puzzles

In the 21 March 2006 bi-weekly meeting, after I confessed that I felt as if I hadn't really developed a positive view on anything in the vicinity of the problem of de re modality or conventionalism, Ludwig suggested that what was important at this stage was not the beginning of an articulation of a view on the subject but rather the collection of various puzzles relating to the topic. So, with this suggestion in mind, I'm starting a puzzle archive in this entry. I believe there are already some puzzles set down in previous posts efforts at solving which may ultimately prove fruitful, but this entry is the formal repository for new puzzles.

1. One puzzle of marginal interest has to do with Carnap's assertion (§38 of Meaning and Necessity) that for the semantical system S₂ which includes intensional operators, there can be a metalanguage M_e in which terms such as 'Human' are neutral between extension and intension, but which is itself only extensional. It's easy to see that the object language term 'N' won't occur in M_e, only a name for 'N' which is given extensionally. But what aboutoccurrencese of terms beginning with 'L-', it seems like this terms will be intensional? Carnap claims that of the four requirements for a complete semantic description of a system S would include: (i) formation rules for formulas, (ii) rules of designation for individual constants and predicates, (iii) rules of truth, (iv) rules of ranges, (i), (iii) and (iv) could be formulated in the purely extensional M_e. (A detailed explanation for the availability of extensional treatment is given on p. 170.) As far as (ii) goes, it seems that simple designation is extensional and could be so included in M_e, but L-designation is not. (Why? I assume because L-designation applies to the intensions had by terms of M' which are ex hypothesi not available in M_e.) But we're not in jeopardy because, by knowing the semantical rules of S₂, we are able to extensionallycharacterizee the L-equivalence of sentences of S₂. For instances, the sentences of M_e: ''H' designates Human' and ''H' designates Featherless Biped' are both true, but so is the statement (of M_e) ''H' and 'F •• B' are not L-equivalent', since we can show (having all the semantical tools of S₂ in M_e, that ''H' designates Human' holds according to those rules alone (and this was determined extensionally) and ''H' designates Featherless Biped' does not (and this was determined extensionally). I guess the idea is that since we can see extensionally whether a sentence is true in virtue of semantics alone, then we can use 'L-equivalent' in M_e purely extensionally, and so it looks like we can have a metalanguage for S₂ that is extensional. What does this mean for the interpretive truth theory and an analysis of 'it is necessary that ...' in terms of 'it is analytic that ...'?
   


2. Could Kaplan's proposal for how '' might be understood in terms of 'logical necessity' have any effect on how a conventionalist thesis might go? That is, we can understand what sentences are in the extension of '' by assigning a truth value to $entences given certain sequences by using the technological innovations that Kaplans develops ("arc quotation" and "shifty operators"). Once we can make sense of quantifying into opaque (modal) contexts, there are standard model theoretic ways to assess the truth of these sentences and assess the truth of these sentences in every model. There's also an analogous proof theoretic procedure to determine which sentences with a '' hold in each model. So it seems like we can, with his innovations, assess the truth of these sort of sentences.
    Now, more generally, if it seems that we understand '' as a predicate of sentences, then we have a method for assigning an arbitrary sentence beginning with a single '' a truth value -- that is, we simply pick out the sentences which we want to be in the extension of ''. Since, '' forms an opaque context, it doesn't have to be the case that the usual entailment relations hold between sentence "inside" this context. For example, if 'S' is true (i.e. 'S' is in the extension of '') and 'S' entails 'T', then we're not necessarily guaranteed that 'T' is true (i.e. 'T' is in the extension of '').
    On the other hand, according to the method of $entences, we treat intensional operators as if they were predicates of $entences and then take the sentence which is in the scope of the intensional operator as if it were contained in arc quotes. So, I guess both S = '(∃x)φ(x)' and S_f = 'φ(x)' may be such that both 'S' and '(∃x)S_f' can be understood as intelligible and assigned a truth value. We make sense of the latter is by assuming that since '' is a predicate of $entences (i.e. applies to both sentences and valuated formulas), we can determine whether S_f is in the extension of '' based on our assignment of a value to 'x'. (Finally! I understand why Kaplan says that phrases like 'φ(x)' in arc-quotes are only syncategorematic! It's still the case that only formulas in which all variables are quantified are sentences, it's just that with the method of $entences, we determine whether '(∃x)S_f' is true by checking to see if S_f is in the extension of '' on a particular valuation. We need the prefix '(∃x)' to insure that the sentence contains no free variables.)
    Now where does this fit with Fine? First off, it seems that Kaplan is considering only situations in which quantification is referential because he's assuming that there's an assignment of values to variables such that we can determine whether the $entence 'S_f' is in the extension or not. It seems that a presupposition here is that the 'x' in this formula is such that it can be assigned a value and that the sentence which would result from substituting the name 't' for 'x' in 'S_f(t)' would be have the same truth value as the sentence 'S_f(s)' if s and t are co-referrential. In other words, on Kaplan's picture, it seems that the only way we can understand the method of $entences is if we assume that formulas treceiveve a valuation on this method are referential in the sense of referential quantification.
   


3. Ernie LePore presented a view on which quotation is a semantic phenomenon which can be understood with the help of the Strong Disquotational Scheme (SDS): Only '''Quine'' quotes 'Quine'' literally contains 'q''. A corollary being that ''Quine'' literally contains 'Quine'. We can explain various data that suggests quotation is context sensitive by noticing that we can quote expressions or signs (which are used, in the context of some language or other, to articulate expressions). I'm curious where the conceptual separation of expression and sign (which seems to be a good one) leaves us if we adopt Fine's suggestion for a Universal Abstract Syntax (UAS) (in "The Problem of De Re Modality"). The suggestion was that contra (for instance) Montague, we think of syntax as fundamentally about instances, replacement and substitution in expressions rather than as based on a theory of concatenation. It seems like Fine's suggestion is that we think of syntax as a feature of abstracta differences in which could be spotted by the instances which were written down with the help of a concatencation system.
    The puzzle is whether we can understand quotation on the SDS model in terms of a Finean UAS. On the face of things, it seems that quotation, treated as a semantically substantial phenomenon depends upon features of signs systems which are based on a theory of concatenation.