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LINGUISTIX&LOGIK, Tony Marmo's blog
Friday, 29 October 2004


Semantics for Deflationists

By Christopher Gauker

According to deflationists, [p]is true is in some sense equivalent to p. The problem that the semantic paradoxes pose for the deflationist is to explicate this equivalence without relying on a semantics grounded in the sort of real reference relations that a deflationist thinks do not exist. More generally, the deflationist is challenged to give an account of logical validity that does not force us to countenance such relations. (The usual model-theoretic definition seems to presuppose that there is some special interpretation, the intended interpretation, such that truth simpliciter is truth on that intended interpretation. So if the deflationist adopts this sort of definition, the deflationist will be challenged to identify the intended interpretation without positing real reference relations.)

Fortunately, a precise semantics compatible with the deflationist philosophy can be had as follows: First, we define a context as a certain sort of set constructed from a basis of literals (atomic sentences and negations of atomic sentences). This formal account of contexts has to be supplemented with an account of the conditions under which a structure satisfying the formal definition is the structure of that kind pertinent ot a given conversation. For each syntactic type of sentence, we define the conditions under which a sentence of that type is assertible relative to a context. In particular, we define the conditions under which sentences of the form "[p]is true" are assertible in a context, and we define the conditions under which sentences of the form "[p]is assertible in context G" are assertible in a context. Finally, logical validity is defined as preservation of assertibility in a context. It is demonstrated that this approach to semantics resists the semantics paradoxes.

(To appear in Deflationism and Paradox, ed. by JC Beall and Bradley Armour-Garb,Oxford University Press)


Posted by Tony Marmo at 00:01 BST
Updated: Friday, 29 October 2004 12:28 BST
Thursday, 28 October 2004


Is the Liar Sentence Both True and False?

By Hartry Field

The argument with which I began shows that if we want to disbelieve instances of excluded middle (in the sense of, believe their negations) then we should be dialetheists (not merely that we should accept paraconsistent logics for some purposes). And as Priest has often urged. the most familiar arguments against the coherence of dialetheism are seriously faulty, a result of a refusal to take the doctrine seriously.

To appear in Beall and Armour-Garb, eds., Deflationism and Paradox (Oxford University Press 2004)

See it

Posted by Tony Marmo at 00:01 BST
Updated: Thursday, 28 October 2004 04:27 BST
Wednesday, 27 October 2004


Grim on Vagueness

The text introduced hereinafter could easily be a paper on the semantics of any natural language, such as Latin, English, Spanish, Korean or French. As the reader can see by the specific topic, which is approached by Grim, issues respecting greater philosophical discussions often have to do with puzzles in Linguistics:

The buried quantifier:
an account of vagueness and the sorites

By Patrick Grim

Contrary to the great bulk of philosophical work on vagueness, the core of vagueness is not to be found in vague monadic predicates such as bald, tall, or old. The true source of vagueness - at least vagueness of the type that typically appears in the sorites - lies beneath these, in a mechanism using a buried quantifier operative over the comparatives balder, taller and older.

Or so I propose. Here the quantifier account is presented in its simplest form, with the limited claim that it offers a paradigmatic treatment for paradigmatic vague predicates in the sorites. Questions remain as to whether the account or something like it can be extended to all sorites vulnerable predicates, and qualifications and concessions in this regard are offered in ?9. What the approach promises, however, even in this limited form, is deeper understanding of vagueness through a deeper understanding of non-comparative adjectives derived from comparatives, a central explanation for a range of otherwise puzzling and disparate phenomena, and a new resolution for the sorites.

Source: Analysis Preprints

Go on

It is interesting to notice that in the Semantics of natural languages the question of whether there are covert quantifiers or operators is a top issue nowadays. Their proponents consider that they are necessary to explain many facts associated with the interpretation of sentences.

Posted by Tony Marmo at 00:01 BST
Updated: Tuesday, 26 October 2004 00:04 BST
Tuesday, 26 October 2004


Some more curious inferences

By Jeffrey Ketland

Nominalism denies the existence of numbers, sets and functions. But a widely discussed problem concerns whether nominalism can account for the applicability of mathematics. This is the indispensability argument against nominalism, associated with Godel, Quine and Putnam. Above we examined examples of the application of mathematics to relationships of logical consequence. It seems to me that the `speed-up' phenomenon under discussion suggests a modified version of the indispensability argument, based now on unfeasibility considerations. Presumably the nominalist does not wish to deny the validity of the inferences I, I{2}, and I{3} under consideration. But there is no feasible direct verification for the above inferences, and the short mathematical derivations involve practically indispensable assumptions about numbers, sets and functions. So, how might a nominalist account for our knowledge that such inferences are valid? After all, the anecdotal evidence is that even nonmathematicians find I{2} and I{3} `obvious'.

Source: Analysis Preprints

See more

Setting aside the problems Ketland mentions above, Everett could try to write a Nominalist Semantics for Pirah?, for that would be consistent with Everett's recent works. Nevertheless, in such case any claim Everett made in the case of Pirah? would have to be valid for other natural languages, and, of course, his views would not easily convince those who do not accept nominalism.

Posted by Tony Marmo at 00:01 BST
Updated: Wednesday, 27 October 2004 00:00 BST
Monday, 25 October 2004


Vagueness and Blurry Sets

By Nicholas J. J. Smith

This paper presents a new theory of vagueness, which is designed to retain the virtues of the fuzzy theory, while avoiding the problem of higher-order vagueness. The theory presented here accommodates the idea that for any statement S1 to the effect that `Bob is bald 'is xtrue, for xin [0,1], there should be a further statement S2which tells us how true S1 is, and so on -that is, it accommodates higher-order vagueness -without resorting to the claim that the metalanguage in which the semantics of vagueness is presented is itself vague, and without requiring us to abandon the idea that the logic -as opposed to the semantics -of vague discourse is classical. I model the extension of a vague predicate Pas a blurry set, this being a function which assigns a degree of membership or degree function to each object o, where a degree function in turn assigns an element of [0,1] to each finite sequence of elements of [0,1]. The idea is that the assignment to the sequence [lang] 0.3,0.2 [rang] , for example, represents the degree to which it is true to say that it is 0.2 true that ois Pto degree 0.3. The philosophical merits of my theory are discussed in detail, and the theory is compared with other extensions and generalisations of fuzzy logic in the literature.

blurry sets, degree functions, degrees of truth, fuzzy logic, fuzzy sets, higher-order vagueness, logic, sorites paradox, truth, type nfuzzy logic, vagueness

Source: Journal of Philosophical Logic

Read it

Posted by Tony Marmo at 06:12 BST
Sunday, 24 October 2004


Formal semantics and intentional states

By Emma Borg

My aim in this note is to address the question of how a context of utterance can figure within a formal, specifically truth-conditional, semantic theory. In particular, I want to explore whether a formal semantic theory could, or should, take the intentional states of a speaker to be relevant in determining the literal meaning of an uttered sentence. The answer I'm going to suggest, contrary to the position of many contemporary formal theorists, is negative. The structure of this note is then as follows: first, I'll very briefly sketch three distinct forms of semantic theory. One, `strong formal semantics', will be seen to be immediately problematic, leaving us with two other options: use-based theories and what I'll term `moderate formal semantics'. If we opt for the latter position, the question arises of what kinds of appeals to a context of utterance are legitimate given a formal outlook. I'll suggest that this question arises in two distinct ways and explore the moderate formal semanticist's position in regard to both. However, the conclusion I will reach is that what is characteristic of formal semantics is that it makes only the most minimal semantic concessions to context.


Posted by Tony Marmo at 00:01 BST
Updated: Sunday, 24 October 2004 12:16 BST


Chunk and Permeate, a Paraconsistent Inference Strategy.
Part I: The Infinitesimal Calculus

By Bryson Brown & Graham Priest

In this paper we introduce a paraconsistent reasoning strategy, Chunk and Permeate. In this, information is broken up into chunks, and a limited amount of information is allowed to flow between chunks. We start by giving an abstract characterisation of the strategy. It is then applied to model the reasoning employed in the original infinitesimal calculus. The paper next establishes some results concerning the legitimacy of reasoning of this kind -specifically concerning the preservation of the consistency of each chunk -and concludes with some other possible applications and technical questions.

chunking, infinitesimal calculus, paraconsistent logic

Published version (For Subscribers of the Journal of Philosophical Logic)

Posted by Tony Marmo at 00:01 BST
Updated: Sunday, 24 October 2004 12:14 BST
Saturday, 23 October 2004

Topic: Cognition & Epistemology

Could a machine have a mind?

By Tennessee Leeuwenburg

Attempting to answer poses a frankly massive ontological problem - so great that I believe that could one solve the ontological issues, the answer to the question would be apparent. There is a definite history to understanding the philosophy of the mind, and many of the attempts to describe the mind will be outlined in this essay. However, there is only one logical launching point - the simple fact that humans have minds. It will be my eventualy position that a machine can indeed have a mind, but before this can be argued for, let alone established, the problem must first be understood.


Posted by Tony Marmo at 00:01 BST
Updated: Friday, 22 October 2004 18:30 BST
Friday, 22 October 2004

Coulda,Woulda, Shoulda

By Stephen Yablo

An enormous amount has been done with the metaphysical/conceptual distinction. Yet, and I think this is agreed by everyone, the distinction remains not terribly well understood. One reason it is not well understood is that the conceptual side of the distinction didn't receive at Kripke's hands the same sort of development as the metaphysical side.

This might have been intentional on Kripke's part. He might have thought the conceptual notion to be irremediably obscure, but important to mention lest it obscure our view of metaphysical necessity. Certainly this is the attitude that many take about the conceptual notion today. It could be argued that much of the contemporary skepticism about narrow content is at the same time skepticism about conceptual possibility. Narrow content, if it existed, would give sense to conceptual possibility: holding its narrow content fixed, S could have expressed a truth. If one rejects narrow content, one needs a different explanation, and none comes to mind. Going in the other direction, one might try to define S's narrow content as the set of worlds w whose obtaining conceptually necessitates that S. Lewis remarks somewhere that whoever claims not to understand something will take care not to understand anything else whereby it might be explained. If you don't understand narrow content, you will take care not to understand conceptual possibility either.

But,although many people have doubts about conceptual possibility,a number of other people are entirely gung ho about it. Some even treat it (and narrow content) as more, or anyway no less, fundamental than metaphysical possibility (and broad content).

Read more

Posted by Tony Marmo at 04:06 BST
Updated: Friday, 22 October 2004 04:08 BST
Thursday, 21 October 2004


Why Compositionality Won't Go Away:
Reflections on Horwich's `Deflationary' Theory

By Jerry Fodor and Ernie Lepore

Compositionality is the idea that the meanings of complex expressions (or concepts) are constructed from the meanings of the less complex expressions (or concepts) that are their constituents. Over the last few years, we have just about convinced ourselves that compositionality is the sovereign test for theories of lexical meaning. So hard is this test to pass, we think, that it filters out practically all of the theories of lexical meaning that are current in either philosophy or cognitive science. Among the casualties are, for example, the theory that lexical meanings are statistical structures (like stereotypes); the theory that the meaning of a word is its use; the theory that knowing the meaning of (at least some) words requires having a recognitional capacity for (at least some) of the things that it applies to; and the theory that knowing the meaning of a word requires knowing criteria for applying it. Indeed, we think that only two theories of the lexicon survive the compositionality constraint: viz., the theory that all lexical meanings are primitive and the theory that some lexical meanings are primitive and the rest are definitions. So compositionality does a lot of work in lexical semantics, according to our lights.

Well, so imagine our consternation and surprise when, having just about convinced ourselves of all this, we heard that Paul Horwich has on offer a `deflationary' account of compositionality, according to which,

...the compositionality of meaning imposes no constraint at all on how the meaning properties of words are constituted (154; our emphasis).

Surely, we thought, that can't be right; surely compositionality must rule out at least some theories about what word meanings are; for example, the theory that they are rocks, or that they are sparrows or chairs; for how could the meanings of complex expressions be constructed from any of those? What, we wondered, is going on here?


This essay, together with a number of others on related topics, is reprinted in the book `The Compositionality Papers' by Fodor and Lepore (OUP).

Posted by Tony Marmo at 05:30 BST
Updated: Thursday, 21 October 2004 21:50 BST
Wednesday, 20 October 2004


Dialetheism, logical consequence and hierarchy

By Bruno Whittle

Dialetheism is defined by Graham Priest to be the view that there are true contradictions. It is supposed to offer treatments of the semantic paradoxes that avoid the problems faced by more orthodox resolutions. The advantage of these treatments is supposed to be that they avoid the sort of appeal to a hierarchy of languages or concepts that more orthodox resolutions seem invariably to have to make. For since a dialetheist can simply accept as sound the derivations of contradictions involved in the paradoxes, there is no need for him to invoke a hierarchy to block these derivations.

In this article I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.

In ?1 I explain why and how a dialetheist needs to be able to talk about logical consequence. In ?2 I argue that there are in fact severe restrictions upon how exactly a dialetheist can talk about logical consequence. These restrictions stem from a version of Curry's paradox. I then argue in ?3 that a dialetheist must appeal to a hierarchy of concepts of logical consequence, and, further, that each of these concepts is dialetheically unobjectionable. The justification of this latter claim involves proving that the addition of these concepts together with natural rules for them conservatively extends dialetheic logic. This is proved in the appendix.

Read this article

Posted by Tony Marmo at 00:01 BST
Updated: Wednesday, 20 October 2004 04:23 BST
Tuesday, 19 October 2004


Lockean and Logical Truth Conditions

By James Dreier
Source: Online Papers in Philosophy

The distinction between logical and Lockean truth conditions helps Expressivism to distinguish itself from Subjectivism. Expressivism is the view that moral judgements lack logical truth conditions. Subjectivism says that moral judgements have logical truth conditions involving the speaker's attitudes. Both theories may allow that moral judgements have Lockean truth conditions involving the speaker's attitudes.

See more

Posted by Tony Marmo at 00:01 BST
Updated: Tuesday, 19 October 2004 05:18 BST
Monday, 18 October 2004


Indicative versus subjunctive in future conditionals

By Adam Morton

There are both Indicative and Subjunctive future-tense conditionals. And moreover sometimes the same words can be used to express both.

Jonathan Bennett (2003), in his wonderfully clear and persuasive book, A Philosophical Guide to Conditionals, continues a debate concerning conditionals about the future. For conditionals about the past there is a clear contrast between so-called indicative and subjunctive conditionals. For most people the contrast is typified by a familiar family of incompatible pairs of sentences such as
If Shakespeare did not write Hamlet someone else did.
If Shakespeare had not written Hamlet someone else would have.

The first of these is assertable, given normal beliefs about the world, and the second is not, so the `did/would have' contrast seems to mark a difference in meaning. I'll call these `Adams pairs', since the first examples were due to Ernest Adams.
I'll assume familiarity with the basic use of Adams pairs to make an indicative/subjunctive distinction. Most people on absorbing the distinction are inclined to classify many future tense conditionals, such as

If Bill won't write the play, someone else will.

with subjunctive `did/would have' past-tense conditionals. Bennett argues against this, urging us to classify `will/will' and `is/will' conditionals with indicative `did/did' ones. Bennett's claim is strong: not only are future tense conditionals usually of the indicative variety, but we cannot use these grammatical forms to express subjunctive conditionals. In this paper I shall contest this latter claim, focusing on paired examples in the familiar family. So the central task is to show that there are Adams pairs set in the future.


Posted by Tony Marmo at 19:24 BST
Updated: Monday, 18 October 2004 19:28 BST


Binding alongside Hamblin alternatives calls for variable-free semantics

Chung-chieh Shan
Source: Semantics Archive

The compositional, bottom-up computation of alternative sets was first introduced by Hamblin (1973) into Montague grammar to treat in-situ wh-questions. In the thirty years since then, alternative sets have found their way into theories of focus (Rooth 1985), indeterminate pronouns (Shimoyama 2001), and free-choice indefinites (Kratzer and Shimoyama 2002). These theories often position alternatives as a scope-taking mechanism that operates separately from Quantifier Raising (May 1977), Quantifying In (Montague 1974), or some other scope-taking mechanism for "genuine" quantifiers like most. On these theories, then, it is not surprising that (say) in-situ who takes scope di erently from most, as is empirically observed.
In particular, if "genuine" scope requires syntactic movement but alternative scope does not, then constraints on movement apply only to the former, and we predict--correctly--that the scope of most is more restricted than the scope of in-situ who.

(1) Who denied that who left?
`Which x and y are such that x denied that y left?'
(2) Who denied that most people left?
*`Which x is such that, for most y, x denied that y left?'

Many theories of quantification, including Quantifier Raising and Quantifying In, make essential use of variables for binding. In the first half of this paper, I show that using variables for binding is incompatible with computing alternatives bottom-up. For example, a theory on which who denotes an alternative set and most books binds a variable cannot account for who read most books. To fix this problem, we can either perform binding without variables (Jacobson 1999, 2000) or compute alternatives non-compositionally. Since Karttunen (1977) has already explored the latter option, I consider the former here: in the second half of this paper, I spell out how to compute alternatives compositionally in a variable-free theory of binding and quantification. Both options fix the problem.


Posted by Tony Marmo at 00:01 BST
Updated: Monday, 18 October 2004 19:09 BST
Sunday, 17 October 2004


Indexicals, Fictions, and Ficta

by Eros Corazza and Mark Whitsey

We defend the view that an indexical uttered by an actor works on the model of deferred reference. If it defers to a character which does not exist, it is an empty term, just as `Hamlet' and `Ophelia' are. The utterance in which it appears does not express a proposition and thus lacks a truth value. We advocate an ontologically parsimonious, anti-realist, position. We show how the notion of truth in our use and understanding of indexicals (and fictional names) as they appear within a fiction is not a central issue. We claim that our use and understanding of indexicals (and names) rests on the fact that their cognitive contribution is not exhausted by their semantic contribution.


Posted by Tony Marmo at 00:01 BST
Updated: Sunday, 17 October 2004 04:46 BST

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