tag:blogger.com,1999:blog-6940841.post2793435350105782882..comments2022-09-08T10:27:01.967-04:00Comments on The Headpiece for the Staff of Ra: The indispensability of identity conditionsMosBenhttp://www.blogger.com/profile/14396378353702882073noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6940841.post-58702394007356538412007-09-24T23:37:00.000-04:002007-09-24T23:37:00.000-04:00"One can use a sentence of that form provided one ..."One can use a sentence of that form provided one has given a non-circular analysis of it. If Quine isn't asking for such an analysis, I really have no idea what the demand for identity conditions is supposed to come to."<BR/><BR/>Agreed: Quine is demanding the PB give a non-circular analysis of sentences of the form [x is the same proposition as y] before she goes around asserting them. For the PB to concede to this demand, fail to do so, and yet still go around asserting such sentences is begging the question. <BR/><BR/>The subordinate clause `While the issue of identity conditions is still up for debate' is a critical qualifier. The sentence you put in quotes is still true when the argument is over the legitimacy of asserting sentences of the form [x is the same proposition as y]. But it's not what I said. And I'm not sure why you think the sentence I said is false.Noumenahttps://www.blogger.com/profile/02442204504120141558noreply@blogger.comtag:blogger.com,1999:blog-6940841.post-8789262194755583172007-09-18T11:22:00.000-04:002007-09-18T11:22:00.000-04:00"The Proposition-Believer (PB) cannot assert any s..."The Proposition-Believer (PB) cannot assert any sentence of the form [x is the same proposition as y] without begging the question against Quine."<BR/><BR/>False. One can use a sentence of that form provided one has given a non-circular analysis of it. If Quine isn't asking for such an analysis, I really have no idea what the demand for identity conditions is supposed to come to. <BR/><BR/>"Now, I don't see how to formalise [x is the same proposition as y] using the standard identity relation except as [x=y]. Perhaps the PB might want identity-with-respect-to-being-propositions, or some such, but this wouldn't be the standard identity relation. So, when we formalise, the sentences that the PB must abjure from if she does not give identity conditions just are the sentences involving the logic of the identity relation."<BR/><BR/>Numerical identities are easy to translate into first order logic. But sortal-relative identities can be translated too. The standard translation of `x is the same proposition as y' is: `x=y and x is a proposition and y is a proposition.'<BR/><BR/>The sort-relativity disappeared in this translation. Perhaps that's a cost. And if you think it is, it's easy to see what motivates the introduction of relative identity predicates by Geach and van Inwagen. Incidentally, one can, so far as I can tell, help oneself to these resources without saying the crazy things Geach says (eg, that *all* identity is sortal relative and that there's no most general sortal).Andrew M. Baileyhttps://www.blogger.com/profile/12606675886229313577noreply@blogger.comtag:blogger.com,1999:blog-6940841.post-76344472732433214672007-09-17T19:45:00.000-04:002007-09-17T19:45:00.000-04:00While the issue of identity conditions is still up...While the issue of identity conditions is still up for debate, the Proposition-Believer (PB) cannot assert any sentence of the form [x is the same proposition as y] without begging the question against Quine. That's just the debate between Quine and the PB: Quine says that, without identity conditions for propositions, [x is the same proposition as y] is nonsense (or nearly so), and hence the PB must provide identity conditions as a necessary (but probably not sufficient) condition on her sentences making sense (or any significant amount of sense). He writes, for example, that `little sense has been made of the term [`proposition', but I believe this applies more generally to any term for Quine] until we have before us some standard of when to speak of propositions as identical and when as distinct' (WO 200). <BR/><BR/>Now, I don't see how to formalise [x is the same proposition as y] using the standard identity relation except as [x=y]. Perhaps the PB might want identity-with-respect-to-being-propositions, or some such, but this wouldn't be the standard identity relation. So, when we formalise, the sentences that the PB must abjure from if she does not give identity conditions just are the sentences involving the logic of the identity relation. <BR/><BR/>Chisholm's definition might do the trick. Quine would object that the entities and relations Chisholm is giving here are just as dubious and in need of identity conditions themselves, but that's another debate. One worry that occurs to me, however, is that it seems to make the identity of propositions -- necessary things -- dependent upon the mental abilities of subjects -- contingent beings (excluding a necessarily-existent divine subject for the moment). At worlds with no subjects at all, for example, all true propositions are identified. It would just be a contingent fact that `2+2=4' and `All bachelors are unmarried' aren't identical. You could start talking about all possible subjects, but Al would complain (just like he did on Friday -- though, did you leave town before then?). <BR/><BR/>Finally, I don't see the circularity in<BR/><BR/>x=y <-> (z)(z€x <-> z€y)<BR/><BR/>(where € is my easier-to-type surrogate for the epsilon of set-inclusion). One side has =, and the other side doesn't.Noumenahttps://www.blogger.com/profile/02442204504120141558noreply@blogger.comtag:blogger.com,1999:blog-6940841.post-5031911420039553342007-09-17T17:15:00.000-04:002007-09-17T17:15:00.000-04:00Quine says `no entity without identity conditions....Quine says `no entity without identity conditions.' The Deniers disagree. And I don't think you've done the Deniers justice--your criticism isn't sensitive to an important distinction any Denier worth her salt would make. Doing philosophy without identity conditions is one thing. Doing philosophy without identity is another.<BR/><BR/>The Denier can freely abstain from giving identity conditions for propositions while nonetheless employing an identity relation in her logic. You've simply assumed that to abjure identity conditions is to abjure the logic of the identity relation. But why assume this without argument?<BR/><BR/>Two other points. First, it's never been clear what Quine actually wanted when asking for identity conditions for Fs. The clearest statement of the Quinean slogan I've found is something like this: don't posit the existence of Fs without a non-circular analysis of the open sentence `x is the same F as y.' But analyzing such open sentences without circularity (even for such well-behaved entities as sets) is notoriously difficult. That sets don't submit to this charge (but there apparently are such things) is good reason, I think, to jettison the requirement.<BR/><BR/>Second, Chisholm answered Quine's specific charge long ago--he gave identity conditions for properties that just might do the trick. F is the same property as G iff for all x, Fx iff Gx and for any subject S, S apprehends (I forget Chisholm's technical vocabulary here--but it was an epistemic relation) F iff S apprehends G. Combine this with the standard Chisholmian take on propositions as a special sort of property to answer Quine's charge. Coextensivity along two dimensions suffices (and is necessary) for identity.<BR/><BR/>So the believer in propositions has options.Andrew M. Baileyhttps://www.blogger.com/profile/12606675886229313577noreply@blogger.com