I'm an associate researcher at UNAM 's Institute for Philosophical Research, and a member of the Mexican National System of Researchers (SNI), level I . Formerly I was a research fellow at the University of Tartu (Estonia).
I work mainly on the philosophical bases of universal logic. Particularly, I'm interested in the axiomatic emptiness of logical consequence, an abstract view of what the relata of logical consequence are, and the debate logical monism-logical pluralism. However, I've also made some incursions in philosophy of mathematics, metaphysics and philosophy of language.
It is part of the logical orthodoxy that quantifiers are interdefinable and that the rules of Uni... more It is part of the logical orthodoxy that quantifiers are interdefinable and that the rules of Universal Instantiation (UI) and Existential Generalization (EG) hold or fail together. Christopher Gauker has presented some cases which seemingly undermine the validity of UI but nonetheless leave EG untouched, and has developed a very sophisticated theory to explain why this is so. In the process, he has rejected several attempts to explain the asymmetry, especially those aiming at saving the logical orthodoxy by showing what is wrong with the counterexamples to UI. In this paper I argue that some of those proposals are better grounded than Gauker thinks and that ultimately they should be preferred over his since they explain satisfactorily the apparent counterexamples.
The most widespread criterion for the admission of a logic into the connexive family is the satis... more The most widespread criterion for the admission of a logic into the connexive family is the satisfaction of the pairs of formulas known as Aristotle's and Boethius' theses, along with the non-symmetry of implication. In this paper, we discuss whether this is enough to characterize a connexive logic or if more can be said about the issue. Our strategy is the following: first, we introduce a logic that has origins and motivations that have little to do with connexive logic. We then present a list of additional criteria found scattered throughout the literature on connexivity and propose to use this list to compare this logic and some of the well-known non-bivalent truth-functional connexive logics. This comparison gives us several interesting results: when every condition is given the same weight, the introduced logic can score as high as some of the well-known systems. Furthermore, a connection between the satisfaction of the most conditions and the loss of intuitiveness or an increase in the complexity of certain structural properties of the system seems to arise. We take these results to motivate the more general open problem of finding the most adequate way of judging systems of connexive logic.
Logical Studies of Paraconsistent Reasoning in Science and Mathematics
In this paper I argue, contra Mortensen, that there is a case, namely that of a degenerate topos,... more In this paper I argue, contra Mortensen, that there is a case, namely that of a degenerate topos, an extremely simple mathematical universe in which everything is true, in which no mathematical "catastrophe" is implied by mathematical triviality. I will show that either one of the premises of Dunn's trivialization result for real number theory –on which Mortensen mounts his case– cannot obtain (from a point of view " external " to the universe) and thus the argument is unsound, or that it obtains in calculations "internal" to such trivial universe and the theory associated, yet the calculations are possible and meaningful albeit extremely simple.
Morgan Thomas has recently shown that a family of naïve set theories based on Asenjo-Priest's "lo... more Morgan Thomas has recently shown that a family of naïve set theories based on Asenjo-Priest's "logic of paradox" (LP) and other related logics suffer from serious expressive limitations. At first sight these results could seem a serious drawback for the prospects of inconsistent mathematics, since these naïve set theories either lack even the most elementary concepts needed to express basic notions of classical mathematics or are nearly trivial. I will argue that these results are not a doom for LP-mathematics, but rather suggest a different, non-foundational role of set theory in non-classical mathematics.
En este trabajo nos ocupamos de la afirmación de Peter Vickers de que los infinitesimales de Bern... more En este trabajo nos ocupamos de la afirmación de Peter Vickers de que los infinitesimales de Bernoulli y, con ello, toda su versión del cálculo, son inconsistentes. Siguiendo la misma metodología que Vickers usa para evaluar, y rechazar, los cargos de inconsistencia contra el cálculo de la primera época, evaluamos su propio cargo de inconsistencia contra el cálculo de Bernoulli. Argumentaremos que el Postulado I de Die Differentialrechnung, la proposición en la que se centra Vickers, no es una contradicción explícita ni nos conduce a una sin ciertos supuestos debatibles, por lo que la teoría formal del cálculo de Bernoulli no necesariamente tendría que ser inconsistente. También argumentaremos que la relatividad de la inconsistencia a una lógica y la falta de evidencia histórica también impiden armar que la justificación bernoulliana de su cálculo sea inconsistente, por lo que Vickers no tiene elementos suficientes para catalogar el cálculo de Bernoulli como inconsistente.
In this paper we present a proposal that (i) could validate more relations in the square than tho... more In this paper we present a proposal that (i) could validate more relations in the square than those allowed by classical logic (ii) without a modification of canonical notation neither of current symbolization of categorical statements though (iii) with a different but reliable semantics.
The geometric analogy is often mentioned to make logical pluralism plausible, nonetheless, how fa... more The geometric analogy is often mentioned to make logical pluralism plausible, nonetheless, how far the analogy should be taken is an issue hardly ever discussed. Rescher in [24] gave one of the most detailed analyses of the analogy, and at the same time one of the most severe critiques to the idea of taking the analogy seriously. More recently Priest in [20] has argued for the legitimacy of the geometric analogy, trying to reject some of Rescher's criticisms, but I will show that he failed. Here I will argue that Rescher's arguments against the idea that the subject matter of logic is not necessarily its canonical application, but a pure mathematical subject akin to that of geometry, are not conclusive. In particular, I will show that Rescher's denial of the analogy and his rejection of the idea of a pure logic are grounded on some historical fallacies regarding the development of geometry, as well as on an uncritically assumption about the nature of logic as an essentially applied theory.
In this position paper we reconstruct and evaluate three arguments by Jean-Yves Béziau put forwar... more In this position paper we reconstruct and evaluate three arguments by Jean-Yves Béziau put forward to show that paraconsistent logics may replace non-monotonic logics in the analysis of situations what the latter were created for, namely updating of databases by increment of information. As originally put forward they might seem too colorful or unserious and easily dismissible, but they really call into question the foundations of non-monotonic logic. We will show that non-monotonic logic may go off well of Béziau's challenging arguments, though.
The subjunctive conditional associated to an intensional disjunction is a bit more complex than u... more The subjunctive conditional associated to an intensional disjunction is a bit more complex than usually thought, and it does not have the fatalist consequences attributed to it.
According to logical non-necessitarianism, every inference may fail in some situation. In his def... more According to logical non-necessitarianism, every inference may fail in some situation. In his defense of logical monism, Graham Priest has put forward an argument against non-necessitarianism based on the meaning of connectives. According to him, as long as the meanings of connectives are fixed, some inferences have to hold in all situations. Hence, in order to accept the non-necessitarianist thesis one would have to dispose arbitrarily of those meanings. I want to show here that non-necessitarianism can stand, without disposing arbitrarily of the meanings of connectives, based on a minimalist view on the meanings of connectives.
In this paper I present a couple of examples of inconsistency-tolerant mathematical theories and ... more In this paper I present a couple of examples of inconsistency-tolerant mathematical theories and some of their most interesting properties. I outline some philosophical issues surrounding this kind of logics and mathematics, and suggest that they can help to expand the concept we have of mathematics, noting that the limits of the mathematically acceptable can be much broader than we thought.
En este artículo presento algunos ejemplos de teorías matemáticas tolerantes a la inconsistencia y algunas de sus propiedades más interesantes. Esbozo algunas cuestiones filosóficas surgidas en torno a ese tipo de lógicas y matemáticas y sugiero que ellas pueden contribuir a ampliar la concepción que se tiene de la matemática, señalando que los límites de lo matemáticamente aceptable pueden ser mucho más amplios de lo que hemos creído.
According to logical non-necessitarianism, every inference may fail in some situation. In his def... more According to logical non-necessitarianism, every inference may fail in some situation. In his defense of logical monism, Graham Priest has put forward an argument against non-necessitarianism based on the meaning of connectives. According to him, as long as the meanings of connectives are fixed, some inferences have to hold in all situations. Hence, in order to accept the non-necessitarianist thesis one would have to dispose arbitrarily of those meanings. I want to show here that non-necessitarianism can stand, without disposing arbitrarily of the meanings of connectives, based on a minimalist view on the meanings of connectives.
En esta nota crítica trato de (i) dar una breve descripción de cada uno de los artículos que comp... more En esta nota crítica trato de (i) dar una breve descripción de cada uno de los artículos que componen Orayen: de la forma lógica al significado, (ii) señalar algunas cuestiones que no están claras en ellos o en las réplicas de Orayen y, (iii) en la medida de lo posible, tratar de señalar si los autores hacen desarrollos ulteriores acerca de los problemas abordados en sus artículos.
The aim of this note is threefold: (i) briefly describe and comment each of the articles of Orayen: de la forma lógica al significado; (ii) to identify some issues that may not be clear enough or not fully developed whether in the articles or even in Orayen’s replies; (iii) to the extent possible, to refer to further studies by the authors themselves on the same as, or quite related to, the subjects addressed by them in their papers.
We argue here that the meanings of logical connectives need not to differ in different logics. Ba... more We argue here that the meanings of logical connectives need not to differ in different logics. Based on the category-theoretic treatment of the logical connectives, we argue against the well-known Quinean thesis that a difference between logics implies a difference in the meanings of connectives. We thus locate this change in the difference between certain objects rather than in the difference between the meaning of connectives. Finally, we try to show that the category-theoretic treatment of logical connectives is a form of semantic minimalism, according to which not all the usual semantic components are relevant in fixing the meaning of a connective.
En este artículo tratamos de hacer plausible la hipótesis de que las conectivas de diferentes lógicas no necesariamente difieren en significado. Utilizando el tratamiento categorista de las conectivas, argumentaremos contra la tesis quineana de que la diferencia de lógicas implica diferencia de significado entre sus conectivas, y ubicamos el cambio de tema en la diferencia de objetos más bien que en una tal diferencia de significado. Finalmente, intentamos mostrar que ese tratamiento categorista es una forma de minimalismo semántico, de acuerdo con el cual no todos los elementos semánticos usuales son relevantes para determinar el significado de las conectivas.
In this paper I probe the idea that neither possibilism nor trivialism could be ruled out on a pu... more In this paper I probe the idea that neither possibilism nor trivialism could be ruled out on a purely logical basis. I use the apparatus of relational structures used in the semantics for modal logics to engineer some models of possibilism and trivialism and I discuss a philosophical stance about logic, truth values and the meaning of connectives underlying such analysis.
Overemphasizing the features of abduction as it occurs in scientifi c practices and daily life sc... more Overemphasizing the features of abduction as it occurs in scientifi c practices and daily life scenarios has led to overlook some features that abduction in those circumstances shares with other phenomena in which some given outputs fail to stand in a certain relation with some given inputs, and thus a modifi cation on those inputs is in order. We propose here a top-down, conceptual and taxonomic investigation on what the most general purely logical features of abduction could be, as well as a research program to investigate to what extent it is a pervasive notion in logic. We start by motivating some broadenings in the most common approaches to abduction, then we characterize inferential problems and finally give general characterizations of the notions of abductive problem, abductive solution and abductive inference.
Si ese viejo profesor no creyera que la teoría de categorías es una vieja moda francesa, él diría... more Si ese viejo profesor no creyera que la teoría de categorías es una vieja moda francesa, él diría que este artículo es una buena aproximación a lo que todo lógico educado debería saber de teoría de topos. Ahora sí, la última versión.
It is part of the logical orthodoxy that quantifiers are interdefinable and that the rules of Uni... more It is part of the logical orthodoxy that quantifiers are interdefinable and that the rules of Universal Instantiation (UI) and Existential Generalization (EG) hold or fail together. Christopher Gauker has presented some cases which seemingly undermine the validity of UI but nonetheless leave EG untouched, and has developed a very sophisticated theory to explain why this is so. In the process, he has rejected several attempts to explain the asymmetry, especially those aiming at saving the logical orthodoxy by showing what is wrong with the counterexamples to UI. In this paper I argue that some of those proposals are better grounded than Gauker thinks and that ultimately they should be preferred over his since they explain satisfactorily the apparent counterexamples.
The most widespread criterion for the admission of a logic into the connexive family is the satis... more The most widespread criterion for the admission of a logic into the connexive family is the satisfaction of the pairs of formulas known as Aristotle's and Boethius' theses, along with the non-symmetry of implication. In this paper, we discuss whether this is enough to characterize a connexive logic or if more can be said about the issue. Our strategy is the following: first, we introduce a logic that has origins and motivations that have little to do with connexive logic. We then present a list of additional criteria found scattered throughout the literature on connexivity and propose to use this list to compare this logic and some of the well-known non-bivalent truth-functional connexive logics. This comparison gives us several interesting results: when every condition is given the same weight, the introduced logic can score as high as some of the well-known systems. Furthermore, a connection between the satisfaction of the most conditions and the loss of intuitiveness or an increase in the complexity of certain structural properties of the system seems to arise. We take these results to motivate the more general open problem of finding the most adequate way of judging systems of connexive logic.
Logical Studies of Paraconsistent Reasoning in Science and Mathematics
In this paper I argue, contra Mortensen, that there is a case, namely that of a degenerate topos,... more In this paper I argue, contra Mortensen, that there is a case, namely that of a degenerate topos, an extremely simple mathematical universe in which everything is true, in which no mathematical "catastrophe" is implied by mathematical triviality. I will show that either one of the premises of Dunn's trivialization result for real number theory –on which Mortensen mounts his case– cannot obtain (from a point of view " external " to the universe) and thus the argument is unsound, or that it obtains in calculations "internal" to such trivial universe and the theory associated, yet the calculations are possible and meaningful albeit extremely simple.
Morgan Thomas has recently shown that a family of naïve set theories based on Asenjo-Priest's "lo... more Morgan Thomas has recently shown that a family of naïve set theories based on Asenjo-Priest's "logic of paradox" (LP) and other related logics suffer from serious expressive limitations. At first sight these results could seem a serious drawback for the prospects of inconsistent mathematics, since these naïve set theories either lack even the most elementary concepts needed to express basic notions of classical mathematics or are nearly trivial. I will argue that these results are not a doom for LP-mathematics, but rather suggest a different, non-foundational role of set theory in non-classical mathematics.
En este trabajo nos ocupamos de la afirmación de Peter Vickers de que los infinitesimales de Bern... more En este trabajo nos ocupamos de la afirmación de Peter Vickers de que los infinitesimales de Bernoulli y, con ello, toda su versión del cálculo, son inconsistentes. Siguiendo la misma metodología que Vickers usa para evaluar, y rechazar, los cargos de inconsistencia contra el cálculo de la primera época, evaluamos su propio cargo de inconsistencia contra el cálculo de Bernoulli. Argumentaremos que el Postulado I de Die Differentialrechnung, la proposición en la que se centra Vickers, no es una contradicción explícita ni nos conduce a una sin ciertos supuestos debatibles, por lo que la teoría formal del cálculo de Bernoulli no necesariamente tendría que ser inconsistente. También argumentaremos que la relatividad de la inconsistencia a una lógica y la falta de evidencia histórica también impiden armar que la justificación bernoulliana de su cálculo sea inconsistente, por lo que Vickers no tiene elementos suficientes para catalogar el cálculo de Bernoulli como inconsistente.
In this paper we present a proposal that (i) could validate more relations in the square than tho... more In this paper we present a proposal that (i) could validate more relations in the square than those allowed by classical logic (ii) without a modification of canonical notation neither of current symbolization of categorical statements though (iii) with a different but reliable semantics.
The geometric analogy is often mentioned to make logical pluralism plausible, nonetheless, how fa... more The geometric analogy is often mentioned to make logical pluralism plausible, nonetheless, how far the analogy should be taken is an issue hardly ever discussed. Rescher in [24] gave one of the most detailed analyses of the analogy, and at the same time one of the most severe critiques to the idea of taking the analogy seriously. More recently Priest in [20] has argued for the legitimacy of the geometric analogy, trying to reject some of Rescher's criticisms, but I will show that he failed. Here I will argue that Rescher's arguments against the idea that the subject matter of logic is not necessarily its canonical application, but a pure mathematical subject akin to that of geometry, are not conclusive. In particular, I will show that Rescher's denial of the analogy and his rejection of the idea of a pure logic are grounded on some historical fallacies regarding the development of geometry, as well as on an uncritically assumption about the nature of logic as an essentially applied theory.
In this position paper we reconstruct and evaluate three arguments by Jean-Yves Béziau put forwar... more In this position paper we reconstruct and evaluate three arguments by Jean-Yves Béziau put forward to show that paraconsistent logics may replace non-monotonic logics in the analysis of situations what the latter were created for, namely updating of databases by increment of information. As originally put forward they might seem too colorful or unserious and easily dismissible, but they really call into question the foundations of non-monotonic logic. We will show that non-monotonic logic may go off well of Béziau's challenging arguments, though.
The subjunctive conditional associated to an intensional disjunction is a bit more complex than u... more The subjunctive conditional associated to an intensional disjunction is a bit more complex than usually thought, and it does not have the fatalist consequences attributed to it.
According to logical non-necessitarianism, every inference may fail in some situation. In his def... more According to logical non-necessitarianism, every inference may fail in some situation. In his defense of logical monism, Graham Priest has put forward an argument against non-necessitarianism based on the meaning of connectives. According to him, as long as the meanings of connectives are fixed, some inferences have to hold in all situations. Hence, in order to accept the non-necessitarianist thesis one would have to dispose arbitrarily of those meanings. I want to show here that non-necessitarianism can stand, without disposing arbitrarily of the meanings of connectives, based on a minimalist view on the meanings of connectives.
In this paper I present a couple of examples of inconsistency-tolerant mathematical theories and ... more In this paper I present a couple of examples of inconsistency-tolerant mathematical theories and some of their most interesting properties. I outline some philosophical issues surrounding this kind of logics and mathematics, and suggest that they can help to expand the concept we have of mathematics, noting that the limits of the mathematically acceptable can be much broader than we thought.
En este artículo presento algunos ejemplos de teorías matemáticas tolerantes a la inconsistencia y algunas de sus propiedades más interesantes. Esbozo algunas cuestiones filosóficas surgidas en torno a ese tipo de lógicas y matemáticas y sugiero que ellas pueden contribuir a ampliar la concepción que se tiene de la matemática, señalando que los límites de lo matemáticamente aceptable pueden ser mucho más amplios de lo que hemos creído.
According to logical non-necessitarianism, every inference may fail in some situation. In his def... more According to logical non-necessitarianism, every inference may fail in some situation. In his defense of logical monism, Graham Priest has put forward an argument against non-necessitarianism based on the meaning of connectives. According to him, as long as the meanings of connectives are fixed, some inferences have to hold in all situations. Hence, in order to accept the non-necessitarianist thesis one would have to dispose arbitrarily of those meanings. I want to show here that non-necessitarianism can stand, without disposing arbitrarily of the meanings of connectives, based on a minimalist view on the meanings of connectives.
En esta nota crítica trato de (i) dar una breve descripción de cada uno de los artículos que comp... more En esta nota crítica trato de (i) dar una breve descripción de cada uno de los artículos que componen Orayen: de la forma lógica al significado, (ii) señalar algunas cuestiones que no están claras en ellos o en las réplicas de Orayen y, (iii) en la medida de lo posible, tratar de señalar si los autores hacen desarrollos ulteriores acerca de los problemas abordados en sus artículos.
The aim of this note is threefold: (i) briefly describe and comment each of the articles of Orayen: de la forma lógica al significado; (ii) to identify some issues that may not be clear enough or not fully developed whether in the articles or even in Orayen’s replies; (iii) to the extent possible, to refer to further studies by the authors themselves on the same as, or quite related to, the subjects addressed by them in their papers.
We argue here that the meanings of logical connectives need not to differ in different logics. Ba... more We argue here that the meanings of logical connectives need not to differ in different logics. Based on the category-theoretic treatment of the logical connectives, we argue against the well-known Quinean thesis that a difference between logics implies a difference in the meanings of connectives. We thus locate this change in the difference between certain objects rather than in the difference between the meaning of connectives. Finally, we try to show that the category-theoretic treatment of logical connectives is a form of semantic minimalism, according to which not all the usual semantic components are relevant in fixing the meaning of a connective.
En este artículo tratamos de hacer plausible la hipótesis de que las conectivas de diferentes lógicas no necesariamente difieren en significado. Utilizando el tratamiento categorista de las conectivas, argumentaremos contra la tesis quineana de que la diferencia de lógicas implica diferencia de significado entre sus conectivas, y ubicamos el cambio de tema en la diferencia de objetos más bien que en una tal diferencia de significado. Finalmente, intentamos mostrar que ese tratamiento categorista es una forma de minimalismo semántico, de acuerdo con el cual no todos los elementos semánticos usuales son relevantes para determinar el significado de las conectivas.
In this paper I probe the idea that neither possibilism nor trivialism could be ruled out on a pu... more In this paper I probe the idea that neither possibilism nor trivialism could be ruled out on a purely logical basis. I use the apparatus of relational structures used in the semantics for modal logics to engineer some models of possibilism and trivialism and I discuss a philosophical stance about logic, truth values and the meaning of connectives underlying such analysis.
Overemphasizing the features of abduction as it occurs in scientifi c practices and daily life sc... more Overemphasizing the features of abduction as it occurs in scientifi c practices and daily life scenarios has led to overlook some features that abduction in those circumstances shares with other phenomena in which some given outputs fail to stand in a certain relation with some given inputs, and thus a modifi cation on those inputs is in order. We propose here a top-down, conceptual and taxonomic investigation on what the most general purely logical features of abduction could be, as well as a research program to investigate to what extent it is a pervasive notion in logic. We start by motivating some broadenings in the most common approaches to abduction, then we characterize inferential problems and finally give general characterizations of the notions of abductive problem, abductive solution and abductive inference.
Si ese viejo profesor no creyera que la teoría de categorías es una vieja moda francesa, él diría... more Si ese viejo profesor no creyera que la teoría de categorías es una vieja moda francesa, él diría que este artículo es una buena aproximación a lo que todo lógico educado debería saber de teoría de topos. Ahora sí, la última versión.
En esta plática muestro algunas conexiones conceptuales entre la teoría cantoriana de Mengen, la ... more En esta plática muestro algunas conexiones conceptuales entre la teoría cantoriana de Mengen, la filosofía aristotélica de la matemática y la teoría de categorías. Mi objetivo es mostrar que las teorías axiomáticas de conjuntos basadas en la noción de pertenencia, como ZF, no reflejan fielmente el contenido conceptual de la teoría que dicen continuar, a saber, la teoría cantoriana de los Mengen. Esto nos ayuda a exhibir por qué una fundamentación de la matemática basada en teorías como ZF es radicalmente distinta a una fundamentación en términos categoristas. Si tengo tiempo, mostraré que autores como Frege o Zermelo hicieron muy poco para probar los cargos de incoherencia que lanzaron contra la teoría cantoriana.
El objetivo general es que adviertas la importancia lógica y filosófica de la noción lógica de re... more El objetivo general es que adviertas la importancia lógica y filosófica de la noción lógica de relevancia, en particular para cuatro grandes temas en filosofía de la lógica: las críticas a la lógica clásica, la definición de validez o consecuencia lógica, el debate entre monismo y pluralismo, y el significado de las conectivas lógicas.
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Papers by Luis Estrada-González
idea of a pure logic are grounded on some historical fallacies regarding the development of geometry, as well as on an uncritically assumption about the nature of logic as an essentially applied theory.
En este artículo presento algunos ejemplos de teorías matemáticas tolerantes a la inconsistencia y algunas de sus propiedades más interesantes. Esbozo algunas cuestiones filosóficas surgidas en torno a ese tipo de lógicas y matemáticas y sugiero que ellas pueden contribuir a ampliar la concepción que se tiene de la matemática, señalando que los límites de lo matemáticamente aceptable pueden ser mucho más amplios de lo que hemos creído.
The aim of this note is threefold: (i) briefly describe and comment each of the articles of Orayen: de la forma lógica al significado; (ii) to identify some issues that may not be clear enough or not fully developed whether in the articles or even in Orayen’s replies; (iii) to the extent possible, to refer to further studies by the authors themselves on the same as, or quite related to, the subjects addressed by them in their papers.
En este artículo tratamos de hacer plausible la hipótesis de que las conectivas de diferentes lógicas no necesariamente difieren en significado. Utilizando el tratamiento categorista de las conectivas, argumentaremos contra la tesis quineana de que la diferencia de lógicas implica diferencia de significado entre sus conectivas, y ubicamos el cambio de tema en la diferencia de objetos más bien que en una tal diferencia de significado. Finalmente, intentamos mostrar que ese tratamiento categorista es una forma de minimalismo semántico, de acuerdo con el cual no todos los elementos semánticos usuales son relevantes para determinar el significado de las conectivas.
idea of a pure logic are grounded on some historical fallacies regarding the development of geometry, as well as on an uncritically assumption about the nature of logic as an essentially applied theory.
En este artículo presento algunos ejemplos de teorías matemáticas tolerantes a la inconsistencia y algunas de sus propiedades más interesantes. Esbozo algunas cuestiones filosóficas surgidas en torno a ese tipo de lógicas y matemáticas y sugiero que ellas pueden contribuir a ampliar la concepción que se tiene de la matemática, señalando que los límites de lo matemáticamente aceptable pueden ser mucho más amplios de lo que hemos creído.
The aim of this note is threefold: (i) briefly describe and comment each of the articles of Orayen: de la forma lógica al significado; (ii) to identify some issues that may not be clear enough or not fully developed whether in the articles or even in Orayen’s replies; (iii) to the extent possible, to refer to further studies by the authors themselves on the same as, or quite related to, the subjects addressed by them in their papers.
En este artículo tratamos de hacer plausible la hipótesis de que las conectivas de diferentes lógicas no necesariamente difieren en significado. Utilizando el tratamiento categorista de las conectivas, argumentaremos contra la tesis quineana de que la diferencia de lógicas implica diferencia de significado entre sus conectivas, y ubicamos el cambio de tema en la diferencia de objetos más bien que en una tal diferencia de significado. Finalmente, intentamos mostrar que ese tratamiento categorista es una forma de minimalismo semántico, de acuerdo con el cual no todos los elementos semánticos usuales son relevantes para determinar el significado de las conectivas.