In particular, those in attendance did not object to the following constituting a proof of the existence of numbers (p. 357):
- There are prime numbers.
- Therefore there are numbers.
Tuesday, October 27, 2009
Schaffer's Permissivism
A couple of weeks ago we discussed Schaffer's 'On What Grounds What'. Although we discussed quite a bit about different, non-equivalent ways of characterizing 'permissivism' in detail, I got the sense that there was a general sympathy towards the spirit of the contention that existential questions about numbers etc. were somehow easy, and the harder questions concerned what grounds what, and thus what is fundamental.
In particular, those in attendance did not object to the following constituting a proof of the existence of numbers (p. 357):
In particular, those in attendance did not object to the following constituting a proof of the existence of numbers (p. 357):
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7 comments:
Hey Dan,
My own take on the matter is that we need some kind of hyperintensional notion in metaphysics, and various people -- Ted, Kit, Ross, Jonathan -- have put different options on the table. And I think anyone tempted towards those views will look upon the (1)-(2) inference as being obviously sound. What I've found interesting is (i) how lots of metaphysicians don't like these kinds of views -- eyes roll when you mention naturalness or quantificational structure. (Not in Leeds, of course ;)) but (ii) how lots of non-metaphysicians tend to find the views natural and appealing. So I'd be interested to hear what the demographic was in the session when you read it, and especially whether the metaphysicians were more reticent to accept the (1)-(2) proof, and the move to fundamentality.
FWIW, and since you mentioned the paper, I'm not totally happy with Schaffer's view. On reason is that he's focusing mainly on the case of entity-grounding, whereas we want a more general account of grounding that tells us what grounds the truth of propositions. I can see how this might go, within Schaffer's setting, but I'm a bit concerned it either (i) collapses into Ross's view (truth-grounding = truth-making, and entity-grounding drops out) or (ii) needs to invoke ugly primitives (i.e. states of affairs, facts, or somesuch structured entities).
Hi Rich!
We were mainly people working partly on metaphysics, but I know the kind of eye-rolling you mention.
Interesting stuff about the relation between the relation between (say) parts grounding the wholes they compose and that between (say) these parts (or wholes) making some truths true.
Re Ross, if I don't misremember he holds two relatively unorthodox views about truth-making, right? (i) That it is a relation between truths as opposed to things such as myself and truths and (ii) that (truths corresponding to) non-fundamental, derived things such as myself don't truthmake. Hmmm...
I'm no expert on the truthmaker literature, but I'm pretty sure Ross would accept (ii): things like me and you don't serve as truthmakers. I think that's because he wants fundamentality and truthmaking to be tied together: to be fundamental is to do truthmaking work. Or at least he's up for something like that.
I'd be surprised if Ross was okay with (i) though.
So, just for the record: I certainly accept (ii). To be real/fundamental is to be a truthmaker, and to be derivative is for the fact that you exist to be made true by something other than yourself.
RE (i). I think that A makes p true iff p is true in virtue of the truth of [A exists]. So truthmaking itself isn't a relation between truths (at least, not always): it's a relation between some thing(s) and some truth. But it goes hand in hand with the obtaining of the in virtue of relation between truths.
That on its own doesn't say anything about whether one of these relations is prior to the other, of course. But I'm somewhat tempted by the view (and I think this is what Dan has in mind by attributing (i) to me) that it's the in virtue of relation that's prior, with truthmaking defined in terms of it via the above biconditional. Why? Economy, and I don't think there's a neat way to define in virtue of in terms of truthmaking.
Thanks, Ross, this clarifies things for me! I was under the impression that you were willing to call ‘truthmaking’ the underlying in virtue of relation between truths itself. (I think this is what Yablo decided to do in recent work, but I might be wrong here again ;-)!) I see how your choice allows you to keep the talk about entities other than truths making truths true. Arguably, some of the traditional motivations for truthmakers would still be not available---appealing to the “insight” of truths requiring anchoring in reality, as to be about things, not free-float in a void, etc. But I seem to remember from the discussion in Barcelona that you were not very impressed by these motivations anyway.
Regarding the other issue, things are clearer to me now as well. I thought you thought I didn’t truthmake because I wasn’t fundamental, but now I see that I am not fundamental for you because I don’t truthmake, right?
Right!
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