Walter the banker: the conjunction fallacy reconsidered,Stephan Hartmann · Wouter Meijs

Abstract

In a famous experiment by Tversky and Kahneman (Psychol Rev 90:293–

315, 1983), featuring Linda the bank teller, the participants assign a higher probability

to a conjunction of propositions than to one of the conjuncts, thereby seemingly committing

a probabilistic fallacy. In this paper, we discuss a slightly different example

featuring someone namedWalter, who also happens to work at a bank, and argue that,

in this example, it is rational to assign a higher probability to the conjunction of suitably

chosen propositions than to one of the conjuncts. By pointing out the similarities

between Tversky and Kahneman’s experiment and our example, we argue that the participants

in the experiment may assign probabilities to the propositions in question in

such a way that it is also rational for them to give the conjunction a higher probability

than one of the conjuncts.

VII Congreso de la Sociedad de Lógica, Metodología y Filosofía de la Ciencia en España

VII Congreso de la Sociedad de Lógica, Metodología y Filosofía de la Ciencia en España

VII CONGRESO DE LA SOCIEDAD DE LÓGICA, METODOLOGÍA Y FILOSOFÍA DE LA CIENCIA EN ESPAÑA La Sociedad de Lógica, Metodología y Filosofía de la Ciencia en España y el Departamento de Lógica y Filosofía Moral de la Universidad de Santiago de Compostela organizan el VII Congreso de la mencionada sociedad que se celebrará en Santiago de Compostela del 18 al 20 de julio de 2012. Como novedad, este congreso de la Sociedad incorpora la celebración de la serie CONFERENCIAS LULIUS de la Sociedad de Lógica y Filosofía de la Ciencia en España. Esta serie de conferencias contará con la presencia de filósofos de prestigio que den a conocer sus últimos trabajos en el seno de nuestra Sociedad. En su primera edición las conferencias correrán a cargo de Philip Kitcher (Columbia University). Las conferencias se distribuirán a lo largo de los tres días de duración del congreso en sesión plenaria. Además, desde la Junta directiva de la SLMFCE se organizará un simposio dedicado a analizar la obra de Philip Kitcher. INFORMACIÓN GENERAL Fechas: 18-20 de Julio de 2012 Lugar de celebración: http://www.usc.es/opencms/es/centros/filosofia/ Facultad de Filosofía Praza de Mazarelos, s/n 15782 Santiago de Compostela, España Organizan: - Sociedad de Lógica, Metodología y Filosofía de la Ciencia en España (SLMFCE) - Departamento de Lógica y Filosofía Moral de la Universidad de Santiago de Compostela. Comité organizador: Concha Martínez Vidal (Presidenta del congreso, Universidad de Santiago de Compostela),  José Luis Falguera López (Secretario, Universidad de Santiago de Compostela), Xavier de Donato (Vocal, Universidad de Santiago de Compostela), José Miguel Sagüillo Fernández-Vega (Vocal, Universidad de Santiago de Compostela), María José Frápolli Sanz (Vocal, Universidad de Granada, Presidenta de la SLMFCE), Pierdaniele Giaretta (Vocal, Universidad degli Studi di Padova), Stephen McLeod (Vocal, University of Liverpool), Sofía Miguens (Vocal, Universidade de Porto), Uxía Rivas Monroy (Vocal, Universidad de Santiago de Compostela), Alejandro Sobrino Cerdeiriña (Vocal, Universidad de Santiago de Compostela),  Charles Travis (King?s College/ Porto), Juan Vázquez Sánchez (Vocal, Universidad de Santiago de Compostela), Jesús Vega Encabo (Vocal, Universidad Autónoma de Madrid, Secretario de la SLMFCE), Víctor Verdejo Aparicio (Vocal, Universidad de Santiago de Compostela), Luis Villegas (Vocal, Universidad de Santiago de Compostela). Comité científico: Juan José Acero (Universidad de Granada), John Corcoran (Buffalo University, EEUU), Javier Echeverría (Ikerbasque/ Universidad del País Vasco), Manuel García-Carpintero (Universidad de Barcelona), María Manzano (Universidad de Salamanca), Grzegorz Malinowski (Universidad de Lódz, Polonia), C. Ulises Moulines (Ludwig-Maximilians-Universität de München, Alemania), León Olivé  (Universidad Nacional Autónoma de México), Javier Ordoñez (Universidad Autónoma de Madrid), Stewart Shapiro (Ohio University/St Andrews University). Comunicaciones y simposios: Serán bienvenidas las comunicaciones y propuestas de simposios en español, gallego o inglés, sobre estas secciones: A. Lógica, historia y filosofía de la lógica B. Filosofía del lenguaje, filosofía de la mente, epistemología C. Filosofía y metodología de la ciencia D. Historia de la ciencia E. Ciencia, tecnología y sociedad *Fecha límite para la recepción de los resúmenes de comunicaciones y simposios: 15 de marzo de 2012. *Fecha límite para la comunicación de aceptación de comunicaciones: 22 de abril de 2012. *La fecha límite para la recepción de la versión definitiva de las comunicaciones y presentaciones a simposios aceptadas (a efectos de su publicación en las actas) será el 3 de junio de 2012. (Máximo 2.000 palabras, Times New Roman 12, doble espacio, en formato Word). Se reservará para cada comunicación aceptada un tiempo de exposición de 30 minutos, discusión incluida. Se reservará para cada simposio aceptado un tiempo máximo de 2 horas con la participación máxima de 5 personas. Las propuestas de comunicaciones y simposios se remitirán electrónicamente a: https://www.easychair.org/conferences/?conf=7thslmfce Para garantizar la revisión ciega de las comunicaciones y simposios, se ruega que el correspondiente resumen o propuesta se suba en un documento en el que no figure el nombre del autor o autores. Los resúmenes de las comunicaciones deberán tener una extensión de 1.000 palabras, en Times New Roman 12, y a doble espacio (se admiten varios formatos de documento). En el caso de las propuestas de simposio, deberá incluirse en el documento un breve resumen de la presentación de cada interviniente (sin incluir sus nombres en el resumen) y una justificación del interés del mismo. Para garantizar la evaluación ciega, los nombres de los autores de las comunicaciones y de los intervinientes en los simposios quedarán registrados en el sistema independientemente del resumen o propuesta. PREMIOS/BOLSAS DE VIAJE PARA JÓVENES INVESTIGADORES  Con el fin de seguir incentivando el trabajo de jóvenes investigadores, la SLMFCE convoca tres premios-bolsas de viaje para las tres mejores contribuciones al congreso por parte de investigadores jóvenes. Los candidatos deben cumplir las siguientes condiciones: (a) ser estudiante de máster o doctorado, o haber defendido la tesis doctoral en los tres últimos años a contar desde el plazo de envío de comunicaciones, es decir, haber defendido la tesis con posterioridad al 31 de mayo del 2009. (b) ser socio de la Sociedad o asociarse a la misma en el momento en que se envíe la comunicación. (c) obtener una evaluación de Excelente en la evaluación ciega de su contribución llevada a cabo por el comité científico del congreso. La dotación de la ayuda será para cubrir los gastos ocasionados por el viaje, alojamiento e inscripción del congreso, hasta un máximo de 500 euros para cada premiado.  La SLMFCE acreditará documentalmente la obtención del premio. En caso de que haya más de tres candidatos que cumplan las condiciones y que presenten trabajos de alta calidad, el comité organizador podrá dividir la suma total disponible (1500 euros) entre todos aquellos que sean considerados merecedores del premio.  Más información: Las novedades sobre el congreso irán apareciendo en la página de la Sociedad(http://www.solofici.org/) o en la del Departamento  (http://dlvisit.usc.es/dloxfmrl/pub/Index) y eventualmente en la propia del congreso. Puede obtenerse información adicional sobre alojamiento y viaje en http://www.santiagoturismo.com/ Para solicitar cualquier información sobre el congreso también puede dirigirse a: Para más información.AQUI 1) Por correo electrónico: viislmfce@usc.es 2) Por correo ordinario: VII Congreso de la SLMFCE Departamento de Lógica y Filosofía Moral Facultad de Filosofía Universidade de Santiago de Compostela Praza de Mazarelos,  s/n 15782 SANTIAGO DE COMPOSTELA

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

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.

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