The opposition prose/verse can only be established in the heart of literal language. The only way of producing nonliteral language is in conversation. . . . Enrique Anderson Imbert published a book in 1958 titled ¿Qué es la prosa? , in which he says: 'No, we do not speak in prose. Prose is not a projection of everyday speech, but rather artistic elaboration."1 But my adherence to his intelligent point of view is not total because he situates prose in the (...) heart of written language, and I think that it should be ascribed to literal language. For Anderson Imbert such an idiomatic modality results in an artistic elaboration; but the intention of prose can be quite different. The reader, for instance, by virtue of his reading, can transform prose into literature; and unwritten prose does exist, as has been stated. In many cases it is impossible to compose the texts in verse; structurally, then, an opposition cannot be established, just as in the case of the student who takes notes following the explanations of the professor. These texts can only be what they are: a more or less truthful transcription, a "copy" of oral language, a mere change of substance, abbreviated in order to bring it closer, as a simple memento, to the elliptical articulations of inner language. · 1. "No, no hablamos en prosa. La prosa no es proyección del habla corriente, sino elaboración artística." Enrique Anderson Imbert, ¿Que es la prosa? 4th ed. , p. 31. Fernando Lázaro Carreter is the director of the department of Spanish at the Universidad Autónoma in Madrid and a member of the Real Academia Española. The author of books on both linguistics and criticism, his published works include: Las ideas lingüísticas en España durante el siglo XVIII; Diccionario de términos filológicos; Estilo barroco y personalidad creadora; Ensayos de Poética ; and Lazarillo de Tormes en la picaresca. This article is a preliminary statement of a problem he is currently investigating: literary language understood as "literal language.". (shrink)

Frente a la teoría de la pena, con sus sutiles matices y fines comunicativos, encontramos una realidad que diverge sustancialmente de aquella. Donde, con frecuencia, la denominada prevención general no acontece, porque la resolución no llega a esta, a la generalidad a la que se apela como fundamento del castigo. Pero, en particular, cuando tal comunicación acontece, tiene lugar en un inquietante marco discursivo que va dando nombre a nuestro tiempo: la era de la posverdad. Se revela aquí un contexto (...) comunicativo hostil al discurso experto y a los hechos, que se ven desplazados por su valoración, donde los interlocutores se alejan del modelo del ciudadano racional sobre el que se teoriza en Derecho, y donde actores políticos desarrollan estrategias comunicativas propagandistas, de modo que, en ocasiones, se termina comunicando un mensaje contrario a lo que enuncia literalmente la resolución judicial. (shrink)

Recesión de J. M.ª Blanco White, Ensayos sobre la intolerancia. edición de M. Moreno Alonso, Caja San Fernando, Sevilla, 2001.

Medieval controversies between Jews and Christians in the Spanish Kingdoms. In the old spanish Kingdoms there were big controversies between Christians and Jews. The two religions based their own credencies on the Old Testament, but the Christians one also added the New Testament. Another difference lies on the different interpretation of the textual tradicion: the Christians use the allegorical method, the Jews follow the litteral one.

En los antiguos Reinos hispánicos hubo grandes controversias entre cristianos y judíos. Las dos religiones fundamentan sus creencias en el Antiguo Testamento, pero los cristianos añaden también el Nuevo Testamento. Otra diferencia estriba en la distinta manera de interpretar la tradición textual: los cristianos emplean el método alegórico y los judíos el método literal.In the old spanish Kingdoms there were big controversies between Christians and Jews. The two religions based their own credencies on the Old Testament, but the Christian one (...) also added the New Testament. Another difference lies on the different interpretation of the textual tradicion: the Christians use the allegorical method, the Jews follow the litteral one. (shrink)

If personhood is the quality or condition of being an individual person, brainhood could name the quality or condition of being a brain. This ontological quality would define the `cerebral subject' that has, at least in industrialized and highly medicalized societies, gained numerous social inscriptions since the mid-20th century. This article explores the historical development of brainhood. It suggests that the brain is necessarily the location of the `modern self', and that, consequently, the cerebral subject is the anthropological figure inherent (...) to modernity (at least insofar as modernity gives supreme value to the individual as autonomous agent of choice and initiative). It further argues that the ideology of brainhood impelled neuroscientific investigation much more than it resulted from it, and sketches how an expanding constellation of neurocultural discourses and practices embodies and sustains that ideology. (shrink)

This paper seeks to establish whether the categories of MacIntyrean virtue ethics as applied to business organizations are meaningful in a non-western business context. It does so by building on research reported in Moore : 363–387, 2012) in which the application of virtue ethics to business organizations was investigated empirically in the UK, based on a conceptual framework drawn from MacIntyre’s work. Comparing these results with an equivalent study in Sri Lanka, the paper finds that the categories are meaningful but (...) that there are both similarities to and considerable differences in the content of these categories from the UK study. The paper draws on aspects of institutional theory to explore and explain these findings. Overall, there is supportive evidence that the categories of MacIntyrean virtue ethics are generalizable, and so can be used to characterize problems of organizational virtue and vice around the world, while providing evidence that there may be polities which are more conducive to the ‘practice-like conduct of production’ : 77–91, 2008). (shrink)

En el terreno de la moral, el contraste entre lo ¿que el filósofo Wilfrid Sellars denominó «la ¿imagen manifiesta» y la «imagen científica» es enorme y tiene unas consecuencias prácticas ineludibles. Este libro reduce la distancia entre esa imagen manifiesta y la imagen científica, dotando al lector de referencias fundamentales, enfoques diversos y un amplio abanico de temáticas a partir de investigaciones experimentales sobre nuestra conducta moral.

English translates ‘genos’ as kind and ‘eidos’ as form, which differ in meaning as much as ‘herd’ and ‘brand’ do. But there are hard passages where ‘genos’ and ‘eidos’ have appeared to be synonyms, usually given the new meaning class. We show that, although ‘genos’ and ‘eidos’ are never synonyms and continue to mean kind and form, the word ‘eidos’ can be used figuratively, as a metonym, for a genos.

A dilemma has stymied interpretations of the Stranger’s method of dividing kinds into subkinds in Plato’sSophistandStatesman. The dilemma assumes that the kinds are either extensions or intensions. Now kinds divide like extensions, not intensions. But extensions cannot explain the distinct identities of kinds that possess the very same members. We propose understanding a kind as like an animal body—the Stranger’s simile for division—possessing both an extension and an intension. We find textual support in the Stranger’s paradigmatic four steps for collecting (...) a subkind. (shrink)

In "'Yes" and "No'" (2000), Ian Rumfitt proposed bilateralism--a use-based account of the logical words, according to which the sense of a sentence is determined by the conditions under which it is asserted and denied. One of Rumfitt's key claims is that bilateralism can provide a justification of classical logic. This paper raises a techical problem for Rumfitt's proposal, one that seems to undermine the bilateralist programme.

We show how to interpret intuitionistic propositional logic into a predicative second-order intuitionistic propositional system having only the conditional and the universal second-order quantifier. We comment on this fact. We argue that it supports the legitimacy of using classical logic in a predicative setting, even though the philosophical cast of predicativism is nonrealistic. We also note that the absence of disjunction and existential quantifications allows one to have a process of normalization of proofs that avoids the use of "commuting conversions.".

As public administrations adopt artificial intelligence (AI), we see this transition has the potential to transform public service and public policies, by offering a rapid turnaround on decision making and service delivery. However, a recent series of criticisms have pointed to problematic aspects of mainstreaming AI systems in public administration, noting troubled outcomes in terms of justice and values. The argument supplied here is that any public administration adopting AI systems must consider and address ambiguities and uncertainties surrounding two key (...) dimensions: the algorithms’ results, and how public managers make decisions for and about AI systems’ design. The article is based on bibliographic research in institutional theory perspective that relates the design of AI systems and relevant literature on the decision-making process in public policy. The main finding is to explain why autonomous decision systems continue to reproduce ambiguities and uncertainties when applied in public administration and propose a reflection on AI governance in public administration. This article points to the need for design institutions that immerse themselves in understanding the nuances, details, and potential outcomes of AI governance for public administration. Such institutions would reconcile consequentialist logic with a logic of appropriateness to help navigate and mediate ambiguities and uncertainties. (shrink)

There is no systematic knowledge about how individuals with Locked-in Syndrome experience their situation. A phenomenology of LIS, in the sense of a description of subjective experience as lived by the ill persons themselves, does not yet exist as an organized endeavor. The present article takes a step in that direction by reviewing various materials and making some suggestions. First-person narratives provide the most important sources, but very few have been discussed. LIS barely appears in bioethics and neuroethics. Research on (...) Quality of Life provides relevant information, one questionnaire study explores the sense of personal continuity in LIS patients, and LIS has been used as a test case of theories in “embodied cognition” and to explore issues in the phenomenology of illness and communication. A systematic phenomenology of LIS would draw on these different areas: while some deal directly with subjective experience, others throw light on its psychological, sociocultural and materials conditions. Such an undertaking can contribute to the improvement of care and QOL, and help inform philosophical questions, such as those concerning the properties that define persons, the conditions of their identity and continuity, or the dynamics of embodiment and intersubjectivity. (shrink)

The war in Iraq has reignited the passionate humanitarian intervention debate. President George W. Bush surprised many observers in his second inaugural address when he promised to oppose tyranny and oppression, and this in a world not always willing or ready to join in that fight. Humanitarian intervention is again on the forefront of world politics.

It has been known for six years that the restriction of Girard's polymorphic system $\text{\bfseries\upshape F}$ to atomic universal instantiations interprets the full fragment of the intuitionistic propositional calculus. We firstly observe that Tait's method of “convertibility” applies quite naturally to the proof of strong normalization of the restricted Girard system. We then show that each $\beta$-reduction step of the full intuitionistic propositional calculus translates into one or more $\beta\eta$-reduction steps in the restricted Girard system. As a consequence, we obtain (...) a novel and perspicuous proof of the strong normalization property for the full intuitionistic propositional calculus. It is noticed that this novel proof bestows a crucial role to $\eta$-conversions. (shrink)

In Frege’s logicism, numbers are logical objects in the sense that they are extensions of certain concepts. Frege’s logical system is inconsistent, but Richard Heck showed that its restriction to predicative quantification is consistent. This predicative fragment is, nevertheless, too weak to develop arithmetic. In this paper, I will consider an extension of Heck’s system with impredicative quantifiers. In this extended system, both predicative and impredicative quantifiers co-exist but it is only permissible to take extensions of concepts formulated in the (...) predicative fragment of the language. This system is consistent. Moreover, it proves the principle of reducibility applied to concepts true of only finitely many objects. With the aid of this form of reducibility, it is possible to develop arithmetic in a thoroughly Fregean way. (shrink)

We introduce a new typed combinatory calculus with a type constructor that, to each type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}, associates the star type σ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma ^*$$\end{document} of the nonempty finite subsets of elements of type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}. We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory (...) calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements. (shrink)

Commuting conversions were introduced in the natural deduction calculus as ad hoc devices for the purpose of guaranteeing the subformula property in normal proofs. In a well known book, Jean-Yves Girard commented harshly on these conversions, saying that ‘one tends to think that natural deduction should be modified to correct such atrocities.’ We present an embedding of the intuitionistic predicate calculus into a second-order predicative system for which there is no need for commuting conversions. Furthermore, we show that the redex (...) and the conversum of a commuting conversion of the original calculus translate into equivalent derivations by means of a series of bidirectional applications of standard conversions. (shrink)

My aim in this paper is twofold: I will try to clarify what the conditions developed in EN I a discipline or an argument must meet to be assumed as precise are, and, then, try to present evidence that the exam of akrasia in EN VII 3 meets these conditions. In the first part of this paper, I will select passages in which such conditions are displayed, and also distinguish between practical precision and theoretical precision. In the second part, where (...) the analysis of the senses of having but not using knowledge in EN VII 3 is carried on, I will claim that Aristotle’s objective is reaching the adequate statement of the explanandum that will be the subject of causal enquiry of akrasia. My concluding remarks will claim that the conditions displayed in this paper’s first part are met by Aristotelian procedure in EN VII 3. (shrink)

Both questions as abstract objects and the speech acts, here called requests, by which we ask them play an enormous role in all argumentative practices. Nonetheless, there is hardly a proper systematic treatment of questions and requests in current argumentation theories. This paper is a first attempt at providing such a systematic treatment. This is achieved by following the ideal model of a critical discussion as elaborated over the years by the Amsterdam school of pragma-dialectics. After introducing the distinction between (...) questions and requests, the paper sets forth and illustrates the norms of questioning which implicitly underlie the four stages of a critical discussion in the standard order: confrontation, opening, argumentation, and conclusion. Among other things, it is shown that crucial insights of pragma-dialectics are illuminated by the questioning perspective, in particular the distinction between single and multiple differences of opinion, the duties of the antagonist and protagonist roles, the precise character of the argumentation stage, and the different ways in which a disagreement can be resolved. (shrink)

When is humanitarian intervention legitimate and how should such interventions be conducted? This article sets out eight liberal principles that underlie humanitarian intervention, some of them abstract principles of international ethics and others more concrete principles that apply specifically to humanitarian intervention. It argues that whilst these principles do not determine the legitimacy of particular interventions, they should ?incline? our judgments towards approval or disapproval. The basic principles include the liberal idea that governments are the mere agents of the people, (...) that tyrannical governments forfeit their legal protections, that human rights entail obligations for governments, that justifiable intervention must intend the end of tyranny or anarchy, that the doctrine of double-effect should be respected, that intervention is only warranted in severe cases, that intervention be welcomed by those it is intended to save, and that ideally it is welcomed by the community of democratic states. (shrink)

Nesse artigo, eu procuro mostrar que a leitura tradicional que atribui um procedimento dialético à abordagem aristotélica da acrasia, em Ética Nicomaquéia VII 1-3 provoca um sério problema interpretativo ao tentar compatibilizar a posição socrática acerca da acrasia e os phanomena. Primeiramente, tento mostrar, baseando-me numa análise de Tópicos I 1-2, que o procedimento metodológico, em EN VII 1 1145b2-7, não se caracteriza como dialético. Em segundo lugar, proponho uma leitura em que Aristóteles, passo a passo refuta a tese socrática (...) que nega a existência da acrasia, uma vez que esse tese não é contada entre os phainomena que se quer preservar. (shrink)

La relación que este monográfico pretende establecer entre los dos conceptos fundamentales en torno a los que gira el título, a saber, teoría y crítica, no debe considerarse ni como una casualidad ni como algo asentado, sino que supone un problema fundamental, de ahí que sean objeto de atención a la hora de fijar los contenidos de este número. Si bien la teoría responde a un conocimiento especulativo a propósito de lo dado en lo real, la crítica es una acción (...) formal, fundada y razonada, conforme a una normativa acerca de aquello mismo dado en lo real. Esta presentación quiere dar cuenta de los contenidos de este número de Fragmentos de Filosofía. ---- The relationship that this monograph seeks to establish between the two fundamental concepts around which the title revolves, namely, theory and criticism, should not be considered either as a coincidence or as something settled, but rather as a fundamental problem, which is why they are the object of attention when it comes to establishing the contents of this issue. While theory responds to a speculative knowledge about what is given in the real, criticism is a formal, founded and reasoned action, in accordance with a norm about what is given in the real. This presentation aims to give an account of the contents of this issue of Fragmentos de Filosofía. (shrink)

This electronic document serves as a guide on how to get a LAMP stack running on a Google Compute Engine virtual machine instance running Debian.

Economists generally agree that free trade leads to economic growth. This proposition is supported both by theoretical models and empirical data. Further, while the empirical evidence is more limited on this question, the general consensus among economists holds that trade restrictions are likely to hurt the poor. Even if the latter consensus turns out to be wrong, if free trade leads to superior growth, governments would have more resources to redistribute to the poor. It is surprising then that philosophers and (...) human rights scholars do not advocate liberalizing trade as a way to improve the welfare of the poor as a class. While many scholars in these fields are silent with respect to the effect of free trade on the poor, some actually argue that liberalized trade is harmful for the poor, contrary to the claims of economists. In this article, we argue that any serious scholar concerned with the plight of the poor needs to address the theory and evidence regarding the effects of trade liberalization on economic growth, suggesting that the standard policy prescriptions of the philosophers and human rights scholars are, at best, of second order concern and, at worst, likely to be counterproductive in terms of improving the welfare of the poor. (shrink)

Con relativa frecuencia el pensamiento de Martin Heidegger es presentado como el de un crítico exacerbado contra la ciencia. Esa crítica es puesta bajo sospecha por su participación política en el nacionalsocialismo y es tachada, en muchos casos sin fundamento alguno, de reaccionaria, de suponer un paso atrás en la línea del progreso. Sin embargo, el propio Heidegger muestra que no hay nada más alejado de la realidad: Su pretensión no es anular la ciencia, sino reconducirla, servir de faro para (...) todas las ciencias, sin distinción entre ciencias de la naturaleza y ciencias del espíritu. El propósito heideggeriano es establecer una suerte de pre-ciencia que sirva para orientar a todas las ciencias (sean de la naturaleza o del espíritu). Este estudio pretende exponer como esa pre-ciencia sirve de guía para la ciencia y como puede convertirse en un puente que sirva para unir las dos orillas de la ciencia. ---- Relatively often Martin Heidegger's thought is presented as that of an exacerbated critic of science. This criticism is put under suspicion for his political participation in National Socialism and is accused, in many cases without any basis, of being reactionary, of being a step backwards in the line of progress. However, Heidegger himself shows that nothing is further from the truth: His intention is not to annul science, but to redirect it, to serve as a beacon for all sciences, without distinction between the sciences of nature and the sciences of the spirit. The Heideggerian purpose is to establish a kind of pre-science that serves to guide all sciences (whether of nature or of the spirit). We will seek to expose how this pre-science serves as a guide for science and how it can become a bridge that serves to unite the two shores of science. (shrink)

This paper explores the notion of cosmotechnics in the context of the history of Latin American philosophy. Since the nineteenth century, Latin American philosophy has developed through an ongoing confrontation between conceptions of “civilization and barbarism.” This tension in turn has impacted the relationship between Latin American philosophy and technology. Consequently, a certain “absence of technique” is visible as a recurring topos in Latin American philosophies. To overcome this apparent absence, this paper criticizes the notion of mestizaje using Silvia Rivera (...) Cusicanqui’s concept of ch’ixi (‘motley’) as an alternative framework. From this perspective, Guaman Poma de Ayala’s description of colonial violence reveals some hints for deconstructing the idea of “Latin Americanness”, while retaining the notion of cosmotechnics. Thus, this paper goes beyond geocultures and metatechnology by formulating a theory of cosmotechnics that is able to articulate politically antagonistic narratives in terms of technical materiality. (shrink)

Edward Nelson published in 1986 a book defending an extreme formalist view of mathematics according to which there is an impassable barrier in the totality of exponentiation. On the positive side, Nelson embarks on a program of investigating how much mathematics can be interpreted in Raphael Robinson's theory of arithmetic Q. In the shadow of this program, some very nice logical investigations and results were produced by a number of people, not only regarding what can be interpreted in Q but (...) also what cannot be so interpreted. We explain some of these results and rely on them to discuss Nelson's position. (shrink)

Em um artigo influente publicado em meados dos anos 80, Jacques Brunschwig defendeu a ideia de que o debate dialético, para Aristóteles, não resultaria em vencedores e derrotados. Sua defesa é baseada no debate dialético como sendo um trabalho comum entre questionador e respondedor (cláusula koinon ergon [cf. Tópicos VIII.11 161a20-21]) e como um tipo de teste de consistência de uma dada proposição (cláusula dia tēn thesis [cf. Tópicos VIII.4 159a20]). Apesar dos muitos méritos do artigo, penso que o argumento (...) de Brunschwig não considera adequadamente aspectos importantes do debate dialético no que concerne à performance dos debatedores, especialmente acerca dos recursos que o questionador deve usar. Ao não considerarmos esses aspectos, temos dificuldades para interpretar passagens em que Aristóteles recomenda o uso de táticas para enganar o respondedor. Meu objetivo nesse artigo será oferecer uma explicação diferente das cláusulas dia tēn thesis e koinon ergon, de modo que isso implicará uma conclusão segundo a qual o debate dialético honesto pode envolver vencedores e derrotados e manter a observância das duas cláusulas. Palavras-chave: Dialética; Aristóteles; Debate. Winners and losers in Aristotle’s dialectical debate. Abstract: In the mid-eighties Jacques Brunschwig published an influential paper of whose main claim consists in a defence of the Aristotelian conception of dialectical debate as a game without winners and losers. His claim is based on the dialectical debate as being a common work between answerer and questioner (koinon ergon clause [cf. Topics VIII.11 161a20-21]) and as a kind of test of the consistency of a given proposition (dia tēn thesis clause [cf. Topics VIII.4 159a20]). Despite its many merits, I think Brunschwig’s argument overlooks important aspects of the dialectical debate concerning the debaters’ performance, especially the resources that should be used by the questioner. By overlooking these aspects, we end up with several troubles to interpret passages in which Aristotle recommends deceptive tactics in the debate. My objective in this paper is to give a different account the dia tēn thesis and the koinon ergon clauses, which will imply a conclusion by which fair dialectical debates can still have winners and losers and observe both clauses. Key-words: Dialectics; Aristotle; Debate. Ganadores y perdedores en el debate dialéctico según Aristóteles. Resumen: En un influyente artículo publicado a mediados de los años 1980, Jacques Brunschwig defendió la idea de que el debate dialéctico, para Aristóteles, no resultaría en ganadores y perdedores. Su defensa se basa en el debate dialéctico como trabajo común entre el que pregunta y el que responde (cláusula koinon ergon [cf. Tópicos VIII.11 161a20-21]) y como una especie de prueba de la consistencia de una proposición dada (cláusula dia tēn thesis [cf. Tópicos VIII.4 159a20]). A pesar de los muchos méritos del artículo, creo que el argumento de Brunschwig no considera adecuadamente aspectos importantes del debate dialéctico con respecto a la actuación de los debatientes, especialmente con respecto a los recursos que debe utilizar el interrogador. Al no considerar estos aspectos, nos resulta difícil interpretar pasajes en los que Aristóteles recomienda el uso de tácticas para engañar al que responde. Mi objetivo en este artículo será ofrecer una explicación diferente de las cláusulas dia tēn thesis y koinon ergon, de modo que esto implique una conclusión de que el debate dialéctico honesto puede involucrar a ganadores y perdedores y mantener la observancia de las dos cláusulas. Palabras-clave: Dialéctica; Aristóteles; Debate. 1 Pesquisa desenvolvida no âmbito do Edital Universal Nº28/2018 financiada pelo CNPq sob o número 433825/2018-9. Data de registro: 01/08/2023 Data de aceite: 24/04/2024. (shrink)

We give an elementary proof of the strong normalization of the atomic polymorphic calculus Fat.

Relations computed by finite-state transducers are applied to interpret temporal propositions in terms of strings representing finite contexts or situations. Carnap–Montague intensions mapping indices to extensions are reformulated as relations between strings that can serve as indices and extensions alike. Strings are related according to information content, temporal span and granularity, the bounds on which reflect the partiality of natural language statements. That partiality shapes not only strings-as-extensions (indicating what statements are about) but also strings-as-indices (underlying truth conditions).

Finite-state methods are applied to determine the consequences of events, represented as strings of sets of fluents. Developed to flesh out events used in natural language semantics, the approach supports reasoning about action in AI, including the frame problem and inertia. Representational and inferential aspects of the approach are explored, centering on conciseness of language, context update and constraint application with bias.

Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the Grundgesetze is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this (...) extended system. (shrink)

A modal logic for translating a sequence of English sentences to a sequence of logical forms is presented, characterized by Kripke models with points formed from input/output sequences, and valuations determined by entailment relations. Previous approaches based (to one degree or another) on Quantified Dynamic Logic are embeddable within it. Applications to presupposition and ambiguity are described, and decision procedures and axiomatizations supplied.

We present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic (Peirce’s Existential Graphs α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}). The straightforward construction of a presheaf category EGα∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {E}}}{{\mathcal {G}}}_{\alpha ^{*}}$$\end{document} of cuts-only Existential Graphs (equivalent to the well-studied category of finite forests) provides a basis for the further construction of the category EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {E}}}{{\mathcal {G}}}_\alpha $$\end{document} which introduces variables in a reconstructedly generic, or label-free, mode. Morphisms in these categories represent syntactical embeddings or, equivalently but dually, extensions. Through the example of Peirce’s system, it is shown how the generic figures approach facilitates the formal investigation of relations between syntax and semantics in such diagrammatic systems. (shrink)