Dummett speaks

Dummett suggests that we take a look at two roles for sentence truth: the first is truth as the aim of assertion; the second is truth as the output of a compositional semantics. These two roles for sentence truth can be associated with two notions of semantic value, "[assertoric] content" and "ingredient sense" (416-417, 447, 449: a hard-fought search.)

Here is Lewis on the same distinction:

"We seem to have a happy coincidence. To do their first job [emph added] of determining whether truth-in-English would be achieved if a given sentence were uttered [assertively!--MF] in a given context, it seems that the semantic values of sentences must provide information about the dependence of truth on features of context. That seems to be the very information that is also needed, in view of shiftiness, if semantic values are to do their second job [emph added] of helping to determine the semantic values of sentences with a given sentence as constituent. How nice.

...No; we shall see that matters are more complicated." (Index, Context, and Content, 28)

Dummett stresses that it's possible to know a sentence's assertability conditions without knowing how it behaves compositionally:

"We must distinguish...between knowing the meaning of a statement in the sense of grasping the content of an assertion of it, and in the sense of knowing the contribution it makes to determining the content of a complex statement in which it is a constituent: let us refer to the former simply as knowing the content of the statement, and to the latter as knowing its ingredient sense." (447)

[is the reverse situation possible--is it possible to know how a sentence embeds without knowing its assertability conditions?---perhaps, if we consider, for example, sentences whose truth-value we couldn't possibly know.]

Dummett suggests, strangely, that if it were not for what Lewis calls the second role of sentences--the embedding role--we should not have a clear distinction between two kinds of truth, the assertion kind, aka 'correctness', and the merely semantical kind (of which it seems safer to say that the former isn't really truth(!):)

"We left the notion of the correctness of an assertion quite vague...the use of the word 'true' normally involves a distinction beyond [one of e.g. tact]: a distinction between the case when what is asserted actually fails to be true from that in which the speaker merely lacks sufficient warrant for his assertion. If the sentence whose utterance effects the assertion were not one that was capable of occurring as a constituent in more complex sentences, no such distinction could be drawn: the use of the sentence would be completely characterized by saying that it was held appropriate to utter it assertively in such-and-such circumstances, and there would be no room for distinguishing, among those circumstances, those which constituted the assertion as true from those which provided the speaker with a ground or other warrant for holding it to be true." (449-450)

I can see Lewis agreeing on this condition: we should gloss assertability as truth at a context, and truth at a context as truth at a context and the index determined by that context. This seems right as far as the Kaplanian machinery is concerned. Dummett is worried about the same kinds of considerations that would lead one to claim that e.g. "I am speaking" and "I exist" are metaphysically necessary truths. They is always assertable, and we can give a good treatment of that; the need to be careful in this treatment is brought out for Kaplan and Lewis by considering the falsity of sentences like "necessarily, I am speaking" and for Dummett (in much the same vein--compositionally) by considering the non-equivalence of "If I am speaking, then I exist" and "If I exist, then I am speaking."

Conclusion: we have excellent grounds for NOT conflating assertability with truth: while it is true the truth-conditions of p determine the truth-conditions of sentences embedding p, it is not true that the assertability-conditions for p determine the assertability conditions of sentences embedding p.

Dummett writes that "it is not from a consideration of the notions of truth and falsity as they are needed for an account of assertoric force that we can find a justification for Frege's thesis that a sentence containing a name without a bearer has no truth-value" (421). That thesis needs to be grounded in compositional concerns.

Dummett notes that assertoric content of a sentence can lend itself to three-valued logics, since the analogue of bivalence in terms of assertability is surely false (meaning: it's plain false that for any sentence p, either p is assertable or p is deniable.) [This is only one of the natural routes to three-valued logics he suggests--the other is the case of denotation-less sentence constituents like empty names.] But doesn't the above then show that a many-valued logic with this kind of motivation--the kind that comes from wanting to capture the non-bivalence of assertability--rests on a misconceived conflation of truth with assertability?

***The quotes***

"In speaking of sentences themselves...there are two different ways in which we may regard them; and these may give rise to two distinct notions of truth-value. On the one hand, we may think of sentences as complete utterances by means of which, when a specific kind of force is attached, a linguistic act may be effected: in this connection, we require that notion of truth-value in terms of which a particular kind of force may be explained. On the other hand, sentences may also occur as constituent parts of other sentences, and, in this connection , may have a semantic role in helping to determine the truth-value of the whole sentence: so here we shall be concerned with whatever notion of truth-value is required in order to explain how the truth-value of a complex sentence is determined from that of its components. There is no a priori reason why the two notions of truth-value should coincide." (417, emph added)

"Under one use of 'true' or 'false', a thought may be called true just in case the assertion of it would be correct, and false otherwise. (419)

[Dummett here employs a notion of 'correctness' which can be extended to other kinds of speech act, in the vein of Searle's 'conditions of satisfaction.']

[This notion of truth is supposed to be 'pragmatic': "the pragmatic part provides the point of so classifying sentences as true or false, by describing the use that can be made of any given sentence in terms of its truth-conditions." (417) ]

A definition of truth entails a notion of consequence. Then again, it doesn't.

A definition of truth entails a notion of consequence. A definition of truth will define truth relative to (a language L and) a formal object x--"truth at x"--which could be (i) an index, (ii) a context, (iii) an index-context pair, (iv) a suitably restricted set of index-context pairs, e.g., those pairs where the index and context are related in a certain way (as in "the index of the context", or "the index initialized by the context"). Suppose we have some such formal object x relative to which truth (in L) is defined. Then, given a set of sentences \Gamma and a sentence s, s is a consequence of \Gamma iff, when all the sentences in \Gamma are true relative to x, s is also true relative to x. We are done.

Then again, a definition of truth does not entail a notion of consequence. In our search for a notion of consequence, we are seeking to do justice to plausible-seeming inference patterns, such as Lukasiewicz's Principle, De Morgan's Law, the Choice Inference, or Stalnaker's "Direct Argument".

It could turn out that our inference patterns do not track the notion of consequence defined above. What they could be giving us data about is (i) the constraints the context places on the index--how to define a "index of the context." (ii) in a more dynamic (or "reasonable inference") vein, perhaps we should see the premises in \Gamma as being true at an ordered series of contexts, rather than a single context, where the inference is valid if the conclusion is true "after" all the premises are true (here, and not in the first definition of consequence, is it the case that the order of the premises matters). (iii) in an "informational consequence" vein, we could think of the inferences as preserving something other than truth (or, what comes to the same thing, we could define a new kind of truth--truth relative to only one parameter of the index.*) Following the first convention rather than the second, we will say that an inference pattern may preserve acceptance (aka certainty or Supertruth) rather than truth.

If our formal semantics can account for the inference pattern in question in any of these ways, we may consider our semantics to have dealt satisfactorily with the inference pattern, even if it is not "valid" in the sense first defined above (valid with regard to truth at L and x).

We achieve synthesis of the two points of view on truth and consequence by noting that it's true that a definition of truth entails A notion of consequence, but there may be many notions of consequence which are of interest to us, and which are useful in explaining inference patterns.

*truth relative only to the i-parameter, and not the w-parameter. For e.g. supervaluationist Supertruth, this is indeed truth relative to only part of the index. Sentences (the full battery of sentences--both modalized and unmodalized) are true at a world and a set of worlds accessible from that world, but given S5 (which defines an i for any w) and an interest in preserving supertruth, we actually don't need the world parameter. We have effectively cut down on the battery of sentences by considering only the preservation of supertruth.

Hypothesis regarding [[?]] and [[metalinguistic negation]]

...there is no such thing.

Quotations

We begin with Davidson's general gloss on theories of quotation---what it is all of them are trying to explain. Then we look at his gloss on different competing theories, and problems therefor.

General: "Quotation is a device used to refer to typographical or phonetic shapes by exhibiting samples, that is, inscriptions or utterances that have those shapes."

1) The Proper-name Theory. "A quotation, consisting of an expression flanked by quotation marks, is like a single word and is to be regarded as logically simple. The letters and spaces...are viewed as accidents in the spelling of a longer word...A quotation mark name is thus, Tarski says, like the proper name of a man." (81-82).

Thus: [[`Ann']] = Ann (the word, not the person) [?--not sure if this is right]

Davidson writes: "The merit of this approach...is the emphasis it puts on the fact that the reference of a quotation cannot be construed as owed, at least in any normal way, to the reference of the expressions displayed within the quotation marks. But...[i]f quotations are structureless singular terms, then there is no more significance to the category of quotation-mark names than to the category of names that begin and end with the letter 'a'. On this view, there is no relation, beyond an accident of spelling, between an expression and the quotation-mark name of that expression. And so no echo remains, as far as this theory of quotation goes, of the informal rules governing quotation that seem so clear: if you want to form a quotation-mark name of an expression, flank that expression with quotation marks." (83)

[I'm not sure what's so wrong with that...it's not accidental, but also not entirely necessary, that e.g. `the n-word' is a name for a particular word.]

The big objection: "on this theory we cannot give a satisfactory account of the conditions under which an arbitrary sentence containing a quotation is true...on the theory of quotation we are considering, quotation-mark names have no significant structure. It follows that a theory of truth could not be made to cover generally sentences containing quotations. We must reject the proper-name interpretation of quotation is we want a satisfactory theory for a language containing quotations" (83).

[I'm not sure this is right, either. It might be right for theories of mixed quotation: "Quine said that quotation Fred" is pretty strange. But why couldn't e.g. `the n-word' be the name of a word construed as a particular part of speech--that is, a word construed as a member of a particular semantic type? That seems fine: "Joe called Bill the n-word" seems well-formed.]

2) The picture-theory of quotation. This is the Fregean-inspired notion that quotation marks create a special context within which words name themselves. On this view, the quotation does have internal structure, since the quotation marks are distinct from what comes within. (No more "Quine said that quotation Fred.") It is, as Davidson remarks, "reminiscent of Frege's theory of opaque (what he called oblique) contexts such as those created by [attitude verbs.]"

Objection: "The trouble with the picture theory, as with Frege's treatment of opaque contexts generally, is that the references attributed to words or expressions in their special contexts are not functions of their references in ordinary contexts, and so special context-creating expressions...cannot be viewed as functional expressions." (85).

[Well, we could always generalize to the worst case! Here, one case that needs to be generalized to is "Lagadonian."]

3) The Spelling (aka Description) Theory. A single word in quotation marks names itself, but a quoted longer expression is structured. For example `Alice swooned' is 'the expression got by writing 'Alice' followed by `swooned.'"

Davidson writes that "there is no difficulty about extending a truth definition to these devices of spelling suggested." But he complains:

"nothing of the idea of quotation marks is captured by this theory--nothing of the idea that one can form the name of an arbitrary expression by enclosing it in quotation marks. On the spelling theory, no articulate item in the vocabulary corresponds to quotation marks, and so the theory cannot reflect a rule for this use." (87)

Davidson then goes on to present as damning evidence the availability of inferences like

`Alice swooned' is a sentence.

Ex (`x swooned' is a sentence).

which, for the spelling theory, would be e.g.

alc^`swooned' is a sentence. [where `alc' denotes the name `Alice']

Ex (x^`swooned' is a sentence )

The deficiencies in accounting for the natural language use of quotation are then that it cannot account for mixed quotation, and it cannot account for the introduction of new notation: "An important use for quotation in natural language is to introduce new notation by displaying it between quotation marks; this is impossible on the spelling theory provided the new notation is not composed of elements that have names." [This confuses me bit, because, in English, at least, the elements always *do* have names...also, given Lagadonian conventions, this is not a problem, because as soon as you know the name, you know the element it names, and vice-versa.]

Now, we have list of desiderata for a theory of quotation:

1. It "merge[s] with a general theory of truth for the sentences of the language." (Not knowing what this means in Davidsonian-ese, I will gloss this as: "it must be compositional.")

2. The theory must provide a semantic role for devices of quotation (marks or hand gestures, etc.) [Is this tendentious?...it seems that Washington/Reimer will reject this.) This is because there is a "rule of quotation" that speakers are able to learn and apply in countless ways.

3. The theory must "explain the sense in which a quotation pictures what is referred to, otherwise it will be inadequate to account for important uses of quotation, for example, to introduce novel pieces of notation in new alphabets." [I'm not so sure about this. The latter half can be taken care of by assuming a Lagadonian convention. The first part is just a question of how well a metaphor is cashed. That's elusive to someone like me, who had a poor grip on the metaphor in the first place.]

4. [inferred from remarks on pg 90] We must balance the conflicting demands of the picture theory (which somehow pushes is towards an unstructured view) and the demand for structure imposed by the requirement of compositionality. The punchline: "enough structure will be too much so long as we regard the quoted material as part of the semantically significant syntax of a sentence. The cure is therefore to give up this assumption."

So the idea is that the quotation marks are demonstrating a shape by ostending something (an inscription) with that shape (this is deferred ostenstion, then...perhaps the only way we can ostend universals like shape.) The semantically significant part of a sentence like

"cat" has three letters.

is the quotation marks themselves, which (jointly?) constitute a demonstrative, as in

That_1 has three letters.

[wait...doesn't this fly in the face of all of those claims that demonstratives are "directly referential"?:

``the position that the semantic content of a name or other directly referring expression is nothing more than the referent: the referent is all that the name contributes to a proposition expressed by a sentence containing it. (SEP)"]

semantic value of question = semantic value of disjunction?

Is this a problem? --e.g., if one's right, is the other wrong? I used to think so--in particular, I used to think that Hamblin disjunction semantics was incompatible with Hamblin question semantics--but Lewis's "General Semantics" has showed me the error of my ways.

Lewis points out that some grammatical (read: syntactical?) transformations of underlying semantic material may only be appropriate if the material is being put to a certain pragmatic use. So, for example, for him [[speak French! ]] = [[you speak French]], even though they don't have the same embedding behavior:

(ok) John knows that you speak French.

(#) John knows that speak French!

this is alright as long as a proposition is the semantic value of [[speak French!]] (which it is, for him.) The unembeddability of [[speak French!]] is explained, not in terms of its semantic value, but in terms of the fact that the proposition is subjected to a transformation

you shut the door --> shut the door

that is only appropriate if it is to be used to make a command.

The same thing can be said for questions and disjunctions, since, for Hamblin, sets of propositions are obviously used interrogatively.

[[which Stooge do you like]] = [[you like Larry or Moe or Curly]] =

{you like Larry, you like Moe, you like Curly}.

Does this mean that e.g. the question mark has a certain semantic value--or a certain metasemantic value? This is worth investigating!...

***

NB I still have no inkling of a compositional account of Hamblin's account of questions that present only one propositional alternative, like

(1) You like coffee?

(2) Have you been to Paris?

...why? For Hamblin, [[(1)]] = {you like coffee, you don't like coffee}. But it's not clear how to get this from the semantic values of the constituents of (1). Still, we can differentiate (1) and (2) from

(1') You like or you don't like coffee.

(2') You have been to Paris or you haven't been to Paris.

...in the way glossed above: they do not differ in semantic value, but in assertoric force.

Lewis, "General Semantics" II: Semantic Values for Nondeclarative Sentences

Lewis contrasts two ways of making sense of the content of nondeclarative speech acts. The two camps are (i) the "sentence radical" view, and (ii) the "paraphrased performative" view.

(i) The Sentence Radical view postulates that an uninflected declarative sentence like "you be late" is a sentence radical which is concatenated a text-scope with a mood-node: this mood-node can be declarative, imperative, interrogative, etc. The sentence radical is not itself a declarative sentence; and "fundamentally...the entire apparatus of referential semantics...pertains to sentence radicals and constituents thereof" (56). To account for moods--not a part of referential semantics, mind you--the quoted philosopher, Stenius 1967, makes reference to what sound like constitutive speech-act rules, like "(declaratively) assert s, with meaning p, iff you believe that p is true."

Lewis notes that the Sentence Radical view will have trouble with any speech act that appears not to have a complete sentence-radical as a constituent; his example is "Hurrah for Porky!"

(ii) Lewis's own view, the performative view, is advertised as having a simpler interface with `referential' semantics [I guess that would be: the semantics of the interpretation function]. We consider a complicated transformational component of the grammar which paraphrases LFs of basically this form:

[.S

[.I

]

[.VP

[.ask/command/declare

]

[.V-bar

[.you

]

[.S*

]

]

]

]

...where S* is the sentence that referential semantics tells us about. Such a transformational component would equate e.g.

I command you to be late.

with

Be late!

Thus "I [Lewis] propose that there is no difference in kind between the meanings of these performaives and non-declaratives and the meanings of the ordinary declarative sentences considered previously" (57).

NB that while Lewis appears to have the same problem as Stenius, he paraphrases "Hurrah for Porky!" as "I cheer Porky."

NB also that Lewis then assigns truth-values to non-declaratives like "Hooray for Porky" and "What time is it?" They are true, because (assuming appropriate felicity conditions) the speaker does thereby succeed in cheering for Porky and asking what time it is. Thus we must keep in mind two uses (rather than two senses) of e.g. "I command you to be late": one use is imperative, while the other is descriptive. Only the former use permits of the paraphrase "Be late!" (Which is odd, because the associated transformation is syntactic.*)

This seems like an unintuitive view (even if Stenius's is too). Why prefer it? Lewis notes that "On the method of sentence radicals, the difference between the performative and self-descriptive uses of performative sentences must be treated as a difference of meaning" (61). But this doesn't seem right to him. He compares this two the two sentences

(1) I am talking in trochaic hexameter.

(2) In hexameter trochaic am I talking.

We would want to say that the sentence have the same meaning, even though they have different available uses: "whether a sentence can be used to talk in trochaic hexameter is not a matter of its meaning" (60). Note that this example provides an interesting riposte to the asterisk-ed complaint above. It is obviously a (series of) syntactic operation(s) that account for the inter-derivability of (1) and (2). While the syntactic operations have no effect on the semantic content of the sentence, they have nonequivalent results for the usability profile of the outputs: in particular, (2) can be used to performatively, while (1) cannot. (Note strangely, then, that (1) may be false and (2) may be true at a context even if everything is held fixed prior to the utterance. Lewis will say that the difference in truth is a result of taking (2) to be used performatively, while (1) cannot be used performatively.)

****

"Index, Context, Content" revisited

...in search of disagreements between that article and "General Semantics"...

...This is found only on the issue of constant-but-complicated vs. variable-but-simple semantic values. Lewis writes that in "General Semantics," he went for the constant-but-complicated.

The difference is elusive to me. (And to Lewis, in the sense that he finds the distinction to be an unimportant one!). Lewis writes:

"...[considerations about the objects of the attitudes] does not mean that we need to equate the propositional content and the semantic value of a sentence in context. It is enough that the assignment of semantic values should somehow determine the assignment of propositional content. And it does, whether we opt for variable-but-simple values or for constant-but-complicated ones. Either way, we have the relation: sentence s is true at context c at index i. From that we can define the propositional content of a sentence s in context c as that proposition which is true at world w iff s is true at c at the index i^w_c that results if we take the index i_c of the context c and shift its world coordinate to w.

...It would be a convenience, nothing more, if we could take the propositional content of a sentence in context as its semantic value. But we cannot. The propositional contents of sentences do not obey the compositional principle, therefore they are not semantic values. Such are the ways of shiftiness that the propositional content of `Somewhere the sun is shining' in a context c is not determined by the content in c of the constituent sentence `The sun is shining.' For an adequate treatment of shiftiness we need not just world-dependence but index-dependence--dependence on all the shiftable features of context. World is not the only shiftable feature." (38-39)

(I remember being terribly confused by this passage, especially the unhelpful "such are the ways of shiftiness that...") The argument here is that we cannot take propositions to be the semantic value of sentences because sentences can embed in operators that shift indices other than the world parameter; the operator "somewhere: ..." is a case in point. The argument would also work with operators like "strictly speaking:...", "it was: ..." and the imaginary "as for you: ...".

This is a polemic against propositions as semantic values, though, which is only a special case of the variable-but-simple semantic value camp.

Lewis, "General Semantics," I

Reading: Lewis's "General Semantics" (1970).

General reflections on "General Semantics": this is a fully intensional, "generalize-to-the-worst-case" system. It appears that what inspired Lewis to generalize to the worst case was intensional adjectives like "alleged." He writes that an adjective like [[alleged]] is a function from adjectives to adjectives--but

"It is best to foresake extensions and Carnapian intensions...most adjectives do not have extensions. What is the set of things to which `alleged' applies?...[there is none.]

In general, an adjective takes a common noun to make a new, compound common noun; and the intension of the new common noun depends on the intension of the original common noun in a manner determined by the meaning of the adjective...

More generally, let us say that an appropriate intension for a [D_ node]...is any n-place function from \pi intensions to \tau intensions.

...We will call these intensions for derived categories compositional intensions." (27-28)

The important thing here is the distinction between compositional intensions and Carnapian intensions; I suspect the distinction corresponds to the Prof.-MacFarlane-recommended Dummettian distinction between Assertoric and Ingredient senses. I have a fair idea at this point of what the compositional intension is. But what is a Carnapian Intension?--

"We call the truth-value of a sentence the extension of that sentence; we call the thing named by a name the extension of that name; we call the set of things to which a common noun applies the extension of that common noun. The extension of something in one of these categories depends on its meaning and, in general on other things as well: on facts about the world, on the time, place, speaker and surrounding discourse of the utterance, etc. It is the meaning which determines how the extension depends upon the combination of other relevant factors. What sort of things determine how something depends on something else? Functions, of course...We have now found something to do at least part of what a meaning for a sentence, name, or common noun does: a function which yields as output an appropriate extension when given as input a package of the various factors on which the extension may depend. We will call such an input package of relevant factors an index; and we will call any function from indices to appropriate extensions for a sentence, name, or common noun an intension.

Thus an appropriate intension for a sentence is any function from indices to truth-values; an appropriate intension for a name is any function from indices to things; an appropriate intension for a common noun is any function from indices to sets. The plan to construe intensions as extension-determining functions originated with Carnap (1947 and 1963). Accordingly, let us call such functions Carnapian intensions. But whereas Carnap's extension-determining functions take as their arguments models or state-descriptions representing possible worlds, I will adopt the suggestion (Montague, 1968; Scott, 1970) of letting the arguments be packages of miscellaneous factors relevant to determining extensions."

...That was a mouthful. But the idea should be clear now. The distinction between Carnapian intension and compositional intension appears here to come from the assumption that an intensional adjective like `alleged' is still an adjective (aka a `common noun.') It is a common noun with no Carnapian intension because there is no set of alleged things. (Not even one that is enumerable with the help of free variables for w, t, and the like...and the problem is obviously not due to an insufficiently rich index.) Yet `alleged' obviously has a compositional intension because it combines in a systematic way with another predicate g, such that the meaning (compositional or Carnapian intension) of [[alleged g]] depends systematically on the compositional intensions of [[g]] and [[alleged]].

...What to say here? It seems like the problem comes in part from taking the term ``adjective" at face-value. [[Alleged]] and [[Communist]] are of different semantic types: one is in D_et, et, and one is in D_et. They have the same output types--both [[g]] and [[alleged g]] are of the same type--but that means they are a type match only in their ranges.

It seems right to say that for Lewis, anything with a Carnapian intension has a compositional intension, but not vice-versa (`alleged' is a case in point.) But with our emendation, we could just as easily say that the Carnapian intension of [[alleged]] is a function from indices to a function from adjectives to adjectives. In fact, that is the kind of semantic entry we give it in H & K, Ch 13:

[[alleged]]^w, t = \lambda f \in D_et . \lambda x \in D . \forall w' \in W compatible with what is alleged in w at t, f(x) = 1.

Here is Lewis defending the ``generalize to the worst case" strategy: basically, it preserves the underlying simplicity of FA.

"I promised simplicity; I deliver functions from functions from functions to functions to functions from functions to functions. ... Yet I think no apology is called for. Intensions are complicated constructs, but the principles of their construction are extremely simple.

...In some cases, it would be possible to find simpler intensions, but at exorbitant cost: we would have to give up the uniform function-and-arguments form for semantic projection rules. We have noted already that some adjectives are extensional, though mot are not. The extensional adjectives could be given sets as extensions and functions from indices to sets as Carnapian intensions...'Grunts,' for instance, is an extensional verb phrase; its extension at an index i is the set of things that grunt at the world and the time given by the world coordinate and the time coordinate of the index i.

There is no harm in noting that extensional adjectives and verb phrases have Carnapian intensions as well as compositional intensions. However, it is the compositional intension that should be used to determine the intension of an extensional-adjective-plus-common-noun or extensional-verb-phrase-plus-name combination. If we used Carnapian intensions, we would have a miscellany of semantic projection rules rather than the uniform function-and-arguments rule....Moreover, we would sacrifice generality: non-extensional adjectives and verb phrases would have to be treated separately fro the extensional ones, or not at all. This loss of generality would be serious in the case of adjectives.

I am a little confused by what is going on here. The point is surely that we need intensions to be the arguments taken in FA, because while e.g. Ext(renate) = Ext(cordate), their intensions differ, and it is that difference that is responsible for the nonequivalence of e.g. [[alleged renate]] and [[alleged cordate]]. But it seems that if we assign [[renate]] and [[cordate]] mere Carnapian intensions, we are ok--since their Carnapian intensions differ. Lewis must be thinking that they don't differ (they don't differ if you fix the w variable at w = actual world...)

Hmm. I'm not sure this is giving me the ingredient/assertoric sense distinction I need.

Must. Think. Harder.

I think weak conjunction is a step in the wrong direction, but I can't prove it. Grrr.

Even if we embrace weak conjunction, we are stuck with a problem with modal necessity: Must(p v q) = Must-p and Must-q

(using the entry for "must" that doesn't break the symmetry between "must" and "might")

***

In broad outline:

if you pick existential quantification, you get wide-scope, "...I can't remember which" type truth-conditions. But this seems to really be a case where the ''or'' has wide scope at LF and is subject to grammatical surface deletion. So the semantics is totally wrong--it's assigning wide-scope truth conditions to the narrow-scope LFs.

On the other hand, if you pick universal quantification, you get things easy for conjunctive readings of "or" (choice situations) but everything goes wrong in downward-entailing environments like negation,

If you try to split the difference--some existential and some universal--then, at the very least, the symmetry between "must" and "might" is broken.

...This seems to me to be an intrinsic limitation of doing Hamblin semantics for disjunction in this way. A recent grad student of Kratzer's, Alonso-Ovalle, did his dissertation on this in 2005 and, though I've only read the introduction, his work seems to bear this out. He designed his semantics so that the quantification over the disjuncts was existential--hence the choice inference isn't valid after all. Then he said it was a conversational implicature.

That seems disappointing to me...why posit so much extra complication just to give the felt inference the status of an implicature? I don't mean to denigrate the study of implicature--it's just that then a Prof. Bach-style, "why'd ya add a disjunct if it wasn't doing any work?"-type response seems good enough. Its sort of like "why'd ya say 'produced a series of sounds which corresponded closely to the score of...' instead of 'sang'?" Surely, there's an answer here, but it has nothing to do with compositionality!

...Am I totally wrong?