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LINGUISTIX&LOGIK, Tony Marmo's blog
Friday, 1 June 2007


Sylvan's Box: A Short Story and Ten Morals

By Graham Priest

The paper contains a short story which is inconsistent, essentially so, but perfectly intelligible. The existence of such a story is used to establish various views about truth in fiction and impossible worlds.

Source: Notre Dame Journal of Formal Logic Volume 38, Number 4 (1997), 573-582.
 Check peer's review here

Posted by Tony Marmo at 18:45 BST
Updated: Friday, 1 June 2007 18:58 BST


Properties and Paradox in Graham Priest's

Towards Non-Being


 By Daniel Nolan
Graham Priest's book is a treasure-trove, with many interesting things to discuss, but in these remarks, I want to address two main questions.  The first concerns what properties and relations Priest's non-existent objects should have simpliciter.  The second is the question of whether Priest's framework needs dialetheism - should the framework only be attractive to those who accept true contradictions?  In these remarks I plan to grant, for the sake of discussion at least, that there are non-existent objects.  I take it that the question of whether there really are things that don't exist is one that is to be settled once  we see how well the rival theories do - and so developing a theory of non-existent objects seems to me an important preliminary to the judgement of whether there are, after all, such things.


To appear in a book symposium in Philosophy and Phenomenological Research.

Source: Online Papers in Philosophy 

Posted by Tony Marmo at 09:21 BST
Updated: Friday, 1 June 2007 09:46 BST

A Consistent Reading of Sylvan's Box
By Daniel Nolan

This paper argues that Graham Priest's story Sylvan's Box has an attractive, consistent reading. Priest's hope to use that story as an example of a non-trivial essentially inconsistent story is thus threatened. The paper then makes some observations about the role Sylvan's Box might play in a theory of unreliable narrators.
Source: Online Papers in Philosophy 

Posted by Tony Marmo at 09:01 BST
Updated: Friday, 1 June 2007 09:30 BST
Friday, 20 April 2007

Inconsistency Theories:
The Importance of Being Metalinguistic
By Douglas Patterson 
This is a discussion of different ways of working out the idea that the semantic paradoxes show that natural languages are somehow 'inconsistent'. I take the workable form of the idea to be that there are expressions such that a necessary condition of understanding them is that one be inclined to accept inconsistent claims (a conception also suggested by Matti Eklund). I then distinguish 'simple' from 'complex' forms of such views. On a simple theory, such expressions are meaningless, while on a complex theory they are not. I argue that complex theories are incompatible with truth conditional semantics and that simple theories are only coherent when the inconsistent claims are metalingusitic attributions of meaning. I close with a discussion of the version of the simple metalinguistic theory I have defended in 'Understanding the Liar' and other papers.
Source: Online Papers in Philosophy 

Posted by Tony Marmo at 08:41 BST
Updated: Friday, 20 April 2007 08:50 BST
Sunday, 29 October 2006



By Janusz Ciuciura

In the late forties, Stanislaw Jaskowski published two papers on the discursive (or discussive) sentential calculus, D2. He provided a definition of it by an interpretation in the language of S5 of Lewis. The known axiomatization of D2 with discursive connectives as primitives was introduced by da Costa, Dubikajtis and Kotas in 1977. It turns out, however, that one of the axioms they used is not a thesis of the real Ja?›kowski's calculus. In fact, they built a new system, D*2 for short, that differs from D2 in many respects. The aim of this paper is to introduce a direct Kripke-type semantics for the system, axiomatize it in a new way and prove soundness and completeness theorems. Additionally, we present labeled tableaux for D*2.

Keywords: discursive (discussive) logic, D2, paraconsistent logic, labelled tableaux.
Published in Logic and Logical Philosophy, Volume 14 (2005), 235-252

Posted by Tony Marmo at 01:47 BST
Saturday, 8 April 2006


Flexible Temporal Consistency for Fixed-Time Constraint Verification in Grid Workflow Systems

By Jinjun Chen & Yun Yang

To verify fixed-time constraints in grid workflow systems, the consistency and inconsistency conditions have been defined in the conventional work. However, in this paper, we argue that although the conventional consistency condition is reasonable, the conventional inconsistency condition is too rigorous and covers several different situations. These situations which are handled conventionally by the same exception handling should be handled differently for cost saving. Therefore, we divide the conventional inconsistency into weak consistency,weak inconsistency and strong inconsistency and treat the conventional consistency as strong consistency. Correspondingly, we discuss how to verify them. Especially, for the weak consistency, we present a method on how to adjust it to the strong consistency. For the weak inconsistency, we analyse why it can be handled by simpler and more economical exception handling. The final comparison and discussion further demonstrate that our research can achieve better cost effectiveness than the conventional work.

Appeared in Lecture Notes in Computer Science, Volume 3795 / 2005

Posted by Tony Marmo at 01:16 BST
Updated: Saturday, 8 April 2006 01:18 BST
Wednesday, 3 August 2005


An Inconsistency in Direct Reference Theory

By George Bealer

My goal [here] is to expose a series of internal difficulties in direct reference theory, ultimately revealing an inconsistency which concerns neither meaning nor the propositional attitudes but rather our standard logic of identity itself. I will not focus on specific formulations, such as those put forward at one time or another by David Kaplan, John Perry, Jon Barwise, Nathan Salmon, Scott Soames, Mark Richard, Mark Crimmins, and many others. By the end it should nonetheless be evident that direct reference theory’s basic tenets make this inconsistency inevitable.

Source: Online Papers in Philosophy

Posted by Tony Marmo at 03:44 BST
Friday, 8 July 2005


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


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


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


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
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
Sunday, 8 May 2005

Another interesting introduction to Paraconsistent Logic:


By Anthony Hunter
In practical reasoning, it is common to have “too much” information about some situation. In other words, it is common for there to be classically inconsistent information in a practical reasoning database [Besnard et al., 1995]. The diversity of logics proposed for aspects of practical reasoning indicates the complexity of this form of reasoning. However, central to practical reasoning seems to be the need to reason with inconsistent information without the logic being trivialized [Gabbay and Hunter, 1991; Finkelstein et al., 1994]. This is the need to derive reasonable inferences without deriving the trivial inferences that follow the ex falso quodlibet proof rule that holds in classical logic.
[Ex falso quodlibet]
α ¬α

So for example, from a database {α, ¬α, α→β, δ} reasonable inferences might include α, ¬α, α→β, and δ by reflexivity, β by modus ponens, α^;β by introduction, ¬α→¬β and so on. In contrast, trivial inferences might include γ, γ^¬δ, etc, by ex falso quodlibet.
Solutions to the problem of inconsistent data include database revision and
paraconsistent logics. The first approach effectively removes data from the database to produce a new consistent database. In contrast, the second approach leaves the database inconsistent, but prohibits the logics from deriving trivial inferences. Unfortunately, the first approach means we may loose useful information— we may be forced to make a premature selection of our new database, or we may not even be able to make a selection. We consider here the advantages and disadvantages of the paraconsistent approach.
The primary objective of this chapter is to present a range of paraconsistent logics that give sensible inferences from inconsistent information.

Posted by Tony Marmo at 09:36 BST
Saturday, 12 March 2005

Now Playing: REPOSTED

Supervaluationism and Paraconsistency

by Achille C. Varzi

Supervaluational semantics have been applied rather successfully to a variety of phenomena involving truth-value gaps, such as vagueness, lack of reference, sortal incorrectedness. On the other hand, they have not registered a comparable fortune (if any) in connection with truth-value gluts, i.e., more generally, with semantic phenomena involving overdeterminacy or inconsistency as opposed to indeterminacy and incompleteness. In this paper I review some basic routes that are available for this purpose. The outcome is a family of semantic systems in which (i) logical truths and falsehoods retain their classical status even in the presence gaps and gluts, although (ii) the general notions of satifiability and refutability are radically non-classical .

Posted by Tony Marmo at 00:01 GMT
Updated: Sunday, 13 March 2005 01:04 GMT


Paraconsistent logic from a modal viewpoint

By Jean-Yves Beziau

In this paper we study paraconsistent negation as a modal operator, considering the fact that the classical negation of necessity has a paraconsistent behavior. We examine this operator on the one hand in the modal logic S5 and on the other hand in some new four-valued modal logics.

Keywords: Modal logic; Paraconsistent logic; Negation; Square of opposition

Appeared at the Journal of Applied Logic.

Posted by Tony Marmo at 00:01 GMT
Updated: Sunday, 13 March 2005 01:05 GMT

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