We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional type theory. The key concept we employ is that of a Lawvere hyperdoctrine for which we describe a notion of quotient completion. That notion includes the exact completion on a category with weak finite limits as an instance as well as examples from type theory that fall apart from this.

We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin.One level is given by an intensional type theory, called Minimal type theory. This theory extends a previous version with collections.The other level is given by an extensional set theory that is interpreted in the first one by means of a quotient model.This two-level theory has two main features: it is minimal among the most relevant foundations for constructive mathematics; it is constructive thanks (...) to the way the extensional level is linked to the intensional one which fulfills the “proofs-as-programs” paradigm and acts as a programming language. (shrink)

In this paper we analyze an extension of Martin-Löf s intensional set theory by means of a set contructor P such that the elements of P are the subsets of the set S. Since it seems natural to require some kind of extensionality on the equality among subsets, it turns out that such an extension cannot be constructive. In fact we will prove that this extension is classic, that is “ true holds for any proposition A.

We give arguments explaining why, when adopting a minimalist approach to constructive mathematics as that formalized in our two-level minimalist foundation, the choice for a pointfree approach to topology is not just a matter of convenience or mathematical elegance, but becomes compulsory. The main reason is that in our foundation real numbers, either as Dedekind cuts or as Cauchy sequences, do not form a set.

We present and study the category of formal topologies and some of its variants. Two main results are proven. The first is that, for any inductively generated formal cover, there exists a formal topology whose cover extends in the minimal way the given one. This result is obtained by enhancing the method for the inductive generation of the cover relation by adding a coinductive generation of the positivity predicate. Categorically, this result can be rephrased by saying that inductively generated formal (...) topologies are coreflective into inductively generated formal covers. The second result is that unary formal covers are exponentiable in the category of inductively generated formal covers and hence, thanks to the coreflection, unary formal topologies are exponentiable in the category of inductively generated formal topologies. From a localic point of view the exponentiability of unary formal topologies means that algebraic dcpos are exponentiable in the category of open locales. But, the coreflection theorem states that open locales are coreflective in locales and hence, as a consequence of well-known impredicative results on exponentiable locales, it allows to prove that locally compact open locales are exponentiable in the category of open locales. (shrink)

Here, we present a category ${\mathbf {pEff}}$ which can be considered a predicative variant of Hyland's Effective Topos ${{\mathbf {Eff} }}$ for the following reasons. First, its construction is carried in Feferman’s predicative theory of non-iterative fixpoints ${{\widehat {ID_1}}}$. Second, ${\mathbf {pEff}}$ is a list-arithmetic locally cartesian closed pretopos with a full subcategory ${{\mathbf {pEff}_{set}}}$ of small objects having the same categorical structure which is preserved by the embedding in ${\mathbf {pEff}}$ ; furthermore subobjects in ${{\mathbf {pEff}_{set}}}$ are classified by (...) a non-small object in ${\mathbf {pEff}}$. Third ${\mathbf {pEff}}$ happens to coincide with the exact completion of the lex category defined as a predicative rendering in ${{\widehat {ID_1}}}$ of the subcategory of ${{\mathbf {Eff} }}$ of recursive functions and it validates the Formal Church’s thesis. Hence pEff turns out to be itself a predicative rendering of a full subcategory of ${{\mathbf {Eff} }}$. (shrink)

Consistency with the formal Church’s thesis, for short CT, and the axiom of choice, for short AC, was one of the requirements asked to be satisfied by the intensional level of a two-level foundation for constructive mathematics as proposed by Maietti and Sambin From sets and types to topology and analysis: practicable foundations for constructive mathematics, Oxford University Press, Oxford, 2005). Here we show that this is the case for the intensional level of the two-level Minimalist Foundation, for short (...) MF, completed in 2009 by the second author. The intensional level of MF consists of an intensional type theory à la Martin-Löf, called mTT. The consistency of mTT with CT and AC is obtained by showing the consistency with the formal Church’s thesis of a fragment of intensional Martin-Löf’s type theory, called \, where mTT can be easily interpreted. Then to show the consistency of \ with CT we interpret it within Feferman’s predicative theory of non-iterative fixpoints \ by extending the well known Kleene’s realizability semantics of intuitionistic arithmetics so that CT is trivially validated. More in detail the fragment \ we interpret consists of first order intensional Martin-Löf’s type theory with one universe and with explicit substitution rules in place of usual equality rules preserving type constructors -rule which is not valid in our realizability semantics). A key difficulty encountered in our interpretation was to use the right interpretation of lambda abstraction in the applicative structure of natural numbers in order to model all the equality rules of \ correctly. In particular the universe of \ is modelled by means of \-fixpoints following a technique due first to Aczel and used by Feferman and Beeson. (shrink)

We present and study the category of formal topologies and some of its variants. Two main results are proven. The first is that, for any inductively generated formal cover, there exists a formal topology whose cover extends in the minimal way the given one. This result is obtained by enhancing the method for the inductive generation of the cover relation by adding a coinductive generation of the positivity predicate. Categorically, this result can be rephrased by saying that inductively generated formal (...) topologies are coreflective into inductively generated formal covers. The second result is that unary formal covers are exponentiable in the category of inductively generated formal covers and hence, thanks to the coreflection, unary formal topologies are exponentiable in the category of inductively generated formal topologies. From a localic point of view the exponentiability of unary formal topologies means that algebraic dcpos are exponentiable in the category of open locales. But, the coreflection theorem states that open locales are coreflective in locales and hence, as a consequence of well-known impredicative results on exponentiable locales, it allows to prove that locally compact open locales are exponentiable in the category of open locales. (shrink)

Razón, poesía, historia.--La cuestión del estoicismo español.--El querer.

Dibujar el pensamiento de Seneca es dibujar su figura viva, trazar el esquema de su persona. Seneca es un mediador que para alzarse sobre nosotros necesita de nuestra necesidad, pues solo apoyado en nuestra indigencia tiene sentido. Maria Zambrano lleva a cabo un lucido estudio de la figura y significacion del pensador cordobes y presenta una seleccion de sus escritos.

Spectroscopy is a scientific topic at the interface between Chemistry and Physics, which is taught at high school level in relation with its fundamental applications in Analytical Chemistry. In the first part of the paper, the topic of spectroscopy is analyzed having in mind the well-known Johnstone’s triangle of chemistry education, putting in evidence the way spectroscopy is usually taught at the three levels of chemical knowledge: macroscopic/phenomenological, sub-microscopic/molecular and symbolic ones. Among these three levels, following Johnstone’s recommendations the macroscopic (...) one is the most useful for high school students who learn spectroscopy for the first time. Starting from these premises, in the second part of the paper, we propose a didactic sequence which is inspired by the historical evolution of spectroscopic instruments from the first spectroscopes invented by Gustav Kirchhoff and Robert Bunsen in 1860 to the UV–vis spectrophotometers which became common since the 1960s. The idea behind our research is to analyze the conceptual advancements through the history of spectroscopy and to identify the key episodes/experiments and spectroscopic instruments. For each of them, a didactic activity, typically an experiment, is then proposed underlining the relevant aspects from the chemistry education point of view. The present paper is the occasion to reflect on the potentialities of an historical approach combined with a laboratorial one, and to discuss the role of historical instruments and related technological improvements to teach spectroscopy. (shrink)

Hilary Putnam is one of the world’s leading philosophers. His highly original and often provocative ideas have set the agenda for a variety of debates in philosophy of science, philosophy of mind and philosophy of language. His now famous philosophical thought experiments, such as the ‘Twin earth’ and ‘the brains in the vat’ have become part of the established canon in philosophy and cognitive science. _Reading Putnam_ is an outstanding overview and assessment of Hilary Putnam’s work by a team of (...) international contributors, and includes replies by Putnam himself. Divided into clear sections, it contains chapters on key aspects of Putnam’s large body of writing, including: Scientific realism and the changes that Putnam’s thought has undergone on this topic analyticity and ontology, including the important interconnections between the views of Putnam and Quine Putnam’s arguments concerning externalist views of meaning and reference, questions of conceptual relativity, and his preoccupation with ethics through a denial of the fact–value dichotomy Putnam’s developing views on perception. Offering an excellent survey of Putnam’s work, _Reading Putnam_ is essential for those studying philosophy of mind, philosophy of language, and philosophy of science, as well as for anyone interested in contemporary philosophy. (shrink)

In the literature, the pragmatic dimension of metaphors has been clearly acknowledged. Metaphors are regarded as having different possible uses, especially pursuing persuasion. However, an analysis of the specific conversational purposes that they can be aimed at achieving in a dialogue and their adequacy thereto is still missing. In this chapter, we will address this issue focusing on the classical distinction between the explanatory and persuasive uses of metaphors, which is, however, complex to draw at an analytical level and often (...) blurred and controversial also from a theoretical point of view. Building on the analysis of explanation in different theories and fields of study, we show how it can be conceived as characterized by a cognitive and a pragmatic dimension, where the transference of understanding is used pragmatically for different dialogical goals - such as informing, making a joint decision, and most importantly persuading. In this sense, the cognitive effects of understanding are not incompatible with a persuasive dialogical purpose. This theoretical proposal will be applied to examples drawn from the medical context, to show how a pragmatic approach to explanation can account for the complexity of the cases that can be found in actual dialogical contexts. (shrink)

This paper argues that the so-called ‘paradox’ of dehumanization is a mirage arising from misplaced abstraction. The alleged ‘paradox’ is taken as challenge that arises from a skeptical stance. After reviewing the history of that skeptical stance, it is reconstructed as an argument with two premises. With the help of an epistemologically structured but pluralistic frame it is then shown how the two premises of the Skeptic’s argument can both be debunked. As part of that it emerges that there are (...) a couple of ways how dehumanization can be realized, and one such realization can be sufficient for affirming the reality of dehumanization for a specific case. (shrink)

Probability as understood today, namely as a quantitative notion expressible by means of a function ranging in the interval between 0–1, took shape in the mid-17th century, and presents both a mathematical and a philosophical aspect. Of these two sides, the second is by far the most controversial, and fuels a heated debate, still ongoing. After a short historical sketch of the birth and developments of probability, its major interpretations are outlined, by referring to the work of their most prominent (...) representatives. The final section addresses the question of whether any of such interpretations can presently be considered predominant, which is answered in the negative. (shrink)

My aim in this paper is to investigate what epistemic role, if any, do appeals to representations play in cognitive neuroscience. I suggest that while at present they seem to play something in between a minimal and a substantive explanatory role, there is reason to believe that representations have a substantial contribution to the construction of neuroscientic explanations of cognitive phenomena.

Dal "disegno su sabbia" delle donne australiane alle terrecotte delle donne del Camerun, dai retablos peruviani agli altari vodou degli immigrati haitiani a New York, dalla "Casa del popolo" del regno di Bandjoun alle "vetrinette" italiane degli anni Sessanta, dai malanggan e dai manufatti annodati dell'Oceania alla topologia dei nodi, dai bologan del Mali alla "Potlatch Collection" rimpatriata nei nuovi musei indigeni del Canada, dalle maschere gelede degli Yoruba alla figura ubiqua e mediatica di Mami Wata, i saggi di questo (...) volume evidenziano le valenze operative dell'arte: sia nell'arena sociale e politica contemporanea, cui appartengono anche le "tradizioni", sia nel campo cognitivo e religioso. A lungo confinata ai soli territori esotici delle culture "primitive" e limitata da un'eccessiva dipendenza dalle categorie interpretative occidentali, la riflessione antropologica sull'arte e sull'estetica trova oggi un nuovo respiro teorico, e un nuovo fascino. (shrink)

_Jane and Louise Wilson_ With Essays by Jeremy Millar and Claire Doherty London: Ellipsis, 2000 ISBN 1-84166-027-2 84 pp., inc. 120 b/w photograph.

Drawing on recent findings, this study examines whether valence concordant electromyography (EMG) responses can be explained as an unconditional effect of mere stimulus processing or as somatosensory simulation driven by task-dependent processing strategies. While facial EMG over the Corrugator supercilii and the Zygomaticus major was measured, each participant performed two tasks with pictures of album covers. One task was an affective evaluation task and the other was to attribute the album covers to one of five decades. The Embodied Emotion Account (...) predicts that valence concordant EMG is more likely to occur if the task necessitates a somatosensory simulation of the evaluative meaning of stimuli. Results support this prediction with regard to Corrugator supercilii in that valence concordant EMG activity was only present in the affective evaluation task but not in the non-evaluative task. Results for the Zygomaticus major were ambiguous. Our findings are in line with the view that EMG activity is an embodied part of the evaluation process and not a mere physical outcome. (shrink)

This paper investigates the emotive (or expressive) meaning of words commonly referred to as “loaded” or “emotive,” which include slurs, derogative or pejorative words, and ethical terms. We claim that emotive meaning can be reinterpreted from a pragmatic and argumentative perspective, which can account for distinct aspects of ethical terms, including the possibility of being modified and its cancellability. Emotive meaning is explained as a defeasible and automatic or automatized evaluative and intended inference commonly associated with the use of specific (...) terms, which can be represented and assessed considering its logical structure and its defeasibility conditions. This automatic inference is conceived as part of the connotation of an ethical term, and is not necessarily stable. By means of quasi-definitions, it is possible to modify the emotive meaning while maintaining the descriptive one, automaticizing the inferences drawn from an ethical word. Through examples drawn from the recent US presidential campaign, we show how re-contextualization and emotive contexts can affect emotive meaning. (shrink)

Scholars have long been intrigued by the Buddha's defining action (karma) as intention. This book explores systematically how intention, agency, and moral psychology were interpreted in all branches of early Theravada thought, paying special attention to the thought of the 5th-century commentator Buddhaghosa.

Leibniz's metaphysics appears to go a long way towards monism: it supports a strong dependence of limited things on the absolute or God and understands this dependence not only as causal dependence but also as a pervasive ontological dependence which involves the communality of nature between absolute and limited. Yet, Leibniz stops short of affirming monism. Why? This paper takes a fresh look at Leibniz's reasons for opposing monism through the lens of a virtually unknown text of 1698 on the (...) metaphysical foundations of the infinite. Against the backdrop of the present-day monistic proposals of Jonathan Schaffer and Michael Della Rocca, the paper identifies and evaluates four different types of monism: 1. Whole-Part Monism; 2. World-Animal Monism; 3. God-Nature Monism and 4. Eleatic Monism. It argues that Leibniz's opposition to Whole-Part Monism, World-Animal Monism, and God-Nature Monism, is due to his conceptions of the infinite and of what it is to be “an absolutely absolute Being”. Furthermore, it argues that the only type of monism which could preserve Leibniz's demanding notions of real infinite and absolute is Eleatic Monism. The latter, however, is also rejected by Leibniz due to our first-hand experience of what it is to be a substance. (shrink)

: The coloniality of power is understood by Anibal Quijano as at the constituting crux of the global capitalist system of power. What is characteristic of global, Eurocentered, capitalist power is that it is organized around two axes that Quijano terms "the coloniality of power" and "modernity." The coloniality of power introduces the basic and universal social classification of the population of the planet in terms of the idea of race, a replacing of relations of superiority and inferiority established through (...) domination with naturalized understandings of inferiority and superiority. In this essay, Lugones introduces a systemic understanding of gender constituted by colonial/modernity in terms of multiple relations of power. This gender system has a light and a dark side that depict relations, and beings in relation as deeply different and thus as calling for very different patterns of violent abuse. Lugones argues that gender itself is a colonial introduction, a violent introduction consistently and contemporarily used to destroy peoples, cosmologies, and communities as the building ground of the "civilized" West. (shrink)

Mental causation is notoriously threatened by the causal exclusion argument. A prominent strategy to save mental causation from causal exclusion consists in subscribing to an interventionist account of causation. This move has, however, recently been challenged by several authors. In this paper, we do two things: We (i) develop what we consider to be the strongest version of the interventionist causal exclusion argument currently on the market and (ii) propose a new way how it can in principle be overcome. In (...) particular, we propose to replace strict supervenience in the assumption that the mental supervenes on the physical by probabilistic supervenience and show how this move has the potential to license the inference to mental causation. Finally, we argue that probabilistic supervenience captures some of the most important intuitions that strict supervenience captures and discuss possible objections to weakening strict supervenience in the way we suggest. (shrink)

El presente artículo hace a una reflexión sobre Kant y su énfasis en el apriorismo moral, sobre todo en cuanto se refiere al concepto de deber en la pura razón. Dicho concepto juega un papel fundamental como criterio de valor de la acción moral; una acción es moral en tanto sea hecha por deber y nada más que por deber. ¿Qué es el deber y dónde se fundamenta?, es de lo que se va a tratar el presente texto; igualmente nos (...) vamos a encontrar con el análisis y las características del imperativo categórico, junto con otras ideas morales, abordadas, eso sí, desde la perspectiva del apriorismo. (shrink)

In this Chapter, Maria Kronfeldner discusses whether psychological essentialism is a necessary part of dehumanization. This involves different elements of essentialism, and a narrow and a broad way of conceptualizing psychological essentialism, the first akin to natural kind thinking, the second based on entitativity. She first presents authors that have connected essentialism with dehumanization. She then introduces the error theory of psychological essentialism regarding the category of the human, and distinguishes different elements of psychological essentialism. On that basis, Kronfeldner (...) connects historical, socio-psychological, and philosophical insights in order to show that although essentialism can act as a catalyst for dehumanization, it is not necessary for it. Examples relate to dehumanization in the context of colonialism and evolutionary thinking, to the history of dehumanizing women from Aristotle to 19th-century craniology, and to contemporary self-dehumanization and ‘lesser mind’ attribution. (shrink)

The coloniality of power is understood by Anibal Quijano as at the constituting crux of the global capitalist system of power. What is characteristic of global, Eurocentered, capitalist power is that it is organized around two axes that Quijano terms “the coloniality of power” and “modernity.” The coloniality of power introduces the basic and universal social classification of the population of the planet in terms of the idea of race, a replacing of relations of superiority and inferiority established through domination (...) with naturalized understandings of inferiority and superiority. In this essay, Lugones introduces a systemic understanding of gender constituted by colonial/modernity in terms of multiple relations of power. This gender system has a light and a dark side that depict relations, and beings in relation as deeply different and thus as calling for very different patterns of violent abuse. Lugones argues that gender itself is a colonial introduction, a violent introduction consistently and contemporarily used to destroy peoples, cosmologies, and communities as the building ground of the “civilized” West. (shrink)

The coloniality of power is understood by Anibal Quijano as at the constituting crux of the global capitalist system of power. What is characteristic of global, Eurocentered, capitalist power is that it is organized around two axes that Quijano terms “the coloniality of power” and “modernity.” The coloniality of power introduces the basic and universal social classification of the population of the planet in terms of the idea of race, a replacing of relations of superiority and inferiority established through domination (...) with naturalized understandings of inferiority and superiority. In this essay, Lugones introduces a systemic understanding of gender constituted by colonial/modernity in terms of multiple relations of power. This gender system has a light and a dark side that depict relations, and beings in relation as deeply different and thus as calling for very different patterns of violent abuse. Lugones argues that gender itself is a colonial introduction, a violent introduction consistently and contemporarily used to destroy peoples, cosmologies, and communities as the building ground of the “civilized” West. (shrink)

Es reseña del libro: Carlos POSE, _La antropología de Xavier Zubiri: una perspectiva actual_, Madrid: Sindéresis, 2022, pp. 290.