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LINGUISTIX&LOGIK, Tony Marmo's blog
Sunday, 12 September 2004


Underdetermination and Meaning Indeterminacy:

What is the Difference?

by Ian McDiarmid

Source: PhilSci Archive

The first part of this paper discusses Quine's views on underdetermination of theory by evidence, and the indeterminacy of translation, or meaning, in relation to certain physical theories. The underdetermination thesis says different theories can be supported by the same evidence, and the indeterminacy thesis says the same component of a theory that is underdetermined by evidence is also meaning indeterminate. A few examples of underdetermination and meaning indeterminacy are given in the text. In the second part of the paper, Quine's scientific realism is discussed briefly, along with some of the difficulties encountered when considering the `truth' of different empirically equivalent theories. It is concluded that the difference between underdetermination and indeterminacy, while significant, is not as great as Quine claims. It just means that after we have chosen a framework theory, from a number of empirically equivalent ones, we still have further choices along two different dimensions.


Posted by Tony Marmo at 01:01 BST
Updated: Tuesday, 14 September 2004 15:14 BST
Saturday, 11 September 2004


Semantics for more plausible
deontic logics

By Sven Ove Hansson

In order to avoid the paradoxes of standard deontic logic, we have to give up the semantic construction that identifies obligatory status with presence in all elements of a subset of the set of possible worlds. It is proposed that deontic logic should instead be based on a preference relation, according to the principle that whatever is better than something permitted is itself permitted. Close connections hold between the logical properties of a preference relation and those of the deontic logics that are derived from it in this way. The paradoxes of SDL can be avoided with this construction, but it is still an open question what type of preference relation is best suited to be used as a basis for deontic logic.


Posted by Tony Marmo at 20:28 BST


An Intensional Schr?dinger Logic

By Newton C. A. da Costa and D?cio Krause
Source: Notre Dame J. Formal Logic 38 (1997), no. 2, 179-194

We investigate the higher-order modal logic SwI, which is a variant of the system Sw presented in our previous work. A semantics for that system, founded on the theory of quasi sets, is outlined. We show how such a semantics, motivated by the very intuitive base of Schr?dinger logics, provides an alternative way to formalize some intensional concepts and features which have been used in recent discussions on the logical foundations of quantum mechanics; for example, that some terms like 'electron' have no precise reference and that 'identical' particles cannot be named unambiguously. In the last section, we sketch a classical semantics for quasi set theory.


General Logic
See also on Kai von Fintel's blog:
Klement on Logical Grammar in Frege, Russell, and Wittgenstein.

Posted by Tony Marmo at 01:01 BST
Updated: Saturday, 11 September 2004 20:12 BST
Friday, 10 September 2004


Semantic Properties of Split Topicalization in German

By Kimiko Nakanishi

Source: Semantics Archive

This paper examines semantic properties of measure phrases (MPs), in particular, MPs adjacent to their host NP (non-split MPs) and MPs split from their host NP in Split Topicalization (split MPs). I show that both non-split and split MPs are subject to semantic restrictions on the nominal domain, while only split MPs are subject to restrictions on the verbal domain. I argue that this is because non-split MPs measure in the nominal domain (the amount of individuals in the extension of the nominal predicate), while split MPs measure in the verbal domain (the amount of events in the extension of the verbal predicate). The present analysis reveals that there is an algebraic parallelism between the nominal and verbal domains. Furthermore, this analysis can be extended to various cross-linguistic constructions.


Posted by Tony Marmo at 17:18 BST
Updated: Friday, 10 September 2004 17:22 BST

The Semantics and Pragmatics of the Russian Factual Imperfective

by Atle Gr?n
Source: Semantics Archive


Posted by Tony Marmo at 17:08 BST
Updated: Friday, 10 September 2004 17:19 BST


On Comparative Quantification in the Verbal Domain

Kimiko Nakanishi

Source: Semantics Archive

The central goal of this paper is to provide a mechanism of comparative
quantification in the verbal domain, where the degree of comparison is associated
with an event argument. The empirical data comes from the comparative
construction in Japanese with sugiru, which is an intransitive verb meaning eto pass,
to exceedi, as in (1)a. Sugiru can attach to an adjective or a verb and express
excessiveness just like too in English, as in (1)b-c.


Posted by Tony Marmo at 16:56 BST


Domains of Measurement: Formal Properties of Non-Split/Split Quantifier Constructions

by Kimiko Nakanishi

Source: Semantics Archive

This dissertation examines the semantics and the syntax-semantics interface properties of constructions involving measurement _ namely, non-split and split quantifier constructions in Japanese and German, and comparative constructions in Japanese and English. One of my central goals is to investigate formal properties of these measurement constructions. I show that these constructions can be categorized into two classes based on Schwarzschildis (2002) notion of emonotonicityi, where a measure function is monotonic relative to the denotation of some element if and only if a measure obtained for that element is larger than a measure obtained for proper subparts of it.

In particular, while non-split quantifier constructions are monotonic to the denotation of a nominal predicate, split quantifier constructions and the relevant comparative constructions are monotonic to the denotation of a verbal predicate. The monotonicity analysis further extends to other cross-linguistic measurement constructions, suggesting that monotonicity is a formal property of a wide range of measurement constructions. The two groups of constructions categorized by monotonicity differ in their domains of measurement: the constructions with nominal monotonicity measure in the nominal domain and the constructions with verbal monotonicity measure in the verbal domain. In split quantifier constructions, the split quantifier syntactically combines with, and semantically operates on, a verbal predicate, yet there is a strong intuition that it somehow measures a nominal predicate as well. This intuition is captured by using a homomorphism (i.e. a structure-preserving mapping) from events to individuals, which makes the split quantifier indirectly measure events by measuring individuals. With this mechanism, it is possible to maintain the compositionality of grammar. Furthermore, the proposed mechanism enables us to satisfactorily account for three characteristic semantic properties of constructions involving measurement in the verbal domain, namely, incompatibility with single-occurrence events, incompatibility with individual-level predicates, and (un)availability of collective readings. The proposed analysis also accounts for the cross-categorial distribution of measure phrases (e.g. two feet of rope, walk two feet, two feet long). A distinction is made between measure phrases and measure functions: while measure phrases are always predicates of scalar intervals (Schwarzschild 2002), measure functions are cross-categorial.


Posted by Tony Marmo at 16:45 BST
Updated: Friday, 10 September 2004 16:50 BST


The Correspondence Theory and Its Critics

By Gerald Vision

In Veritas, Gerald Vision defends the correspondence theory of truth -- the theory that truth has a direct relationship to reality -- against recent attacks, and critically examines its most influential alternatives. The correspondence theory, if successful, explains one way in which we are cognitively connected to the world; thus, it is claimed, truth -- while relevant to semantics, epistemology, and other studies -- also has significant metaphysical consequences. Although the correspondence theory is widely held today, Vision points to an emerging orthodoxy in philosophy that claims that truth as such carries no significant weight in philosophical explanations.

He devotes much of the book to a criticism of that outlook and to a less vulnerable formulation of the correspondence theory. Vision defends the correspondence theory by both presenting evidence for correspondence and examining the claims made by such alternative theories as deflationism, minimalism, and pluralism. The techniques of the argument are thoroughly analytic, but the problem confronted is broadly humanistic. The question examined -- how we, as thinking beings, are connected to and manage to cope in a world that was not designed for our comfort or convenience -- is more likely to be raised by continentalists, but is approached here with the tools of clarity and precision more highly prized in analytic philosophy. The book seeks to avoid both the obscurantism that infects much continental thought and the overly technical concerns and methodology that limit the interest of much work in analytic philosophy. It thus provides a rigorous but largely nontechnical treatment of the topic that will be of interest not only to readers familiar with philosophy but also to those with a background in literary theory and linguistics.


Posted by Tony Marmo at 02:09 BST
Updated: Friday, 10 September 2004 02:11 BST
Thursday, 9 September 2004




da Costa & Krause
(excerpt, page 5)

It should be remarked that in the `classical world', which at first glance can be described by using standard logic and mathematics, if alpha and beta are both theses or theorems of a theory (founded on classical logic), then alpha & beta is also a thesis of that theory. This is what we intuitively mean when we say that on the grounds of classical logic, a true proposition cannot `exclude' another true proposition.

In classical logic, if from some group Delta1 of axioms of a theory T we deduce gamma, and if from another group Delta2 we deduce non-gamma, then gamma & non-gamma is also deductible in T.

Normally, our group Delta of axioms of T is finite, so that we may talk of the conjunction of its sentences instead of Delta itself. Then, if alpha and beta are respectively the conjunctions associated to Delta1 and Delta2, as above, we are looking for a theory T such that in T we may have alpha |- gamma and beta |- non-gamma, but in which gamma & non-gamma is not a theorem of T.

Therefore, our goal is to describe a way to formally avoid that Delta1 U Delta2 (or alpha&beta) entails a contradiction, since we do not intend to rule out `complementary situations'.

Posted by Tony Marmo at 01:53 BST
Updated: Thursday, 9 September 2004 01:57 BST


The Logic of Confusion

by Jean-Yves Beziau
The logic of confusion is a way to handle together incompatible viewpoints.
These viewpoints can be information data, physical experiments, sets of opinions or believes. Logics of confusion are obtained by generalizing Jaskowski-type semantics and combining it with many-valued semantics.

Keywords: paraconsistent logic, discussive logic, many-valued logic, quantum physics


Posted by Tony Marmo at 01:01 BST
Updated: Tuesday, 7 September 2004 01:15 BST
Tuesday, 7 September 2004


The Dialogical Dynamics of Adaptive Paraconsistency

Shahid Rahman & Jean Paul van Bendegem

The dialogical approach to paraconsistency as developed by Rahman and Carnielli ([1]), Rahman and Roetti ([2]) and Rahman ([3], [4] and [5]) suggests a way of studying the dynamic process of arguing with inconsistencies.
In his paper on Paraconsistency and Dialogue Logic ([6]) Van Bendegem suggests that an adaptive version of paraconsistency is the natural way of capturing the inherent dynamics of dialogues. The aim of this paper is to develop a formulation of dialogical paraconsistent logic in the spirit of an adaptive approach and which explores the possibility of eliminating inconsistencies by means of logical preference strategies.

One way to formulate paraconsistent logic within the dialogical approach as developed in Rahman and Carnielli ([1]), Rahman and Roetti ([2]) and Rahman ([4]) can be achieved in the following way. Assume that to the structural rules of the standard dialogical logic [i] we add the following:

Negative Literal Rule:
The Proponent is allowed to attack the negation of an atomic (propositional) statement (the so called negative literal) if and only if the Opponent has already attacked the same statement before.

This structural rule can be considered in analogy to the formal rule for positive literals. The idea behind this rule is the following: An inconsistency of the Opponent may be tolerated by using a type of charity principle. The inconsistency might involve different semantic contexts in which, say, aand ?ahave been asserted. Now, if the Opponent attacks ?awith ahe concedes thereby that there is some common context between ?aand awhich makes an attack on ?apossible. This allows the Proponent to attack the corresponding negation of the Opponent.

In Rahman and Carnielli ([1]) the logics produced by this rule were called Literal Dialogues , or shorter: L-D. In order to distinguish between the intuitionistic and the classical version Rahman and Carnielli wrote L-D i(for the intuitionistic version) and L-D c(for the classical version). To be precise we should call these logical systems literal dialogues with classical structural rules and literal dialogues with intuitionistic structural rules respectively.
The Proponent loses because he is not allowed to attack the move (5) (see negative literal rule). In other words the Opponent may have contradicted himself, but the semantic context of the negative literal is not available to the Proponent until the Opponent starts an attack on the same negative literal ?an attack which in this case will not take place.


Posted by Tony Marmo at 01:01 BST
Updated: Tuesday, 7 September 2004 16:52 BST



by Newton C. A. da Costa & D?cio Krause

Bohr's Principle of Complementarity is controversial and there has been much dispute over its precise meaning. Here, without trying to provide a detailed exegesis of Bohr's ideas, we take a very plausible interpretation of what may be understood by a theory which encompasses complementarity in a definite sense, which we term C-theories. The underlying logic of such theories is a kind of logic which has been termed `paraclassical', obtained from classical logic by a suitable modification of the notion of deduction. Roughly speaking, C-theories are non-trivial theories which may have `physically' incompatible theorems (and, in particular, contradictory theorems). So, their underlying logic is a kind of paraconsistent logic.

Keywords: Complementarity, Paraconsistency, Paraclassical Logic.


Posted by Tony Marmo at 01:01 BST
Updated: Thursday, 9 September 2004 02:00 BST
Monday, 6 September 2004



Roman Tuziak

Paraconsistent logic was introduced in order to provide the framework for inconsistent but nontrivial theories. It was initiated by J. Lukasiewicz (1910) in Poland and, independently, by N. A. Vasilev (1911-13) in Russia, but only in 1948 the first paraconsistent formal system was designed. Since then thousands of papers have been published in this field. Paraconsistency became one of the fastest growing branches of logic, due to its fruitful applications to computer science, information theory, and artificial intelligence. K. R. Popper touched on the problem in his paper ,,What is Dialectic?" (1940). Although only mentioned, his basic idea of the possibility of a formal system of such a logic was fresh and original. Another attempt of exploring the logic of contradiction, this time as a dual to intuitionistic logic, was made by Popper in his paper ,,On the Theory of Deduction I and II" (1948). The same idea was formalized by N. D. Goodman (1981) and developed by D. Miller (1993) under a label ,,Logic for Falsificationists".
Popper`s contribution to the subject of paraconsistent logic has not been properly recognized so far. Since Lukasiewicz`s and Vasilev`s works were still not translated into any West European languages in the 1940s, he should be undoubtedly regarded as an independent forerunner of paraconsistency. On the other hand, it seems tempting to adapt some of Popper`s other ideas for the theory of paraconsistent logic (the way it was done with Vasilev`s very general concepts) and, especially, for the theory of artificial intelligence.


Posted by Tony Marmo at 14:46 BST
Sunday, 5 September 2004


Paraconsistent Logics and Paraconsistency:
Technical and Philosophical Developments

by Newton C. A. da Costa, D?cio Krause & Ot?vio Bueno

Saying in a few words, paraconsistent logics (PL) are the logics that can be the logics of inconsistent but non-trivial theories. A deductive theory is paraconsistent if its underlying logic is paraconsistent. A theory is inconsistent if there is a formula (a grammatically well formed expression of its language) such that the formula and its negation are both theorems of the theory; otherwise, the theory is called consistent. A theory is trivial if all formulas of its language are theorems. Roughly speaking, in a trivial theory 'everything' (expressed in its language) can be proved. If the underlying logic of a theory is classical logic, or even any of the standard logical systems like intuitionistic logic, inconsistency entails triviality, and conversely. So, how can we speak of inconsistent but non trivial theories? Of course by exchanging the underlying logic to one which may admit inconsistency without making the system trivial. Paraconsistent logics do the job.
Let us remark that our use of terms like 'consistency', 'inconsistency', 'contradictory' and similar ones is syntactical, what is in accord with the original metamathematical terminology of Hilbert and his school. On the other hand, in order to treat such terms from the semantical point of view, in the field of paraconsistency, one must be able to build, for instance, a paraconsistent set theory beforehand. This is possible, as we shall see, although most semantics for paraconsistent logics are classical, i.e., constructed inside classical set theories. So, the best, to begin with, is to employ the above terms syntactically.

Source: CLE


See also:

Science and Partial Truth - A Unitary Approach to Models and Scientific Reasoning

by Newton C. A. da Costa & Steven French

Da Costa and French explore the consequences of adopting a 'pragmatic' notion of truth in the philosophy of science. Their framework sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate, as well as the nature of scientific models and their heuristic development.

Check it

Posted by Tony Marmo at 01:01 BST
Updated: Sunday, 5 September 2004 13:56 BST
Saturday, 4 September 2004


Towards a Logic for Pragmatics. Assertions and Conjectures

by Gianluigi Bellin and Corrado Biasi

The logic for pragmatics extends classical logic in order to characterize the logical properties of the operators of illocutionary force such as that of assertion and obligation and of the pragmatic connectives which are given an intuitionistic interpretation. Here we consider the cases of assertions and conjectures : the assertion that a mathematical proposition _ is true is justified by the capacity to present an actual proof of _, while the conjecture that _ is true is justified by the absence of a refutation of _. We give sequent calculi of type G3i and G3i m inspired by Girard's LU , with subsystems characterizing intuitionistic reasoning and some forms of classical reasoning with such operators. Extending Godel, McKinsey, Tarski and Kripke's translations of intuitionistic logic into S4 , we show that our sequent calculi are sound and complete with respect to Kripke's semantics for S4 .


See also
G. Bellin and Corrado Biasi.
Cut-Elimination for the logic of pragmatics
(This is work in progress, which summarizes dr Corrado Biasi's Tesi di Laurea. It substantially refines and develops the ideas and the direction of research presented at the IMLA-FLOC'02 conference.)


Posted by Tony Marmo at 01:01 BST
Updated: Saturday, 4 September 2004 12:03 BST

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