# [FOM] The Irrelevance of definite descriptions in the Slingshot Argument?

Kenny Easwaran easwaran at berkeley.edu
Thu Sep 28 13:26:47 EDT 2006

```The issue is just that set abstract terms _are_ definite descriptions.
Instead of "the x such that ..." you are talking about "the set
containing all and only x such that ...".

And of course, neither argument is clearly valid.  It seems that the
identity is logically equivalent to either s or t only on the
Russellian reading of definite descriptions - but in that case, the
definite descriptions aren't referring terms at all, so they can't
co-refer.  So one of the two types of substitution is blocked on any
reading.  (Unless there is a referential reading of definite
descriptions that can make the whole sentence equivalent to something
simpler.)

Best,
Kenny Easwaran

On 9/28/06, A.S.Virdi at lse.ac.uk <A.S.Virdi at lse.ac.uk> wrote:
>
>
> Dear FOMers,
>
> Can anyone think of any significant mathematical difference between the
> following two arguments?
>
> 1. s                                                    Premise
> 2. {x: x = d & s} = {x: x = d}  From 1., given substitution salva
> veritate of logical equivalents
> 3. {x: x = d & t} = {x: x = d}  From 2., given substitution salva
> veritate of co-referring terms
> 4. t                            From 3., given substitution salva
> veritate of logical equivalents
>
> And (with i is the iota/definite-description operator)
>
> 1. s                                                    Premise
> 2. ix(x = d & s) = ix(x = d)    From 1., given substitution salva
> veritate of logical equivalents
> 3. ix(x = d & t) = ix(x = d)    From 2., given substitution salva
> veritate of co-referring terms
> 4. t                            From 3., given substitution salva
> veritate of logical equivalents
>
> Both arguments seem valid (don't they?). So why has there been much
> philosophical ado about nothing concerning the status of definite
> descriptions in setting up this slingshot argument? Replace definite
> descriptions with their set abstract counterparts and there are no
> iota-expressions to be concerned with. Am I missing something here?
>
> Arhat Virdi
>
>
>
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
>
```