmatic intermediary between the logical and the empirical. The essence of this idea is that mathematical concepts can be looked at from two perspectives, from the perspective of their pure logical structure and from the perspective of the empirical concepts through which they are applied. The one treats the axioms which define a certain concept as meaningless posits the consequences of which simply need to be worked out, and the other treats these axioms as explicating something which is independently meaningful. The interplay between these perspectives is what drives progress in mathematics. This is of course a terribly crude picture, but it raises an interesting question for my account if it’s right. If mathematics is an intermediary between the logical and the empirical, and metaphysics is also an intermediary between the logical and the empirical, then how do we understand the difference between mathematics and metaphysics, and do their different intermediary roles overlap? Much thinking to be done here.

3. Planned Projects

i) Hegel: I’ve been invited to give a paper at the 21st Century Idealism Conference in Dundee this year. It is tentatively titled ‘The Greatest Mistake: A Case for the Failure of Hegel’s Idealism’. I’ll be straight to work on this as soon as the first draft of the thesis is finished.

ii) Modal Logic: I’ve been toying with a way of generating alternative inferentialist semantics for modal logic. It involves adding some additional features to Brandom’s scorekeeping pragmatics, but it’s general enough to produce a whole host of modal operators (far more than Kripke semantics and Lewis’ restricted accessibility and closeness relations can get you). On this front it’s really more of a meta-semantics for modal operators. It also has interesting ties to semantics for conditionals, including counterfactuals, as well as providing the necessary resources to formalise my distinction between different kinds of conceptual content (transcendental, mathematical, empirical, interpretational, etc.). Another interesting consequence of this is that the additional features that need to be added to the pragmatics amount to a generalisation of something already involved in Brandom’s account, and enable us to give a strong response to McCullagh’s objections regarding Brandom’s account of non-extensional contexts (because they account for all such contexts).

iii) Quantifiers: I’m also working on a way of generalising Brandom’s account of quantifiers so that it can represent all the standard kinds of quantifiers (objectual, substitutional, and free, with domain restrictions and various arities). This involves using some of the resources I’ve been developing to tackle modal logic, but it’s in pretty early stages at the moment. However, this does mean that it should be easy to tie the two stories together and get meta-semantics for quantified modal logic (woo).

iv) Book: Finally, I’ve been toying around with a book idea that I might have a crack at once I’ve finished the thesis and gotten a few papers written (see above). The provisional title I’m working with is Reintroduction to Metaphysics. It’s obviously a play on Heidegger’s Introduction to Metaphysics, but there’s more to it than that, insofar as it’s supposed to be a book concerned with what metaphysics is that isn’t trying to simply to classify the various metaphysical problems passed down by the tradition, but to present a revisionary picture of metaphysics that excludes some of those problems while tying the others together in a single framework of inquiry. The basic idea is to presented a reconstruction of the history of metaphysics from the pre-socratics to the present day, focusing on the genealogy of the notion of metaphysics itself rather than the specific metaphysical theories that are adopted along the way. This focuses upon three different traditions: the mainstream tradition (Plato, Spinoza, Leibniz, Hegel, Bergson, Deleuze, Lewis, etc.), the revisionary tradition (Aristotle, Kant, Heidegger, Quine, Ladyman & Ross, etc.) and the anti-metaphysical tradition (Hume, Wittgenstein, Carnap, Van Fraasen, etc.). The idea is then to explain the thematic issues underlying this history (e.g., the generality of metaphysics, the relationship between metaphysics and science, the relationship between metaphysics, epistemology and semantics, etc.) and to formulate an argument that it is necessary to define metaphysics in order to fight off the challenges of the anti-metaphysical tradition (placing me firmly in the revisionist camp). The book will then of course culminate in a (hopefully) more detailed version of the account of metaphysics presented in the TR essay, which responds to all the relevant anti-metaphysical challenges and takes stances on all the different thematic questions. Still on the drawing board, but it’s pretty exciting.

Anyway, those are my half formed ideas. Hope they’ll do until I can put down something more thorough.