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LINGUISTIX&LOGIK, Tony Marmo's blog
Friday, 8 July 2005


Posted by Tony Marmo at 02:26 BST


Dialectical Considerations on the Logic of Contradiction: Part I

By John Woods

This is an examination of the dialectical structure of deep disagreements about matters not open to empirical check. A dramatic case in point is the Law of Non-Contradiction (LNC). Dialetheists are notoriously of the view that, in some few cases, LNC has a true negation. The traditional position on LNC is that it is non-negotiable. The standard reason for thinking it non-negotiable is, being a first principle, there is nothing to negotiate. One of my purposes is to show that the first-principle defence of LNC is inadequate. A second purpose is to argue that it flows from this inadequacy that LNC stands or falls on economic considerations, much in the spirit of Quine's pragmatism about logic generally. This is a tactical victory for dialetheists. It gives them room to make the case against LNC on cost-benefit grounds. As things presently stand, no such case can be considered decisive. But, given that costs and benefits shift with changing circumstances, it is possible that a winning case for the dialetheist may present itself in the future. Notwithstanding the rivalry between consistentists and dialetheists, they share a common opponent. This is trivialism, the doctrine that everything whatever is true. It is an ironic alliance, in as much as the dialetheist's case against the consistentist can be adapted to a defence of trivialism. How damaging this turns out to be depends on the adequacy of the reasons for the dialetheist's rejection of trivialism. My further purpose is to show that the damage is slighter than dialetheists commonly believe.

Key Words: antinomy, Aristotle, contradiction, costs and benefits, consistentism, Curry Paradox, detonation, dialetheism, Frege, Law of Non-Contradiction, Liar Paradox, Locke, proof, Russell, near-trivialism, paraconsistency, Philosophy's Most Difficult Problem, set theory, semantics, Solving Paradox, Tarski, truth

Appeared in the Logic Journal of IGPL 2005 13(2):231-260

Posted by Tony Marmo at 00:01 BST
Updated: Friday, 8 July 2005 02:20 BST


Modality and Paraconsistency

By João Marcos

Paraconsistent logic was born in the vicinity of modal logic. Moreover, as every other non-classical logicians, paraconsistentists have very often flirted with modalities. The first known system of paraconsistent logic was in fact defined as a fragment of S5, in the late 40s. But a fragment of a modal system is not necessarily a modal system. I will show here, indeed, that Jaškowski’s D2 is not a modal logic, in the contemporary usual meaning of the term. By contrast, I will also show, subsequently, that any non-degenerate normal modal system is inherently paraconsistent.

Appeared in
[i.] Marta Bilkova and Libor Behounek (eds), The Logica Yearbook 2004, Filosofia, Prague, 2005, pp.213-222.
[ii.] Marcos (2005), Logics of Formal Inconsistency, Chapter 3.2, pp. 211-219. Unicamp press.

Posted by Tony Marmo at 00:01 BST
Updated: Friday, 8 July 2005 02:21 BST


Logics of essence and accident

By João Marcos

We say that things happen accidentally when they do indeed happen, but only by chance. In the opposite situation, an essential happening is inescapable, its inevitability being the sine qua non for its very occurrence. This paper will investigate modal logics on a language tailored to talk about essential and accidental statements. Completeness of some among the weakest and the strongest such systems is attained. The weak expressibility of the classical propositional language enriched with the non-normal modal operators of essence and accident is highlighted and illustrated, both with respect to the definability of the more usual modal operators as well as with respect to the characterizability of classes of frames. Several interesting problems and directions are left open for exploration.

Keywords: philosophy of modal logic, non-normal modalities, formal metaphysics, essence, accident

Appeared in
[i.] Bulletin of the Section of Logic, 34(1):43-56, 2005
[ii.] Marcos (2005) Logics of Formal Inconsitency, Chapter 3.1: 199-210

Sources: João Marcos' Webpage, Paraconsistency group, Paraconsistent Newsletter.

Posted by Tony Marmo at 00:01 BST
Updated: Friday, 8 July 2005 02:19 BST


A Paraconsistent -preservationist approach to a common confusion concerning predicate-extensions

By Martin W. Allen

The existence of multiple criteria for the introduction of a predicate may lead to confusion when the criteria diverge as to whether or not some object falls under the predicate. It can be dicult to represent the semantics of sentences featuring such a predicate-term, and it is not obvious how a person is supposed to employ such confused terms in the business of language and reasoning. I consider [here] two approaches to the problem: dialethism, which allows both a sentence and its negation to be true at once; and disambiguation, which represents any such confused predicate in terms of other ,distinct predicates. I show the equivalency of plausible formal treatments of these approaches, discuss reasons for this equivalency, and present an alternative approach|a preservationist one, which does not interpret the confused predicates but rather seeks to contain the confusion present. I argue that a meaningful, and useful, concept of inference is available, even where the semantics of certain predicate-terms remain confusing.

Posted by Tony Marmo at 00:01 BST
Updated: Friday, 8 July 2005 02:19 BST
Thursday, 7 July 2005

Now Playing: UPDATED
Update: Today I received Jo?o Marcos' book, Logics of Formal Inconsistency.Thanks Jo?o!!

Paraconsistency For Beginners

Joao Marcos' book has an important section for beginners. From page 16 to page 30, Chapter 1.0 (it would be Chapter 2 or an appendix to Chapter 1, but Jo?o liked the idea of calling it 1.0), there is a very easy exposition of what is Paraconsistent Logic. Section 2 of the same Chapter requires more attention from the reader, but by reading the first Section one is relatively prepared to understand Section 2, which is not very difficult.
So, teachers, here is my recommendation: Joao Marcos? Chapter 1.0 for your undergraduates.

February the 17th 2005

Yesterday, Joao Marcos defended his PhD dissertation, as the Unicamp Portal infoms us. Here is an abstract with a link:

Logics of Formal Inconsistency

By Joao Marcos

According to the classical consistency presupposition, contradictions have an explosive character: Whenever they are present in a theory, anything goes, and no sensible reasoning can thus take place. A logic is paraconsistent if it disallows such presupposition, and allows instead for some inconsistent yet non-trivial theories to make perfect sense. The Logics of Formal Inconsistency, LFIs, form a particularly expressive class of paraconsistent logics in which the metatheoretical notion of consistency can be internalized at the object-language level. As a consequence, the LFIs are able to recapture consistent reasoning by the addition of appropriate consistency assumptions. So, for instance, while classical rules such as disjunctive syllogism (from A and not-A-or-B, infer B) are bound to fail in a paraconsistent logic (because A and not-A could both be true for some A, independently of B), they can be recovered by an LFI if the set of premises is enlarged by the presumption that we are reasoning in a consistent environment (in this case, by the addition of consistent-A as an extra hypothesis of the rule).
The present monograph introduces the LFIs and provides several illustrations of them and of their properties, showing that such logics constitute in fact the majority of interesting paraconsistent systems from the literature. Several ways of performing the recapture of consistent reasoning inside such inconsistent systems are also illustrated. In each case, interpretations in terms of many-valued, possible-translations, or modal semantics are provided, and the problems related to providing algebraic counterparts to such logics are surveyed. A formal abstract approach is proposed to all related definitions and an extended investigation is made into the logical principles and the positive and negative properties of negation.

Keywords: Universal Logic, negation, paraconsistency, possible-translations semantics, modalities, formal philosophy.

PhD Dissertation, Cooperation Agreement between the State University of Campinas and the Technical University of Lisbon

Note: As the members of the Commission have offered Jo?o Marcos many suggestions, it is possible that a new revised text will appear sooner or later, though most of the Chapters have been already published as separate papers in different journals.

Posted by Tony Marmo at 00:01 BST
Updated: Friday, 8 July 2005 02:24 BST
Monday, 4 July 2005

Topic: Interconnections

The Elimination of Self-Reference
(Generalized Yablo-Series and the Theory of Truth)

By Phillippe Schlenker

Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo showed that this is not so by displaying an infinite series of non-referential sentences which, taken together, are paradoxical (e.g. Yablo 2004). We generalize Yablo's result along two dimensions.
1. First, we investigate the behavior of Yablo-style series of the form {<s(i), [Qk: k> i] f[(s(k)) k≥i ]>: i≥0}, where for each i s( i) is a term that denotes the sentence [Qk: k> i] f[(s(k)) k≥i] ] (for some generalized quantifier Q and for some (fixed) truth function f). We show that for any n-valued compositional semantics and for any quantifier Q that satisfies certain natural properties, all the sentences in the series must have the same value. We derive a characterization of those values of Q for which the series is paradoxical in a natural trivalent logic.
2. Second, we show that in the Strong Kleene trivalent logic, Yablo's results are a special case of a much more general phenomenon: given certain assumptions, any semantic phenomenon that involves self-reference can be reproduced without self-reference (Cook 2004 proves a special case of this result, which only applies to logical paradoxes).

Specifically, we can associate to each pair <s, F> of a formula F named by a term s in a language L' a series of translations {<s( i), [Qk: k> i] [F] k>: i≥0} (where [F] kis a certain modification of F) in a quantificational language L* in such a way that
(i) none of the translations are self-referential,
(ii) in any fixed point I* of L*, all the translations of a given formula of L have the same value according to I*, and
(iii) there is a correspondence between the fixed points of L' and the fixed points of L* which ensures that the translations really do have the same semantic behavior as the sentences they translate.

We give a characterization of those generalized quantifiers Q which can be used in the translation.
Source: Online Papers in Philosophy

Posted by Tony Marmo at 07:15 BST
Updated: Monday, 4 July 2005 07:24 BST
Saturday, 2 July 2005

Topic: Cognition & Epistemology

Reference Determination and Conceptual Change

By Ingo Brigandt

The paper discusses reference determination from the point of view of conceptual change in science. The first part of the discussion uses the homology concept, a natural kind term from biology, as an example. It is argued that the causal theory of reference gives an incomplete account of reference determination even in the case of natural kind terms. Moreover, even if descriptions of the referent are taken into account, this does not yield a satisfactory account of reference in the case of the homology concept. I suggest that in addition to the factors that standard theories of reference invoke the scientific use of concepts and the epistemic interests pursued with concepts are important factors in determining the reference of scientific concepts. In the second part, I argue for a moderate holism about reference determination according to which the set of conditions that determine the reference of a concept is relatively open and different conditions may be reference fixing depending on the context in which this concept is used. It is also suggested that which features are reference determining in a particular case may depend on the philosophical interests that underlie reference ascription and the study of conceptual change.

Source: Online Papers in Philosophy

Posted by Tony Marmo at 07:20 BST
Tuesday, 28 June 2005


On the Lumping Semantics of Counterfactuals

By Makoto Kanazawa, Stefan Kaufmann and Stanley Peters

Kratzer (1981) discussed a naïve premise semantics of counterfactual conditionals, pointed to an empirical inadequacy of this interpretation, and presented a modification— partition semantics— which Lewis (1981) proved equivalent to Pollock's (1976) version of his ordering semantics. Subsequently, Kratzer (1989) proposed lumping semantics, a different modification of premise semantics, and argued it remedies empirical failings of ordering semantics as well as of naïve premise semantics. We show that lumping semantics yields truth conditions for counterfactuals that are not only different from what she claims they are, but also inferior to those of the earlier versions of premise semantics.

See also the Journal of Semantics 2005 22(2):129-151

Constraining Premise Sets for Counterfactuals

By Angelika Kratzer

This note is a reply to "On the Lumping Semantics of Counterfactuals" by Makoto Kanazawa, Stefan Kaufmann, and Stanley Peters. It argues first that the first triviality result obtained by Kanazawa, Kaufmann, and Peters does not apply to the analysis of counterfactuals in Kratzer (1989). Second, and more importantly, it points out that the results obtained by Kanazawa, Kaufmann, and Peters are obsolete in view of the revised analysis of counterfactuals in Kratzer (1990, 2002).

Posted by Tony Marmo at 00:01 BST
Updated: Tuesday, 28 June 2005 08:39 BST
Friday, 24 June 2005


On the practice of indirect reports

by Alessandro Capone

In this paper, I shall deal with the practice of indirect speech reports. I shall argue that indirect speech reports are transformations of original speech events (or speech acts), subject to severe limitations, which it is my aim in this paper to spell out in detail. I shall study the interactions with the theory of pragmemes, of indexicals, and of modes of presentation. I end this paper suggesting, given appropriate evidence, that a key to the understanding of indirect reports is the exploration of analogies with the theory of speech acts and that analogies with the theory of propositional attitudes may be misleading.

Source: Semantics Archive

Posted by Tony Marmo at 23:19 BST
Wednesday, 22 June 2005


On the Storeyed Revenge of Strengthened Liars

By Jordan Howard Sobel

The Strengthened Liar observes that if we follow a partiality theorist and declare the Liar sentence neither true nor false (or failing to express a proposition, or suffering from some sort of grave semantic defect), then the paradox is only pushed back. For we can go on to conclude that whatever this status may be, it implies that the Liar sentence is not true. This claim is true, but it is just the Liar sentence again. We are back in paradox. (Glanzberg 2002, p. 468; 2004, p. 29; 2001, p. 222, “We are back in our contradiction.”)

There are problems with this charge that strengthened liar sentences avenge would be disparagements that they do not express propositions, by reappearing as claims that are easy consequences of these disparagements. For one thing, if, as one supposes, claims would be propositions not sentences, [t]his claim cannot be the Liar sentence again. (Cf., Grim 1991, p. 19.) For another thing, while it does follow from the disparagement that a Liar sentence does not express a proposition, that this sentence does not express a true proposition, it is a consequence of that disparagement that this claim or proposition is not expressed by the Liar sentence itself. However, there are ways in which informal and formal revelations that Liar sentences do not express propositions and seem to bring them back with vengeance. This is their story.

Source: Online Papers in Philosophy

Posted by Tony Marmo at 03:55 BST
Updated: Wednesday, 22 June 2005 04:03 BST
Tuesday, 21 June 2005


Standard and Non-Standard Quantifiers in Natural Language

By Edward L. Keenan

Since the early 1980s we have been witnessing an explosive growth in our knowledge of natural language quantifiers, specifically of their denotations as opposed to their form, distribution, or compositional interpretation. Our concern here is to unify and extend these results, highlighting generalizations of linguistic interest. We present first an inventory of semantically defined classes of quantifiers expressible in English, and then a list of linguistic generalizations stated in terms of these classes and their defining concepts. We close with two types of quantification that lie outside these classes and which invite further research as less is known about them.

Source: Online Papers in Philosophy

Posted by Tony Marmo at 03:03 BST
Thursday, 16 June 2005


Zero Tolerance for Pragmatics

By Christopher Gauker

The proposition expressed by a sentence is relative to a context. But what are the values of the context variables? Many theorists would include among these values aspects of the speaker's intention in speaking. My thesis is that, on the contrary, the values of the context variables never include the speaker's intention. My argument for this thesis turns on a consideration of the role that the concept of proposition expressed in context is supposed to play in a theory of linguistic communication and on a consideration of what a speaker and a hearer can reasonably expect of one another. Although I call this thesis zero tolerance for pragmatics, it is not an expression of intolerance for everything that might be called pragmatics.

Source: Online Papers in Philosophy

Posted by Tony Marmo at 07:48 BST
Updated: Thursday, 16 June 2005 07:59 BST
Friday, 10 June 2005


Questioning Contextualism

By Brian Weatherson

There are currently a dizzying variety of theories on the market holding that whether an utterance of the form S knows that p is true depends on pragmatic or contextual factors. Even if we allow that pragmatics matters, there are two questions to be answered. First, which kind of pragmatic factors matter? Broadly speaking, the debate here is about whether practical interests (the stakes involved) or intellectual interests (which propositions are being considered) are most important. Second, whose interests matter? Here there are three options: the interests of S matter, the interests of the person making the knowledge ascription matter, or the interests of the person evaluating the ascription matter.
This paper is about the second question. I’m going to present some data from the behaviour of questions about who knows what that show it is not the interests of the person making the knowledge ascription that matter. This means the view normally known as contextualism about knowledge-ascriptions is false. Since that term is a little contested, and for some suggests merely the view that someone’s context matters, I’ll introduce three different terms for the three answers to the second question.
• Environmentalism – The interests of S, i.e. her environment, matter.
• Indexicalism – The interests of the person making the knowledge ascription matter, so ‘know’ behaves like an indexical term.
• Relativism – The interests of the person evaluating the knowledge ascription matter, so knowledge ascriptions are not true or false simpliciter but only relative to an evaluator.

Posted by Tony Marmo at 05:40 BST
Updated: Friday, 10 June 2005 05:42 BST
Saturday, 4 June 2005

This post is also available here.

The Stanley-Rett Debate

Nominal Restriction

By Jason Stanley

Extra-linguistic context appears to have a profound effect on the determination of what is expressed by the use of linguistic expressions. For a bewildering range of very different linguistic constructions, adhering to relatively straightforward linguistic intuition about what is expressed leads us to the conclusion that facts about the nonlinguistic context play many different roles in determining what is said. Furthermore, that so many different constructions betray this sort of sensitivity to extra-linguistic context understandably leads to pessimism about rescuing the straightforward intuitions while preserving any sort of systematicity in the theory of meaning.
A presumption motivating the pessimistic inclination is that, if we accept the ordinary intuitions, what appears to be very different ways in which context affects semantic content in fact are different ways in which context affects linguistic content. Pessimism is a natural reaction to those who adopt this presumption, because if appearance is a good guide to the facts in this domain, then there are just too many ways in which context affects semantic content to preserve systematicity. One common and natural reaction to these facts is, therefore, to deny the semantic significance of the ordinary intuitions, thereby relegating the project of explaining the apparent effects of extra-linguistic context on semantic content to a domain of inquiry outside the theory of meaning proper. So doing removes the threat context poses to the systematicity of semantic explanation, but at the cost of reducing the interest of the semantic project.
In this paper, I explore a different reaction to the situation. My purpose is to undermine the presumption that what appear to be very different effects of context on semantic content are very different effects. My challenge is of necessity rather limited, since it is too implausible to trace all effects of extra-linguistic context on semantic content to the very same source. Rather, I will take, as a case study, three superficially very different effects of context on semantic content, and show that they are due to the very same mechanism, what I call Nominal Restriction. I thereby hope to provide convincing evidence of the promise of the project of reducing all apparent effects of context on semantic content to a small number of sources.

Published in Logical Form and Language, edited by Peters and Preyer, Oxford University Press (2002)

Context, Compositionality and Calamity

By Jessica Rett

This paper examines an attempt made in a series of articles (Stanley 2002, a.o.) to create a syntactic placeholder for contextual information. The initial shortcoming of Stanley’s proposal is that it does not easily integrate these placeholders with domain-restricting information syntactically encoded elsewhere in the utterance. Thus, Stanley erroneously predicts that a sentence in which quantifier restricting information encoded in (for example) a prepositional phrase conflicts with quantifier-restriction valued by context is internally incoherent.
I continue by exploring the space of possible solutions to this problem that are available to Stanley, demonstrating how each of these possible solutions results in its own interpretation problem and, ultimately, fails. In doing so, I argue that Stanley’s syntactic/semantic approach to context is ultimately untenable.

Source: Semantics Archive
To appear in Mind & Language

Of related interest:

Context Dependence and Compositionality

By Francis Jeffrey Pelletier

Some utterances of sentences such as ?Every student failed the midterm exam? and ?There is no beer? are widely held to be true in a conversation despite the facts that not every student in the world failed the midterm exam and that there is, in fact, some beer somewhere. For instance, the speaker might be talking about some particular course, or about his refrigerator. Stanley and Szabo (in Mind & Language , 15, 2000) consider many different approaches to how contextual information might give meaning to these ?restricted quantifier domains?, and find all of them but one wanting. The present paper argues that their considerations against one of these other theories, considerations that turn on notions of compositionality, are incorrect.

Appeared in Mind & Language, April 2003, vol. 18, no. 2, pp. 148-161(14)

Posted by Tony Marmo at 00:01 BST
Updated: Saturday, 4 June 2005 12:55 BST

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