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Claudio Conforti

miércoles, 30 de noviembre de 2011

Logic, Epistemology and the Unity of Science, Vol 25: Between Logic and Reality

Majda Trobok · Nenad Mišcevi ˇ c´ · Berislav Žarnic´
Editors
Between Logic and Reality

Modeling Inference, Action
and Understanding


Preface
The papers collected in this book analyse the logic-mathematics-reality relationship
from different approaches and perspectives. It connects logical theory with more
concrete issues of rationality, normativity and understanding, thus pointing to a wide
range of potential applications.
Let us say a few words about the context in which the book was created. Continuing a longer tradition that started in the 1980s by the members of the Rijeka Analytic
Philosophy Circle (V. Muškardin, N. Smokrovic, B. Ber ´ ciˇ c, S. Priji ´ c-Samaržja, the ´
editors of the present volume, and others), the Department of Philosophy at the
University of Rijeka has been active in organizing international philosophical conferences and other philosophical events in Croatia establishing thus global and vital
connections between the philosophers from all sides of the world with those from
the local region, in particular those coming from academic communities in Bulgaria,
Croatia, Hungary, Italy, Serbia and Slovenia. Thanks to its cosmopolitan atmosphere
and a regard for logic, the Department of Philosophy at University of Rijeka, the
only analytic department of philosophy in Croatia, has provided a supporting environment for promoting logico-philosophical research. The book originated from two
recent conferences that took place in Rijeka.

We were also lucky to have on our side the hospitality of the Inter-University
Center Dubrovnik, where we organized or helped organizing a series of conferences,
most notably the yearly courses/conferences Analytic Philosophy: Epistemology
and Metaphysics, in particular the 2010 conference The Philosophy of Logical Consequence organized by Stewart Shapiro, and the Mind, World and Action course.
Also, two larger scientific projects funded by the Ministry of Science, Education
and Sports of Republic of Croatia have offered further institutional framework for
the initiatives that have led to the assembling of the book: Logic and Reality, and
Logical Structures and Intentionality.


Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1
Majda Trobok, Nenad Mišcevi ˇ c, and Berislav Žarni ´ c´

Part I Logical and Mathematical Structures
2 Life on the Ship of Neurath: Mathematics in the Philosophy
of Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
Stewart Shapiro
3 Applied Mathematics in the Sciences . . . . . . . . . . . . . . . . . . . . . . . . . . . .  29
Dale Jacquette
4 The Philosophical Impact of the Löwenheim-Skolem Theorem . . . . .  59
Miloš Arsenijevic´
5 Debating (Neo)logicism: Frege and the Neo-Fregeans . . . . . . . . . . . . . .  83
Majda Trobok

Part II Epistemology and Logic
6 Informal Logic and Informal Consequence . . . . . . . . . . . . . . . . . . . . . . .  101
Danilo Šuster
7 Logical Consequence and Rationality . . . . . . . . . . . . . . . . . . . . . . . . . . . .  121
Nenad Smokrovic´
8 Logic, Indispensability and Aposteriority . . . . . . . . . . . . . . . . . . . . . . . .  135
Nenad Mišcevi ˇ c´

Part III Dynamic Logical Models of Meaning
9 Extended Game-Theoretical Semantics . . . . . . . . . . . . . . . . . . . . . . . . . .  161
Manuel Rebuschi
10 Dynamic Logic of Propositional Commitments . . . . . . . . . . . . . . . . . . .  183
Tomoyuki Yamada

sábado, 19 de noviembre de 2011

Logical Constants: a pragmatist approach María José Frapolli & Stavros Assimakopulos

Abstract
There is currently no general definition of logical constanthood with which all philosophers of logic agree. In this paper, we address this issue by putting forward a proposal regarding the distinctive feature of logical constants. Our background position is that by focusing too much on structural features, we have forgotten central aspects of the original motivation that gave rise to the modern study of logic along Fregean/Peircian lines. On the basis of this realization, we argue that a logical constant has to be seen as encoding some kind of dynamic meaning, which marks the presence of an inferential transition among propositional contents. Following a pragmatist rationale, according to which some notion can be identified as a logical constant by considering the way in which it is used in our everyday reasoning practices, we put forth a characterization of logical constants that takes into account their syntactic, semantic and pragmatic roles. What follows from our proposal is that logical constanthood can be best understood as a functional property that is satisfied only by certain uses of the natural-language counterparts of the conditional, negation, disjunction and the compound of conditional-plus-quantifiers. After briefly discussing these cases, we turn to conjunction in order to show why it needs to be excluded from our set of genuine logical constants.

miércoles, 16 de noviembre de 2011

Reference to numbers in natural language Friederike Moltmann

Abstract A common view is that natural language treats numbers as abstract
objects, with expressions like the number of planets, eight, as well as the number
eight acting as referential terms referring to numbers. In this paper I will argue that
this view about reference to numbers in natural language is fundamentally mistaken.
A more thorough look at natural language reveals a very different view of the
ontological status of natural numbers. On this view, numbers are not primarily
treated abstract objects, but rather ‘aspects’ of pluralities of ordinary objects,
namely number tropes, a view that in fact appears to have been the Aristotelian view
of numbers. Natural language moreover provides support for another view of the
ontological status of numbers, on which natural numbers do not act as entities, but
rather have the status of plural properties, the meaning of numerals when acting like
adjectives. This view matches contemporary approaches in the philosophy of
mathematics of what Dummett called the Adjectival Strategy, the view on which
number terms in arithmetical sentences are not terms referring to numbers, but
rather make contributions to generalizations about ordinary (and possible) objects.
It is only with complex expressions somewhat at the periphery of language such as
the number eight that reference to pure numbers is permitted.

Keywords Numbers Abstract objects Tropes Frege Referential terms
Adjectival Strategy Abstraction

The Nature of Information: A Relevant Approach Edwin Mares

Introduction
In (Mar09), I advocate replacing the notion of a truth condition in the
semantics for relevant logic with the notion of an information condition.
In the present paper, I explore the notion of information that underlies
this reading of the semantics and explain my motivations for using it.
In (Mar09) I use an objective notion of information. In this paper
I give a more detailed characterization of the notion of objective in-
formation and outline how it …ts with the semantics for relevant logic.
The notion of objective information is of information that is available
in an environment, as opposed to information that is available in one’s
mind or in a database. The key notion here is that of availability in an
environment, and I try in this paper to make that notion rather precise.
As we shall see, I am very liberal in my understanding of availability,
and this liberality is important to the relationship between information
in the present sense and logic.
The notion of information itself, although interesting, is only a means
to an end for me. I want it to be a central feature of a semantics for a
logical system. So, after my general remarks on the nature of availabil-
ity, I outline how the notion of objective information is incorporated
into the interpretation of the semantics for relevant logic. But before I
do this, I present a natural deduction formulation of relevant logic. This
natural deduction formulation itself not only provides a target system
for the semantics to characterize, but also helps with the interpretation
of the semantics itself. The natural deduction system helps to explain
what sort of information can be used to support inferences and how it
can be used in this way.

“Inference versus consequence” revisited: inference, consequence, conditional, implication Göran Sundholm

Abstract Inference versus consequence, an invited lecture at the LOGICA 1997
conference at Castle Liblice, was part of a series of articles for which I did research
during a Stockholm sabbatical in the autumn of 1995. The article seems to have been
fairly effective in getting its point across and addresses a topic highly germane to the
Uppsala workshop. Owing to its appearance in the LOGICA Yearbook 1997, Filosofia
Publishers, Prague, 1998, it has been rather inaccessible. Accordingly it is republished
here with only bibliographical changes and an afterword.

Keywords Inference · Consequence · Validity · Judgement · Proposition ·
Type theory