Paloma Pérez-Ilzarbe | Universidad de Navarra (original) (raw)
Papers by Paloma Pérez-Ilzarbe
Springer eBooks, 2022
WOMEN IN PRAGMATISM INTERNATIONAL CONFERENCE (University of Barcelona, 28 - 30 January 2020) The ... more WOMEN IN PRAGMATISM INTERNATIONAL CONFERENCE (University of Barcelona, 28 - 30 January 2020) The Ladd-Franklin formula is a simple mathematical expression that represents the logical form of syllogisms in a completely general way. The use of symmetrical copulas makes the distinction of syllogistic figures unnecessary (since the positions of subject and predicate are interchangeable). In addition, the distinction of syllogistic moods is also made unnecessary: the choice of E-forms and I-forms reduces the number of possible combinations, and then, by putting the syllogism into the form of an inconsistency (which is again a symmetrical structure), the possibilities are reduced to one. This formula is very valuable indeed from the perspective of the construction of an abstract calculus, but here I wish to focus on two further aspects of Ladd’s innovation, both related to her decision to take symmetrical structures as canonical forms of expression, and both very much in the spirit of the Peircean conception of logic. First, I want to stress the visual character of the antilogistic structure. The canonical expression of propositions allows one to detect validity by mere visual inspection, just by checking the arrangement of universal/particular copulas and positive/negative terms. The antilogism is, in some sense, a diagram that exhibits the logical form of syllogisms in a way that makes validity visible (manifest to the trained eye). Second, I want to join Ladd herself in valuing the non-inferential character of her canonical expression of syllogisms (an inconsistent triad where the idea of a “succession” from premises to conclusion is lost). In spite of its apparent unnaturalness when presented as “the form of syllogisms”, the inconsistency reflects the structure of a very natural way of arguing (rebuttal). Thus the antilogism is offered by Ladd not only as a tool for calculation, but also as a fruitful insight into our actual reasoning process.
No somos islas. Homenaje al profesor Jaime Nubiola, 2023
In this paper I offer a new look at the semiotic ideas that underlie Susanne Langer’s philosophic... more In this paper I offer a new look at the semiotic ideas that underlie Susanne Langer’s philosophical project. Based on these ideas, I present a Langerian defense of philosophy, in its two main senses: philosophy as the reflection upon our own life (to which anyone should, ideally, aspire) and philosophy as the expert knowledge of the broadest concepts for the categorization of the world (which is the task of academic philosophy). In the first section I focus on the semiotic theory that Langer develops in Philosophy in a New Key (1942), highlighting the strictly logical aspects of her notions and distinctions. The second section studies the notion of “abstraction”, with which Langer captures the human ability of “seeing one thing in another”, which is the basis of metaphorical thinking. The key to understanding the semantic mechanism of metaphor lies in the idea that “presentational” symbols (in contrast to “discursive” symbols) are natural symbols, which exemplify the abstract form they symbolize. This peculiarity allows for the non-arbitrary extension of meaning which characterizes metaphor. Thus, metaphorical meaning can be understood, in Langer, not as a deviation from literal meaning, but as a semantic development towards a higher level of abstraction. The final section focuses on the role of metaphorical forms in human understanding (and on the important role this still leaves for philosophy). As a conclusion, the connection between philosophy and life that inspires Langer's thought is highlighted, and the effective role of academic philosophy in human life is defended.
Patristica et mediaevalia, 2001
This paper examines Buridan's conception of scientia as opposed to error, opinio and fides. S... more This paper examines Buridan's conception of scientia as opposed to error, opinio and fides. Since scientia (as well as error, opinio and fides) is the intellectual assent to some proposition, I will try to support the hypothesis that the specific nature and structure of propositions plays an essential role in Buridan's theory of human knowledge. On the one hand, the fact that a proposition is not a mere complexio but an enunciatio, capable of being true or false, determines that human knowledge is open to error. On the other hand, since a proposition may be not only apprehended but also judged to be true, there must be some causes that move the intellect from apprehensio to assensus. Given the natural inclination of the intellect to truth, the fact that some propositions are such that they can manifest their own truth and some others are not, seems to be the explanation of why the human mind wavers between scientific knowledge and opinion, and also of the difference between science and faith. As Buridan explains the truth conditions of propositions in terms of the semantic property of suppositio, the hypothesis that propositions play a role in knowledge can be tested by examining the contribution of suppositio to the grasping of truth
Pragmatism in the Americas
Anuario Filosófico, 2011
Formal Approaches and Natural Language in Medieval Logic, 2017
In what follows I will present Pardo' s analysis of the threat that singular trinitarian ... more In what follows I will present Pardo' s analysis of the threat that singular trinitarian terms pose to the formality of expository syllogism. My interest is more doctrinal than historical: I am looking for an understanding of the terminist conception of logical form (what can count as a formal element for a terminist logician, and what kind of tools they have developed for the analysis of logical form). In addition, Pardo's pages on the expository syllogism not only offer a general inquiry into the terminist understanding of the logical form of singular syllogistic premises, but they contain a lucid exposition of the limits of a non-formalised analysis of logical form. The chapter is structured in two main parts. In the first of these, I will give a brief introduction to put the discussion in context: first, I will present the problem of the formality of expository syllogism; second, I will outline the main features of the semantics of trinitarian terms and the logical device that was designed to solve trinitarian paralogisms (namely, the construction of new artificial propositions to effect the logical analysis of syllogistic premises). After that, the core of the chapter will deal with Pardo's analysis of this device: first, I will present his arguments concerning the logical properties of these new propositions; second, I will examine his arguments concerning the suitability of the new propositions for the analysis of the formal validity of expository syllogisms.
Servicio de Publicaciones de la Universidad de Navarra, 2003
Presentación 1 los problemas del mundo tecnificado en el que vivimos: a través de una realidad ta... more Presentación 1 los problemas del mundo tecnificado en el que vivimos: a través de una realidad tan cercana y omnipresente como la publicidad. Confiamos en que este Cuaderno ofrezca sugerencias interesantes, no sólo para los docentes de filosofía sino en general para cualquiera que pretenda comprender los problemas del mundo en que vivimos.
The complexity of the scholastic view of descent stems from the attempt to find a reply to three ... more The complexity of the scholastic view of descent stems from the attempt to find a reply to three different questions at the same time: those pertaining to the meaning of propositions, the relationships of inference between propositions, and the truth conditions of propositions. From each of these issues there arises a different sequence of developments to this doctrine, each of which has its own problems and solutions. Initially, the concept of descent is introduced in response to the problem of determining the meaning of quantified propositions. This is the first axis of the development of the doctrine of descent, according to which descent consists of the construction of individual propositions which make explicit the meaning of the quantified proposition. The appearance of these new propositions, however, gives rise to the second axis in the development of the doctrine of descent. As soon as we have this multiplicity of singular propositions, it is possible to forget where they came from and how, simply considering the problem of their logical relationship with the original quantified proposition. This is how descent comes to be viewed not as an analysis of the meaning of the proposition, but as a relationship of consequence: that which could be established between a quantified proposition and a set of singular propositions. Lastly, when descent is considered as a relationship of consequence, it is possible to develop this doctrine in a third direction, given that this relationship between a quantified proposition and a set of singular propositions can be used as a means of showing the truth or falsehood of the quantified proposition. Pardo’s text is a good example of the problems which the concept of descent inevitably encounters when it is approached from three points of view which are superimposed upon each other without regard for their radical diversity.
The first section offers a reconstruction of Buridan’s theory of propositions, along the followin... more The first section offers a reconstruction of Buridan’s theory of propositions, along the following lines: on the syntactic plane, propositions obtain a special type of unity from the presence of a copula; on the semantic plane, the fact that a proposition does not have any specific significate (different from the significate of terms), does not erase the distinction between propositions and terms: the copula performs an act of “saying”, in virtue of which propositions can be true or false. The second section summarises Pardo’s theory of propositions, showing how in this case a Buridanian starting point led to a result very different from that which Buridan reached
espanolEn este articulo estudio como Jeronimo Pardo (un autor espanol del terminismo tardio) intr... more espanolEn este articulo estudio como Jeronimo Pardo (un autor espanol del terminismo tardio) introduce subdivisiones en la nocion de “significacion” para analizar la posibilidad y limites de la suposicion material como instrumento de autorreferencialidad. Estas subdivisiones no son ad hoc, puesto que distintos conceptos median de distintos modos en la significacion del lenguaje vocal. EnglishI study the way in which Jeronimo Pardo (a late terminist Spanish author) introduces subdivisions in the notion of “signification”, in order to analyse the possibility and limits of material supposition as a device of self-reference. The non-ad-hoc character of these subdivisions is guaranteed by the fact that different concepts act as intermediaries, in different ways, in the signification of vocal language.
Springer eBooks, 2022
WOMEN IN PRAGMATISM INTERNATIONAL CONFERENCE (University of Barcelona, 28 - 30 January 2020) The ... more WOMEN IN PRAGMATISM INTERNATIONAL CONFERENCE (University of Barcelona, 28 - 30 January 2020) The Ladd-Franklin formula is a simple mathematical expression that represents the logical form of syllogisms in a completely general way. The use of symmetrical copulas makes the distinction of syllogistic figures unnecessary (since the positions of subject and predicate are interchangeable). In addition, the distinction of syllogistic moods is also made unnecessary: the choice of E-forms and I-forms reduces the number of possible combinations, and then, by putting the syllogism into the form of an inconsistency (which is again a symmetrical structure), the possibilities are reduced to one. This formula is very valuable indeed from the perspective of the construction of an abstract calculus, but here I wish to focus on two further aspects of Ladd’s innovation, both related to her decision to take symmetrical structures as canonical forms of expression, and both very much in the spirit of the Peircean conception of logic. First, I want to stress the visual character of the antilogistic structure. The canonical expression of propositions allows one to detect validity by mere visual inspection, just by checking the arrangement of universal/particular copulas and positive/negative terms. The antilogism is, in some sense, a diagram that exhibits the logical form of syllogisms in a way that makes validity visible (manifest to the trained eye). Second, I want to join Ladd herself in valuing the non-inferential character of her canonical expression of syllogisms (an inconsistent triad where the idea of a “succession” from premises to conclusion is lost). In spite of its apparent unnaturalness when presented as “the form of syllogisms”, the inconsistency reflects the structure of a very natural way of arguing (rebuttal). Thus the antilogism is offered by Ladd not only as a tool for calculation, but also as a fruitful insight into our actual reasoning process.
No somos islas. Homenaje al profesor Jaime Nubiola, 2023
In this paper I offer a new look at the semiotic ideas that underlie Susanne Langer’s philosophic... more In this paper I offer a new look at the semiotic ideas that underlie Susanne Langer’s philosophical project. Based on these ideas, I present a Langerian defense of philosophy, in its two main senses: philosophy as the reflection upon our own life (to which anyone should, ideally, aspire) and philosophy as the expert knowledge of the broadest concepts for the categorization of the world (which is the task of academic philosophy). In the first section I focus on the semiotic theory that Langer develops in Philosophy in a New Key (1942), highlighting the strictly logical aspects of her notions and distinctions. The second section studies the notion of “abstraction”, with which Langer captures the human ability of “seeing one thing in another”, which is the basis of metaphorical thinking. The key to understanding the semantic mechanism of metaphor lies in the idea that “presentational” symbols (in contrast to “discursive” symbols) are natural symbols, which exemplify the abstract form they symbolize. This peculiarity allows for the non-arbitrary extension of meaning which characterizes metaphor. Thus, metaphorical meaning can be understood, in Langer, not as a deviation from literal meaning, but as a semantic development towards a higher level of abstraction. The final section focuses on the role of metaphorical forms in human understanding (and on the important role this still leaves for philosophy). As a conclusion, the connection between philosophy and life that inspires Langer's thought is highlighted, and the effective role of academic philosophy in human life is defended.
Patristica et mediaevalia, 2001
This paper examines Buridan's conception of scientia as opposed to error, opinio and fides. S... more This paper examines Buridan's conception of scientia as opposed to error, opinio and fides. Since scientia (as well as error, opinio and fides) is the intellectual assent to some proposition, I will try to support the hypothesis that the specific nature and structure of propositions plays an essential role in Buridan's theory of human knowledge. On the one hand, the fact that a proposition is not a mere complexio but an enunciatio, capable of being true or false, determines that human knowledge is open to error. On the other hand, since a proposition may be not only apprehended but also judged to be true, there must be some causes that move the intellect from apprehensio to assensus. Given the natural inclination of the intellect to truth, the fact that some propositions are such that they can manifest their own truth and some others are not, seems to be the explanation of why the human mind wavers between scientific knowledge and opinion, and also of the difference between science and faith. As Buridan explains the truth conditions of propositions in terms of the semantic property of suppositio, the hypothesis that propositions play a role in knowledge can be tested by examining the contribution of suppositio to the grasping of truth
Pragmatism in the Americas
Anuario Filosófico, 2011
Formal Approaches and Natural Language in Medieval Logic, 2017
In what follows I will present Pardo' s analysis of the threat that singular trinitarian ... more In what follows I will present Pardo' s analysis of the threat that singular trinitarian terms pose to the formality of expository syllogism. My interest is more doctrinal than historical: I am looking for an understanding of the terminist conception of logical form (what can count as a formal element for a terminist logician, and what kind of tools they have developed for the analysis of logical form). In addition, Pardo's pages on the expository syllogism not only offer a general inquiry into the terminist understanding of the logical form of singular syllogistic premises, but they contain a lucid exposition of the limits of a non-formalised analysis of logical form. The chapter is structured in two main parts. In the first of these, I will give a brief introduction to put the discussion in context: first, I will present the problem of the formality of expository syllogism; second, I will outline the main features of the semantics of trinitarian terms and the logical device that was designed to solve trinitarian paralogisms (namely, the construction of new artificial propositions to effect the logical analysis of syllogistic premises). After that, the core of the chapter will deal with Pardo's analysis of this device: first, I will present his arguments concerning the logical properties of these new propositions; second, I will examine his arguments concerning the suitability of the new propositions for the analysis of the formal validity of expository syllogisms.
Servicio de Publicaciones de la Universidad de Navarra, 2003
Presentación 1 los problemas del mundo tecnificado en el que vivimos: a través de una realidad ta... more Presentación 1 los problemas del mundo tecnificado en el que vivimos: a través de una realidad tan cercana y omnipresente como la publicidad. Confiamos en que este Cuaderno ofrezca sugerencias interesantes, no sólo para los docentes de filosofía sino en general para cualquiera que pretenda comprender los problemas del mundo en que vivimos.
The complexity of the scholastic view of descent stems from the attempt to find a reply to three ... more The complexity of the scholastic view of descent stems from the attempt to find a reply to three different questions at the same time: those pertaining to the meaning of propositions, the relationships of inference between propositions, and the truth conditions of propositions. From each of these issues there arises a different sequence of developments to this doctrine, each of which has its own problems and solutions. Initially, the concept of descent is introduced in response to the problem of determining the meaning of quantified propositions. This is the first axis of the development of the doctrine of descent, according to which descent consists of the construction of individual propositions which make explicit the meaning of the quantified proposition. The appearance of these new propositions, however, gives rise to the second axis in the development of the doctrine of descent. As soon as we have this multiplicity of singular propositions, it is possible to forget where they came from and how, simply considering the problem of their logical relationship with the original quantified proposition. This is how descent comes to be viewed not as an analysis of the meaning of the proposition, but as a relationship of consequence: that which could be established between a quantified proposition and a set of singular propositions. Lastly, when descent is considered as a relationship of consequence, it is possible to develop this doctrine in a third direction, given that this relationship between a quantified proposition and a set of singular propositions can be used as a means of showing the truth or falsehood of the quantified proposition. Pardo’s text is a good example of the problems which the concept of descent inevitably encounters when it is approached from three points of view which are superimposed upon each other without regard for their radical diversity.
The first section offers a reconstruction of Buridan’s theory of propositions, along the followin... more The first section offers a reconstruction of Buridan’s theory of propositions, along the following lines: on the syntactic plane, propositions obtain a special type of unity from the presence of a copula; on the semantic plane, the fact that a proposition does not have any specific significate (different from the significate of terms), does not erase the distinction between propositions and terms: the copula performs an act of “saying”, in virtue of which propositions can be true or false. The second section summarises Pardo’s theory of propositions, showing how in this case a Buridanian starting point led to a result very different from that which Buridan reached
espanolEn este articulo estudio como Jeronimo Pardo (un autor espanol del terminismo tardio) intr... more espanolEn este articulo estudio como Jeronimo Pardo (un autor espanol del terminismo tardio) introduce subdivisiones en la nocion de “significacion” para analizar la posibilidad y limites de la suposicion material como instrumento de autorreferencialidad. Estas subdivisiones no son ad hoc, puesto que distintos conceptos median de distintos modos en la significacion del lenguaje vocal. EnglishI study the way in which Jeronimo Pardo (a late terminist Spanish author) introduces subdivisions in the notion of “signification”, in order to analyse the possibility and limits of material supposition as a device of self-reference. The non-ad-hoc character of these subdivisions is guaranteed by the fact that different concepts act as intermediaries, in different ways, in the signification of vocal language.
Anuario Filosófico, 2011
Reseña del libro "Lógica aristotélica" de José Miguel Gambra y Manuel Oriol: "una fundamentación ... more Reseña del libro "Lógica aristotélica" de José Miguel Gambra y Manuel Oriol: "una fundamentación aristotélica, sistemática y actualizada de la lógica aristotélica elemental". Este manual interesará no solamente a quienes tengan que impartir una asignatura de lógica aristotélica, sino a quienes se hayan formado en la lógica matemática pero deseen conocer, con cierta profundidad (con las limitaciones de espacio y complejidad de un manual, pero con todo el rigor de una investigación seria), una lógica distinta de la que aprendieron.
Anuario Filosófico, 2022
The third edition of Logic Primer: very useful for instructors, as a source of ideas to organize ... more The third edition of Logic Primer: very useful for instructors, as a source of ideas to organize an introductory logic course, and as a repository of exercises of different levels of difficulty.
Anuario Filosófico, 2020
Este voluminoso libro es una recopilación de algunos trabajos del matemático y filósofo William B... more Este voluminoso libro es una recopilación de algunos trabajos del matemático y filósofo William Boos (1943-2014), situados en la zona fronteriza entre matemáticas y filosofía. El estilo que comparten todos los trabajos es un ir y venir alegórico, en el que, por un lado, la metamatemática se usa como metáfora para entender los grandes temas de la historia de la filosofía y, por otro lado, los problemas filosóficos sirven para iluminar el sentido de los resultados de la metamatemática del siglo XX.
Anuario Filosófico, 2018
A book devoted to predication from a philosophical point of view, which deals with the main probl... more A book devoted to predication from a philosophical point of view, which deals with the main problems on the topic: the nature of predication, the history of the notion, the role of the copula, the role of names, the ontology of propositions, the syntactic and semantic analysis of propositions, the pragmatics of saying, the connection between logic and ontology.
Two rival paradigms are distinguished, the Aristotelian and the Fregean analysis of predication, and the impression is transmitted that the Fregean one has some limits and might be refined.
The most promising orientations in this book are: the attention paid to ontological questions, the search for alternatives to the dominant paradigm, and, in sum, the sense that there is something special in the act of "saying".
Anuario Filosófico, 2018
ANUARIO FILOSÓFICO 51/1 (2018) en la realidad natural, y la idea puesta por el Creador en el homb... more ANUARIO FILOSÓFICO 51/1 (2018) en la realidad natural, y la idea puesta por el Creador en el hombre haciéndolo captador de ideas" (p. 117). La segunda, que el hombre, al ser el culmen de la creación, es la única criatura capaz de abrirse a una relación más allá de lo intra-mundano, que trascienda los modos de ser para llegar hasta el que simplemente Es (pp. 122-123). Y la tercera, que en virtud de su especial participación respecto del Divino Artífi ce, el hombre se hace a la vez co-creador, cultivando el mundo con la simiente de sus ideas, o sea, desenvolviendo la cultura (p. 121). La edición se cierra con dos Excursus: "En busca del absolutola vía de la indigencia", y "Evolución y creación".
Reseña de la obra de Aliseda, Atocha, "La lógica como herramienta de la razón. Razonamiento ampli... more Reseña de la obra de Aliseda, Atocha, "La lógica como herramienta de la razón. Razonamiento ampliativo en la creatividad, la cognición y la inferencia", College Publications, Milton Keynes, 2014, 90 pp.
http://hdl.handle.net/10171/39246
I would like to present Articulating Medieval Logic as the outline of a research program for medi... more I would like to present Articulating Medieval Logic as the outline of a research program for medieval logic scholars. The book can be seen to belong to the first stage of a huge project: a serious attempt at considering together two different logical paradigms (the ‘medieval’ and the ‘post-Fregean’), in the belief that they are comparable. The first stage, represented here, is the development of an artificial language that can translate both, and (accompanied by the corresponding semantics and deductive apparatus) can act as a medium for comparison.
http://hdl.handle.net/10171/42316
Mathematical Reviews
The book contains both a set of technical proposals and a philosophical reflec- tion about the n... more The book contains both a set of technical proposals and a philosophical reflec-
tion about the nature of logic. The technical part is fairly developed: in sum,
Slater’s articles show how the Epsilon Calculus provides a satisfactory formal-
ization of natural language, seems to avoid paradoxes (with the advantage of
being a conservative extension of classical Predicate Logic), and allows a natu-
ral treatment of fictional discourse. The philosophical part, which is reflected
in the title of the compilation, is in fact the core of the author’s research pro-
gramme: “logic is not mathematical”, that is, logical analysis must attend to
natural language, rather than to mathematical structures independently con-
strued.
http://hdl.handle.net/10171/29696
Mathematical Reviews
This book is a significant contribution to the semantics of time and change. The title reveals t... more This book is a significant contribution to the semantics of time and change.
The title reveals the author’s option for temporalism, that is, the thesis that
propositions can be affected by the passage of time: the backdrop of Brogaard’s
research is her idea that propositions can change their truth values over time.
This temporalist framework allows for interesting developments in two direc-
tions, one more metaphysical in character (in accordance with the subtitle) and
the other strictly logical: on the one hand, the book investigates the nature of
‘temporal’ (as opposed to ‘eternal’) propositions; on the other hand, it tries to
offer a correct account of the logical form of tensed sentences.
http://hdl.handle.net/10171/29695
Mathematical Reviews
This is a weighty and daring book. It proposes a new philosophy of mathe- matics, based on a det... more This is a weighty and daring book. It proposes a new philosophy of mathe-
matics, based on a detailed knowledge of the most recent work in advanced
mathematics, and constructed in explicit contrast with the traditional analyti-
cal approach. A brief yet illuminating introduction summarizes the spirit of the
work in four theses: a) contemporary mathematics must not be reduced to Set
Theory, and neither must it to elementary mathematics; b) real contemporary
work in mathematics is the source of new, as yet unattended, philosophical prob-
lems; c) philosophy of mathematics should be synthetic rather than analytic, in
order to capture the dialectical tensions that are present in actual mathematical
activity; d) there is in fact a fruitful exchange between philosophy and mathe-
matics that must be fostered in order to promote both mathematical creativity
and philosophical reflection. Going beyond the dualistic schemas that have tra-
ditionally oppressed the philosophy of mathematics, such as the dichotomies re-
alism/idealism, necessity/contingency, unity/plurality, among others, Zalamea
undertakes a study of the living and evolving mathematics from an unbiased
philosophical perspective.
http://hdl.handle.net/10171/29694
Mathematical Reviews
The book is a short introduction to five non-classical logics (temporal, modal, conditional, rel... more The book is a short introduction to five non-classical logics (temporal, modal,
conditional, relevantistic, and intuitionistic). In its 153 pages it has room for
several items that students and non-specialists will thank: the philosophical
motivations of the technical developments are treated; some useful suggestions
for further readings are given (in particular, the reader is provided with sources
of “second opinions”); and a number of technical proofs of the main results
are given or at least sketched, leaving nonetheless to the reader the option of
skipping them. Understandably, the book has not room for any compilation
of “end-of-chapter problem sets” (sometimes offered as a complement to logic
textbooks); it also has to neglect a systematic history of the different non-
classical developments; and, finally, as a general rule, the technical results have
preeminence over the discussion of the philosophical issues that underlie or are
raised by them.
http://hdl.handle.net/10171/29677
WOMEN IN PRAGMATISM INTERNATIONAL CONFERENCE (University of Barcelona, 28 - 30 January 2020) The... more WOMEN IN PRAGMATISM INTERNATIONAL CONFERENCE
(University of Barcelona, 28 - 30 January 2020)
The Ladd-Franklin formula is a simple mathematical expression that represents the logical form of syllogisms in a completely general way. The use of symmetrical copulas makes the distinction of syllogistic figures unnecessary (since the positions of subject and predicate are interchangeable). In addition, the distinction of syllogistic moods is also made unnecessary: the choice of E-forms and I-forms reduces the number of possible combinations, and then, by putting the syllogism into the form of an inconsistency (which is again a symmetrical structure), the possibilities are reduced to one.
This formula is very valuable indeed from the perspective of the construction of an abstract calculus, but here I wish to focus on two further aspects of Ladd’s innovation, both related to her decision to take symmetrical structures as canonical forms of expression, and both very much in the spirit of the Peircean conception of logic.
First, I want to stress the visual character of the antilogistic structure. The canonical expression of propositions allows one to detect validity by mere visual inspection, just by checking the arrangement of universal/particular copulas and positive/negative terms. The antilogism is, in some sense, a diagram that exhibits the logical form of syllogisms in a way that makes validity visible (manifest to the trained eye).
Second, I want to join Ladd herself in valuing the non-inferential character of her canonical expression of syllogisms (an inconsistent triad where the idea of a “succession” from premises to conclusion is lost). In spite of its apparent unnaturalness when presented as “the form of syllogisms”, the inconsistency reflects the structure of a very natural way of arguing (rebuttal). Thus the antilogism is offered by Ladd not only as a tool for calculation, but also as a fruitful insight into our actual reasoning process.
No somos islas. Homenaje al profesor Jaime Nubiola (Pamplona: Eunsa), 2023
Este volumen colectivo reúne trabajos de distintas áreas de la filosofía. Es un regalo que alguno... more Este volumen colectivo reúne trabajos de distintas áreas de la filosofía. Es un regalo que algunos colegas ofrecen al profesor Jaime Nubiola con motivo de su jubilación, como símbolo de agradecimiento por su amistad y magisterio. Las veintiséis contribuciones, agrupadas en cuatro bloques temáticos, abarcan autores, temas, corrientes filosóficas y momentos históricos muy variados, pero están en todos los casos conectadas con la vida intelectual que Jaime ha ido cultivando a su alrededor.
I. “El profesor universitario”. Junto con unas semblanzas que presentan a Jaime Nubiola como maestro y como amigo, esta primera parte contiene también dos capítulos de investigación propiamente dicha, en los que las nociones de “interdisciplinariedad” y “persona” ayudan a comprender la unidad de dimensiones complementarias (distintas pero interrelacionadas) que debe tener lugar, de modo privilegiado en la enseñanza universitaria, y en general en toda vida propiamente humana.
II. “Pensar, escribir, dialogar: hacer el mundo más razonable”. El hilo conductor de esta segunda parte es el lenguaje (o, más ampliamente, los signos compartidos) y el tema de fondo es la búsqueda de sentido, que se lleva a cabo en comunidad. Las nociones de “juegos de lenguaje”, “abstracción”, “narración”, “formas de vida”, “razonabilidad”, “amor personal” y “juego”, por nombrar solamente las más centrales, son herramientas para comprender realidades tan presentes en nuestras vidas como el crecimiento de nuestros hijos, la necesidad de saber quiénes somos, la transmisión de la fe, la orientación de las acciones de acuerdo con fines, la importancia de la amistad o las peculiaridades de la investigación científica.
III. “Filosofía para el siglo XXI”. En la tercera parte se trata de mostrar la conexión real de la filosofía académica con algunas de las grandes cuestiones del mundo contemporáneo: el debilitamiento moderno de las antiguas convicciones compartidas sobre el mundo y la vida, el eclipse de la verdad en el discurso público, la relación del ser humano con la naturaleza, la lucha de las mujeres por la superación de barreras, el papel de las emociones en la vida política, la presencia de lo sagrado en la cultura laica y la posibilidad de la ética en la sociedad neoliberal. Las nociones filosóficas con las que se trata de comprender estas cuestiones son: “sospecha” y “confianza”, “verdad” y “posverdad”, “naturaleza” y “finalidad”, “autonomía” y “simpatía”, “reconocimiento” e “identidad”, “inspiración” y “fiesta”, “poder” y “amabilidad”.
IV. “La comprensión histórica de la filosofía”. La última parte quiere reflejar el modo de hacer filosofía que Jaime practicó y enseñó durante toda su carrera. Por una parte, el diálogo con los filósofos Nicolás de Cusa, Tomás de Aquino, Saul Kripke, Michel Foucault y Friedrich Nietzsche; por otra parte, la mirada al contexto en el que se desarrollan el arte de Manuel de Falla, la epistemología empirista y la comunidad pragmatista mediterránea; en conjunto, estos capítulos nos ayudan a profundizar en cuestiones como las siguientes: ¿qué son la mente y el conocimiento?, ¿qué es eso que llamamos Dios?, ¿qué se esconde en un nombre?, ¿cómo encontrar la verdad sobre nosotros mismos?, ¿cómo enfrentarnos a nuestra fragilidad?, ¿qué relación tiene el arte con la vida?, ¿son las matemáticas algo más que lógica? y, finalmente, ¿qué es una comunidad de pensamiento?