On Penguins
Doing a PhD is not just about writing a PhD. Fortunately, you can distract yourself with other philosophical activities, that are supposed to be good for you, so that you don't feel so guilty for not being at home working on your thesis in that very moment.
So a good source of educative distraction are the Friday Seminars in my Department. Yesterday it was specially interesting and touching, since we had a Sheffield graduate doing the seminar. It was my good old friend David Liggins, who was a PhD student not long ago, and yesterday he was an invited speaker at the seminar! Quite an event. He suggested a very interesting and somehow intriguing view about how we can communicate using matehmatical statements. For instance, we can communicate something by using the sentence 'The number of penguins at Ely is zero' (which, according to nominalists, is false since it is committed to the existence of numbers), because we all share the belief 'The number of penguins at Ely is Zero iff there are no penguins at Ely'. Therefore, when we hear the former, we can come to believe that there are no penguins at Ely.
This sounds plausible, but I was puzzled by one consequence of the view: if you are a philosopher who does not believe in numbers, then you do not share such a belief, because you think that the right-hand sentence is true while the left-hand sentence is false. Then, this view is not supposed to be true of the very same people that propose it, becase they do not believe in the existence of numbers!
posted by Esa @ 9:31 PM
9 Comments:
Just two quick questions: Why should a nominalist hold false 'The number of penguins at Ely is Zero,' instead of explaining its truth paraphrasing it away as 'There are no penguins at Ely'? And what does the claim that one does not "believe in numbers" really amount to? If, possibly, that one holds that apparently numerical statements are to be paraphrased away in the envisaged way, then perhaps one might not believe in numbers but share the relevant (analytic) belief all the same, no?
Sure, there are 'hermeneutic' nominalists who hold that sentences such as 'the number of penguins at Ely is zero' can be true, even if there are no numbers, because they paraphrase those numbers-invoking sentences in terms of sentences not involving them. In my post (following david) I was focusing on error-theorist nominalists, who claim that most of our mathematical sentences are false (or trivially true). Thanks for the clarification.
Oh, I see. So is David's view then that one might think that 'The number of penguins at Ely is zero' is false, that 'There are no penguins at Ely' is true, and still believe that the former is true iff the later is true?
No, of course THAT is not David's view! He does not think we are all irrational! He thinks that the folk (minus the error-theory nominalists) tend to think that 'The number of penguins in Ely is zero' is true, and by that they understand that 'There are no penguins in Ely', because they believe the biconditional. Those who believe that 'the number of penguins in Ely is zero' is false, but that 'there are no penguins in Ely' is true, do not longer believe the biconditional, obviously.
Still don't get it, sorry. Let us label the three relevant statements:
(i) 'The number of penguins at Ely is zero;'
(ii) 'There are no penguins at Ely;'
(iii) [(i) iff (ii)].
Now "the folk" think that (i), (ii), and (iii) are all true. The DL-nominalist rejects (i) and thereby rejects (iii). In which sense then sharing the belief about (iii) explains communication, if only "the folk" do belief this? Was this your original worry?
Thanks for this, it is helpful. Yes, that was my worry. I guess David might say that (iii) can explain communication FOR the folk, and this is all he wanted to explain.
Mmm, good that we agree on this! What I don't get now is which is David's project: how "the folk" manage to communicate with each other does not require anything very special -- provided that communicating is transmitting beliefs.
What if you invite David to contribute here?
I think I get your worry now, thanks.
David's project was, if I got it correctly, to explain how the folk can communicate thoughts about the physical, concrete world, by using mathematical sentences (which, by assumption, are about abstract objects and therefore false, or trivially true). So he suggests that if the folk believe, say,(iii), then it's clear to see how they can communicate (ii) by saying (i).
ok, ic
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