Thursday, December 06, 2007

Truthmaker theorists should be priority monists.

I’ve written a paper arguing that the truthmaker theorist has to be a priority monist, on pain of being committed to mysterious necessary connections. That is, if you think that for every true proposition there is an entity which couldn’t exist and that proposition be false then you should also think that there is only one fundamental existent, with every other entity being ontologically dependent on The One, otherwise you violate my suggested version of the Humean ban on necessary connections.

The full paper is here, and any comments will be much appreciated. But here’s the argument in outline. The first step is to identify when necessary connections are acceptable. A completely die-hard Humean would say: never. I’m interested in how to be less die-hard and still have a principled position (one that can be justified independently of considerations concerning truthmaker theory). One popular option is: necessary connections are bad when they’re between wholly distinct existents, but acceptable when they’re between distinct but not wholly distinct entities – i.e. entities that overlap. I don’t like that. In general, things have the parts they do, and belong to the complexes they do, as a matter of contingency; and if that’s the case then necessary connections between overlapping entities are as mysterious as necessary connections between wholly distinct entities. I suggest instead that necessary connections are acceptable iff there is an appropriate relationship of ontological dependence between the entities. I want to analyse ontological dependence in terms of truthmaking: B is ontologically dependent on A iff B exists in virtue of A’s existence, which is to say just that A is the truthmaker for the fact that B exists. In that case, it’s no surprise if the existence of A necessitates the existence of B – that just follows from truthmaker maximalism. With a caveat that I won’t go into here (but I do in the paper), I suggest we limit the necessary connections in our ontology to those where the necessitated entity is ontologically dependent on the necessitating entity. Those necessary connections are explainable just by what ‘ontological dependence’ means, so if all the necessary connections are of that kind, we’re okay.

If that’s right the argument to priority monism is pretty quick. The truthmaker theorist needs not only truthmakers for atomic truths but also a totality truthmaker that says that all the first-order truthmakers are all the first-order truthmakers. The existence of the higher-order truthmaker necessitates the existence of each of the first-order truthmakers: if it didn’t, it wouldn’t be doing the job it was introduced to do. If that necessary connection is to be explainable, then, the first-order truthmakers must be ontologically dependent on the higher-order truthmaker. The fact that the first-order truthmakers exist must be true in virtue of the existence of the higher-order truthmaker. And so we’re driven to the view that the only fundamental being is the higher-order truthmaker – the totality fact that says how the world as a whole is; other things exist – such as the states of affairs of proper parts of the world being some way – but these will all be ontologically derivative entities, dependent on the totality fact.

I don’t particularly care as to whether one should modus ponens and be a priority monist or modus tollens and reject truthmaker theory. I care about the conditional; any thoughts on it will be welcome.


Carrie Jenkins said...

Your constraint means no two-way necessitation, I guess?

Ross Cameron said...

That's the caveat that I didn't go into the post, but do in the paper. I do want to hold that both, e.g., the singleton of a necessitates a and vice-versa; but obviously while {a} is ontologically dependent on a, a is not OD on {a}. But: I think the extra necessitation can be explained because, while many truths could have been made true by different possible truthmakers, '{a} exists' can *only* be made true by a. That's why {a} necessitates a: if {a} is around, a needs to be around to make it the case that {a} is around. (And I don't think there's a big mystery as to why a is the only possile TM for '{a} exists' - I think that's really just linguistic: it's just how we use the sentence '{a} exists'. Anyway, I say a bit more about this in the paper, but that's what I want to say when the necessary connection goes both ways.

Louis said...

Hi Ross,

Let P be a run of the mill first-order fact.
You argue from:
(1)The existence of the higher-order truthmaker necessitates the existence of P
(2) P is ontologicaly dependent on the higher-order truth-maker.

Here's a parody which does not involve 2-way necessitation:
(1)* the existence of the pair set {a, b} necessitates the existence of each of a (and not vice versa).
(2)* So a is ontologically dependent on (a, b}.

This argument is intuitively invalid. Here's a diagnosis: you need an implicit "solely" in your explanation of ontological dependence: B is ontologically dependent on A iff B exists *solely* in virtue of A's existence. But {a, b} does not exist solely in virtue of a's existence, so there's necessitation without ontological dependence. Thus, the restriction on A's necessitation of B will require some sort of fix in light of this qualification. I worry that, so-fixed, the truthmaker theorist can decline priority monism.

Obviously, I'm looking forward to reading the paper.

- Louis

Ross Cameron said...

Excellent question Louis, and that's going to force me to be more explicit about some things in the paper than I am at the moment: thanks.

But I think the pluralist is still in trouble.

The existence of {a,b} is necessitated by the existence of a and b. No problem, because a and b make it true that {a,b} exists.

The existence of {a,b} also necessitates the existence of a, and of b (and, hence, of them both). Explanation? a and b are the only possible truthmaker for the fact that {a,b} exists.

So can the pluralist say something similar in the totality fact case? Call the higher-order truthmaker ‘TOTALITY’. The existence of TOTALITY necessitates the existence of each of the first-order truthmakers. Explanation for the pluralist? The analogous explanation would be that those first-order truthmakers are the only possible truthmakers for the fact that TOTALITY exists. But that can’t be right! They’re not actually truthmakers for the fact that TOTALITY exists, because they could all exist and TOTALITY fail to exist. So the pluralist can’t explain the necessary connection between TOTALITY and each of its first-order constituents in the way the set theorist can explain the necessary connections between non-unit sets and each of its members.

Ross Cameron said...
This comment has been removed by the author.
Louis said...

Hi Ross,

If I understand you correctly, the qualification you suggest is this: a is necessitated by {a,b} in virtue of {a,b} necessitating the only possible truthmaker for the existence of {a,b}, which in turn necessitates a. The latter necessitation is unmysterious for the Humean, since it arises from a transparent entailment via conjunction elimination. So you seem to have in mind the following constraint on necessitation:
If Y necessitates X, then either (i) X ontologically depends on Y, (ii) X is transparently entailed by Y (e.g. by conjunction elim), or (iii) X is necessitated by the only possible truthmaker for the existence of Y.

(The necessitation of a by {a, b} requires clauses (ii) and (iii). A necessitation relation that requires all three clauses is, e.g., the necessitation of the singleton {a} by {a, b}.)

But now why can't the Humean TM theorist claim that P is transparently necessitated (e.g. by conjunction elim) by the only possible truthmaker for the existence of TOTALITY?

- Louis

Ross Cameron said...

Hi Louis,

Can I point you to the paper? The details of the 'no nec conns' principle are dealt with there - it would be a bit much to wrtie them out again here. If you still have worries, please let me know.

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