Minimal Truthmakers

I've been working on a paper on minimal truthmakers with an ex-colleague of mine from Durham, Donnchadh O'Conaill (we've previously written a paper together on monism). The paper is now at the stage where we could use some feedback. Rather than posting a link to the draft here, I'll post this general call for volunteers -- drop me a message if you think you might like to read it and could perhaps provide some feedback, or even just a general impression. We make some use of the work of Armstrong, Fine, Correia, Sider, and Schaffer, among others. The goal is to defend the usefulness of the notion of minimal truthmakers and to provide a definition of them, as well as give some reasons to think that there indeed are some minimal truthmakers. Our two primary arguments concern the explanatory value of minimal truthmakers, and the idea that at least 'joint-carving' (or fundamental) propositions are likely to have minimal truthmakers. The draft is about 8,000 words. The abstract is below.

A minimal truthmaker for a given proposition is the smallest portion of reality which can make this proposition true. Minimal truthmakers are frequently mentioned in the literature, and have been referred to as “of quite special importance for metaphysics” (Armstrong 2004, 19). However, there has been no systematic account of what minimal truthmakers are or of their importance. In this paper we shall clarify the notion of a minimal truthmaker for a given proposition, and argue that there is reason to think that at least some propositions have minimal truthmakers. We shall then argue that the notion of a minimal truthmaker can play a useful role in truthmaker theory, by helping to explain the truth of certain propositions as precisely as possible.

Comments

[Marcus Arvan]

Nice paper. Just a couple of worries.

On p.10 you write: "It might be objected here that if all propositions turn out to be vague, then our response to the argument we have just been considering would entail that there are no minimal truthmakers. This would be a worrying development, but there are a number of possible responses we can make to this objection. If it is granted that there are some predicates that carve nature perfectly at its joints, then propositions involving these joint-carving predicates are plausibly not subject to vagueness."

Question: what if someone denies that any predicates carve natures at its joints for the very reasons raised in the objection (i.e. vagueness)? After all, your example -- using electrons -- seems problematic precisely this way. Electrons aren't the "point-particles" assumed in Newtonian theory; they have *no* determinate spatial location/velocity but rather exist in a "blur" called an orbital. Isn't this like the case of a cloud (where does the cloud begin? where does it end?). If vagueness is all around, shouldn't one think there are *no* propositions that carve nature at its joints?

A different issue: what about hyperintensionality? The fact that all triangles have internal angles adding up to 180-degrees and the proposition that triangles have three interconnected sides are different truths, yet they would seem to have the same minimal truth-maker. Is this a problem? (I have no idea: just thought I'd ask!).

Also on p.10, you write: "Finally, even if it turns out that there are no minimal truthmakers, we would still argue that the concept of a minimal truthmaker can play a useful role in metaphysics. For one thing, it would allow us to state the fact that the world is such that there are no minimal truthmakers, which would itself be of metaphysical interest. More generally, the notion of a minimal truthmaker could function as a limit case, allowing us to understand explanations of the truth-values of different propositions as more or less precise."

Maybe it's just me, but I don't think this is enough. I think you need to establish that there really are minimal truthmakers. If I were a reviewer, I don't think I would be happy recommending "accept" for a paper which said: "Here's our account of X...and oh, by the way, there may be no Xs. But we still think it is important to give a theory of Xs." As a reviewer, I don't think I'd buy this.

Otherwise, I like a lot of what you have here. The paper's very well-written and well-argued!

-M

[Tuomas Tahko]

Thanks a lot for the comments Marcus!

Let me briefly reply to your comments, although I'll have to discuss these with Donnchadh as well.

Vagueness: This issue came up in some previous comments as well, but we don't feel that it's so serious. We don't attempt to claim that electrons *necessarily* carve at the joints, this is simply stipulated in the paper. But we do believe that there are very good reasons to think that at least some propositions must carve at the joints. I defend this in another forthcoming paper (here: www.ttahko.net/papers/boundaries.pdf). In general, we are fallibilist about which propositions carve at the joints, but if nothing does, then I think that a Dummettian 'amorphous lump' view of reality threatens. So, this is perhaps a more general problem, although one that I think can be addressed. In the paper we also hint towards a supervaluationist treatment of vagueness, which might be one way to address the problem even if vagueness is all around. Well, we may try to say a little bit more about this.

Hyperintensionality: We are happy to acknowledge that the same truthmaker can (and will) act as a minimal truthmaker for several propositions. This shouldn't cause any problems for our view. It should be no more problematic than the same truthmaker making true several propositions in general.

Substance: Your general worry about the substance of our claim might require some more work on our part. We do of course think that we have a reasonable case for the existence of at least some minimal truthmakers (this is what the argument from joint-carving is for). But I do think that a lot of papers out there give an account of some issue which may not turn out to be quite so relevant, or even true -- that's what philosophy is most of the time. At least we can say that, because several philosophers think that minimal truthmakers *are* important, we should have a rigorous definition of them, even if it did turn out that nothing satisfies that definition (so much worse for those who thought they were important).

Once again, thanks for taking the time to read the paper, we appreciate your input!

[Marcus Arvan]

Thanks for the explanations. They all sound pretty reasonable! Anyway, I do hope that my comments were at least somewhat helpful. Again, I'm not a metaphysician, but I tried my best!