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

Michael Zeleny zeleny at post.harvard.edu
Thu Sep 28 16:14:12 EDT 2006

```Various published versions of the slingshot argument turn on the
deployment of class abstracts and other variable-binding term
operators. No mathematical substance depends on this choice. The key
assumption in this regard is that the ensuing terms be interpreted
categorematically, as required for taking them as concurrent or
co-denoting, and hence subject to being substituted salva veritate.
This is the crucial element in Church's attribution of crushing
cogency to Frege's informal argument that declarative sentences denote
truth values.

--
Michael Zeleny at post.harvard.edu
http://larvatus.livejournal.com/
7576 Willow Glen Road, Los Angeles, CA 90046 -- 323.363.1860
All of old. Nothing else ever. Ever tried. Ever failed. No matter. Try
again. Fail again. Fail better. -- Samuel Beckett

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
> 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
>
```