armchair investigations

Monsters in Kaplan's Logic of Demonstratives

2012-01-04T21:07:00.000-08:00

This paper started its life as a post awhile back and is now officially forthcoming in Philosophical Studies.

variables are not directly referential

2011-12-12T13:07:00.000-08:00

Here is an argument that variables are not directly referential:

(1) A term t is directly referential iff the semantic content of t is the designatum of t.

(2) The semantic content of a term t is X iff for every linguistic environment E, the semantic content that t contributes to E(t) is X [i.e Semantic Innocence].

(3) Thus, a term t is directly referential iff for every linguistic environment E, the semantic content that t contributes to E(t) is the designatum of t.

(4) In a bound environment (e.g. ∀xFx) a variable does not contribute its designatum (since 'Fx' must contribute a set of assignments).

(5) Thus, variables are not directly referential.

I'm interested in how people who advocate direct reference theory maneuver out of this argument. Denying either premise (1) or premise (2) are really the only options for not accepting the conclusion.

Premise (1) is an attempted definition of "direct reference". So perhaps I got the rough definition wrong. One alternative idea that would avoid the conclusion is this: a term t is "directly referential" iff the designatum of t is "directly" determined by the interpretation or assignment function, in the sense that its designatum is assigned independently of the world and time parameters. But to my ear this is a definition of rigidity de jure---it's a fact about a terms designatum across worlds/times and how it is built in by law that it be independent of worlds/times. Direct reference, however, is supposed to make a further claim about "semantic content". Kaplan defines it thusly: "When what is said in using an indexical in a context c is to be evaluated with respect to an arbitrary circumstance, the relevant object is always the referent of the indexical with respect to the context c." It's a familiar point that "direct reference" simply amounts to rigidity de jure, unless we construe it in terms of Russellian structured contents. But I'm not sure how one might want to tinker with the definition to avoid the conclusion.

In any case, I think the real action is with premise (2). And it seems that many will somehow want to deny it, and thus deny semantic innocence (e.g. see Salmon's "A theory of bondage", which develops a Fregean referential shift semantics for variable binding (although he doesn't exactly endorse the occurrence-based semantics he outlines)).

But if a term can be "directly referential" even though the value it contributes across all environments (i.e. its compositional semantic value) isn't its designatum, what is the significance of calling the term "directly referential"? For example, the direct reference theory of names is controversial precisely because of its commitments on embedded occurrences, e.g. names embedded in belief reports. (Perhaps this is where the distinction between Millianism and Direct Reference is important.) Can one accept that 'Hesperus' and 'Phosphorus' are directly referential (and thus have the same "semantic content" in some important sense) even though the semantic content of their occurrences in belief contexts are different? It's hard for me to get a grip on "semantic content", if it is detached from the semantic contribution an expression makes to the complex expressions of which it is a constituent.

I'm left wondering what "direct reference" is exactly and what important (and plausible) thesis about language it is committed to. Any ideas?

I could have been Barack Obama

2011-06-04T17:19:00.000-07:00

(1) My parents could have named me "Barack Obama".
(2) If my parents had named me "Barack Obama", I would have been a Barack Obama.
(3) Necessarily, every Barack Obama is identical to someone who is Barack Obama.
(4) Therefore, I could have been Barack Obama.

I imagine people will question premise (3) or question whether or not (4) follows from (3). But (3) just says that it is necessary that for any x such that Barack Obama(x) there exists a y such that x=y and Barack Obama(y). So...

(3.1) If I had been a Barack Obama, I would have been identical to someone who is Barack Obama.
(3.2) If I had been identical to someone who is Barack Obama, I would have been Barack Obama.
(3.3) So, if I had been a Barack Obama, I would have been Barack Obama.

...I could have been Barack Obama.

I am not, of course, saying that I could have been the current and actual president of the US---I couldn't have been that Barack Obama. But I could have been a different one, if I had been named appropriately. The Barack Obama I could have been would have been Barack Obama the philosopher.

formulating a donkey sentence in first-order logic

2011-04-29T10:33:00.000-07:00

Here is a standard donkey sentence:

(1) Every farmer that owns a donkey beats it.

It is often said that such sentences cannot be formulated in the language of first-order logic. There is a formulation in first-order logic that gets the correct truth conditions but it differs radically from the surface structure of (1)---most significantly it interprets the indefinite article as a universal quantifier.

(1') ∀x∀y[(farmer(x) & donkey(y) & owns(x,y)) --> beat(x,y)]

There are numerous novel semantic frameworks that attempt to deal with the problem, e.g. various dynamic semantics. But the following seems to be a reasonable formulation of the donkey sentence in first-order logic.

(1'') ∀x[(farmer(x) & ∃y(y=z & donkey(z) & owns(x,z)) --> beat(x,z)]

What's wrong with this?

syntax for definitions

2011-04-14T10:00:00.000-07:00

How should one write a definition? The mathematician Douglas West (The Grammar According to West) provides the following advice:

Definitions. Words being defined should be distinguished by italics (or perhaps boldface in a textbook context). When italics are used to indicate a word being defined, it is unnecessary to use "called" or "said to be"; the use of italics announces that this is the term being defined and replaces these words.

Many definitions are phrased as "An object has property italicized term if condition holds." We use just "if" even though subsequently it is understood that an object has the property if and only if the defining condition holds. The italicization alerts the reader to this situation. The convention can be justified by saying that the property or object does not actually exist until the definition is complete, so one does not yet in the definition say that the named property implies the condition.

This seems confused to me for a number of reasons---especially the justification for the convention: "the property or object does not actually exist until the definition is complete". What does that mean?

Definition. An object x is a firath if and only if x is a female giraffe.

Obviously, firaths existed long before I defined "firath"! They just were not so-called.

But what I mostly don't like is that the "definition" schema appears to merely give a sufficient condition for falling under the definiendum. The following is not a good definition of "firath".

Definition. An object x is a firath if x is a giraffe.

Does his advice seem reasonable or not? Presumably, a lot of mathematicians are adhering to his grammar suggestions.

Negation as an interpretation shifting operator

2011-03-28T00:29:00.000-07:00

In propositional logic a formula φ of language L is only true (1) or false (0) relative to an interpretation M. The semantics of the negation symbol ~ is usually given as follows:

[[~φ]]^M = 1 iff [[φ]]^M = 0.

But we could do it differently. We could conceive of negation as analogous to a modal operator (or quantifier). In this case it doesn't shift the world parameter or the assignment of values to individuals variables---instead it shifts the interpretation, i.e. the assignment of truth-values to propositional letters.

[[~φ]]^M = 1 iff [[φ]]^M* = 1, where M* is just like M except it assigns 1 - M(φ) to φ.

As far as I can tell, that is a perfectly fine semantics for negation in propositional logic.

What is the aim of natural language semantics?

2011-02-02T20:03:00.000-08:00

The answer seems clear.

Tarski (1936): "Semantics is a discipline which, speaking loosely, deals with certain relations
between expressions of a language and the objects (or `states of affairs') referred to by those expressions."

Davidson (1967): "There is no need to suppress, of course, the obvious connection between a definition of truth of the kind Tarski has shown how to construct, and the concept of meaning. It is this: the definition works by giving necessary and sufficient conditions for the truth of every sentence, and to give truth conditions is a way of giving the meaning of a sentence. To know the semantic concept of truth for a language is to know what it is for a sentence -- any sentence -- to be true, and this amounts, in one good sense we can give to the phrase, to understanding the language."

Montague (1968): "semantics...is primarily concerned with the notion of truth (in a model, or under an interpretation)."

Lewis (1970): "Semantics with no treatment of truth conditions is not semantics."

Heim and Kratzer (1998) Semantics in Generative Grammar: "A theory of meaning...pairs sentences with their truth-conditions."

Portner and Partee (2002) Formal semantics: the essential readings: "At the most basic level, a formal semantic analysis postulates a compositional, functional pairing between syntactically analyzed sentences of a language and their truth-conditional meaning."

Büring (2005) Binding Theory: "The task of the semanticist is to devise basic meanings for the words of the language and systematic ways of combining them so as to arrive at intuitively correct truth conditions for entire sentences."

Schlenker (forthcoming) `Semantics', The Linguistics Encyclopedia: "Minimally, a semantic theory should specify rules by which the truth conditions of complex sentences are computed on the basis of memorized properties of words or morphemes, together with a specification of the syntax (derivation tree) of the sentence at hand."

I find similar things said in Chierchia and McConnell-Ginet (2000) Meaning and grammar: An introduction to semantics and in Larson and Segal (1995) Knowledge of Meaning (the aim here is to specify our tacit knowledge of an internal compositional T-theory).

In Partee (2004) Compositionality in formal semantics, Barbara Partee describes her first introduction to Montague's work at a UCLA seminar in 1968 (attended also by David Lewis). She describes how at the time Montague's approach was different from anything she had seen and reports that she was especially excited by "...the revolutionary (to a linguist) idea that the core data were the truth conditions of sentences. Suddenly there was a non-subjective criterion of `observational adequecy' for semantics".

Any good quotes along these lines that I've missed? I'd especially like a better quote from Montague -- but he doesn't provide much actual prose to choose from.

Who disagrees with this answer? The Davidsonian project seems to get a lot of criticism (e.g. Soames) but its unclear to me what the fundamental difference is between the Montagovian and Davidsonian approaches. And the Montague inspired approach seems to be the dominate approach of the actual practitioners of semantics.

Another related set of good questions are these: What are truth conditions exactly? What are the things that have to meet a certain condition for truth to be achieved? Worlds? Centered worlds? Contexts? Points of evaluation? And do the truth conditions of sentences have to be the same as the propositions expressed by sentences? What is the relationship between truth conditions and the things we say?

new paper

2011-01-14T09:48:00.000-08:00

I have just recently posted a new paper online. Comments are very welcome.

Against the identification of assertoric content with compositional value

Abstract. This essay investigates whether or not we should think that the things we say are identical to the things our sentences mean. It is argued that these theoretical notions should be distinguished, since assertoric content does not respect the compositionality principle. As a paradigmatic example, Kaplan's formal language LD is shown to exemplify a failure of compositionality. It is demonstrated that by respecting the theoretical distinction between the objects of assertion and compositional values certain conflicts between compositionality and contextualism are avoided. This includes the conflict between eternalism and the semantics of tense, the embedding problems for contextualism about epistemic modals and taste claims, and the conflict between direct reference and the semantics of bound pronouns (and monstrous operators). After presenting the theoretical picture which distinguishes assertoric content from compositional semantic value, some objections to the picture are addressed. In so doing, the objection from King (2003) stemming from apparent complications with the interaction of temporal expressions and attitude reports is assessed and shown to be non-threatening.

some links

2010-12-06T09:54:00.000-08:00

* Landon has a new website and a redesigned weblog. And he just had a new paper come out in the Journal of Graph Theory.

* Wo is back at ANU and has an interesting new post on quantum mechanics and relativistic semantics.

* I visited NYU this (northern) fall and attended Barker & Pryor's linguists course (What Philosophers and Linguists Can Learn From Theoretical Computer Science But Didn't Know To Ask). The very detailed and interesting lecture notes are online here.

* I recently gave a presentation on Kripke's "A puzzle about belief" for Graeme Forbes' course on Fregean models of compositionality. The handout is available here.

* Graham Priest in the New York Times ("The Stone") has a piece on Paradoxical Truth.

* I like the thesis that names are predicates and have given a talk on it (see the weird pre-beamer slides here). I have also played around with the thesis on this blog, e.g. "Are proper names general terms?" and "Names or what?". In a new paper Delia Graff Fara defends the view in detail. I am looking forward to the responses.

my recent conversation with a robot

2010-09-12T10:24:00.000-07:00

you ==> Is the next thing you say going to be "no"?
splotchy ==> negative

you ==> Is the next thing you say going to be "negative"?
splotchy ==> no way jose

you ==> Is the next thing you say going to be "no way jose"?
splotchy ==> heck no!

you ==> Is the next thing you say going to be something other than "yes"?
splotchy ==> no way

you ==> haha, stupid machine
splotchy ==> ;-)



Click here to talk to splotchy.

objects of attitudes & modal operators: king's criticism of richard

2010-09-10T10:29:00.000-07:00

Jeffery King 2003 criticizes Mark Richard's 1982 semantics for attitudes reports and tense and modal operators. King's criticism is the following:

One problem with Richard's account is that since tense and modal operators operate on the same thing, since these are not propositions and since propositions are the objects of the attitudes, for Richard the objects of the attitudes and the things modal operators operate on are not the same. But that means that on Richard's view, the following inference should not be valid...But this inference certainly does seem valid:

(i) Shannon believes that God exists,
(ii) It is possible that God exists,
(iii) Therefore, Shannon believes something that is possibly true.

Such arguments leave me completely unmoved, since there has been no actual demonstration that the argument is not valid according to Richard's semantics? Show me the semantics! It seems that if we do crunch through a semantics according to which the objects of the attitudes and the things modal operators operate on are not the same, the argument actually comes out as valid.

In order to assess the validity of this argument we need to know what the logical form and semantics of the premises are -- especially premise (iii). We might analyze `Shannon believes something' as `There is something that Shannon believes'. Let's give that the following semantics: [[∃q(Believes(Shannon, q)]]^{c,w,t} = 1 iff there is a q such that BEL(Shannon, q). Importantly, here we need not assume that the things that individuals stand in the BEL relation to are propositions -- they can be non-propositional semantic values of some sort. This in no way commits one to the claim that the objects of belief are non-propositional semantic values. It is completely consistent to say that `Shannon believes something' is true just in case there is a semantic value q that is so-and so, while at the same time maintaining that the the things we believe are propositions. That is why it is not enough to just allude to a problem here without actually looking at the details of the semantics. If we tack on the conjunct about possibility we get the logical form of (iii): [∃q(Believes(Shannon, q) & Poss(q)]. From here is follows fairly straightforwardly that (i) [Believes(Shannon, G)] and (ii) [Poss(G)] entail (iii) by conjunction introduction and existential quantification.

Have I missed something?

J. King. (2003). Tense, modality, and semantic values. Philosophical Perspectives, 17(1):195–246.

M. Richard. (1982). Tense, propositions, and meanings. Philosophical Studies, 41(3):337–351.

compositionality and the predicate abstraction rule

2010-08-13T08:22:00.000-07:00

The semantic account given in Heim and Kratzer (1998) is not strictly compositional and the failure is very similar to the composition failure in Kaplan below. The failure in this case is due to their Predicate Abstraction Rule (see Heim and Kratzer 1998, p. 186). According to their theory there are lambda terms in the object language syntax such as 'λx.Fx' but there is not a lexical entry for the lambda binder ‘λx’ itself. And the semantic value of 'λx.Fx' isn’t (and can't) be calculated by composing the semantic value of ‘λx’ with the semantic value of ‘Fx’ but instead such lambda terms must be handled by the following non-compositional rule.

Predicate Abstraction Rule: Let α be a branching node with daughters β and γ, where β dominates only a lambda binder λx. Then, for any variable assignment g, [[α]]^g = λz. [[α]]^g[z/ x].

Why not instead have the semantic value of `Fx' be a function from assignments to extensions -- and the semantic value of `λx' be a function from functions from assignments to extensions to functions from individuals to extensions? Then the semantic value of `λx.Fx' can be calculated from the semantic values of `λx' and `Fx' as follows.

[[λx.Fx]]^g = [[λx]]^g (λg.[[Fx]]^g) = λi. [[Fx]]^g[i/x]

To see the similarity to the discussion of Kaplan's LD below notice that we could add a non-compositional rule to patch up the semantics of Kaplan's LD.

Quantifier Construction Rule: Let α be a branching node with daughters β and γ, where β dominates only a quantifier ∀x. Then, for any variable assignment g, [[α]]^g = ∀z. [[γ]]^g[z/ x)].

This would allow semantic calculations of the relevant constructions but would be explicitly non-compositional.

Why would one opt for having these non-compositional rules when the system can easily be transformed into a compositional system with no such non-compositional rules? Is it that much of a cost to have a few non-compositional rules like the predicate abstraction rule?

In the discussions of temporalism/eternalism in relation to the operator argument why don't the eternalists just respond by claiming that temporal constructions need special non-compositional rules?

Past Tense Construction Rule: Let α be a branching node with daughters β and γ, where β dominates only the temporal operator PAST. Then, for any time t, [[α]]^c,t = ∀t' before t. [[γ]]^t'.

In this case it seems that the eternalist theory with a few non-compositional tense rules is a bad theory. But if we are happy with the Predicate Abstraction Rule why should a few more such rules really bother us?

I guess what I have ended up doing was pushing some kind of slippery slope worry -- predicate abstraction is a gateway rule that will lead to nasty ones like the past tense construction rule. That is probably not a very threatening argument. But I just don't understand why we would opt for predicate abstraction in the first place when a truly compositional semantics is close at hand.

use and mention on a train

2010-05-15T21:24:00.001-07:00

Kaplanian content is not compositional

2010-01-31T10:36:00.000-08:00

I claim that Kaplanian content isn't compositional. The tension lies in Kaplan's treatment of variables and the compositional semantics for quantifiers -- there is an inconsistent tetrad between the direct reference of variables, the semantics of quantification and the compositionality principle.

To see this let's just focus on a fragment of Kaplan's LD that has to do with variables and quantification (if you know it you can skip down to after the semantic clauses).

In the syntax of LD we have an infinite set of individual variables, V = {x₁, x₂, x₃,...}, an infinite set of n-place predicates Π = {F₁, F₂, F₃,...} and the two quantifiers ∀, ∃. For these we have the following (relevant) formation rules:

* If π is an n-place predicate and α₁,..., α_n are variables, then πα₁,..., α_n is a formula.

* If φ is a formula and α ∊ V, then ∀αφ and ∃αφ are formulae.

For the semantics we have a structure A = {C, W, T, U, I}, where C is the set of contexts, W is the set of worlds, T is the set of times, U is the set of individuals, and I is an interpretation function (which gives extensions to predicates at t,w).

A point of evaluation is a quadruple (c,f,t,w) where c ∊ C, t ∊ T, w ∊ W and f is an assignment function. An assignment function f is a function from variables to individuals, f: V → U. We write f[α/x] to denote the assignment that is just like f except it assigns x to α . And we write [[γ]]^c,f,t,w for "the extension of γ at (c,f,t,w)" (we omit the structure).

Given this we recursively define 1 ("truth") at a point of evaluation as follows.

* [[α ]]^c,f,t,w = f(α ).

* [[πα₁,..., α_n]]^c,f,t,w = 1 iff ([[α₁]]^c,f,t,w ,..., [[α_n]]^c,f,t,w ) ∊ I_π(t,w).

* [[∀αφ]]^c,f,t,w = 1 iff for all i ∊ U, [[φ]]^{c,f[α/i],t,w} = 1.

* [[∃αφ]]^c,f,t,w = 1 iff there is an i ∊ U, [[φ]]^{c,f[α/i],t,w} = 1.

That is the basics. I wanted to make sure I didn't leave anything out. And that is all fine as far as it goes. The lexical entries for the quantifiers here are syncategorematic, so its left implicit what the exact compositional mechanisms are -- what is it that quantifiers are functions from function from? Yet its obvious what they must be. Back to this in a second.

The Kaplanian content of an expression (at a context) is meant to be the propositional contribution that the expression makes. This generally means two things: (i) content is "what is said" or expressed by an expression, and (ii) content is compositional, i.e. the content of a compound expressions is a function of the contents of its parts. Ignore the first bit. What we are interested in here is refuting the contention that Kaplanian content is compositional.

Kaplan says "A variables first and only meaning is its value" and "Free variables under an assignment of values are paradigms of ... directly referential terms". Saying that a variable α is directly referential is to say that the propositional (semantic) contribution of α at an assignment f is simply the object f(α) (or in non-Russellian lingo a constant function from W x T to that object). And this is just what Kaplan tells us in the "Remarks..." on LD. He introduces the notation {γ}_c,f to mean "the Content of γ in the context c under the assignment f" and tells us that the content of a variable is as follows.

* If α is a variable, then {α}_c,f = that function which assigns to each t ∊ T, w ∊ W, [[α ]]^c,f,t,w .

That is, the content of α at a context c and assignment f is λt,w.[[α ]]^c,f,t,w, where for any (t',w'), λt,w.[[α ]]^c,f,t,w(t',w') = f(α), i.e. a constant function from circumstances to f(α).

Now there is a clash between the claim that the content of a quantified sentence, like `∀xGx', is compositionally determined by the contents of its parts and Kaplan's statement above about what the content of a variable is (i.e. the claim that variables are directly referential).

The content of the formula `Gx' at a context and assignment (c,f) is a function which assigns 1 to a circumstance (t,w) iff f(x) is in the extension of G at (t,w). In other words, the content of `Gx' is a "singular proposition" to the effect that f(x) is G. A function from circumstances to truth-values may be the right entity for modal and temporal operators to take as argument but it is not the right input to a quantifier over individuals. We can't get the right result by compositionally combining a function of this type with the semantic value of the quantifier ∀x!

What the quantifier needs to take as argument is a function over individuals (or assignments) -- a functon like this: λi.[[Fx]]^c,f[x/i],t,w. This is because the semantic value of ∀α at a context c is something like λp. for all i, p(f[x/i]) = 1 at t,w, i.e. a function from assignments to truth-values. Thus, the compositional semantic value of `Gx' at a context is different from the Kaplanian content. Kaplanian content is not compositional.

Someone might respond by insisting that I've simply taken Kaplan's claims about "free" variables and applied them to "bound" variables. But there is no such distinction between different kinds of variables in LD. There are simply the members of V which can occur both free and bound and there is no semantic/syntactic difference made between them. So my argument restricted to the language of LD is undeniable.

It is true, however, that Kaplan seems to want to make a distinction between the semantics of free and bound occurrences of a variable (note the similarity here between deictic and anaphoric uses of pronouns). But what is this distinction exactly? In the formula `∀xFx & Fx' is it something about binding one of the occurrences of `x' that "changes" the semantic value? How does that work compositionally? Is is ambiguity? Are there two homographic expressions `x' and `x' in the formula - a variable and a schmariable? Then in LD we should actually have two syntactic categories of variables V_free and V_bound. And we can give these different contents (semantic values) in contexts.

It seems to me the much better options are either (i) to adjust the commitments about the contents of variables, i.e. to give up the claim that free variables are directly referential or (ii) to give up the claim that Kaplanian contents do the compositional work.

So, Kaplan followers what do you do?

Random randomly silent

2009-11-09T09:48:00.000-08:00

In a new paper by Gabriel Uzquiano called ``How to solve the hardest logic puzzle ever in two questions" he shows how to solve the puzzle in two questions -- one way uses the ignorance of the gods with respect to Random's future answers (if such there be) and the other way uses potentially unanswerable self-referential questions. In either case, the trick is to get information from a god's inability to answer certain questions. Uzquiano suggests a further amendment to the puzzle to avoid such two question solutions: have Random randomly say 'ja', 'da' or remain silent (instead of silence one could have the god randomly suffer a head explosion -- doesn't matter as the logic is the same).

Puzzle. Three gods A, B and C are called, in some order, True, False and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely or whether Random speaks at all is a completely random matter. Your task is to determine the identities of A, B and C by asking yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for ‘yes’ and ‘no’ are ‘da’ and ‘ja’, in some order. You don't know which word means which.

With the further condition:

* Whether Random answers ‘da’ or ‘ja’ or whether Random answers at all should be thought of as depending on the toss of a fair three-sided dice hidden in his brain: if the dice comes down 1, he doesn't answer at all; if the dice comes down 2, he answers ‘da’; if 3, ‘ja’.

It is left as an open question, whether this puzzle can be solved in two questions. Landon proves that it cannot be solved in two questions here.

`He' and `she' demonstrating me

2009-10-15T05:57:00.000-07:00

Say I point to myself and utter,

(1) He is a student.

It was a bit awkward of me to do that but it seems to me that my utterance was true. But what if I point to myself and utter,

(2) She is a student.

It seems that here something much worse has happened. On some treatments of deictic pronouns both (1) and (2) would be undefined, i.e. they get no truth-value. The pronouns have certain "dominating features" and if the purported value doesn't satisfy one of the features it gets rejected as a value and the pronoun goes unassigned. For `he' the features are masculine, 3rd person, and singular -- where 3rd person is understood as being neither the speaker nor the audience of an utterance.

Pointing at yourself in the mirror without realizing that it is you is enough to remove the awkwardness of uttering (1). Is pointing at yourself in the mirror without realizing that it is you and without realizing that you are dressed as a female enough to remove the awkwardness of uttering (2)? Not sure.

Doesn't seem like `I' can refer to someone who fails to satisfy the 1st person feature. But maybe there is a strange case that removes the awkwardness.

A.N. Prior on double indexing

2009-07-21T20:41:00.000-07:00

``Hans Kamp devised in 1967 a consistent semantic interpretation for `now' which can be presented, with slight modifications, as a new sort of UT-calculus, in which T ties each tense-logical proposition not to one instant but to two, i.e. our basic form is not Tap but Tabp. The proposition p is related to the instants a and b in different ways; the essential difference is that the elimination of complexities from what is put after Tab may take us to other instants than a, but never to other instants than b. And wherever we may have been taken from a by operators like G and H, the one place to which we are always immediately taken by J [`It is now the case that'] is the instant b, i.e. the instant represented by the second argument of T. We might read the form Tabp as `From b it is the case at a that p', and `From b it is that case at a that p--now' = `From b it is the case at b that p'." -- Prior, A. N.: 1968, `"Now"', Nous 2(2), 101–119.

The 1967 work that Prior refers to is Kamp, H.: 1967, "The treatment of `now' as a 1-place sentential operator", multilith circulated to a graduate seminar at the University of California in Los Angeles. The results were reported in A.N. Prior (1968) and full treatment was published in Kamp (1971),`The formal properties of ``Now"', Theoria 37, pp. 227-274.

Prior presents problematic sentences such as,

(A) It will be the case that it is now the case that I am sitting,

and attributes to Kamp the above ``the first solution offered" to such problems. Prior agrees that this works but goes on to present an alternative (singly-indexed) treatment by introducing an instant-constant n for a designated instant (and then doing some other tricks due to Prior & Meredith (1953) -- I don't think he just gives extensional treatment of the operators but it seems very similar).

necessity, rigidity and co-extensionality

2009-06-08T19:41:00.000-07:00

I have heard people say things like the following.

(K1) A true identity statement is necessary just in case the identity sign is flanked by two rigid designators.

Such a principle seems to work alright for singular terms but it gets tricky when applying it to general terms -- it is notoriously tricky just how to extend the notion of `rigidity' to general terms.

I prefer to extend the notion of rigidity to all expressions in the most straightforward manner: An expression is rigid (w.r.t. worlds) iff it has the same extension in all worlds. (This generalizes to temporal-rigidity, spacial-rigidity, agential-rigidity, etc.)

With this conception expressions like `water' and `H2O' are not rigid. This result is thought to be a reason against generalizing the notion of rigidity in this way. The statement `Water is identical to H2O' is necessary so according to (K1) we should expect that the expressions that flank the identity sign be rigid designators. But with my preferred understanding of rigidity this is not the case, so such an explanation of the necessity of identity statements cannot be given.

I think (K1) is a bad principle. It is somewhat close, however, to the true principle, which is the following.

(B1) A true identity statement is necessary just in case the identity sign is flanked by two necessarily co-extensional expressions.

It is easy to see why one might mistakenly think that (K1) was the correct principle since all rigid designators that flank a true identity statement will be necessarily co-extensional. But it is not the case that all necessarily co-extensional expressions that flank a true identity statement are rigid designators. Consider,

(1) The inventor of bifocals is identical to the extension of `the inventor of bifocals'.*

This is a necessary truth in which the identity sign is not flanked by two rigid designators. Instead the identity sign is merely flanked by two necessarily co-extensional expressions. What is important for the necessity of identity statements is that the pattern of extension across worlds of their flanking expressions is the same not that they are rigid expressions. It just so happens that in cases like

(2) The successor of one is identical to the smallest prime number,

the fact that the flanked expressions are rigid guarantees that their the patterns of trans-world extension agree. But it is the pattern not the rigidity which is of primary importance to the necessity of identity statements.

The same is true of the following identity statement.

(3) Water is identical to H2O.

The expression `water' and the expression `H2O' have the same pattern of counterfactual extensions. If `water' designates a certain set at world w, then `H2O' designates a certain set at world w. This is true even though on my preferred understanding of rigidity `water' and `H2O' are not rigid. This seems like a nice simple way to make sense of these issues. What more do we want?

Homework: Think of necessary identity statements in which the expressions that flank the identity sign are non-rigid (but, of course, necessarily co-extensional).

[*Ignore scope and assume this is an identity statement not a Russellian existentially quantified statement. And note that the expression "the extension of `the inventor of bifocals'" concerns our expression `the inventor of bifocals' not some other homophonic expression.]

The quick argument for double-indexing

2009-05-10T02:29:00.000-07:00

Consider the following logical truths (or indexical validities) of English:

(1) It rains if and only if it rains now.

(2) It rains now if and only if it always rains now.

Assume (to reach a contradiction) a singly-indexed semantics. Given that (1) is a logical truth, then the semantic clause for the indexical sentential operator `Now' (or `It is now the case that') must be as follows:

[[Now(φ)]]^t =1 iff [[φ]]^t =1

But then (2) is not valid (as long as there are times in structures where it rains and fails to rain). But (2) is valid. Contradiction.

[This is basically the argument given in Kamp (1971), "The formal properties of `now'"]

defense of two question solution

2009-04-08T18:13:00.000-07:00

I have put a new paper online called "In defense of the two question solution to the hardest logic puzzle ever". It is mostly a reaction to a few blog post, e.g. this one (and some others that I can't find right now) and a manuscript. And we briefly discuss the generalization from this one.

metalinguistic predicates vs. object language operators

2009-03-16T16:28:00.000-07:00

I am interested in the distinction between metalinguistic predicates (sentential predicates) and object language operators (or sentential functors). This distinction seems to be very important for topics like (i) the Kripkean necessary aposteriori & contingent apriori, (ii) various implementations of two-dimensional semantics (especially metalinguistic versions?), (iii) issues surrounding context-dependence and monstrous operators, and probably many more things.

But I don't have much to say about it because I don't fully understand the distinction and how exactly metalinguistic predicates work (how are they treated in the formal system?) So this is just a plea for help. Where is this distinction discussed? Where are metalinguistic predicates discussed? I can't seem to find anything but perhaps I am searching for the wrong thing.

The distinction I have in mind is illustrated below:

(1) It is F that S.

(2) `S' is F.

(1a) It is necessary that two is prime.

(2a) `Two is prime' is necessary.

(1b) It is true that I am hungry.

(2b) `I am hungry' is true.

(1c) It is believed by John that Cicero is Tully.

(2c) `Cicero is Tully' is believed by John.

(1d) It is a priori that bachelors are unmarried.

(2d) `Bachelors are unmarried' is a priori.

(1e) It is true at 2:00am that its raining now.

(2e) `Its raining now' is true at 2:00am.

etc.

Any help would be greatly appreciated.

inconstants?

2009-02-18T18:39:00.000-08:00

Some expression are rigid in the sense that they have a constant (secondary) intension, while others are nonrigid. And some expressions are stable, in the sense that they have a constant character, while others are unstable. Moreover, some expressions have combinations of the rigidity and stability properties.

Constants (e.g. logically proper names?) are both rigid and stable. Indexicals (e.g. `I', `tall') are rigid but unstable. Vacillators (e.g. `kangaroo', `the inventor of bifocals') are stable but nonrigid.

Are there any expressions that are both unstable and nonrigid?

anaphoric pronouns with indexical antecedents

2009-02-07T20:28:00.000-08:00

This probably has a simple and not very interesting explanation having to do with syntactic constraints or morphological constraints or something. But why is it that the starred sentences below go wrong, given that they are obtained from the relevant non-stars by substitution of co-extensive expressions (i.e. `I' for `Brian')? The source of the problem here is obviously not intensionality!

(1) Brian left his wallet on the table.
(1*) I left his wallet on the table.

(2) Brian is such that John believes that he is a spy.
(2*) I am such that John believes that he is a spy.

(3) Brian went to the store and he bought tofu.
(3*) I went to the store and he bought tofu.

Can you think of an example where the referent of `I' can be picked up by an anaphoric pronoun? Is `I' itself sometimes an anaphoric pronoun? How does this relate to the following Heim example?

(4) Only I got a question I understood.

philpapers

2009-01-27T15:15:00.000-08:00

Here is a great new tool: philpapers. Its a massive directory of online philosophy articles with many useful features. Read more about it here.

Heimson = Hume

2009-01-20T18:46:00.000-08:00

Proof that Heimson is Hume. Heimson believes that he is Hume. Hume believes that too. Hume is right. Thus, Heimson is Hume.

The action here is the second sentence. Isn't the reading Lewis intended monstrous?

Cases of referential shift?

2009-01-05T00:25:00.000-08:00

Case 1. In the sentence ‘It is necessary that Cicero is Tully’, ‘Cicero is Tully’ denotes not the True but rather its intension (i.e. a function from indices to truth-values), the role of the functor ‘It is necessary that’ is two-fold. It both denotes a function and induces a linguistic context in which the embedded term denotes something other than what it would otherwise denote: namely the intension of that term. Hence, ‘It is necessary that’ denotes the necessity function, nec, and induces an intensional context such that ‘Cicero is Tully’ denotes its intension, which nec takes as argument.

Case 2. In the expression ‘(3)^2 ’, ‘3’ denotes not 3 but rather 9, the role of the functor ‘( )^2’ is two-fold. It both denotes a function and induces a linguistic context in which the embedded term denotes something other than what it would otherwise denote: namely the square of the denotation of that term. Hence, ‘( )^2’ denotes the identity function, id, and induces a "squared context" such that ‘3’ denotes the square of its customary denotation, which id takes as argument.

* This is adapted from Humberstone, Lloyd (2008), “Can every modifier be treated as a sentence modifier?”, Philosophical Perspectives 22. I have changed it a bit to make the analogy tighter.

Expressions designate intensions

2008-12-22T18:24:00.000-08:00

It is absurd to think that sentences with the same truth-value are about the same thing; e.g. 'Grass is green' and 'Snow is white' don't refer to the same thing! Instead, sentences that refer to the same thing are the ones that have the same truth-conditions, e.g. 'Snow is white' and 'Schnee ist weiss'. Let's assume, then, that the extension of a sentence is a truth-condition. Truth-conditions are functions from indices to truth-values (i.e. intensions). Thus we get the following principle.

Intensional extensionality: The extension of a sentence is an intension.

Combine this with a plausible Fregean thesis about composition.

Extensional compositionality: The extension of a sentence is determined by the extensions of its sub-sentential parts.

And we can derive the following.

Thesis. Sub-sentential expressions designate intensions.

Proof. Assume (to reach a contradiction) that sub-sentential expressions do not designate intensions. Consider a pair of non-cointensive sentences Ψa and Ψb that only differ on the sub-sentential parts 'a' and 'b', where 'a' and 'b' are coextensive but not cointensive. Since every sub-sentential part of Ψa is coextensive with a sub-sentential part of Ψb (and vice versa), it follows by Extensional Compositionally that Ψa and Ψb are coextensive. By Intensional Extensionality it follows that Ψa and Ψb are cointensive. Contradiction.

*************************************************************

This is some kind of "modus tollens-ing" of the Frege-Church-Goedel slingshot argument that sentences refer to truth-values. The argument above starts with the assumption (which I tried to give some [insincere] motivation) that sentences designate intensions; functions from indicies to truth-values. The slingshot, on the other hand, starts with the assumption that it is not the case that all sub-sentential expressions designate intensions. Its not clear, to me, that this is a substantial issue (see reference in last post).

The semantic value of a sentence is determined by the semantic values of its parts. Whatever these "semantic values" of sentences are, we should ensure them to be the same in kind as the semantic values of the sub-sentential parts.

intensions as extensions

2008-12-16T21:44:00.000-08:00

"I have a problem for those who, like myself, admire intensional formal semantics and think it a key to understanding natural language. We can go to extremes of intensionality, if we like. Semantic rules can be stated entirely in terms of intensions, while extensions go unmentioned. But when we do, it seems for all the world as if we've gone purely extensional instead!"

David Lewis (1974), "'Tensions", Semantics and Philosophy, M. Munitz & P. Unger

sense and direct reference

2008-11-28T22:27:00.000-08:00

Even harder than The Hardest Logic Puzzle Ever

2008-11-21T02:44:00.000-08:00

Tom Ellis at the University of Cambridge has written a good article (find it here) summarizing and extending Boolos' puzzle. There is a nice presentation of how we can screen off the fact that the gods do not speak English and the issue of whether they speak Daisyesjaisno or Jaisyesdaisno and the fact that some of them are liars and the fact that Boolos' random sometimes lies, etc.

The generalization of the puzzle is this: Amongst 2N+1 English speaking gods there are at least N+1 truth tellers, and the others are randomers. In 2N questions determine whether φ is true (where φ is an arbitrary proposition).

sleeping beauty analog?

2008-11-06T13:54:00.000-08:00

A procedure is going to be run to give values for an ordered pair (a,b). The value of the first parameter, a, is decided by a fair coin. The value of the second parameter, b, is decided as follows: (i) if a = 0, then b = 0, and (ii) if a = 1, then b = 0 or b = 1 (decided again by a fair coin). The procedure is run; to what degree ought you believe that the procedure output 0 for the first parameter?

The answer is obvious. So in what important respect does the procedure above differ from the sleeping beauty scenario (if at all)?

2008-10-04T02:35:00.000-07:00

the nature of apriori contingencies

2008-09-06T17:42:00.000-07:00

Here is a familiar story. "Once upon a time, it was thought that if a truth was knowable a priori, then it is a necessary truth (i.e. the truths of pure reason are the necessary ones). Then along came Saul Kripke in the early 1970's and shook everything up. He provided putative examples of truths that are knowable apriori yet contingent (e.g. the meter stick truth). Thus, the traditional conception of the relationship between the truths of reason and the truths that couldn't have been otherwise was shattered. And, the philosophers have been trying to pick up the pieces ever after."

This story seems to be fairly accurate. What I am interested in is the following two quesitons: (i) why did pre-Kripkean theorists think that aprioricity entails necessity, and (ii) which implicit premise of the pre-Kripkean reasoning does the post-Kripkean theorist deny?

Before introducing his counterexamples, Kripke provides the following intuitive argument on behalf of the traditional theorist.

I guess it is thought that...if something is known a priori it must be necessary, because it was known without looking at the world. If it depended on some contingent feature of the actual world, how could you know it without looking? Maybe the actual world is one of the possible worlds in which it would have been false. This depends on the thesis that there can't be a way of knowing about the actual world without looking that wouldn't be a way of knowing the same thing about every possible world. - Saul Kripke, Naming and Necessity (1980), p. 38.

Interestingly, Kripke never tells us what is wrong with this reasoning. He just provides (alleged) counterexamples of the conclusion. It would be nice to formulate this quote into a valid (non-circular) argument and see what premise Krikpe and the post-Kripkean theorists are denying. Unfortunately, I have found it difficult to whip it into shape by brute force. But a more delicate approach will provide some insight. Here is an analogous argument.

I guess it is thought that if it is known that the output of a function is 1 without knowing the input, then the function must give 1 on every input. If some inputs gave 0, how could you know what the output was without knowing what the input was? Maybe the input is one of the ones on which it gives 0. This depends on the thesis that there can't be a way of knowing the output of a function without knowing the input that wouldn't be a way of knowing the same thing about every input.

This argument has a sort of intuitive appeal but if you think about it for a second it is obviously fallacious. For example, say the function we are dealing with is division. In general, you needn't know the input in order to know the output; if you know that the input is of the form (x,x), you thereby know the output is 1. So as long as you have some minimal information about the input you can deduce the output (e.g. knowing that the input is in the domain of a constant function and knowing that this constant function is a subset of the function in question).

I think this is a perfect analogy for understanding the nature of apriori contingencies. There is a level of abstraction upon which all the various (and conflicting) accounts of the contingent apriori have something important in common. Here is a scheme that all accounts of the contingent a priori trivially fall into.

Ψ is both apriori and contingent iff f(Ψ) = (h1,h2) and A(h1) & C(h2)

Every account will trivially accord to this scheme if we let Ψ=h1, Ψ = h2, and let A and C be the properties apriority and contingency, respectively. But there is a more interesting level of similarity that can be captured by the scheme. Lets start with a broadly two-dimensionalist account (what I will call "bifurcationalism") and then see how the other accounts (i.e. disquotationalism and exportationalism) have a similar structure.

The bifurcationalist (Tichy, Stalnaker, Evans, Davies and Humberstone, Kaplan, Chalmers, Jackson, Fragments-of-Kripke) holds that Ψ is both a priori and contingent if and only if two functions h1 and h2 associated with Ψ have certain properties, namely if h1, is a constant function to TRUE and h2 is not constant but gives TRUE at w@. There are different ways to understand h1 and h2, but the basic idea is that they are functions from world pairs (w,v) to truth-values, where h1 tracks the epistemic profile of Ψ [it takes inputs of the form (x,x)] and h2 tracks the metaphysical profile of Ψ [it takes inputs of the form (x,y)].

Understood this way the analogy is clear. If we know that the input is in the domain of a h1, h1 is a constant function and that h1 is a subset of h2, then we can know the output of h2 even though its output varies across worlds. For example, consider the sentence (or proposition) `The inventor of bifocals is the actual inventor of bifocals'. The associated function h1, which is a function from world-pairs to truth-values, is such that for every pair of worlds (x,x), h1 delivers as output TRUE [since in every world considered as actual the inventor of bifocals in that world is the actual inventor of bifocals]. Thus, the sentence (or proposition, if you like) is apriori. But since the other associated function h2 gives FALSE on some world-pairs, the sentence is contingent. So in other words, one can know that the contingent sentence is true without knowing which world is actual simply by knowing that the 2D matrix is constant down the diagonal. This is very much like knowing that the output of the division function is 1 without knowing the exact input.

The disquotationalist (Kripke-of-Soames) and the exportationalist (Soames, Salmon) also hold that Ψ is both a priori and contingent if and only if two functions h1 and h2 associated with Ψ have certain properties, namely if h1, is a constant function to TRUE and h2 is not constant but gives TRUE at w@. Of course they don't express thier views this way but they could.

For the disquoatationalist a contingent proposition Ψ is knowable a priori in virtue of the truth of a sentence S that expresses Ψ being knowable a priori. If it is knowable a priori that sentence S is true, then (via understanding S) it is knowable a priori that Ψ. For the disquotationalist f a function from a proposition Ψ to a ordered pair of functions (h1, h2). h1 is a function from contexts-of-utterance to truth values; it takes a context as argument and assesses whether or not the metalinguistic proposition expressed by a sentence of the form`S is true' in that context, where `S' expresses Ψ in the actual context, is true. If h1 is a constant function Ψ is apriori (the contingency bit is straightforward).

For the exportationalist a contingent proposition Ψ is knowable a priori in virtue of the truth of a necessary proposition φ (knowledge of which exports to knowledge of Ψ) being knowable a priori. If it is knowable a priori that φ, then (via exportation) it is knowable a priori that Ψ. For the exportationalist f is a function from a proposition Ψ to a ordered pair of functions (h1, h2). h1 is a function from worlds to truth values; it takes a world as argument and assesses whether or not the de-actualized cousin of Ψ, φ (i.e. if Ψ looks like this [R(t,@t)], then φ looks like this [R(t,t)] is true). If h1 is a constant function Ψ is apriori (the contingency bit is again straightforward).

If any of these accounts are right then there is an priori way of knowing about the actual world that is not a way of knowing the same thing about every possible world. And that is just what is at issue.

infinite chains of exploding god-heads

2008-08-19T22:07:00.000-07:00

There is an interesting post at XOR's Hammer. He tries to create a question to ask of the truth-telling god (see here for the details on "the hardest logic puzzle ever") that is similar to a revenge problem for the Liar paradox. He tries to extend on the notion of exploding god-heads (see here) such that "we may actually extract an unbounded amount of information from a single yes-or-no question by choosing the question carefully and then observing how much of the universe is destroyed by our asking it". It's a neat idea but as I say in the comments I am not sure exactly how it is going to work...

a novel proof of the heine-borel theorem

2008-08-06T18:46:00.000-07:00

For a couple of years (off and on) landon and I have been playing with stuff at the intersection of graph theory and the semantic paradoxes (mostly Yablo's omega-Liar). The idea was to find graph theoretical necessary and sufficient conditions for paradoxicality. In graph theoretic terms: Yablo showed that there are acyclic reference graphs that support paradoxes, whereas it was traditionally thought that cyclicality (i.e. self-reference or mediated self-reference) was a necessary condition for a reference graph to support a paradox (what we call a "dangerous" reference graph). Anyway, we have some good results and are getting closer to the answer.

A by-product of all this has been some cool stuff intrinsically interesting to graph theory and other areas of math. One such tangent, with a lot of help from Matt Macauley, turned into a proof of Brouwer's fan theorem (one using Goedel compatness) and then into a proof of the Heine-Borel theorem. Matt has also tidied it up into a cute prose-style paper, which can be found here.

The work on the paradoxes is scattered throughout various emails but we are hoping to pull it all together soon. Anyway, this is all a distraction from my real work...so back to a priori contingencies, etc.

Kripke-style anti-referentialist arguments

2008-06-25T04:42:00.000-07:00

The standard anti-descriptivist arguments take the form of either the Modal Argument, the Epistemological Argument, or the Semantical Argument. I think there are parallel anti-referentialist arguments. If so, then it seem that the situation is more of a stand-off than is usually thought, i.e. there are compelling arguments against descriptivism but there are exactly parallel and equally compelling arguments against referentialism. The situation looks like a paradox about proper names.

The parallel Kripkean arguments, I have in mind, go something like this:

Assume (for reductio) that `Hesperus' is referential such that it is semantically equivalent to `Phosphorus'. Then certain counterintuitive modal, epistemological and semantical consequences follow. We will represent the assumption as follows.

Assumption 0. [[Hesperus]] = [[Phosporus]]

Now consider the following sentence:

(1) Hesperus is Phosphorus.

By, Assumption 0, it follows that (1) is semantically equivalent to (2).

(2) Phosphorus is Phosphorus.

We can represent the logical form of the singular proposition that (2) semantically expresses as follows (note: I just stipulate that the `is' in (1) and (2) is the `is' of predication, not the `is' of identity. It ultimately doesn't matter but if you like just reword (1) as `Hesperus has the property of being identical to Phosphorus'.):

P: {Phosphorus, being identical to Phosphorus}

With this set up, we can run arguments completely parallel to the Kripkean anti-descriptivist arguments.

ANTI-REFERENTIALIST MODAL ARGUMENT: Since P is true evaluated with respect to every epistemically possible world (in which Phosphorus exists), P is epistemically necessary. But, surely (1) does not express an epistemically necessary truth. It might turn out that Hesperus is not Phosphorus.

ANTI-REFERENTIALIST EPISTEMIC ARGUMENT: Since one merely needs to entertain P in order to know that it is true, P is knowable a priori. But, surely (1) does not express an a priori truth. One cannot know a priori that Hesperus is Phosphorus.

ANTI-REFERENTIALIST SEMANTIC ARGUMENT: Suppose that Hesperus is not in fact Phosphorus but instead it is a comet with an erratic orbit. What does `Hesperus' refer to? By, Assumption 0, `Hesperus' refers to the same thing as `Phosporus', namely the planet Venus. And since by supposition, Hesperus is not the planet Venus, it follows that 'Hesperus' does not refer to Hesperus. But, surely `Hesperus' refers to Hesperus (regardless of what `Phosphorus' refers to).

australia

2008-04-21T02:09:00.000-07:00

I have just recently arrived in Canberra as a new PhD student in Philosophy at the Research School of Social Sciences, Australian National University. I have somewhat tentative plans to write a dissertation on THE EPISTEMOLOGY OF PHILOSOPHY. So this would probably involve talking about things like intuition, conceptual analysis, conceivability, analyticity, aprioricity, epistemic and metaphysical possibility, semantic theory, meaning, concepts, rationalism, and philosophical methodology. The idea would be to try out some kind of conceptualist defense of the apriori method...

I plan to post more regularly in the coming months and years than I have in the past (well, once I settle in). As usual I will write on whatever philosophical issue is on my mind, thus the posts will (hopefully) be mostly focused around my dissertation project. But given the number of philosophy talks that take place here there will most likely be posts on those as well [and I will probably revisit some old themes as well, e.g. the semantic paradoxes, the names as common nouns hypothesis, the semantic/pragmatics interface, 2D semantics, and philosophy of mind].

This isn't an advertisment. Its just me taking stock and providing a little sign post for you readers out there...

tigers and smiths

2008-04-09T14:04:00.000-07:00

A bearer of the name "Tiger Smith" need not be a tiger nor a smith but such a bearer will be both a Tiger and a Smith.

A refutation of the knowability principle?

2008-02-12T22:02:00.000-08:00

The knowability principle: For all p, if p is true, then it is possible to know p.

But it seems that the following statement is a counterexample.

Ψ: It is impossible to know Ψ.

Claim. Ψ is true (and, thus, it is impossible to know Ψ).

Proof. Assume (to reach a contradiction) that Ψ is not true. Then it is possible to know Ψ. So, there is a world w such that Ψ is known at w. Since Ψ is known at w, Ψ is true at w. But then it is impossible to know Ψ at w. Hence, (assuming T or stronger) Ψ is not known at w. Contradiction.

[Does this work? It is just a "modalized" version of the Knower. Has this already been done?]

The Sixth Way

2008-02-11T08:34:00.000-08:00

The Argument from Knowability

The Sixth Way is taken from the idea of knowability. (1) Now it is certain that all things which are true are capable of being known. (2) But then we find that all truths are known. (3) For if it is true that there is an unknown truth, then a being is capable not only of knowing that truth but knowing that that truth is unknown; (4) and it is impossible that a being both know something and know that it is not known, for the latter is contrary to the former. (5) Therefore, there exists a being in the Universe that possesses intelligence by which all truths are known; and this we call God.

[see Fitch's paradox of knowability; credit due to Phil Atkins and others in the grad lounge (Luke and Ian?) for the original idea and suggestions on the wording]

Reason and value conference

2008-01-02T13:15:00.000-08:00

Reason and Value
The Fourth Steven Humphrey Excellence in Philosophy Conference

February 16th-18th, 2008
Santa Barbara, California

Speakers: Joseph Raz, John Broome, R. Jay Wallace, Peter Railton, David Velleman, Ralph Wedgwood, Thomas Pink, and Connie Rosati.

Commentators: Niko Kolodny, Pamela Hieronymi, Nadeem Hussain, Joshua Gert, Ulrike Heuer, Mark Schroeder, Douglas Lavin, and Pekka Väyrynen.

It should be a great conference! See here for details.

Names or what?

2007-11-22T20:03:00.000-08:00

Are these proper names?

'the Mississippi'
'the Cliffs of Moher'
'the Netherlands'
'the Rockies'
'the Outback'
'the Holy Roman Empire'
'the Sun'
'the Parthenon'

What are these? (and was is their relation to the above?)

'the mighty Mississippi'
'the daunting Cliffs of Moher'
'the peaceful Netherlands'
'the majestic Rockies'
'the desolate Outback'
'the evil Holy Roman Empire'
'the setting Sun'
'the massive Parthenon'

[Aren't they just like 'the table' and 'the brown table'? ]

I think there is a dilemma here: (1) if you treat 'the Parthenon' as a name, then you must give 'the massive Parthenon' a disjoint treatment where 'Parthenon' is a common noun, but then you must allow dropping the 'massive' to get 'the Parthenon' where 'Parthenon' is still a common noun. Thus, 'the Parthenon' is ambiguous between the name and the definite description. This is unappealing. (2) if you concede that 'the Parthenon' is not a name, then either the Parthenon does not have a name (in English) or its name is 'Parthenon' and names can have determiners in front (then there is no reason not to think that 'two David Kaplans', 'every David Kaplan', are somehow to get a different treatment than names in argument position).

So the dilemma is this if the expressions on the first list are names, then the expressions on the second list, force one to the distasteful position that expressions like 'the Mississippi' and 'the Netherlands' are lexically ambiguous. If, instead, the expressions on the first list are not names, then there are a few options. (i) 'the Netherlands' is not a name [= BAD], (ii) 'Netherlands' is a name but interacts with determiners, modifiers, quantifiers, etc. [= names are general terms].

No doubt there are some places to explore in there but these look like the main roads.

Grice's guillotine

2007-11-09T11:38:00.000-08:00

"In every writing on semantic theory, which I have hitherto met with, I have always remarked, that the author proceeds for some time in the ordinary ways of reasoning, making observations about what people say, what they assert and so forth; when all of a sudden I am surprised to find, that instead of sentences containing, 'says' and 'asserts', I meet with no sentence that is not connected with a 'means' or an 'expresses'. This change is almost imperceptible but is, however, of the last consequence. Since this 'means', or 'expresses', indicates some new relation or affirmation; this should be observed and explained and a good reason should be given. For it seems altogether inconceivable, how this new relation can be a deduction from others, which are entirely different from it."

Are proper names general terms?

2007-10-19T11:45:00.000-07:00

Consider these examples from Clarence Sloat [1969: "Proper Nouns in English", Language, Vol. 45, No. 1., pp. 26-30].

A man stopped by.--------------------------A Smith stopped by.
*Some man stopped by.--------------------*Some Smith stopped by.
SOme man stopped by. ---------------------SOme Smith stopped by.
Some men stopped by. ----------------------Some Smiths stopped by.
Men must breathe. -------------------------Smiths must breathe.
The clever man stopped by.-----------------The clever Smith stopped by.
The man who is clever stopped by.----------The Smith who is clever stopped by.
A clever man stopped by. -------------------A clever Smith stopped by.
The men stopped by. -----------------------The Smiths stopped by.
The man stopped by.-----------------------*The Smith stopped by.
*Man stopped by. ---------------------------Smith stopped by.

Cf. Burge, 1973: "Reference and Proper Names", Journal of Philosophy 70, 425-439.

On possible beliefs about actual dudes

2007-09-06T20:03:00.000-07:00

Consider the following sentence.

(1) John believes that the actual king of Sweden is fat.

Lets assume that (1) is false, i.e. that John does not believe that the actual king of Sweden is fat. Although (1) is false it seems clear that it could have been true, i.e. the following sentence is true.

(2) Possibly, John believes that the actual king of Sweden is fat.

If this is correct then we require a semantic analysis of (2) on which it is true. What does the semantics of (2) look like then? Here are some candidates.

(i) exists w[in w, the actual king of Sweden is such that John believes that he is fat]

(ii) exists w[in w, John believes that the king of Sweden (in w) is fat]

(iii) exists w[in w, John believes that the actual king of Sweden (not in w) is fat]

My intuitions about what the right analysis of (2) is are very sketchy at best. (iii) would yield that (2) is false. But since we had some prima facie reason to think that (2) was true an advocate of (iii) should at least give us an explanation of where and why our intuitions are led astray. So if we assume that (2) is true we are left with (i) and (ii) both of which would yield (2) true (although for different reasons). (i) is true iff John could have had a de re belief about the actual king of Sweden, whereas (ii) is true iff John could have had a de dicto belief about the (possibly non-actual) king of Sweden. When I emphasize the ‘actual’ I get a de re feeling and when I don’t I get the de dicto feeling. So maybe it just depends on whether we are talking about de re belief or de dicto and then the analysis is (i) or (ii) respectively. But I can imagine some one saying, “No, we are talking about the possibility that John have a de dicto belief that the actual king of Sweden is fat”. In that case (iii) does start to look plausible. Perhaps our intuitions that (2) is true could be explain away as mistakenly reading (2) as either about the possibility that John have a de re belief about the actual king of Sweden or the possibility that John have a de dicto belief about the king of Sweden in w.

If this is right then it shows that if A does not believe (de dicto) that the actual F is G, then it is not possible that A believe (de dicto) that the actual F is G. Like I said my intuitions here are sketchy so I’m not sure if this is a bad thing. But it would mean that a descriptivist theory that equates the semantics of names with rigidified descriptions has a problem (see Soames (1998)).

The problem is that if the above is correct and names are semantically equivalent to rigidified definite descriptions and A does not believe (de dicto) that n is G, then it is not possible that A believe (de dicto) that n is G.

[*this post is inspired by ideas found in Soames and Chalmers]

Not all logically equivalent designators are co-designative

2007-08-10T13:29:00.000-07:00

Claim. It is not the case that all logically equivalent designators are co-designative.

Proof. Assume (to reach a contradiction) that all logically equivalent designators are co-designative.

Consider the following definite description,

ψ1: ‘the least natural number that is neither designated by an English definite description consisting of exactly twenty-seven words nor designated by “the king of Sweden”’

There are at most n^27 twenty-seven word definite descriptions (where n is the total number of English words). Each definite description designates at most one natural number. Hence, all the 27-word definite descriptions of English can designate at most n^27 natural numbers. But there are infinitely many natural numbers, so there are some numbers (infinitely many in fact) that cannot be designated by an English definite description consisting of exactly twenty-seven words. Thus, there is a least natural number that is neither designated by an English definite description consisting of exactly twenty-seven words nor designated by ‘the king of Sweden’.
Exactly one number satisfies the matrix of the proper definite description ψ1, therefore ψ1 designates that number.

Consider the following definite description, which is logically equivalent to ψ1,

ψ2: ‘the least natural number that is not designated by an English definite description consisting of exactly twenty-seven words and is not designated by “the king of Sweden”’

By assumption, since ψ2 is logically equivalent to ψ1, ψ2 designates the same number as ψ1. It follows that, this number, i.e. the least natural number that is not designated by an English definite description consisting of exactly twenty-seven words (and not designated by ‘the king of Sweden’) is also designated by ψ2, which is an English definite description consisting of exactly twenty-seven words. Contradiction.

Attempted refutation of Leibniz's Law using Cartwright's Puzzle

2007-08-09T07:45:00.001-07:00

Leibniz's Law (LL): x = y ↔ [φ(x) ↔ ψ(y)]

Claim. LL does not hold generally.

Proof. Assume (to reach a contradiction) that LL is true. Let ‘A’ designate the sentence ‘The last word of A is obscene’ and let ‘B’ designate the sentence ‘The last word of A is obscene’. Let ‘G’ denote the property [λx](if x had quotes around its last word, then x would have been true). Since A = B, by LL it follows that G(A) ↔ G(B). A is not such that if it had quotes around its last word it would have been true (since if A had quotes around its last word its last word would have been “obscene” not ‘obscene’). Hence, ~G(B). But B is such that if it had quotes around its last word it would have been true (since if B had quotes around its last word it would have rightly said of A that its last word is ‘obscene’). Thus, G(B). Contradiction.

[There is a plausible premise to deny. Which is it?]

?

2007-06-30T23:52:00.000-07:00

If this sentence is true, then I solved Curry's paradox.

"unintentional actions"

2007-06-27T07:10:00.000-07:00

There are no such things as unintentional actions! There are unintentional results or unintended consequences of certain actions but those things, those events, are not actions.

It is very common to classify actions into two main types, intentional and unintentional. For example, Anscombe states that “actions can be either intentional or unintentional”. And Davidson argues that although we would not usually call the unintentional consequence of an intentional action an ‘action’, “it should not be inferred from this that [the unintentional result] is therefore something different from [the intentional action], say just its consequence.” Both Davidson and Anscombe (and many others) maintain that there are these things called ‘unintentional actions’, which are genuine actions. I think is a confusing, misguided and useless taxonomy.

Why would “unintentional actions” be classified as actions; what interesting property do they have in common with (intentional) actions? Nothing. There is no interesting connection between the unintentional results of actions and the actions themselves, except that they are the unintentional results of an action! J.W. Meiland observed that calling an unintentional result an ‘action’ only “serves to indicate that what happened has some relation to something that someone did.”[1] He argued that the

use of ‘intentional’ and ‘unintentional’ depends on whether or not certain results were intended or unintended; these terms are used to indicate the status of those results. They are not to be regarded as adjectives modifying ‘action’.[2]

This is right. What intentional and unintentional actions have in common is that they both have some relation to an (intentional) action. Intentional actions stand in the relation of being identical to intentional actions, while unintentional actions stand in the relation of being caused by or the consequences of intentional actions. But then actions would be the class of things that either are intentional actions or are the consequences of intentional actions. Clearly, this is not a theoretically interesting category.

For example, say that Gilbert has just bought some coffee and is running late to seminar. In the elevator he checks his wrist-watch and in so doing accidentally spills some of his coffee. Consider the following two sentences about Gilbert.

(1) Gilbert checked his wrist-watch.

(2) Gilbert spilled his coffee.
Are both (1) and (2) are true? It seems that they are. But are they both about actions (perhaps the same action)? No. It does not follow from the truth of (2), if it is actually true, that Gilbert acted or that any an action took place. What if instead of checking his watch, Gilbert thrashed around having a seizure and in so doing spilled his coffee? Is (2) true? It seems that it is. But did Gilbert act? Did an action take place? No. Gilbert spilled his coffee by having a seizure but there was no agency on behalf of Gilbert. The seizure just happened to him. It does not follow from ‘Gilbert seized’ that Gilbert acted. Likewise it does not follow from ‘Gilbert spilled his coffee’ that Gilbert acted. (Consider ‘Gilbert sneezed’, ‘Gilbert bled’, ‘Gilbert fell’, ‘Gilbert snored’, etc.) One must be wary of inferring the existence of an action just from the fact that there is an agent in the subject position of a true sentence.

Perhaps this is just a terminological quibble. Some things that happen are done by agents, some are the consequences of things done by agents, and some are things not done or caused by agents at all (e.g. Gilbert fell down the stairs.) I think we should reserve the term ‘action’ for the first of these categories. The second category, which we could call ‘agent-initiated events’, includes the intentional results of actions as well as the unintentional results of actions (i.e. so-called “unintentional actions”). The third category, of course, is mere events (or to be precise non-agent-initiated events).

Keeping actions, agent-initiated events, and non-agent-initiated events distinct is very important when invesitageing philosophical questions about the practical knowledge and abilities of agents.

[1] Meiland (1963), "Are there unintentional actions?" p. 380.

[2] Ibid.

The Way

2007-05-27T16:16:00.000-07:00

Before two gates stands one gatekeeper on guard. To this gatekeeper comes a man from the country who is searching for the Way. On each gate it is transcribed, “The Way is the Way and the gate that is the Way is not the gate that is not the Way”. From the scriptures, the man recalls that a gatekeeper before the Way, will grant an answer to one yes-no question. And that whether or not the gatekeeper speaks the truth depends on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely. The gatekeeper with his hooded yellow robe and long grey beard, offers the man a stool allowing him to sit and think before the gates. The man deliberates about what question to asked and he is overcome with frustration, for he remembers that the gatekeepers only speak in their native tongue. The words for yes and no are ‘dui’ and ‘shi’, in some order but the man does not know which word means which. The man has come so far and he will not turn back. There he sits for days and years. He often thinks he has come up with the question, but he always finds a flaw. During the long years the man studies the patterns in the gates and compares them to curls in the gatekeepers beard. He becomes convinced that the answer is hidden in these configurations and mutters to himself the intricate theories he has concocted. He becomes old and senile and curses the gatekeeper. Finally, he beckons the gatekeeper to bend down, since the man has become too weak to move and can scarcely speak. The gatekeeper bends down to hear him and the man whispers a question in the gatekeepers ear. The gatekeeper looks astonished, he flips his coin, considers the question for a minute, he smiles and replies ‘shi’. The man stands for the first time in many years; he has lost all strength and he falls to his knees. But he has found the Way. He crawls to the gate on the right and enters.

What question did the man ask?

What's your name?

2007-05-15T22:00:00.000-07:00

A: What's your name?
B: My name is Fred.
A: What is Fred?
B: It is my name.
A: I know, but which name is it?
B: My name is Fred!
A: Alright, how do you spell Fred?
B: F-R-E-D
A: Oh, so Fred is 'Fred'.
B: Well, I 'm Fred.
A: It depends on which Fred you are talking about. If your name is Fred, then you are not Fred.
B: What? I am only talking about one Fred. Fred is my name. I am Fred.
A: Wait Fred, you are not a name! Your name is Fred, so you are not Fred. But since Fred is 'Fred', you are Fred. There are two Freds: one is your name and one is you. Your name is Fred and Fred is 'Fred' and 'Fred' is your name. Do you see what I'm saying Fred?
B: Umm...

The concept horse is not a concept?

2007-03-20T19:01:00.000-07:00

For Frege, the distinction between functions and objects is a fundamental ontological distinction, which corresponds to the linguistic distinction between object-expressions (i.e. expressions that designate objects) and function-expressions (i.e. expressions that "stand for" functions). Frege explains that the crucial difference between a function and an object is that a function by itself is incomplete, in need of supplementation by an object, whereas an object needs no such supplementation.

The expressions '2 + 3 – 3', '2 + 4 – 4', and '1 + 1' all designate the same object, namely the number 2. The first two expressions have something else in common, which the latter expression lacks. There is a “common element” in the first two expressions that exemplify a function. We usually represent the function as ^'2 + x – x^'. The two occurrences of "x" indicate where the expression needs supplementation by an object-expression. Frege thought that the only way to represent a function is to use an expression which is incomplete in this way, i.e. function-expressions must be unsaturated. Object-expressions, in contrast, are saturated or in need of no supplementation.

"The two parts into which a mathematical expression is thus split up, the sign of the argument and the expression of the function, are dissimilar; for the argument is a number, a whole complete in itself, as the function is not." - Function and Concept

There is an absolute metaphysical dichotomy between functions and objects and a parallel linguistic dichotomy between function-expressions and object-expressions. Frege says both that functions are unsaturated and that function-expressions are unsaturated, while both objects and object-expressions are saturated. Obviously, whatever unsaturatedness is, the way in which function-expressions are unsaturated is only analogical to the way in which functions are unsaturated; function-expressions are in need of supplementation by an object-expression, while functions are in need of supplementation by an object.

One of Frege’s greatest insights, which resulted in the development of the propositional calculus and later developments in formal semantics, was to extend this understanding of functional analysis from mathematics to logic and natural language. Frege states,

"Statements in general, just like [mathematical] equations…, can be imagined to be split up into parts; one complete in itself, and the other in need of supplementation…" - Function and Concept

For example, the expression ‘Caesar conquered Gaul’ can be split up into the singular term ‘Caesar’ and the function-expression ‘conquered Gaul’. ‘Caesar’ designates a certain object and ‘conquered Gaul’ stands for a certain function, i.e. a function that takes an object x as argument an gives the True if x conquered Gaul and gives the False if it is not the case that x conquered Gaul. These type of functions, that is functions from objects to truth-values, Frege called “concepts”. Since concepts are just certain functions, they too are unsaturated.

"Such being the essence of a concept, there is now a great obstacle in the way of expressing ourselves correctly and making ourselves understood. If I want to speak of a concept, language, with an almost irresistible force, compels me to use an inappropriate expression which obscures…the thought. One would assume, on the basis of analogy with other expressions, that if I say ‘the concept equilateral triangle’ I am designating a concept…But this is not the case; for we do not have anything with a predicative nature…the [designatum] of the expression…is an object." - Comments on Sense and Designatum

Names and expressions of the form 'the F' are saturated and thus must designate saturated entities, i.e. objects. Concepts cannot be named. For example, if I tried to name my favorite concept, say, 'Conner', the name 'Conner' is a saturated expression and thus cannot designate an unsaturated entity. If 'Connor' designates anything it is an object and therefore cannot designate my favorite concept, even though I stipulated that it should.

It gets worse. Since expressions of the form 'the F' are saturated and must designate saturated entities, it follow that, in particular, expressions of the form 'the concept F' must designatesaturated entities and so cannot designate concepts. This leads Frege to endorse the strange sentence 'The concept horse is not a concept'. The first three words in the strange sentence compose a saturated expression and thus must designate an object; and so since 'the concept horse' designates an object, the concept horse is not a concept. Frege thinks that in this case we are “confronted by an awkwardness of language” that “cannot be avoided”.

In order to designate an unsaturated entity we must use an unsaturated expression. For example, 'x is a horse' designates an unsaturated entity, an entity that we are compelled to call “the concept horse”, but of course the expression is inappropriate, since it designates an object not a concept. Yet, since 'x is a horse' designates an unsaturated entity, there must be a unique entity it designates. The problem is that language does not allow us to say which entity. We cannot even say that 'x is a horse' designates the entity designated by 'x is a horse', without committing ourselves to 'x is a horse' designating an object, since any expression of the form 'the entity designated by A' must designate an object. Hence, in addition to denying that the concept horse is a concept he must deny the apparently analytic principle that for any expression A, A designates the entity designated by A.

Frege explains that identity can only be thought of as holding for objects, not concepts. When we say that object a is the same as object b, we are saying that a falls under all and only the concepts that b falls under. Whereas when we say that concept F is the same as concept G we are not saying that the concept F falls under all and only the concepts that G falls under, instead we are saying that all and only the objects that fall under F also fall under G.

Object-Sameness: a = b iff AF(Fa iff Fb)

Concept-Sameness: Fx ~ Gx iff Ax(Fx iff Gx)

In the Begriffsschrift the unsaturatedness of a concept is represented by an empty place where the object-expression must go. But since this place must be filled in order to have a well-formed expression, we could never have an expression that designates the concept itself flanking one side of an equality, e.g. an expression of the form 'F( ) = A' is not complete until we fill the space between the parentheses with an object-expression; but once we do this the left side of the equality will designate an object. It seems we are limited to either (i) making a claim about an identity between the extensions of concepts, i.e. ÊF(E) = ÊG(E), or (ii) making a universal claim about objects. Neither of these capture the relation we wish to state. Frege concludes that “the only recourse we really have is to say 'the concept F is the same as the concept G' and in saying this we have of course named objects, where what is intended is a relation between concepts.” What we want to say is (lambda x)[Fx] = (lambda x)[Gx], but Frege would insist that these lambda expressions must designate objects since they are saturated expressions (or perhaps we could regard functions as sets of ordered pairs of an element of the domain coupled with an element of the co-domain, but for Frege a set is an object, and thus cannot be a function. So we are left only with suggestions and allusions of what we are talking about, although what we really want to say cannot be said.

"I admit that there is a quite peculiar obstacle in the way of an understanding with my reader. By a kind of necessity of language, my expressions, taken literally, sometimes miss my thought; I mention an object when what I intend is a concept." - On Concept and Object

Frege maintains that he is relying on a reader who will meet him halfway, one "who does not begrudge a pinch of salt". If we concede to Frege that concepts can only be designated by incomplete expressions, while objects only designated by complete expressions, the obstacle we are dealing with immediately arises. If Frege is just introducing us to a formal language, then perhaps we should allow him this oddity. But Frege thinks that this obstacle is necessarily insurmountable. It is not just that German or the Begriffsschrift has this inherent limited expressivity, it is a necessary limitation of any linguistic system. Frege would insist that we cannot just stipulate that an expression like '(lambda x)[Gx]' designates that thing of which we cannot usually speak (i.e. that thing we would like to designate by the inappropriate expression 'the concept G'). Frege is gripped by this analogy between language and thought, where concept-expressions are in need of supplementation just as the concept itself is in need of supplementation. He thinks it is absolutely crucial that thoughts have an unsaturated component, so he transposes this commitment to the expression of thoughts in language: they too must be unsaturated.

We can agree that "not all parts of a thought can be complete; at least one must be unsaturated or predicative; otherwise they would not hold together", I see no reason to transpose this metaphor to the expression of thought.

Let '(lambda x)[Gx]' designates the unsaturated component of the thought usually expressed by the predicative aspect of the sentence 'a is G'. Given this stipulation we now have the means to express this same thought by the expression '(lambda x)[Gx](a)'. If we sever the parallel between language and thought, we can allow that the “saturated” expression '(lambda x)[Gx]' designates an "unsaturated" entity. Although it is clear that Frege would not accept this modification of his theory, it seems like this avoids the obstacle (or has the difficulty only been shifted?)

a proof that god exists

2007-02-03T08:52:00.000-08:00

Assumptions:

Modal Rationalism. C(Φ) --> <>(Φ)[1]

Reflexivity Axiom. [](Φ) --> (Φ)

Euclidian Axiom. <>[](Φ) --> [](Φ)

Theorem 1. [(<>(Φ) & [](Φ <--> Y)) --> <>(Y)]

Assumption 1. [][God exists <--> [](God exists)][2]

Argument:*

1. C(God exists) {given}

2. <>(God exists) {1, Modal Rationalism}

3. [][God exists <--> [](God exists)] {Assumption 1}

4. <>[](God exists) {2, 3, Theorem 1}

5. [](God exists) {4, Euclidian Axiom}

6. God exists {5, Reflexivity Axiom}

see you at church!

(of course by "God" I mean FSM and by "church" I mean a pirate ship.)

pdf version

* Cf. Plantinga (1974), The Nature of Necessity.
[1] Let ‘C’ be an abbreviation for ‘It is conceivable that’, i.e. if it is conceivable that Φ, then it is possible that Φ. For a thorough defense of modal rationalism see David Chalmers’, “Does Conceivability Entail Possibility?”, published in (T. Gendler & J. Hawthorne, eds) Conceivability and Possibility (Oxford University Press, 2002), pp. 145-200.
[2] This is the common assumption that if God exists at all, then he is not a contingent being.

2007-01-21T22:05:00.000-08:00

They're made out of meat

2007-01-14T16:56:00.000-08:00

After years of probing humans in every possible manner, two alien researchers meet at a late night diner to discuss a most unusual discovery about our species.

They're made out of meat

[this is Stephen O'Regan's film based off of Terry Bisson's short story of the same name]

oregon break

2006-12-23T12:06:00.000-08:00

i am spending the break in oregon, visiting family, etc. yesterday we went fishing on the umpqua.

The Hardest Logic Puzzle Ever

2006-10-15T11:57:00.000-07:00

Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for 'yes' and 'no' are 'da' and 'ja' in some order. You do not know which word means which. (Boolos, 1996, p.62) ( illustration of the puzzle)

A Simple Solution to the Hardest Logic Puzzle Ever (with landon)

vegan spy

2006-10-14T11:01:00.000-07:00

K: John knows that x
F: is a vegan
The D: the shortest chinese spy
N: Lee
/x = lamba x

1. (/x. K Fx) the D
2. K (/x. Fx) the D

(1) doesn't imply (2) and (2) doesn't impy (1).

3. (/x. K Fx) the actual D
4. K (/x. Fx) the actual D

(3) doesn't imply (4) and (4) doesn't imply (3).

5. (/x. K Fx) N
6. K (/x. Fx) N

Does (5) imply (6) or visa versa? If so then how do we model the difference between (3)(4) and (5)(6)? It seems that any model on which (5) implies (6), (3) will imply (4). If not...well the semantics of names must involve more than mere extension (maybe?).

meta-philosophy & methodology

2006-09-21T13:09:00.000-07:00

Over at Plurality of Words there is an interesting post on the resurgence of methodological issues in philosophy, e.g. terminological disputes, intuition, conceptual analysis, etc. There are some good links to check out. I found the Williamson article particularly interesting. Here is a bit from the abstract:

"A striking feature of the traditional armchair method of philosophy is the use of imaginary examples: for instance, of Gettier cases as counterexamples to the justified true belief analysis of knowledge. The use of such examples is often thought to involve some sort of a priori rational intuition, which crude rationalists regard as a virtue and crude empiricists as a vice. It is argued here that, on the contrary, what is involved is simply an application of our general cognitive capacity to handle counterfactual conditionals, which is not exclusively a priori and is not usefully conceived as a form of rational intuition."

twins

2006-08-18T02:17:00.000-07:00

Adisyn and Olivia born 8-10-06.

2D reading group

2006-07-15T12:49:00.000-07:00

I have updated my two-dimensional semantics reading group page. I have added a few articles from the new Garcia-Carpintero & Macia book and organized the rest a bit. If this group ever actualizes (there is just too much going on here right now with the modal logic group and the Fodor/concepts group) I will post our discoveries. The page may be of some use to those trying to round up the literature on 2D (although there is really nothing here one can't already find on Chalmers' site this is narrowed down to very specific issues). If there are any glaring omissions please let me know.

I am carefully making my way through Davies' "Reference, Contingency and the Two-Dimensional Framework". The logic of "actually" is much more thorny than I thought (the earlier post is evidence of my recent confusions).

Unrelated interesting problem: How many people do you need at a party to guarantee the existence of either k mutual stangers or k mutual friends? outline of a solution here

thoughts on yachts

2006-07-13T11:33:00.000-07:00

there is a sentence about a yacht that I am thinking about.

(1) I thought that your yacht was larger than it is.

As is well known (1) has two readings.

(1a) I thought that the size of your yacht was greater than the size of your yacht.
(1b) The size that I thought your yacht was is greater than the size that your yacht is.

In order to highlight the logical form of the two readings, (1a) and (1b) can be represented semi-formally using the following scheme of abbreviation and symbolization.

B: I thought that a
S: the size of your yacht
>: a is greater than b

(1a*) B [S > S]
(1b*) Ex [(B(x = S)) ^ x > S]

There is another sentence about a yacht that has a similar type of ambiguity. I wonder if it can be given a similar treatment.

(2) Your yacht could be larger than it is.

I think (2) has the following two readings.

(2a) It could be that the size of your yacht is greater than the size of your yacht.
(2b) The size that your yacht could be is greater than the size that your yacht is.

These readings parallel the treatment of (1) as is clear from the following formalization.

M: it is possible that a
S: the size of your yacht
>: a is greater than b

(2a*) M [S >S]
(2b*) Ex [(M (S = x)) ^ (x > S)

But (2b*) seems to have two readings:

(i) There is a size that the size of your yacht could be equal to, namely x, and x > S
(ii) There is a size that could be equal to the size of your yacht, namely x, and x > S

Spelled out a bit more these become:

(i`) There is a size such that: (it is possible that: the size of your yacht is equal to that size) and (that size is greater than the size of your yacht)

(ii`) There is a size such that: (it is possible that: that size is equal to the size of your yacht) and (that size is greater than the size of your yacht)

Aren’t these the same? Yes. But there is a subtle difference which the different orderings (almost) bring out. This is what I have in mind.

First lets look at (i`): There is a size, say 20’, such that, (it is possible that, the size of my yacht is equal to that size, i.e. 20’), and (that size, i.e. 20’, is greater than the size of my yacht, say 15’). Roughly put, it is possible that the size of my yacht be 20’ instead of 15’.

Turning to (ii`): There is a size, say 20’, such that, (it is possible that, that size, i.e. 20’, is equal to the size of my yacht, say 15’), and (that size, i.e. 20’, is greater than the size of my yacht, i.e. 15’). Roughly put, it is possible that 20 be equal to 15’ instead of being more than 15’.

The reading we want, of course, is (i`).

Putting an ‘actual’ in seems to make it clearer.

(2A) Your yacht could be larger than it actually is.
(2bA) The size that your yacht could be is greater than the size that your yacht actually is.

Adding “actually” to the scheme (A: actually), we get the following symbolization.

(2b*A) Ex [(M (S = x)) ^ (x > AS)

Which reads something like this:

(iA) There is a size such that: (it is possible that: the size of your yacht is equal to that size) and (that size is greater than the actual size of your yacht)

Or should it be this:

(2b*A`) Ex [M (S = x) ^ A(x > S)]

(iA`) There is a size such that: (it is possible that: the size of your yacht is equal to that size) an (actually: that size is greater than the size of your yacht)

I am not sure how best to represent it. We want the definite description represented by ‘S’ in the left conjunct to be non-rigid but we want the ‘S’ in the right conjunct to be rigidified. The actuality operator achieves this but it might be redundant. I keep getting a funny reading like (ii`) and think I must have gone wrong somewhere. Quantifying over sizes is a bit weird. Its not quite right for (1), since as Kripke has pointed out, there is not an exact size you thought my yacht was. That type of problem shouldn’t affect the modal sentence, since there is an exact size (well, many exact sizes) that my yacht could be. I'm not sure....

my thoughts have drifted off of yachts.

the ontology of concepts

2006-07-10T21:38:00.000-07:00

are concepts abstract entities or mental particulars? i don't think this is an interesting question. this is why: in order to trivialize this issue one need simply appeal to a type/token distinction. since, even psychologism-haters such as frege acknowledged that these abstracta must be 'grasped' or somehow mentally accessed, one can identify concepts with abstract entities and still allow concepts to be tokened in the mind. if someone were to make the further claim that concepts are not mentally accessed, then it seems they have changed the subject or are greatly confused. it appears that one can identify concepts with the concept type (i.e. abstract entity) or the concept token (i.e. mental entity) and nothing of much interest turns on this debate. for theoretical purposes, however, it is perhaps best to identify concepts with the abstract entity. for example, two people can have the concept HORSE, while one has a mental image of a black horse and the other a mental image of a white horse (or perhaps one simply has an associated description of a horse). the worry is that identifying concepts with mental particulars individuates concepts too fine-grained, such that we could not rightly say that any two people posses the same concept. we would require too much if we required that two people share the concept HORSE only if they both think of stallions or they both have memories of being kicked by one on their fifth birthday, etc. clearly there is some mental stuff that differs between the black horse person and the white horse person but it isn't clear that they differ in what concepts they posses. what this brings out is that what we identitfy concepts with depends on what we want out of a theory of concepts...

Leibniz on Truth and Modality

2006-06-10T10:57:00.000-07:00

pdf here

Reasons and Rationality

2006-05-19T10:14:00.000-07:00

What is it to be to rational? Some say to be rational is to respond to reasons. Likewise, some may think that if one does something they have no reason to do, then they are irrational. But there are many cases in which someone does something they have no reason to, in which it seems they are completely rational (e.g. I believe there is a glass of gin in front of me and I want some gin, so I drink; but unbeknownst to me the glass is full of petrol. I have no reason to drink the petrol but it seems that my doing so was completely rational). I think a lot of these problems tend to trade on the ambiguity of the English word 'reason'. This is often acknowledged by philosophers in the literature but it is also often underappreciated or ignored. To combat this we should all internalize this bit from a recent paper by John Broome. I doubt that anyone would disagree with this.

"Many philosophers unhesitatingly assume there is some conceptual connection between rationality and reasons. More specifically, they assume that acting contrary to reasons is irrational. Why make this assumption? There are certainly connections between the words 'rational' and 'reason'. For one thing, they have the same Latin root. But, although etymology can be suggestive, it gives no real ground for thinking there is a connection between the concepts. More confusingly, the word 'reason' has various senses, and in one of them it refers to the faculty of reason. 'Reason' used this way is a mass noun - a noun that has no plural. Our faculty of rationality is plainly part of, or perhaps all of, our faculty of reason. So there is certainly a conceptual connection between rationality and reason in this sense. But the word 'reason'...does not have that sense. It is a count noun - a noun that has a plural. Its plural is 'reasons'. Just because rationality is conceptually connected with the faculty of reason, it does not follow that it is conceptually connected with reasons." - John Broome, "Is Rationality Normative"

What should we do?

2006-05-17T16:08:00.000-07:00

A dirt road. A shrub. Evening. Al Hillah, Iraq. Alfah, sitting on a low mound, is trying to kill an ant while balancing one round rock atop another. With a stick in his left hand he jabs at the ant distracting him from the rocks. Bayta stares intensely into the core of the sun and listens as the shrub gains food directly from an inorganic compound using light energy. Alfah gives up, exhausted, turns to Bayta.

Alfah: What should we do?

Bayta: I don’t know.

Alfah: What should we do in order to come to know what we should do?

Bayta: Whatever we usually do in order to come to know what we should do.

Alfah: Why should we do that?

Bayta: In order to come to know what we should do.

Alfah: Why should we come to know what we should do?

Bayta: Because we want to know what we should do.

Alfah: Why should we want that?

Bayta: I don’t know…we just do!

Alfah: No, no. We certainly should want to know what we should do.

Bayta: Then that is what we shall do! (raising his fist to air)

(Curtain)

Soames/Chalmers exchange

2006-05-03T09:33:00.000-07:00

The Soames/Chalmers exchange from the recent central APA in Chicago is now online. There are signs of progress and I have a better understanding of where the disagreement is (although I have loads of questions). (Stalnaker was also a critic but it is not online)

Chalmers: Scott Soames' Two-Dimensionalism

Soames: Reply to Critics

Chlamers: Response to Reply

*there are some additional comments at: fragments of conciousness

Semantic Width, Privileged Access, and the Possibility of Dry Earth

2006-03-27T15:07:00.000-08:00

I posted a new draft of a paper on externalism, dry earth and privileged access. It is based on some of the earlier posts on this blog...

Semantic Width, Privileged Access, and the Possibility of Dry Earth

[html]

Mind, Identity and Possibility

2006-03-19T14:12:00.000-08:00

Identity Theory is committed to necessarily, P=Q. Dualism which contends that it's not necessary that P=Q, is committed to it not being possible that P=Q (after some modal logic). Standard Dualist arguments against Identity Theory start from the conceivability of the physical without qualia to the possibility of P & ~Q; if sound, then identity theory is false. Is there a route from conceivability to the possibility that P=Q and therefore also a counterexample to the denial of identity theory? I posted some brief comments on this here:

Notes on modality, mind, and conceivability

What concept does 'water' express if the actual world is Dry Earth?

2006-03-14T18:33:00.000-08:00

In order to answer this question I propose to make the following distinctions (inspired by distinctions made in Bealer "A priori knowledge and the scope of philosophy" and Chalmers "The Foundations of Two-Dimensional Seamntics").

An expression T is semantically neutral iff which concept T expresses does not depend on how the actual world turns out.

An expression T is semantically sensitive iff which concept T expresses depends on how the actual world turns out.

An expression T is semantically narrow iff we could have still possessed the concept actually expressed by T had the world turned out differently.

An expression T is semantically wide iff we could not have possessed the concept actually expressed by T had the world turned out differently.

An expression T is semantically void iff T does not actually express a concept.

What concept does ‘water’ express if the actual world is Dry Earth?

Clearly, 'water' is semantically sensitive; it expresses the concept twater if the XYZ-world is actual, and it expresses the concept water if the H2O-world is actual, and some other concept if a world where the watery stuff is made up of various different chemicals is actual, etc. But what concept does it express if Dry Earth (a world where all the watery stuff is illusiory) is actual? And under this assumption is 'water' wide, narrow or void?

If the actual world is Dry Earth, could we have possessed the concept that is expressed by ‘water’ (i.e. dwater) had the world turned out differently. This involves two questions :

(i) What concept is actually expressed by ‘water’ (assuming actual world is Dry Earth)?
A. dwaterA = watery-stuff concept
B. dwaterB = empty concept; a concept which necessarily applies to nothing
C. no concept

(ii) Could we have possessed that concept had the world turned out differently?
A. Yes (Narrow)
B. Yes (Narrow)
C. No (Void)

Option A: Assuming the actual world is Dry Earth ‘water’ expresses the concept dwaterA, which applies to all and only watery stuff; a concept we could have possessed even if the world turned out differently (i.e. ‘water’ is semantically narrow).

Option B: Assuming the actual world is Dry Earth ‘water’ expresses the concept dwaterB, an empty concept which necessarily applies to nothing; a concept we could have possessed even if the world turned out differently (i.e. ‘water’ is semantically narrow).

Option C: Assuming the actual world is Dry Earth ‘water’ does not express a concept, so we don’t possess a concept.

Option A seems to be the intuitive answer. (Perhaps this is like 'air').

Option B is also seems ok, though not so intuitive. (Perhaps this is like 'phlogiston')

Option C seems bad, in fact I think it is open to a reductio. (Is this like 'mimsies'?)

Assume for reductio that:

(V) If I am a Dry Earthlian, then ‘water’ is semantically void.

Argument Gamma:
(1g) If ‘water’ is not semantically void, then I am not a Dry Earthian.
(2g) If I am thinking that water is wet, then ‘water’ is not semantically void.
(3g) I am thinking that water is wet.
(4g) Therefore, I am not a Dry Earthian.

All the premises can be know a priori. (1g) is the contrapositive of (V). (2g) is obvious. (3g) by priviliged access. So, (V) is incompatible with priviliged access. I think the content externalist should not and need not accept (V), since it combined with priviliged access entails that we can know a priori that we are not Dry Earthians.

So this leaves options A and B. Notice that both result in 'water' being semantically narrow. So although we can know a priori that 'water' is semantically sensitive we can't know a priori whether 'water' is semantically wide or narrow. This seems to tell against the Mckinsey-style reductios which start from the width of 'water' to knowing that we are not Dry Earthians. If what I have said is right then the first premise cannot not be known a priori, thus no reductio. May others have said this in different words (Brueckner, Tye and Mclaughlin, etc.)

In this way, the Dry Earth example should be a weapon the content externalist weilds against its foes, not vice versa.

The externalist and privileged access

2006-03-04T18:35:00.000-08:00

The Reductio of Strong Externalism

McKinsey's Maxim [1]:

For any propositions E and P the following holds. If E cannot be known a priori and theory X is committed to it being an a priori truth that if one is thinking that P, then E, then either one cannot know a priori that one is thinking that P or theory X is false.[2]

For example, let E and P be the following and lets call the theory, which is committed to it being an a priori truth that if one is thinking that P, then E, strong externalism (SE).

(E) I am not a Dry Earthian.
(P) I am thinking that water is a liquid.

(Dry Earth is a world qualitatively identical to Earth but on Dry Earth all the watery stuff is an illusion.)

Principle of Privileged Access (PA): A normal subject can know what they are thinking by introspection alone.

If the fact that one is not a Dry Earthian cannot be known a priori and strong externalism is committed to it being an a priori truth that if one is thinking that water is a liquid, then they are not a Dry Earthian, then either one cannot know a priori that they are thinking that water is a liquid or it is not an a priori truth that if one is thinking that water is a liquid, then they are not a Dry Earthian. Since giving up (P) would violate (PA) it is clear that strong externalism is incompatible with privileged access.

Using the logic of McKinsey's Maxim we can get the following set up for a reductio ad absurdum of strong externalist compatiblism (SEC) (who is committed to the conjunction of (SE) and (PA).
1s. (SEC) --> (SE) & (PA)
2s. (SE) --> [(P) --> (E)]
3s. (PA) --> (P)
Cs. (E)

The strong externalist compatibilist is committed to both (SE) and (PA), i.e. they are committed to it being an a priori truth that if one is thinking that (P), then (E) and that it is knowable a priori that one is thinking that (P). Thus, it follows that according to (SEC) one can know a priori that (E). Assuming (SEC) the reductio can be written as follows.

(1) If I am thinking that water is a liquid, then I am not a Dry Earthian.
(2) I am thinking that water is a liquid.
(3) Therefore, I am not a Dry Earthian.

The Weak Externalist

"Any externalist thesis that implies that it is a priori true that if one is thinking that P, then E, where E cannot be known a priori, is indeed incompatible with privileged access. Our position is just that no such externalist thesis has as a consequence that it is a priori knowable that if one is thinking that P, then E, where E is not itself knowable a priori."[3]

"Although one can know a priori that one is thinking a thought involving, say, the concept water, one cannot know a priori that this concept is a natural kind concept. It is epistemically possible that water might turn out to be a disjunction of two different substances, as has turned out to be the case with jade. Our reasons for believing that this is not in fact the case are empirical."[4]

When faced with the reductio the externalist should opt for a weaker claim by making the consequent of 2s conditionalized on (N).

(N) Water is a natural kind.

Now the argument looks like this with a weakened conclusion.

1w. (WEC) --> (WE) & (PA)
2w. (WE) --> [(N) --> {(P) --> (E)}]
3w. (PA) --> (P)
Cw. (N) --> (E)

The weak externalist compatibilist is committed to both (WE) and (PA), i.e. they are committed to it being an a priori truth that if water is a natural kind, then {if one is thinking that (P), then (E)} and that it is knowable a priori that one is thinking that (P). Thus, it follows that according to (WEC) one can only know a priori that if (N), then (E). The (WEC) argument can be written as follows.

(1*) If water is a natural kind, then {if I am thinking that water is a liquid, then I am not a Dry
Earthian}.
(2*) I am thinking that water is a liquid.
(3*) Therefore, if water is a natural kind, then I am not a Dry Earthian.

The Dry Earthians are entitled to the same reasoning as we are and all our other intrinsic twin inhabitants of possible worlds. We have all the same intuitions as they do about 'water', we all say if water turns out to be XYZ, then there is XYZ and all water is XYZ, etc. We all say that if it turns out that we are Dry Earthians, then 'water' is a functional kind, i.e. the watery stuff. These intuitions we share about the meaning of 'water' superviene on our identical intrinsic properties?Is this all the internalist wanted? No, the internalist wants the content of 'water' to superviene only intrinsic properties. Perhaps some content does so supervieve but thats not the only content. So that speaks in favor of externalism. On the other hand, the fact that the content of 'water' supervienes on the intrinsic properties of a subject (plus a world) seems to at least be in the spirit of internalism, e.g. it is our semantic intentions that determine the content of 'water' given a world as argument. The external conditions play an important role in individuating content but it is kind of secondary to our semantic intentions. At this point I start to think that externalism is either an absurd thesis like SE above or a very trivial thesis.

[1] McKinsey (1991).
[2] (MM): [~KE & (X --> (KP --> KE)] --> [~KP or ~X], where KE = know a priori that E, X = theory X and KP = know a priori that one is thinking P.
[3] Tye & McLaughlin (1998).
[4] Falvey (2000), p. 139.

infallibility of 'I am thinking that Q'

2006-02-22T20:38:00.000-08:00

Let P express a proposition of the form 'I am thinking that Q' (where Q expresses any proposition).

1. If a subject S sincerely asserts P, then S believes that P (by the nature of sincere assertion).
2. If S believes that P, then it is true that P (by self-verification).

Therefore, if S sincerely asserts P, then P is true (i.e. If S sincerely asserts 'I am thinking that Q', then it is true that S is thinking that Q). By this reasoning one could argue that self-ascriptive assertions of the form 'I am thinking that Q' are infallible (modulo concerns about content externalism??). Perhaps this is not a very substantial conclusion but it's something.

Given an additional premise about knowledge, we can conclude that if S sincerely asserts P, then S knows that P.

3. If S believes that P and it is true that P, then S knows that P.

Since this premise does not mention anything about justification or evidence it would need to be supported by some further argument about the nature of this kind of self-knowledge. I don't know how this would go, but if this reasoning could be sustained it would transform an assertion that P into knowledge that P. A Somewhat magical conclusion but still not very substantial as far as self-knowledge goes. It would need to be extended to different P's that express more substantial attitudes (of which I am very skeptical)... its cool but I think this kind of neo-expressivist reasoning is going about self-knowledge all wrong. I guess I would prefer some kind of unmediated observation model.

a guide to qualia, functions and the physical

2006-02-14T07:13:00.000-08:00

[Is it possible that A-twins differ w.r.t. thier B-properties? (A's vertical, B's horizontal)]

1. Is it possible that qualitative-twins differ w.r.t. thier qualitative properties?
2. Is it possible that qualitative-twins differ w.r.t thier funtional properties?
3. Is it possible that qualitative-twins differ w.r.t thier physical properties?

4. Is it possible that functional-twins differ w.r.t. thier qualitative properties?
5. Is it possible that functional-twins differ w.r.t. thier functional properties?
6. Is it possible that functional-twins differ w.r.t. thier physical properties?

7. Is it possible that physical-twins differ w.r.t. thier qualitative properties?
8. Is it possible that physical-twins differ w.r.t. thier functional properties?
9. Is it possible that physical-twins differ w.r.t. thier physical properties?

I lean towards the answers above. The interesting boxes are 2, 3, 4, 6, and 7.

2 is "inverted-function", (e.g. my red quale picks out red things, my twin's red quale picks out green things).

3 is "multiple-realizability of qualia", (e.g. I have a qualia-twin who is made of silicon, his pain feels like mine).

4 is "inverted-qualia", (e.g. I pick out red things with my red quale, my functional-twin does the same with his green quale).

6 is "multiple-realizability of functions", (e.g. my functional-twin and I have the same belief but he is made of silicon).

7 is "zombies", (e.g. my physical-twin has different qualia or no qualia).

8 might be interesting? Can there be physical-twins who differ functionally? Probably locally but not globally, because of externalism, twater etc. So I am thinking globally on all these but the differences might be interesting and important.

How do YOU fill in the matrix?

Certain combinations of answers are inconsistent. For example one cannot say NO to 3 while holding my answers fixed.

There is a conflict between denying the multiple realizabilty of qualia and accepting inverted-function (while answering NO to 8).

QQ -> PP by NO to 3
PP -> FF by NO to 8
QQ & ~FF by YES to 2

FF & ~FF by logic

This is a problem for those who want to identify qualia with the physical, while allowing for the inversion of qualia and functions. (I think Perry 2003 says something like this? maybe one could accept 8?).

liar liar

2006-02-12T21:54:00.000-08:00

Some thoughts on the Liar paradox...

Let Z be a sentence, A be a name for Z and B be an unassigned name. Assume that there is a language that follows the following principles:

Principle T: A is true <-> Z

Principle S: (A = B) -> (A is true <-> B is true)

Principle B: ~(A is true & A is not true) & (A is true or A is not true)

Now let L be a sentence which says of itself that it is not true:

The Liar Sentence (LS): L = ‘L is not true’

The Liar reasoning proceeds by first assuming that L is not true. Then by Principle T, it follows that ‘L is not true’ is true. Then by Principle S and the Liar sentence it follows that L is true. There is no problem yet. The problem arises by adjunction of the assumption and L is true. This violates Principle B.

The Liar Reasoning:

1. L is not true {Assumption}
2. L is not true -> ‘L is not true’ is true {Principle T}
3. ‘L is not true’ is true {1, 2, MP}
4. (‘L is not true’ = L) -> (‘L is not true’ is true <-> L is true) {Principle S}
5. ‘L is not true’ is true <-> L is true {LS, 4, MP}
6. L is true {3, 5, MP}
7. L is true & L is not true {1, 6, ADJ}
8. ~(L is true & L is not true) {Principle B}

Contextualists and hierarchical theorists take issue with Principle T. They argue that in one way or other Principle T is significantly more complex than our naïve construal would have it and due to this certain instances of it do not hold.[1] Others have taken issue with Principle S. The worry is roughly that two sentences ‘A’ and ‘A is true’ do not always have the same truth-value.[2] Dialetheists, who contend that there are true contradictions, have challenged the left conjunct of Principle B,[3] while others who appeal to truth-values gaps have taken issue with the right conjunct of Principle B.[4] Still others maintain that every principle is faithful to our language and therefore our folk theory is inconsistent. [5] In every case except the latter, the purposed solutions can be seen as attempts to unmask the hidden mistake in our reasoning. Giving up Principle S is very unattractive and counterintuitive. Challenging principle B, means giving up classical logic. Therefore, if there is some explanation of why Principle T does not always hold it would be the path of least resistance. It seems that the contextualist has the best shot at providing a "happy-face solution" to the Liar paradox, but I think they have some huge problems (see Schiffer 2003 for happy-face/unhappy-face distinction).

...and the suggestion that the Liar sentence is meaningless or doesn't express a propostion doesn't solve anything.

Consider this strengthened Liar sentence:

l = ‘l does not express a true proposition’

Let us first assume that l does expresses a proposition; that is let us try to assign a truth-value to l. Suppose first that l is true, then ‘l does not express a true proposition’ is true, so l is not true. If l is not true, then ‘l does not express a true proposition’ is not true, so l does express a true proposition and l is true. Contradiction. This is the familiar paradox.

However, when faced with this paradoxical reasoning one may be tempted to claim that what is really going on is that l does not express a proposition at all, e.g. l is not “truth-evaluable” or l is “meaningless”. Let us follow this suggestion and assume that l does not express a proposition. If l does not express a proposition at all, then it surely follows that l does not express a true proposition. Yet, this is precisely what l says, so l must be true after all and therefore l expresses a proposition. Again we get a contradiction. Now what?

[1]See Parsons (1974), Burge (1979), (1981) Simmons (1993), Glanzberg (2001), (2004), Gauker, (forthcoming).
[2] See Skyrms (1970)
[3] See Priest (1987).
[4] See Kripke (1975).
[5] See Tarski (1956), Chiraha (1979), Eklund (2002a), (2002b). Inconsistency views are of course unhappy-face solutions.

hello

2006-02-12T17:27:00.000-08:00

let the investigations begin!