tag:blogger.com,1999:blog-14117162.post4819643329935647150..comments2024-03-28T02:29:26.853-07:00Comments on Obscure and Confused Ideas: Logical pluralism and brother-in-law pluralismUnknownnoreply@blogger.comBlogger6125tag:blogger.com,1999:blog-14117162.post-74317960264273407492008-03-03T15:18:00.000-08:002008-03-03T15:18:00.000-08:00A couple more notes to myself:- It looks like a co...A couple more notes to myself:<BR/><BR/>- It looks like a common figurative way of putting the difference between lack of specificity and ambiguity is that in ambiguity, we SELECT a sense to give an utterance meaning, whereas in underspecification, we SUPPLY a sense. Using that metaphor, 'case' (and 'thing') don't look that ambiguous.<BR/><BR/>- One of the most common ambiguity tests is the "conjunction reduction test." Consider the two sentences <BR/> <I>Aaron is at the bank<BR/> Beth is at the bank</I><BR/>Consider a circumstance in which both are true, because Aaron is next to the river, and Beth is making a monetary deposit.<BR/>Now, the 'reduced' sentence<BR/> <I>Aaron and Beth are at the bank</I><BR/>cannot express this state of affairs: it can only say that both A and B are at the money depository or at the edge of a body of water. The linguists describe this as 'a cross interpretation' being impossible. This is evidence of ambiguity (instead of generality of sense). Why? Consider 'parent,' which is unspecified between 'mother' and 'father'.<BR/> <I>Aaron is a parent<BR/> Beth is a parent</I><BR/>Consider a case where both are true, because Aaron is a father and Beth a mother. But unlike the above case involving 'bank', cross-interpretation is possible in the reduced sentence:<BR/> <I>Aaron and Beth are parents.</I><BR/>That is, 'parent' means 'mother or father'.<BR/><BR/>Now how does this test fare when it comes to the pluralists' 'case'?<BR/><BR/>Let's suppose that S1 is some situation (of the sort used in semantics for relevant logic), and C1 is a construction (of the sort used in semantics for intuitionistic logic).<BR/><BR/>I <B>think</B> Beall and Restall would say<BR/> <I>S1 is a case</I><BR/>and <BR/> <I> C1 is a case</I><BR/>are both true (at least in the way 'Aaron is at the bank' is true when he is at the edge of a body of water but not at a monetary depository; if B&R say these two are not true, then 'case' is not even ambiguous). The 'conjunction reduction' would then be<BR/> <I>S1 and C1 are cases</I>.<BR/>Now, the question for the ambiguity test is: does this admit of crossed interpretations? (= Is this sentence true in the specified circumstance?) If Yes, then 'case' is not ambiguous; if No, it is ambiguous. The problem is I just don't know whether the answer is Yes or No -- or what evidence for one side or the other would look like.Greg Frost-Arnoldhttps://www.blogger.com/profile/08563986984421570652noreply@blogger.comtag:blogger.com,1999:blog-14117162.post-67907604641125429932008-03-03T12:14:00.000-08:002008-03-03T12:14:00.000-08:00Notes mostly to self:~ If 'case' (and therefore 'c...Notes mostly to self:<BR/><BR/>~ If 'case' (and therefore 'consequence') are ambiguous (as B&R say in "Defending Logical Pluralism" -- see correction in main post), then is 'thing' also ambiguous, and not merely very general in sense? For 'thing' seems to me much closer to 'case' than 'bank' or 'duck' are.<BR/><BR/>~ 'sibling' = 'brother or sister'. But B&R cannot think of 'case' as 'situation or possible world or Tarskian model or...'; if they did, there would be one notion of logical consequence, viz. C is a consequence of P iff there is at least one type of case in which C is true in every case in which P is true. So the question is then: is 'case' really disjunctive/ unspecific (like 'sibling') or not?<BR/><BR/>~ Jay David Atlas's 1989 <I>Philosophy without Ambiguity</I> argues (to a first approximation) that many supposed cases of ambiguity are really just general in sense. So if I ever think about this more, I'm going to have to dig into that book.<BR/><BR/>~ I asked my students today how they would respond to "Is pi a number?" All said yes, nobody was really tempted by the 'one the one hand yes (it's a real number), on the other hand no (it's not a natural number).'<BR/><BR/>~ B&R give (in the book, not the article) a definition of case as (basically) something that makes a sentence true. But does this definition really generate an ambiguous notion? I.e., Might this yield a univocal notion of case? [Student Tommy Lane pushed in this direction]Greg Frost-Arnoldhttps://www.blogger.com/profile/08563986984421570652noreply@blogger.comtag:blogger.com,1999:blog-14117162.post-32275030382049442142008-03-01T10:51:00.000-08:002008-03-01T10:51:00.000-08:00Hi Richard -Thanks, that strikes me as a good way ...Hi Richard -<BR/><BR/>Thanks, that strikes me as a good way to think about the difference between 'brother-in-law' and 'case'. Do you think various conceptions of 'thing' compete (instead of being disjunctive) also?<BR/><BR/>I was also hesitant about using the term "indeterminate", but I recently read a famous paper by the linguists Zwicky and Sadock, "Ambiguity Tests and How to Fail Them," where they say some linguists have called (what they call) 'lack of specificity' by the name of 'indeterminacy' inter alia. I'm not a linguist, so I was deferring to their jargon.<BR/><BR/>I do wonder whether the different notions of case really do compete/ 'implicitly exclude' one another in the way you're envisaging, for B&R. For some cases are proper subsets of others. E.g., one way of spelling out 'situation' is as a part of a world -- but not necessarily a <I>proper</I> part, so that worlds are situations too.<BR/><BR/>Now that I think about this, it strikes me as wrong to conclude that this precludes implicit exclusion/ competition: if someone asks me "Given any two distinct numbers, is there a third distinct number between them?", I have to say "Yes and No -- If by 'number' you mean 'real number', then yes; but if by 'number' you mean 'integer' then no." But the integers are obviously a proper part of the reals.<BR/><BR/>So can we figure out a test that sorts cases of lack of specificity into (implicitly) competing vs. disjunctive ones? (And then, of course, run that test on 'case' in B&R's usage.)Greg Frost-Arnoldhttps://www.blogger.com/profile/08563986984421570652noreply@blogger.comtag:blogger.com,1999:blog-14117162.post-76751809662601199992008-03-01T08:57:00.000-08:002008-03-01T08:57:00.000-08:00Regarding (2), we should distinguish non-maximal-s...Regarding (2), we should distinguish non-maximal-specificity from <I>indeterminacy</I>. 'Parent' is <B>not</B> "indeterminate between 'mother' and 'father'", it determinately includes both! So we may hope to distinguish pluralism on these grounds. It is not that there is some overarching concept of a 'case' which is the disjunction of any number of more specific implementations. Rather, there are <I>competing</I> conceptions of a 'case', each of which implicitly excludes the others, though objectively speaking no one approach is privileged.Richard Y Chappellhttps://www.blogger.com/profile/16725218276285291235noreply@blogger.comtag:blogger.com,1999:blog-14117162.post-80367485078437664482008-02-28T15:59:00.000-08:002008-02-28T15:59:00.000-08:00Hi Kenny --Thanks for the rich comment. A few thi...Hi Kenny --<BR/><BR/>Thanks for the rich comment. A few things occur to me in response:<BR/><BR/>(1) I'm very sympathetic to your basic idea of appealing to what the concept is FOR as a constraint on the problem-area. That said, I don't have a clear and distinct idea of what you mean by "very essential uses" of a term, and why 'brother-in-law' lacks one. <BR/><BR/>(2) Also, though I asserted in the post that 'brother-in-law'-like cases abound, I did not really justify that at all. So here's another extended example: 'sibling' is indeterminate between 'brother' and 'sister'. 'Sister' is indeterminate between 'older sister' and 'younger sister.' 'Parent' is indeterminate between 'mother' and 'father.' And I think it's clear that 'parent,' 'sister,' and 'sibling' are not ambiguous (more specifically, not homophonic) words. Examples of non-maximally-specific words could be multiplied. Will none of these have 'very essential uses'?<BR/><BR/>(3) I'm very sympathetic to your worry about logical pluralism missing something: "If logic is really about truth, and how things actually are, then presumably one of the notions will be the relevant one." I'm not sure how B&R would respond, but here's two tries:<BR/><BR/>(i) When we say C is a logical consequence of P1...Pn, that can't just be saying that the actual world is such that either one of P1...Pn is false or C is true (since then "Grass is purple" entails "The sky is green"). So we can't just be talking about truth (in our world). In my intro classes I say "A valid argument is one whose conclusion is true <I>whenever</I> all the premises are" (= B&R's (V)). What exactly does that 'whenever' quantify over? It's not specified, and (more importantly) it's not clear to me that being a "realist and correspondence theorist about truth and the like" forces you to pick one specification over the other (e.g., does the realist correspondence theorist go with possible worlds or Tarskian models as the domain of quantification for that 'whenever'?).<BR/><BR/>Try (ii): Logic is not about truth simpliciter, it is about (preservation of) true <I>sentences</I>. Sentences are 'made' true by something or another (at least in most projects of philosophical semantics). Is the realist correspondence theorist committed to the idea that there is only one kind of thing that can make sentences true? Or is there still some freedom in specifying what makes sentences true?<BR/><BR/>Those responses are a bit groping, I realize. As I said, I think you're placing pressure on B&R in the right spot.Greg Frost-Arnoldhttps://www.blogger.com/profile/08563986984421570652noreply@blogger.comtag:blogger.com,1999:blog-14117162.post-52446839530431640982008-02-28T13:17:00.000-08:002008-02-28T13:17:00.000-08:00The way I would want to go about these discussions...The way I would want to go about these discussions is to figure out what uses we have for the relevant concept. I don't really understand whether there's a distinction here between pluralism and ambiguity (or perhaps better, homophony between different words). But in the case of "brother-in-law", I think we normally don't have very essential uses for the term, and so it's ok that it sometimes refers to one and sometimes the other. Whereas with logical consequence, I've worried (since reading that paper) that the pluralist position is missing something. If logic is really about truth, and how things actually are, then presumably one of the notions will be the relevant one. Perhaps it'll be a different one for inferential purposes than for truth purposes, but I just don't see why someone would be interested in the intuitionist or relevance notions if they're realists and correspondence theorists about truth and the like.Kennyhttps://www.blogger.com/profile/09588770173317316837noreply@blogger.com