Pro g r ama Primer Simposio Internacional de Investigación
de Lógica y Argumentación
LUNES 7 DE NOVIEMBRE DE 2011
Sede: Universidad Autónoma de la Ciudad de México
Plantel San Lorenzo Tezonco
Calle Prolongación San Isidro 151
Col. San Lorenzo Tezonco
Del. Iztapalapa, México, D.F.
08:00 – 08:30 h
Registro: Laboratorio Filosófico
Salón C-308
08:30 – 09:00 h
Inauguración
Ágora
09:00 – 10:30 h
Conferencia Magistral:
Strategic Manoeuvring in Argumentative Discourse
Frans van Eemeren, UvA
Ágora
10:30 – 11:00 h
Receso
11:00 – 13:30 h
Mesa 1: Paraconsistencia: ¿Para qué? ¿Para quién?
Eje temático: Lógicas paraconsistentes: historia y aplicaciones
Coordinadora: Atocha Aliseda
Salón B-101
Paraconsistencia: Reflexiones sobre los sistemas C de Da Costa
Federico Marulanda
IIF-UMSNH
On the history of paraconsistency and paraconsistent logic
Itala M. L. D´Ottaviano
CLE-UNICAMP
Paraconsistencia y cambio científico: ¿un tratamiento racional de las
contradicciones?
David Gaytán
Academia B de Filosofía e Historia de las Ideas-UACM
13:30 – 15:30 h
Receso
15:30 – 17:30 h
Mesa 2: Lógica y lenguaje matemático
Eje temático: Filosofía de las matemáticas
Coordinador: Cristian Alejandro Gutiérrez Ramírez
Salón A-201
La lógica de las matemáticas: ¿primero o segundo orden?
Max Fernández de Castro Tapia
UAM-I
Los números--¿clases naturales? Una respuesta semántica
Javier García Salcedo
FFyL-UNAM
Teoremas de categoricidad para la teoría de conjuntos
Cristian Alejandro Gutiérrez Ramírez
FFyL-IIF-UNAM
17:30 – 17:45 h
Receso
17:45 – 20:00 h
Taller: The pragma-dialectical method of analyzing and evaluating
argumentative discourse
Frans van Eemeren, UvA
Salón A-201
MARTES 8 DE NOVIEMBRE DE 2011
Sede: Universidad Autónoma de la Ciudad de México
Centro Vlady
Calle Goya 63
Col. Insurgentes Mixcoac
Delegación Benito Juárez, México D.F.
09:00 – 10:30 h
Conferencia Magistral: El miedo a pensar
Una reflexión desde Fromm
Alejandro Herrera Ibáñez
IIF-UNAM
10:30 – 13:00 h
Mesa 3: Aplicaciones formales a la realidad
Eje temático: Lógica,matemáticas y realidad
Coordinador: Jesús Jasso Méndez
La justificación de la deducción
Dr. Pedro Ramos Villegas:
Academia B de Filosofía e Historia de las Ideas-UACM
Matemáticas y realidad. Una teoría de la aplicación matemática
Mtro. Jesús Jasso Méndez
Academia B de Filosofía e Historia de las Ideas-UACM
Lógicas no deductivas en argumentación jurídica
Dra. María Inés Pazos
Academia B de Filosofía e Historia de las Ideas-UACM
Lógica y dialéctica
Mtra. Natalia Luna Luna
Academia B de Filosofía e Historia de las Ideas-UACM
13:00 – 14:30 h
Conferencia Magistral:
Relations between the classical differential calculus and Da Costa’s
Paraconsistent differential calculus
Itala M. L. D´Ottaviano
CLE-UNICAMP
14:30 h Brindis de clausura del SIILA
Pro g r ama
XIV Encuentro Internacional de Didáctica de la Lógica
MIÉRCOLES 9 DE NOVIEMBRE DE 2011
Sede: Universidad Autónoma de la Ciudad de México
Plantel San Lorenzo Tezonco
Calle Prolongación San Isidro 151
Col. San Lorenzo Tezonco
Del. Iztapalapa, México, D.F.
08:00 – 08:30 h
Registro
Laboratorio Filosófico
Salón C-308
08:30 – 09:00 h
Inauguración
09:00 – 10:00 h
Homenaje al Dr. José Alfredo Amor y Montaño
10:00 – 10:30 h
Receso
10:30 – 12:00 h
Conferencia Magistral: Seis modelos de argumentación
Raymundo Morado
IIF-UNAM
Salón A-201
12:00 – 12:30 h
Receso
12:30 – 14:30 h
Mesa 1:
Análisis de modelos de argumentación
Salón A-201
Pertinencia del modelo de Toulmin en la esquematización de la
estrategia argumentativa para ensayos de nivel superior
Eva Paola Meléndez Pérez
UPAEP
Sobre la necesidad de la enseñanza complementaria de las lógicas
formal e informal
Ana Hilda García Gutiérrez
UACM
Reflexiones en torno a Las claves de la Argumentación de Antonhy Weston
Teresita García González
FES-Acatlán-UNAM
ColBach
Teoría de la argumentación y las lógicas erotéticas
Israel Velasco Cruz
IIF-UNAM
14:30 – 16:30 h
Receso
16:30 – 18:00 h
Conferencia Magistral:
Identificación de argumentos y conectores argumentativos
Corina Yoris-Villasana
UCAB
Salón A-201
18:00 – 20:00 h
Mesa 2:
Alternativas de enseñanza de las tablas de verdad y la negación
Salón A-201
Algunos problemas sobre la enseñanza de las negaciones lógicas
Jesús Castañeda Rivera
PREU
UniNova
Estrategia didáctica para la comprensión de textos expositivos a partir
del uso de tablas de valores de verdad
Martha Evelia Pérez Obeso
CETis 107
Utilidad de los diagramas de Venn como herramienta didáctica para la
enseñanza de las principales conectivas de la lógica clásica
proposicional
Nayeli Rodríguez de Jesús
FC-UNAM
Tablas de verdad y sectores de verdad
Héctor Hernández O.
Unicaribe
JUEVES 10 DE NOVIEMBRE DE 2011
Sede: Universidad Autónoma de la Ciudad de México
Plantel San Lorenzo Tezonco
Calle Prolongación San Isidro 151
Col. San Lorenzo Tezonco
Del. Iztapalapa, México, D.F.
09:00 – 10:30 h
Taller:
De la lógica informal a la lógica formal
Federico Marulanda
IIF-UMSNH
Salón B-101
09:00 – 10:30 h
Taller:
Deducción natural, tablas de verdad y árboles semánticos:
diseño de estrategias de exposición
Seminario Lógica Clara
FFyL-UNAM
Salón C-107
10:30 – 12:00 h
Conferencia Magistral:
Programación de cursos de argumentación en filosofía
Huberto Marraud González
DLLMLF-UAM
12:00 – 12:30 h
Receso
12:30 – 14:30 h
Mesa 3:
Comunicación argumentativa, elección de sistemas y análisis de
modelos didácticos de lógica, argumentación y pensamiento crítico
Salón B-101
Las mujeres en la enseñanza de la lógica
Juan Manuel Campos Benítez
Karla Ivonne Caballero Arroyo
BUAP
Sobre la elección de sistemas lógicos
José Martín Castro-Manzano
IIF-UNAM
Proyecto de especialidad en comunicación argumentativa
Gabriel Ramos García
FFyL-UNAM, FES-Acatlán-UNAM
14:30 – 16:30 h
Receso
16:30 – 18:00 h
Conferencia Magistral:
Tomás de Aquino y la práctica de la argumentación
José Luis Rivera
UP
Salón B-101
18:00 – 20:30 h
Asamblea Academia Mexicana de Lógica
Salón B-101
VIERNES 11 DE NOVIEMBRE DE 2011
09:00 – 10:30 h
Taller:
De la lógica informal a la lógica formal
Federico Marulanda
IIF-UMSNH
Salón B-101
09:00 – 10:30 h
Taller:
Deducción natural, tablas de verdad y árboles semánticos:
diseño de estrategias de exposición
Seminario Lógica Clara
FFyL-UNAM
Salón C-010
10:30 – 12:00 h
Conferencia Magistral:
Los diversos significados de la negación. ¿Cuál de ellos enseñar?
Gladys Palau
UNLP
Salón B-101
Receso 12:00 – 12:30 h
12:30 – 14:30 h
Mesa 4:
Metodología, metacognición y filosofía
Salón B-101
La enseñanza de la filosofía como apoyo para la enseñanza de
habilidades del pensamiento lógico
Teresita de Jesús Mijangos Martínez
UNSIS
Ejemplo o teoría: ¿Cuál primero?
Enrique Alfredo Montero Morán
FFyL-UNAM
La metacognición del error como estrategia didáctica en el aprendizaje
del pensamiento crítico
Federico Rafael Arrieta Pensado
UV
Metodología de la comprensión para profesores de lógica;
aplicaciones en el aula
César Manuel López Pérez
FFyL-UNAM
14:30 – 16:30 h
Receso
16:30 – 18:30 h
Mesa 5:
Lógica: de la educación básica a la educación media
Salón B-101
El desarrollo de las estrategias inferenciales y estructuras
argumentativas en niños de primaria
Ytzelt Gónzalez García
UACM
Abel Rubén Hernández Ulloa
UG
Bondades y desventajas de la comunidad de indagación en la
enseñanza de la lógica
José Antonio Olvera González
Escuela de Bachilleres-UAQ
Argumentación filosófica del bachiller
Abigaeli Velázquez
ColBach
Entre lo formal y lo informal: una estrategia didáctica a la mitad del camino
Karen González Fernández
UP
18:30 – 20:30 h
Mesa 6:
Juegos y estrategias
Salón B-101
Acertijos lógicos como herramienta de enseñanza-aprendizaje.
Estrategas de resolución y evaluación de su utilidad
Patricia Díaz Herrera
UACM
Logical Beast
Hansel Morales Murillo
Gerardo Alcalá Padilla
FES-Acatlán-UNAM
Damas lógicas, un verdadero juego de estrategia
Xóchitl Martínez Nava
Samuel Alejandro Lomelí Gómez
FFyL-UNAM
Amílcar Arroyo Medina
UACM
10
SÁBADO 12 DE NOVIEMBRE DE 2011
Sede: Universidad Autónoma de la Ciudad de México
Centro Vlady
Calle Goya 63
Col. Insurgentes Mixcoac
Delegación Benito Juárez, México D.F.
09:00 – 10:30 h
Taller:
De la lógica informal a la lógica formal
Federico Marulanda
IIF-UMSNH
09:00 – 10:30 h
Taller:
Deducción natural, tablas de verdad y árboles semánticos:
diseño de estrategias de exposición
Seminario Lógica Clara
FFyL-UNAM
10:30 – 12:30 h
Mesa 7
Ética y argumentación
La falacia naturalista y los argumentos contra natura
Jorge Pablo Oseguera Gamba
FFyL-UNAM
El video como una herramienta didáctica para argumentar en la clase
de ética
Gabriela Rodríguez Jiménez
ENP-UNAM
Presentación del Libro: ¿Ética para qué?
Gabriela Rodríguez Jiménez
ENP-UNAM
Presentación de libro de texto y cuaderno de trabajo de Lógica
conforme al programa de la ENP de la UNAM
Alejandra M. Ocampo Morales
12:30 – 14:00 h
Conferencia Magistral:
Didáctica de la lógica con enfoque transdisciplinar
Ariel Campirán
UV
14:00 – 14:30 h
Ceremonia de Clausura
14:30 – 15:30 h
Ensamble Coral de la UACM, dirigido por Francisco Grijalva
15:30 h Brindis
11
LISTA DE SIGLAS
Academia B de Filosofía e Historia de las Ideas-UACM AFHIB-UACM
Benemérita Universidad Autónoma de Puebla BUAP
Centro de Estudios Tecnológicos industrial y de servicios No. 107 CETis 107
Centro de Lógica, Epistemologia e História da Ciência CLE
Colegio de Bachilleres ColBach
Departamento de Lingüística, Lenguas Modernas, Lógica y Filosofía de la Ciencia DLLMLFC
Escuela de Bachilleres-Universidad Autónoma de Querétaro UAQ
Escuela Nacional Preparatoria- UNAM ENP-UNAM
Facultad de Ciencias-Universidad Nacional Autónoma de México FC-UNAM
Facultad de Estudios Superiores Acatlán-Universidad Nacional Autónoma de México FES-Acatlán-UNAM
Facultad de Filosofía y Letras-Universidad Nacional Autónoma de México FFyL-UNAM
Instituto de Investigaciones Filosóficas-Universidad Michoacana de San Nicolás de Hidalgo IIF-UMSNH
Instituto de Investigaciones Filosóficas-Universidad Nacional Autónoma de México IIF-UNAM
Instituto Salesiano de Estudios Superiores ISES
Instituto Tecnológico y de Estudios Superiores de Monterrey ITESM
Preparatoria La Salle del Pedregal USLA
PREUniversitaria PREU
Universidad Autónoma de la Ciudad de México UACM
Universidad Autónoma de Madrid DLLMLF-UAM (España)
Universidad Autónoma Metropolitana-Unidad Iztapalapa UAM-I
Universidad Católica Andrés Bello UCAB (Venezuela)
Universidad de Guanajuato UG
Universidad de la Sierra Sur UNSIS
Universidad del Caribe Unicaribe
Universidad Estadual de Campinas CLE–UNICAMP
Universidad Marista campus Tláhuac UMA-Tláhuac
Universidad Nacional de La Plata UNLP (Argentina)
Universidad Nova Spania UniNova
Universidad Panamericana UP
Universidad Panamericana UP
Universidad Popular Autónoma del Estado de Puebla UPAEP
Universidad Veracruzana UV
University of Amsterdam UvA
martes, 25 de octubre de 2011
jueves, 6 de octubre de 2011
Conditionals and Modularity in General Logic de Dov M. Gabbay • Karl Schlechta
This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the authors' uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation.
The book will be of value to researchers and graduate students in logic and theoretical computer science.
lunes, 26 de septiembre de 2011
Journal of Philosophical Logic. Vol.40 N° 5 Logic in India
Logic in India—Editorial Introduction
Hans van Ditmarsch · Rohit Parikh ·
R. Ramanujam
1 History of Indian Logic
In the words of David B. Zilberman,
The most remarkable feature of Indian formal logic (as it was reflected
by the most advanced system of Indian logic, by Navya–Nyaya) is
clearly a close connection of a logical formalism to a linguistic material
. . . A common characteristic of Indian knowledge on all stages of its
existence was a consistent intentionalism, whereas European logic was
still a predominantly extentional one. Important properties appeared to
be also a utilization of non-quantum formalized expressions, presence
of a complicated theory relations, and a unique theory of multi-level
abstraction. (...) According to Bochenski, Indian logic can be of interest
to Western logicians because it was ‘initiated on different foundations’.
[13, p. 119], [3, p. 517]
Logic arose in ancient India from the art of conducting philosophical debate,
prevalent probably as early as the time of the Buddha in the sixth century BCE
but became more systematic and methodical in the subsequent four hundred
years. By the second century BCE, there were several manuals for formal debates,
perhaps the most systematic of them being Nyaayasutras of Aksapaada
Gautama. Aksapaada defined a method of philosophical argumentation called
the nyaya method. It starts with an initial doubt, as to whether p or not-p is the
case, and ends with a decision that p, or not-p as the case may be. There are
five ‘limbs’ in a structured reasoning: the statement of the thesis, the statement
of reason or evidence, the citation of an example, showing of the thesis as a
case that belongs to the general one and the assertion of the thesis as proven.
The Buddhist logicians argued that the first two or three of these were relevant.
In any case, the discussion was on articulation of inference schemata.
There was a continuing tradition of logic and the Jaina logicians were
concerned with epistemological questions. Perhaps themost important ‘school’
in the long list of logician communities was that of the Navya–Nyaya founded
in the 13th century CE by the philosopher Gange´sa. His Tattvacintamani
(“Thought-Jewel of Reality”) dealt with logic, some set theory, and especially
epistemology. This school developed a sophisticated idiom for analysing inference,
one that has been refined over centuries and is still used by scholars.
The systems of Indian logic are a topic of research and debate to this day,
and a community of scholars undertake studies, meet periodically and discuss
their observations.
2 Logic in India in the Twentieth Century
The widespread influence of the eminent philosopher Sarvepalli Radhakrishnan
on Indian schools of philosophy meant that many modern Indian philosophers
focussed on spiritualism in Indian thought rather than formal logic.
While a few did take up studies on formal semantics, modern developments
in mathematical logic were largely unfluential in Indian studies. Modal logic
and incompleteness phenomena attacted some Indian mathematicians [11, 12]
but only in the last two or three decades of the twentieth century did research
in logic come into its own in India.
From the perspective of philosophical logic, the work of Frege and Quine,
and the role of formalization intrigued many philosophers, especially in relation
to similar notions in Indian systems of logic. The influence of thinkers
such as Wittgenstein was also considerable. Towards the end of the century,
notions from non-classical logics such as non-monotonicity and imprecision in
truth, especially in relation to formal epistemology, attracted the attention of
many researchers [4, 5].
On the other hand, mathematical studies in logic were few. Algebraic
logic, inspired by the work of Helena Rasiowa [9] offered a home for some
mathematicians [2]. However, it was the advent of computer science that gave
a tremendous fillip to logic studies in India. Studies in logics of programs,
programming language semantics, temporal logics and artificial intelligence
Logic in India—Editorial Introduction 559
led to interest in mathematical logic per se, and soon, with the exception of
a handful in Mathematics and Philosophy, logic became a subject of teaching
and research in the computer science departments in India. A newly emergent
and confident theoretical computer science community sought to build bridges
with mathematicians in the areas of combinatorics, graph theory and number
theory, and with logicians in the areas of model theory and proof theory,
bringing algorithmic and complexity theoretic notions into the tools [7, 8, 10]
3 The Assocation for Logic in India
It was in such a background that ALI, the Assocation for Logic in India
(see http://ali.cmi.ac.in/) was formed in 2007, with the basic aim of building
a logic community in India, promoting research and education in logic and its
applications. A foundation for this had been provided by the annual meetings
of the Calcutta Logic Circle (a regular feature for two decades), the first two
editions of the Indian Conference on Logic and its Applications (ICLA) at IIT
Bombay (January 2005 and January 2007) and the International Conference
on Logic, Navya–Nyaya and Applications at Kolkata in January 2007. By
now the Indian Conference on Logic and its Applications (ICLA) is biennial,
taking place in the January of odd years, and the two-week long Indian School
on Logic and its Applications (ISLA) is biennial as well, taking place in the
January of even years.
ICLA The biennial Indian Conference on Logic and its Applications (ICLA)
is a forum for bringing together researchers from a wide variety of fields that
formal logic plays a significant role in, along with mathematicians, philosophers
and logicians studying foundations of formal logic in itself. The fourth
conference was held at Delhi University, in January 2011, and the proceedings
published as LNCS 6521 in the FoLLI series [1]. It had as a special feature the
inclusion of studies in systems of logic in the Indian tradition, and historical
research on logic.
ISLA The Indian School on Logic and Applications (ISLA) is a biennial
event as well. The previous editions of the school were held in IIT Bombay
(2006), IIT Kanpur (2008), and University of Hyderabad (2010), and an
upcoming ISLA is at Manipal University (2012). The objective is to present
before graduate students and researchers in India some basics as well as active
research areas in logic. The School typically attracts students and teachers
from mathematics, philosophy and computer science departments. The school
adopts a dual format: the mornings will consist of introductory courses on
fundamental aspects of logic, by eminent researchers in the area. The afternoons
have workshops, which can be of the nature of advanced tutorials, or
presentations on research areas, in different aspects of logic and applications.
4 Contents
This special issue on Logic in India aims to provide a sampler of work from
both traditions, that of Indian logic, as well as work from logicians active in
mathematics and computer science in India.
‘Possible Ideas of Necessity in Indian Logic’ by Sundar Sarukkai is a contribution
motivated by the history of Indian logic, on the conception of necessity.
Logical necessity is presumably absent in Indian logic, where the structure of
the logical argument in Indian logic is often given as a reason for this claim.
In Indian logic, the analysis of ‘invariable concomitance’ (vyapti) is of crucial
importance and its definitions are very complex. The author argues how vyapti
can be understood in terms of contingent necessity in the Leibnizian sense and
also how the complex definitions can be interpreted as an attempt to define
contingent necessity in terms of logical necessity.
‘Fine-grained concurrency with separation logic’ by Kalpesh Kapoor, Kamal
Lodaya and Uday Reddy is a contribution in the area of computer science,
on reasoning about concurrent programs. Such reasoning involves ensuring
that concurrent processes manipulate disjoint portions of memory but the
division of memory between processes is in general not static. The implied
ownership of memory cells may be dynamic and shared, allowing concurrent
access. Concurrent Separation Logic with Permissions, developed byO’Hearn,
Bornat and others (see [6] for various contributions), is able to represent
sophisticated transfer of ownership and permissions between processes. The
authors demonstrate how these ideas can be used to reason about fine-grained
concurrent programs.
‘Context-sensitivity in Jain Philosophy. A Dialogical Study of Siddharsigani’s
Commentary On The Handbook of Logic’ by Nicolas Clerbout, Marie-Hélène
Gorisse, and Shahid Rahman is a contribution on the history of Indian logic. In
classical India, Jain philosophers developed a theory of viewpoints (naya-vada)
according to which any statement is always performed within and dependent
upon a given epistemic perspective or viewpoint. The Jainas furnished this
epistemology with an (epistemic) theory of disputation that takes into account
the viewpoint in which the main thesis has been stated. The paper delves
into the Jain notion of viewpoint contextualisation and develops a suitable
logical system that offers a reconstruction of the Jainas’ epistemic theory of
disputation.
‘A Logic for Multiple-source Approximation Systems with Distributed
Knowledge Base’ by Mohua Banerjee and Aquil Khan is a contribution in
the area of mathematics and computer science, focussing on rough sets, which
are approximations of sets. The primitive notion is that of an approximation
space, which is a pair consisting of a domain of discourse (the knowledge base)
and an equivalence relation on that domain (the granularity of information
about objects in the domain). The authors focus on the situation where
information is obtained from different sources. The notion of approximation
space is extended to define a multiple-source approximation system with
distributed knowledge base, that can reflect how individual sources perceive
the same domain differently (depending on what information the group /
individual source has about the domain). The same concept may then have
approximations that differ with individuals or groups.
It is hoped that this issue will generate interest in Logic in India within the
wider international community of logicians and philosophers.
References
1. Banerjee, M., & Seth, A. (Eds.) (2011). Logic and its applications—4th Indian Conference,
ICLA 2011. Proceedings (Vol. 6521). LNCS: Springer.
2. Banerjee, M., & Chakraborty, M. K. (1996). Rough sets through algebraic logic. Fundamenta
Informaticae, 28(3–4), 211–221.
3. Bochenski, I. M. (1955). Formale logik. München: K. A. Verlag
4. Chakraborty, M. K. (1995). Graded consequence: Further studies. Journal of Applied Non-
Classical Logics, 5(2), 127–137.
5. Chakraborty, M. K., & Chatterjee, A. (1996). On representation of indeterminate identity via
vague concepts. Journal of Applied Non-Classical Logics, 6(2).
6. Gardner, P., & Yoshida, N. (Eds.) (2004). 15th international Conference on Concurrency
Theory (CONCUR) (Vol. 3170). LNCS: Springer.
7. Lodaya, K., & Pandya, P. K. (2006). A dose of timed logic, in guarded measure. In E. Asarin,
& P. Bouyer (Eds.), FORMATS. Lecture notes in computer science (Vol. 4202, pp. 260–273).
Springer.
8. Lodaya, K., Parikh, R., Ramanujam, R., & Thiagarajan, P. S. (1995). A logical study of
distributed transition systems. Information and Computation, 119(1), 91–118.
9. Rasiowa, H., & Sikorski, R. (1970). The mathematics of metamathematics. Warsaw: Polish
Scientific Publishers.
10. Seth, A. (1992). There is no recursive axiomatization for feasible functionals of type ∼2. In
LICS (pp. 286–295). IEEE Computer Society.
11. Shukla, A. (1967). A note on the axiomatizations of certain modal systems. Notre Dame
Journal of Formal Logic, 8(1–2), 118–120.
12. Shukla, A. (1972). The existence postulate and non-regular systems of modal logic. Notre
Dame Journal of Formal Logic, 13(3), 369–378.
13. Zilberman, D. B. (2006). History of Indian logic. In R. S. Cohen, &H. Gourko (Eds.), Analogy
in Indian and Western philosophical thought. Boston studies in the philosophy of science
(Vol. 243, pp. 110–120). Springer
Hans van Ditmarsch · Rohit Parikh ·
R. Ramanujam
1 History of Indian Logic
In the words of David B. Zilberman,
The most remarkable feature of Indian formal logic (as it was reflected
by the most advanced system of Indian logic, by Navya–Nyaya) is
clearly a close connection of a logical formalism to a linguistic material
. . . A common characteristic of Indian knowledge on all stages of its
existence was a consistent intentionalism, whereas European logic was
still a predominantly extentional one. Important properties appeared to
be also a utilization of non-quantum formalized expressions, presence
of a complicated theory relations, and a unique theory of multi-level
abstraction. (...) According to Bochenski, Indian logic can be of interest
to Western logicians because it was ‘initiated on different foundations’.
[13, p. 119], [3, p. 517]
Logic arose in ancient India from the art of conducting philosophical debate,
prevalent probably as early as the time of the Buddha in the sixth century BCE
but became more systematic and methodical in the subsequent four hundred
years. By the second century BCE, there were several manuals for formal debates,
perhaps the most systematic of them being Nyaayasutras of Aksapaada
Gautama. Aksapaada defined a method of philosophical argumentation called
the nyaya method. It starts with an initial doubt, as to whether p or not-p is the
case, and ends with a decision that p, or not-p as the case may be. There are
five ‘limbs’ in a structured reasoning: the statement of the thesis, the statement
of reason or evidence, the citation of an example, showing of the thesis as a
case that belongs to the general one and the assertion of the thesis as proven.
The Buddhist logicians argued that the first two or three of these were relevant.
In any case, the discussion was on articulation of inference schemata.
There was a continuing tradition of logic and the Jaina logicians were
concerned with epistemological questions. Perhaps themost important ‘school’
in the long list of logician communities was that of the Navya–Nyaya founded
in the 13th century CE by the philosopher Gange´sa. His Tattvacintamani
(“Thought-Jewel of Reality”) dealt with logic, some set theory, and especially
epistemology. This school developed a sophisticated idiom for analysing inference,
one that has been refined over centuries and is still used by scholars.
The systems of Indian logic are a topic of research and debate to this day,
and a community of scholars undertake studies, meet periodically and discuss
their observations.
2 Logic in India in the Twentieth Century
The widespread influence of the eminent philosopher Sarvepalli Radhakrishnan
on Indian schools of philosophy meant that many modern Indian philosophers
focussed on spiritualism in Indian thought rather than formal logic.
While a few did take up studies on formal semantics, modern developments
in mathematical logic were largely unfluential in Indian studies. Modal logic
and incompleteness phenomena attacted some Indian mathematicians [11, 12]
but only in the last two or three decades of the twentieth century did research
in logic come into its own in India.
From the perspective of philosophical logic, the work of Frege and Quine,
and the role of formalization intrigued many philosophers, especially in relation
to similar notions in Indian systems of logic. The influence of thinkers
such as Wittgenstein was also considerable. Towards the end of the century,
notions from non-classical logics such as non-monotonicity and imprecision in
truth, especially in relation to formal epistemology, attracted the attention of
many researchers [4, 5].
On the other hand, mathematical studies in logic were few. Algebraic
logic, inspired by the work of Helena Rasiowa [9] offered a home for some
mathematicians [2]. However, it was the advent of computer science that gave
a tremendous fillip to logic studies in India. Studies in logics of programs,
programming language semantics, temporal logics and artificial intelligence
Logic in India—Editorial Introduction 559
led to interest in mathematical logic per se, and soon, with the exception of
a handful in Mathematics and Philosophy, logic became a subject of teaching
and research in the computer science departments in India. A newly emergent
and confident theoretical computer science community sought to build bridges
with mathematicians in the areas of combinatorics, graph theory and number
theory, and with logicians in the areas of model theory and proof theory,
bringing algorithmic and complexity theoretic notions into the tools [7, 8, 10]
3 The Assocation for Logic in India
It was in such a background that ALI, the Assocation for Logic in India
(see http://ali.cmi.ac.in/) was formed in 2007, with the basic aim of building
a logic community in India, promoting research and education in logic and its
applications. A foundation for this had been provided by the annual meetings
of the Calcutta Logic Circle (a regular feature for two decades), the first two
editions of the Indian Conference on Logic and its Applications (ICLA) at IIT
Bombay (January 2005 and January 2007) and the International Conference
on Logic, Navya–Nyaya and Applications at Kolkata in January 2007. By
now the Indian Conference on Logic and its Applications (ICLA) is biennial,
taking place in the January of odd years, and the two-week long Indian School
on Logic and its Applications (ISLA) is biennial as well, taking place in the
January of even years.
ICLA The biennial Indian Conference on Logic and its Applications (ICLA)
is a forum for bringing together researchers from a wide variety of fields that
formal logic plays a significant role in, along with mathematicians, philosophers
and logicians studying foundations of formal logic in itself. The fourth
conference was held at Delhi University, in January 2011, and the proceedings
published as LNCS 6521 in the FoLLI series [1]. It had as a special feature the
inclusion of studies in systems of logic in the Indian tradition, and historical
research on logic.
ISLA The Indian School on Logic and Applications (ISLA) is a biennial
event as well. The previous editions of the school were held in IIT Bombay
(2006), IIT Kanpur (2008), and University of Hyderabad (2010), and an
upcoming ISLA is at Manipal University (2012). The objective is to present
before graduate students and researchers in India some basics as well as active
research areas in logic. The School typically attracts students and teachers
from mathematics, philosophy and computer science departments. The school
adopts a dual format: the mornings will consist of introductory courses on
fundamental aspects of logic, by eminent researchers in the area. The afternoons
have workshops, which can be of the nature of advanced tutorials, or
presentations on research areas, in different aspects of logic and applications.
4 Contents
This special issue on Logic in India aims to provide a sampler of work from
both traditions, that of Indian logic, as well as work from logicians active in
mathematics and computer science in India.
‘Possible Ideas of Necessity in Indian Logic’ by Sundar Sarukkai is a contribution
motivated by the history of Indian logic, on the conception of necessity.
Logical necessity is presumably absent in Indian logic, where the structure of
the logical argument in Indian logic is often given as a reason for this claim.
In Indian logic, the analysis of ‘invariable concomitance’ (vyapti) is of crucial
importance and its definitions are very complex. The author argues how vyapti
can be understood in terms of contingent necessity in the Leibnizian sense and
also how the complex definitions can be interpreted as an attempt to define
contingent necessity in terms of logical necessity.
‘Fine-grained concurrency with separation logic’ by Kalpesh Kapoor, Kamal
Lodaya and Uday Reddy is a contribution in the area of computer science,
on reasoning about concurrent programs. Such reasoning involves ensuring
that concurrent processes manipulate disjoint portions of memory but the
division of memory between processes is in general not static. The implied
ownership of memory cells may be dynamic and shared, allowing concurrent
access. Concurrent Separation Logic with Permissions, developed byO’Hearn,
Bornat and others (see [6] for various contributions), is able to represent
sophisticated transfer of ownership and permissions between processes. The
authors demonstrate how these ideas can be used to reason about fine-grained
concurrent programs.
‘Context-sensitivity in Jain Philosophy. A Dialogical Study of Siddharsigani’s
Commentary On The Handbook of Logic’ by Nicolas Clerbout, Marie-Hélène
Gorisse, and Shahid Rahman is a contribution on the history of Indian logic. In
classical India, Jain philosophers developed a theory of viewpoints (naya-vada)
according to which any statement is always performed within and dependent
upon a given epistemic perspective or viewpoint. The Jainas furnished this
epistemology with an (epistemic) theory of disputation that takes into account
the viewpoint in which the main thesis has been stated. The paper delves
into the Jain notion of viewpoint contextualisation and develops a suitable
logical system that offers a reconstruction of the Jainas’ epistemic theory of
disputation.
‘A Logic for Multiple-source Approximation Systems with Distributed
Knowledge Base’ by Mohua Banerjee and Aquil Khan is a contribution in
the area of mathematics and computer science, focussing on rough sets, which
are approximations of sets. The primitive notion is that of an approximation
space, which is a pair consisting of a domain of discourse (the knowledge base)
and an equivalence relation on that domain (the granularity of information
about objects in the domain). The authors focus on the situation where
information is obtained from different sources. The notion of approximation
space is extended to define a multiple-source approximation system with
distributed knowledge base, that can reflect how individual sources perceive
the same domain differently (depending on what information the group /
individual source has about the domain). The same concept may then have
approximations that differ with individuals or groups.
It is hoped that this issue will generate interest in Logic in India within the
wider international community of logicians and philosophers.
References
1. Banerjee, M., & Seth, A. (Eds.) (2011). Logic and its applications—4th Indian Conference,
ICLA 2011. Proceedings (Vol. 6521). LNCS: Springer.
2. Banerjee, M., & Chakraborty, M. K. (1996). Rough sets through algebraic logic. Fundamenta
Informaticae, 28(3–4), 211–221.
3. Bochenski, I. M. (1955). Formale logik. München: K. A. Verlag
4. Chakraborty, M. K. (1995). Graded consequence: Further studies. Journal of Applied Non-
Classical Logics, 5(2), 127–137.
5. Chakraborty, M. K., & Chatterjee, A. (1996). On representation of indeterminate identity via
vague concepts. Journal of Applied Non-Classical Logics, 6(2).
6. Gardner, P., & Yoshida, N. (Eds.) (2004). 15th international Conference on Concurrency
Theory (CONCUR) (Vol. 3170). LNCS: Springer.
7. Lodaya, K., & Pandya, P. K. (2006). A dose of timed logic, in guarded measure. In E. Asarin,
& P. Bouyer (Eds.), FORMATS. Lecture notes in computer science (Vol. 4202, pp. 260–273).
Springer.
8. Lodaya, K., Parikh, R., Ramanujam, R., & Thiagarajan, P. S. (1995). A logical study of
distributed transition systems. Information and Computation, 119(1), 91–118.
9. Rasiowa, H., & Sikorski, R. (1970). The mathematics of metamathematics. Warsaw: Polish
Scientific Publishers.
10. Seth, A. (1992). There is no recursive axiomatization for feasible functionals of type ∼2. In
LICS (pp. 286–295). IEEE Computer Society.
11. Shukla, A. (1967). A note on the axiomatizations of certain modal systems. Notre Dame
Journal of Formal Logic, 8(1–2), 118–120.
12. Shukla, A. (1972). The existence postulate and non-regular systems of modal logic. Notre
Dame Journal of Formal Logic, 13(3), 369–378.
13. Zilberman, D. B. (2006). History of Indian logic. In R. S. Cohen, &H. Gourko (Eds.), Analogy
in Indian and Western philosophical thought. Boston studies in the philosophy of science
(Vol. 243, pp. 110–120). Springer
The Realism-Antirealism Debate in the Age of Alternative Logics. Vol 23 LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE
Les comparto la aparición del Vol. 23 de LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE
El tema: The Realism-Antirealism
Debate in the Age
of Alternative Logics
Editores: Shahid Rahman · Giuseppe Primiero ·
Mathieu Marion
Contents
1 OnWhen a Disjunction Is Informative . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Patrick Allo
2 My Own Truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Alexandre Billon
3 Which Logic for the Radical Anti-realist? . . . . . . . . . . . . . . . . . . . . . . . 47
Denis Bonnay and Mikaël Cozic
4 Moore’s Paradox as an Argument Against Anti-realism . . . . . . . . . . . 69
Jon Cogburn
5 The Neutrality of Truth in the Debate Realism vs. Anti-realism . . . . 85
María J. Frápolli
6 Modalities Without Worlds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Reinhard Kahle
7 Antirealism, Meaning and Truth-Conditional Semantics . . . . . . . . . . 119
Neil Kennedy
8 Game Semantics and the Manifestation Thesis . . . . . . . . . . . . . . . . . . . 141
Mathieu Marion
9 Conservativeness and Eliminability for Anti-Realistic Definitions . . . 169
Francesca Poggiolesi
10 Realism, Antirealism, and Paraconsistency . . . . . . . . . . . . . . . . . . . . . . 181
Graham Priest
11 Type-Theoretical Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Giuseppe Primiero
12 Negation in the Logic of First Degree Entailment and Tonk . . . . . . . . 213
Shahid Rahman
13 Necessary Truth and Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Stephen Read
14 Anti-realist Classical Logic and Realist Mathematics . . . . . . . . . . . . . 269
Greg Restall
15 A Tale of Two Anti-realisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Sanford Shieh
16 A Double Diamond of Judgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Göran Sundholm
17 Stable Philosophical Systems and Radical Anti-realism . . . . . . . . . . . 313
Joseph Vidal-Rosset
18 Two Diamonds Are More Than One . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Elia Zardini
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Preface
In the preface to the first volume of LEUS, the editors of the series pointed out,
within the context of the failure of the positivist project of the unity of science, the
difference between science as a body of knowledge and science as process by which
knowledge is achieved. In fact, the editors suggested that a ban on the logical analysis
of science as a dynamic process, which in traditional philosophy was overtaken
by ‘gnoseology’, produced a gap between sciences and logic (including philosophy
of science). In gnoseology the main notion was the one of judgement rather than
that of proposition. Judgement delivered the epistemic aspect of logic, namely the
relation between an (epistemic) agent and a proposition. This represented the basis
of the Kantian approach to logic, which seemed to be in conflict with the post-
Fregean approach where only relations between propositions are at stake and where
the epistemic aspect is seen as outside logic.
As it happens quite often in philosophy, the echoes of the old traditions come
back and point to the mistakes of the younger iconoclast movements. This is indeed
the case in the relation between logic and knowledge where the inclusion or exclusion
of the epistemic moment as linked with the concept of proposition provoked a
heated debate since the 1960s. The epistemic approaches, which started to call themselves,
following Michael Dummett, ‘antirealism’, found their formal argument in
the mathematics of Brouwer and intuitionistic logic, while the others persisted with
the formal background of the Frege-Tarski tradition, where Cantorian set theory
is linked via model theory to classical logic. This picture is, however, incomplete.
Already in the 1960s Jaakko Hintikka tried to join both traditions by means of what
is now known as ‘explicit epistemic logic’, where the epistemic content is introduced
into the object language as an operator which yield propositions from propositions
rather than as metalogical constraint on the notion of inference. The debate
had thus three players: classical logicians, intuitionistic logicians (implicit epistemic
logic) and epistemic logicians (explicit epistemic logic), though the mainstream
continued to think that the discussion reduces to the discussion between classical
and intuitionistic logic.
The editors of the present volume think that in these days and age of Alternative
Logics, where manifold developments in logic happen in a breathtaking pace,
this debate should be revisited. In fact, collaborators to this volume took happily
this challenge and responded with new perspectives on the debate from both
the explicit and the implicit point of view, challenging it from the newly arisen
perspectives in logic. This volume aims therefore at presenting standard issues of
the realism-antirealism debate in a new light, shed from the point of view of different
philosophical perspectives. It is therefore appropriate that we open with Patrick
Allo’s contribution, which analyses the meaning of ambiguous connectives (and
in particular of disjunction) from a logical pluralistic viewpoint, in which content
is explained in terms of informativeness. Logical pluralism can be understood as
the larger conceptual umbrella under which one finds today many different understandings
of the realism-antirealism debate. This certainly still grows on Dummett’s
arguments against truth-conditional semantics, which Neil Kennedy reconstructs
and critically analyses; in general, it refers to well known forms of semantic antirealism,
which Sanford Shieh characterizes by means of the distinction between
epistemically-based and conceptually based ones, and it still triggers today huge
debates such as the one on Moorean validities, that Jon Cogburn reconstructs in view
of the different old and new interpretations. But antirealism today profits of the influences
of many different backgrounds: this is the case for example of Martin-Löf’s
type theory, which is conceptually and historically located within the larger frame of
theories of truth and judgement in Göran Sundholm’s contribution, and which meets
for the first time belief revision dynamics in Giuseppe Primiero’s paper. Departure
from classical principles of reasoning is therefore possible in different forms, and
whereas Denis Bonnay and Mikaël Cozic place the justification of radical forms
of anti-realism in the context of the (to them still unjustified) shift to linear logic,
Joseph Vidal-Rosset suggests a larger philosophical frame for the understanding of
radical antirealism. Many are therefore the new branches of logic that are called
upon in this volume to face non-classical issues raising from an antirealistic perspective:
this is the case of modal logic in the interpretations by Reinhard Kahle
and Elia Zardini; the anti-realistic inspired defence of realist mathematics by Greg
Restall, where (implicit) antirealism is understood as a means to defend logical
pluralism: the extension to Paraconsistency, via a defence of a suitable negation
connective in the Kripke-Hintikka reconstruction of intuitionistic logic, suggested
by Graham Priest, which virtually dialogues with the dialogical interpretation of the
same connective given by Shahid Rahman. The relation of antirealism to dialogical
logic and game semantics appears also inMathieu Marion’s contribution, where it is
considered how to make Dummett’s Manifestation Argument work within this new
programme, and it is argued that a derived Thesis fits (with appropriate reformulations)
within game semantics. Stephen Read, takes the proof theoretical approach
to logic of the antirealists to challenge the epistemic constraints of the intuitionists
and Francesca Poggiolesi analyses properties of anti-realistic definitions starting
from the classical requirements imposed by Lesniewski. Truth is of course always
an open field for new interpretations: Alexandre Billon considers the notion of
assessment-sensitive truth to provide solutions to semantic paradoxes and Maria
Frapolli presents a prosentential account of truth showing that our comprehension
of truth and the use we make of truth expressions are strictly independent of our
views about the relation between mind and world
Some years have passed from the initial proposal to collect a number of contributions
from scholars that are reconsidering the realism-antirealism debate from new
philosophical, logical and metaphysical perspectives. This has led to different lineups
of both authors and editors.What we hope to have achieved through this process
is to have selected significant contributions on the different aspects of research on
anti-realism done today at academic level, a representative body of work that can be
of reference and inspiration for further advancements in this field.
Montreal, Canada Mathieu Marion
Ghent, Belgium Giuseppe Primiero
Lille, France Shahid Rahman
December 2010
El tema: The Realism-Antirealism
Debate in the Age
of Alternative Logics
Editores: Shahid Rahman · Giuseppe Primiero ·
Mathieu Marion
Contents
1 OnWhen a Disjunction Is Informative . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Patrick Allo
2 My Own Truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Alexandre Billon
3 Which Logic for the Radical Anti-realist? . . . . . . . . . . . . . . . . . . . . . . . 47
Denis Bonnay and Mikaël Cozic
4 Moore’s Paradox as an Argument Against Anti-realism . . . . . . . . . . . 69
Jon Cogburn
5 The Neutrality of Truth in the Debate Realism vs. Anti-realism . . . . 85
María J. Frápolli
6 Modalities Without Worlds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Reinhard Kahle
7 Antirealism, Meaning and Truth-Conditional Semantics . . . . . . . . . . 119
Neil Kennedy
8 Game Semantics and the Manifestation Thesis . . . . . . . . . . . . . . . . . . . 141
Mathieu Marion
9 Conservativeness and Eliminability for Anti-Realistic Definitions . . . 169
Francesca Poggiolesi
10 Realism, Antirealism, and Paraconsistency . . . . . . . . . . . . . . . . . . . . . . 181
Graham Priest
11 Type-Theoretical Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Giuseppe Primiero
12 Negation in the Logic of First Degree Entailment and Tonk . . . . . . . . 213
Shahid Rahman
13 Necessary Truth and Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Stephen Read
14 Anti-realist Classical Logic and Realist Mathematics . . . . . . . . . . . . . 269
Greg Restall
15 A Tale of Two Anti-realisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Sanford Shieh
16 A Double Diamond of Judgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Göran Sundholm
17 Stable Philosophical Systems and Radical Anti-realism . . . . . . . . . . . 313
Joseph Vidal-Rosset
18 Two Diamonds Are More Than One . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Elia Zardini
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Preface
In the preface to the first volume of LEUS, the editors of the series pointed out,
within the context of the failure of the positivist project of the unity of science, the
difference between science as a body of knowledge and science as process by which
knowledge is achieved. In fact, the editors suggested that a ban on the logical analysis
of science as a dynamic process, which in traditional philosophy was overtaken
by ‘gnoseology’, produced a gap between sciences and logic (including philosophy
of science). In gnoseology the main notion was the one of judgement rather than
that of proposition. Judgement delivered the epistemic aspect of logic, namely the
relation between an (epistemic) agent and a proposition. This represented the basis
of the Kantian approach to logic, which seemed to be in conflict with the post-
Fregean approach where only relations between propositions are at stake and where
the epistemic aspect is seen as outside logic.
As it happens quite often in philosophy, the echoes of the old traditions come
back and point to the mistakes of the younger iconoclast movements. This is indeed
the case in the relation between logic and knowledge where the inclusion or exclusion
of the epistemic moment as linked with the concept of proposition provoked a
heated debate since the 1960s. The epistemic approaches, which started to call themselves,
following Michael Dummett, ‘antirealism’, found their formal argument in
the mathematics of Brouwer and intuitionistic logic, while the others persisted with
the formal background of the Frege-Tarski tradition, where Cantorian set theory
is linked via model theory to classical logic. This picture is, however, incomplete.
Already in the 1960s Jaakko Hintikka tried to join both traditions by means of what
is now known as ‘explicit epistemic logic’, where the epistemic content is introduced
into the object language as an operator which yield propositions from propositions
rather than as metalogical constraint on the notion of inference. The debate
had thus three players: classical logicians, intuitionistic logicians (implicit epistemic
logic) and epistemic logicians (explicit epistemic logic), though the mainstream
continued to think that the discussion reduces to the discussion between classical
and intuitionistic logic.
The editors of the present volume think that in these days and age of Alternative
Logics, where manifold developments in logic happen in a breathtaking pace,
this debate should be revisited. In fact, collaborators to this volume took happily
this challenge and responded with new perspectives on the debate from both
the explicit and the implicit point of view, challenging it from the newly arisen
perspectives in logic. This volume aims therefore at presenting standard issues of
the realism-antirealism debate in a new light, shed from the point of view of different
philosophical perspectives. It is therefore appropriate that we open with Patrick
Allo’s contribution, which analyses the meaning of ambiguous connectives (and
in particular of disjunction) from a logical pluralistic viewpoint, in which content
is explained in terms of informativeness. Logical pluralism can be understood as
the larger conceptual umbrella under which one finds today many different understandings
of the realism-antirealism debate. This certainly still grows on Dummett’s
arguments against truth-conditional semantics, which Neil Kennedy reconstructs
and critically analyses; in general, it refers to well known forms of semantic antirealism,
which Sanford Shieh characterizes by means of the distinction between
epistemically-based and conceptually based ones, and it still triggers today huge
debates such as the one on Moorean validities, that Jon Cogburn reconstructs in view
of the different old and new interpretations. But antirealism today profits of the influences
of many different backgrounds: this is the case for example of Martin-Löf’s
type theory, which is conceptually and historically located within the larger frame of
theories of truth and judgement in Göran Sundholm’s contribution, and which meets
for the first time belief revision dynamics in Giuseppe Primiero’s paper. Departure
from classical principles of reasoning is therefore possible in different forms, and
whereas Denis Bonnay and Mikaël Cozic place the justification of radical forms
of anti-realism in the context of the (to them still unjustified) shift to linear logic,
Joseph Vidal-Rosset suggests a larger philosophical frame for the understanding of
radical antirealism. Many are therefore the new branches of logic that are called
upon in this volume to face non-classical issues raising from an antirealistic perspective:
this is the case of modal logic in the interpretations by Reinhard Kahle
and Elia Zardini; the anti-realistic inspired defence of realist mathematics by Greg
Restall, where (implicit) antirealism is understood as a means to defend logical
pluralism: the extension to Paraconsistency, via a defence of a suitable negation
connective in the Kripke-Hintikka reconstruction of intuitionistic logic, suggested
by Graham Priest, which virtually dialogues with the dialogical interpretation of the
same connective given by Shahid Rahman. The relation of antirealism to dialogical
logic and game semantics appears also inMathieu Marion’s contribution, where it is
considered how to make Dummett’s Manifestation Argument work within this new
programme, and it is argued that a derived Thesis fits (with appropriate reformulations)
within game semantics. Stephen Read, takes the proof theoretical approach
to logic of the antirealists to challenge the epistemic constraints of the intuitionists
and Francesca Poggiolesi analyses properties of anti-realistic definitions starting
from the classical requirements imposed by Lesniewski. Truth is of course always
an open field for new interpretations: Alexandre Billon considers the notion of
assessment-sensitive truth to provide solutions to semantic paradoxes and Maria
Frapolli presents a prosentential account of truth showing that our comprehension
of truth and the use we make of truth expressions are strictly independent of our
views about the relation between mind and world
Some years have passed from the initial proposal to collect a number of contributions
from scholars that are reconsidering the realism-antirealism debate from new
philosophical, logical and metaphysical perspectives. This has led to different lineups
of both authors and editors.What we hope to have achieved through this process
is to have selected significant contributions on the different aspects of research on
anti-realism done today at academic level, a representative body of work that can be
of reference and inspiration for further advancements in this field.
Montreal, Canada Mathieu Marion
Ghent, Belgium Giuseppe Primiero
Lille, France Shahid Rahman
December 2010
miércoles, 21 de septiembre de 2011
What is (not) Logic, and what is it (not) Good for? I. Grattan-Guinness
What is (not) Logic, and what is it (not) Good for?
I. Grattan-Guinness
To the memory of Hans Wussing (1927-2011),
historian and historiographer of mathematics
Building on a previous article on assertion and negating a proposition, an attempt is made to characterise logical knowledge from other kinds, especially mathematics. The tradition of stressing forms of proposition is revived, showing that logic is dependent on the context to which it is applied. Attention is paid to several theories that overlap with both logic and foundational branches of mathematics; they include set theory, model theory, axiomatisation and metamathematics.
Logic is concerned with the real world just as truly as zoology, though with its
more abstract and general features.
Bertrand Russell [1919, 169]
1. Aims
In a previous article [Grattan-Guinness 2011d], named ‘GGan’ here, two features of the assertion of a proposition (that is, the assignment to it of a truth-value) in classical two-valued logic, and various modes of negating it, were examined in some detail and applied to various contexts. Here several features of that study are extended in an attempt to distinguish logic from other kinds of knowledge, especially mathematics.[1]
The uses made in GGan of several technical terms in and around logic are maintained here. So also is the preference to take the proposition rather than the term as the primary notion of logical knowledge. Otherwise the position put forward here is intended to be neutral about various philosophical positions and issues. Of especial pertinence is the question of whether logical knowledge is primarily concerned with (in)valid deduction and truth transmission or with the processing of information [Sagüillo 2009].[2]
To avoid excessive length, the discussion is usually limited to propositions; the consequences for sentences as propositions in a language and to statements as utterances of sentences are not normally explored. The intentions of the utterer include persuading others to share his beliefs and knowledge of what he knows to be true or untrue, improving the cogency of an argument by converting it to a line of reasoning that is already well known, detecting errors in the logic of an argument, using words such as ‘true’ and ‘untrue’ metaphorically, exploiting equivocations, ambiguities and jokes, and even resorting to deliberate lying. There are important issues here, called ‘argumentations’, well captured in [Corcoran 1989] and [Walton 1989, 1996]; they complement the discussion proffered here.
Given any proposition R, the asserted proposition ‘It is true that R’ (symbolised ‘+R’) is the ‘affirmation’ of R, while ‘It is untrue that R’ (‘–R’) is its ‘denial’. R is a proposition about some states of affairs in a context. This can be anything: plasma physics, or structures in piano sonatas, or making wine at home, or the publication of [Russell 1919], or …. . An important special case of self-reference occurs when the context is logic itself. The key question is: what role does logic play in these assertions?
Logical knowledge is notoriously elusive, difficult to detach from its applications. This characterisation starts by proposing four main departments of logic (proposition, propositional function, deduction, assertion), all construed in a way that distinguishes them from other kinds of knowledge, especially “neighbouring” theories such as collections (including set theory), metamathematics, model theory and some “close-by” branches of mathematics such as arithmetic and abstract algebras. The focus remains upon two-valued logic (called ‘bivalent’ and named ‘L2’), comprising both propositional and functional calculi; but some version of our considerations obtains in any other logic, at least ones with explicit organisation and prominent symbolism.
[1] A much more elaborate philosophical and historical version of this article and its predecessor is in preparation as [Grattan-Guinness 2011c].
[2] Other issues include intension versus extension, Platonism versus empiricism versus nominalism versus a priorism versus psychologism versus formalism [Weir 2010], analysis versus synthesis [Otte and Panza 1997], and the status of universals. Some of these issues may well bear less upon logic than upon its applications.
On Assertion and Negations in Logics and Mathematics I. Grattan-Guinness
On Assertion and Negations in Logics and Mathematics
I. Grattan-Guinness
Two features of logic are discussed: 1) the details of asserting a proposition, that is, assigning to it the value ‘true ‘ or ‘untrue’; 2) the extension of negation to cases when a sub-proposition is negated. Various consequences follow for mathematics as well as for logic: we examine the formulation of several paradoxes, and the use of indirect proof-methods when the theorem is asserted.```
1. Aims
In this article the word ‘logic’ or phrase ‘a logic’ is confined to some systematic account of methods of forming propositions, making deductions with and from them, and working with their truth-values. When this logic is axiomatised, uses notations, admits paradoxes, and/or links closely to some branches of mathematics, it is often called a ‘formal’ or symbolic’ logic. We treat almost exclusively two-valued (or ‘bivalent’) formal logic, called ‘L2’, where the truth-values are ‘true’ and ‘untrue’. It divides into the propositional calculus, in which a proposition R is an indivisible “atom”, related to other propositions by logical connectives; and the functional calculus, where a proposition is split to reveal its propositional functions of one or of several variables (of individuals) x, y, …. Existential and universal quantification (‘there exists’, and ‘for all’ or ‘for every’) can apply to propositions, functions and individuals.
The first Part of this article deals with two deviations from normal practice. One concerns the assertion of a proposition, that is, the assignment to it of one of those two truth-values; while commonly done, the details of assertion are not usually pursued. The other concerns negation: normally TUL uses only ‘external’ negation, where an entire proposition is negated; but we take in also an important kind of ‘internal’ negation when a sub-proposition is negated.
The second Part of this article treats three contexts important in logic and mathematics where assertion and negations play significant roles: the propositional paradoxes, such as the liar paradox; indirect proof-methods, especially that by contradiction; and the distinction between implication and inference. Several features of our study contribute to an attempt in a sequel paper to characterise logical knowledge, and to distinguish it especially from mathematical knowledge.
All propositions are in indicative mood, and in either active or passive voice; we do not handle questions or commands, which have their own logical features. We do not treat more informal uses of a logic, such as logistics or the logic of the situation; or theories that have been called ‘inductive logics’, which belong to the philosophy of science and probability theory. However, they are all parts of ‘logical knowledge’, which refers to the totality of logics in general.
viernes, 2 de septiembre de 2011
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