Now Playing: UPDATED
Topic: PARACONSISTENCY
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.

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February the 17^th 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.

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

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

Now Playing: FROM COUNTERFACTUALS WEEK (UPDATED)
Topic: HUMAN SEMANTICS

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

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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).

Topic: HUMAN SEMANTICS

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

Topic: GENERAL LOGIC

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

Topic: HUMAN SEMANTICS

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

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