tag:blogger.com,1999:blog-14117162.post2247057237227433291..comments2024-06-10T02:43:59.211-07:00Comments on Obscure and Confused Ideas: Ontological Commitment, "To be is to be the value of a bound variable," and Schematic Letters in QuineUnknownnoreply@blogger.comBlogger3125tag:blogger.com,1999:blog-14117162.post-6089633241141179102015-09-18T12:34:23.235-07:002015-09-18T12:34:23.235-07:00A relevant question is precisely how Quine reads f...A relevant question is precisely how Quine reads formulas (or whatever he calls them) containing schematic letters. There are several options here. In your L1 free variables are taken to endow the formula in which they occur with generality (Frege in his ideography used Latin letters for this purpose; cf also the generality of axiom schemes). But the letters may also be so read that the formulas they occur in are taken to display a certain form; for instance, I can say that, in predicate logic an atomic formula has the form Fa or Fab or Fabc..., thus using letters (this is one way of understanding Frege's use of the Greek letters xi and zeta in the exposition of his ideography).<br /><br />I would be quite happy to say that the generality reading above, and so PRA, entails an ontological commitment to individuals in the domain of the variables (though maybe not to `all individuals', since this is a notion we assume not to grasp). But this can then not be ontological commitment quite in the sense of `to be is to be etc', since there is no binding here, as explained in the previous comment. <br /><br />As for independent motivation for the reading, one could point to Hilbert. In `On the infinite' he is quite clear that e.g. m + n = n + m (on the generality reading) is a finitistically meaningful statement of the commutative law, but he emphasizes that we cannot hope to make sense in general of negating such schematic generalities.Anstennoreply@blogger.comtag:blogger.com,1999:blog-14117162.post-50857082769694114752015-09-17T17:23:19.322-07:002015-09-17T17:23:19.322-07:00Hi Ansten --
Thanks for that comment! Certainly,...Hi Ansten --<br /><br />Thanks for that comment! Certainly, on your proposal, neither L1 nor L2 would necessarily have ontological commitments.<br /><br />I guess your proposal prompts a few further questions for me:<br /><br />1. (Quine interpretation) Does <b>Quine</b> ever say PRA has no ontological commitments? <br /><br />2. (Defense of this line) Should <b>we</b> say that believing PRA entails no ontological commitments? <br /><br />3. Is there any independent motivation/ justification for your proposal, besides 'It saves the Quinean position from this particular problem'?<br /><br />Those are just the thoughts that occurred to me. Thanks again for stopping by!Greg Frost-Arnoldhttps://www.blogger.com/profile/08563986984421570652noreply@blogger.comtag:blogger.com,1999:blog-14117162.post-2457737722390912802015-09-17T10:27:31.487-07:002015-09-17T10:27:31.487-07:00The language L2 would have to be obtained from L1 ...The language L2 would have to be obtained from L1 by the mere decoration of the formulas of the latter with what has the shape of universal quantifiers. The question is whether in L2 we can speak about a binding of the free variables in L1. For instance, we cannot negate the `quantified' formulas of L2; e.g. something like ~(x)Px is not well-formed in L2 (~Px is well-formed in L1, but its counterpart in L2 is (x)~Px). Likewise, we do not have existentially quantified formulas in L2. <br /><br />What Quine could say, therefore, is that by the binding of variables he means a process the outcome of which is either a universally *or* an existentially quantified formula, and which in turn may be negated. In L2 there is no such binding.Ansten Klevnoreply@blogger.com