In this paper we compare the propositional logic of Frege’s Grundgesetze der Arithmetik to modern propositional systems, and show that Frege does not have a separable propositional logic, definable in terms of primitives of Grundgesetze, that corresponds to modern formulations of the logic of “not”, “and”, “or”, and “if…then…”. Along the way we prove a number of novel results about the system of propositional logic found in Grundgesetze, and the broader system obtained by including identity. In particular, we show that (...) the propositional connectives that are definable in terms of Frege’s horizontal, negation, and conditional are exactly the connectives that fuse with the horizontal, and we show that the logical operators that are definable in terms of the horizontal, negation, the conditional, and identity are exactly the operators that are invariant with respect to permutations on the domain that leave the truth-values fixed. We conclude with some general observations regarding how Frege understood his logic, and how this understanding differs from modern views. (shrink)

Livro-texto de introdução à lógica, com (mais do que) pitadas de filosofia da lógica, produzido como uma versão revista e ampliada do livro Forallx: Calgary. Trata-se da versão de 13 de outubro de 2022. Comentários, críticas, correções e sugestões são muito bem-vindos.

Ce texte est le fruit d’une collaboration entre un astrophysicien, Jean-René Roy, et un philosophe de l’éducation, Normand Baillargeon. Ils ont en commun d’avoir été marqués par la fréquentation des oeuvres de Mario Bunge, auxquelles ils attachent un grand prix, sur un plan personnel, d’abord, mais aussi, et c’est ce qu’ils veulent rappeler dans ces pages : parce qu’ils estiment que les oeuvres de Bunge contribuent de manière extrêmement forte et positive à rendre plus salubre la vie de l’esprit, en (...) enrichissant notre intellect et en luttant contre diverses formes troublantes d’obscurantisme qui y sévissent parfois, notamment dans les domaines familiers aux deux auteurs. (shrink)

The paper argues against Peacocke's moderate rationalism in modality. In the first part, I show, by identifying an argumentative gap in its epistemology, that Peacocke's account has not met the Integration Challenge. I then argue that we should modify the account's metaphysics of modal concepts in order to avoid implausible consequences with regards to their possession conditions. This modification generates no extra explanatory gap. Yet, once the minimal modification that avoids those implausible consequences is made, the resulting account cannot support (...) Peacocke's moderate rationalism. (shrink)

The paper compares the suitability of two different epistemologies of counterfactuals—(EC) and (W)—to elucidate modal knowledge. I argue that, while both of them explain the data on our knowledge of counterfactuals, only (W)—Williamson’s epistemology—is compatible with all counterpossibles being true. This is something on which Williamson’s counterfactual-based account of modal knowledge relies. A first problem is, therefore, that, in the absence of further, disambiguating data, Williamson’s choice of (W) is objectionably biased. A second, deeper problem is that (W) cannot satisfactorily (...) elucidate modal knowledge. Third, from a naturalistic perspective, the nature of this second problem favours (EC) against (W). (shrink)

Departing from Anderson’s (2016) suggestion that there are three communities in Peirce’s thought corresponding to his three normative sciences of logic, ethics, and esthetics, I argue that these communities partake in a relationship of dependence similar to that found among the normative sciences. In this way, just as logic relies on ethics which relies on esthetics, so too would a logical community of inquirers rely on an ethical community of love, which would rely on an esthetic community of artists. A (...) community could conduct inquiry together only if it pursued the same goal; and it could pursue the same goal only if it first imaginatively construed it. Any logical or ethical community requires a shared imaginative repertoire of ideal ends. (shrink)

In this paper, I argue that Plotinus does not limit the sphere of free human agency simply to intellectual contemplation, but rather extends it all the way to human praxis. Plotinus’s goal in the first six chapters of Ennead 6.8 is, accordingly, to demarcate the space of freedom within human practical actions. He ultimately concludes that our external actions are free whenever they actualize, in unhindered fashion, the moral principles derived from intellectual contemplation. This raises the question of how the (...) freedom of practical actions might relate to the freedom of intellectual contemplation. After considering two previously offered models—a model of double activity, and an Aristotelian model of practical syllogism—I offer a third alternative, namely a model of moral attunement, according to which our rational desires assume a kind of ‘care of the soul’ through active supervision. Practical life is thus imbued with freedom to the extent that the soul supervises its actions to conform to its will and choice of the good. (shrink)

We study shared intentions in what we call “loose groups”. These are groups that lack a codified organizational structure, and where the communication channels between group members are either unreliable or not completely open. We start by formulating two desiderata for shared intentions in such groups. We then argue that no existing account meets these two desiderata, because they assume either too strong or too weak an epistemic condition, that is, a condition on what the group members know and believe (...) about what the others intend, know, and believe. We propose an alternative, pooled knowledge, and argue that it allows formulating conditions on shared intentions that meet the two desiderata. (shrink)

In this paper I argue that, to conceive transcendence, Levinas retrieves the Platonic concept of “separation” and deploys it in three ways: metaphysically, semantically, and affectively. Levinas finds in the interaction between being and the Good beyond being of Republic VI 509b a certain “formal structure of transcendence”—one in which a term is conditioned by another while remaining absolutely separated from it. This formal structure is subsequently deployed metaphysically, in the relation between creator and creature; semantically, in the relation between (...) meaning and sense; and affectively, in the relation between the desiring self and its desired aim. (shrink)

Neste artigo propomos uma reconceitualização do amor como um modo de engajamento intersubjetivo normativamente guiado pela busca constante do equilíbrio entre a sub- e a sobredeterminação de seu objeto, que se efetiva em relações deconfiança marcadas pelo cuidado com o(a) outro(a). Esta reconceitualização permite que o amor participe da epistemologia como uma virtude intelectual responsabilista, que nos torna membros mais confiáveis de nossas comunidades epistêmicas e nos aproxima de descrições verdadeiras sobre o mundo, ao deixar que diversos pontos de vista (...) sobre esses objetos sejam reconhecidos e valorizados. (shrink)

In Posterior Analytics II 16-17, Aristotle seems to claim that there cannot be more than one explanans of the same scientific explanandum. However, this seems to be true only for “primary-universal” demonstrations, in which the major term belongs to the minor “in itself” and the middle term is coextensive with the extremes. If so, several explananda we would like to admit as truly scientific would be out of the scope of an Aristotelian science. The secondary literature has identified a second (...) problem in II 16-17: the middle term of a demonstration is sometimes taken as the definition of the minor term (the subject), other times as the definition (or the causal part of the definition) of the major (the demonstrable attribute). I shall argue that Aristotle’s solution to the first problem involves showing that certain problematic attributes, which appear to admit more than one explanation, actually fall into the privileged scenario of primary-universal demonstrations. In addition, his solution suggests a conciliatory way-out to our second problem (or so I shall argue): the existence of an attribute as a definable unity depends on its subject having the essence it has, which suggests that both the essence of subjects and the essence of demonstrable attributes can play explanatory roles in demonstrations. (shrink)

This is an exploration of recent trends in metaphysics, including deflationary and experimental metaphysics.

Miss Arendt is more reticent than, perhaps, she should be, about what actually went on in this public realm of the Greeks. —W. H. Auden.

This paper reconstructs the function argument of Aristotle’s Eudemian Ethics 2.1. The argument seeks to define happiness through the method of division; shows that the highest good is better than all four of the goods of the soul, not only two, as commentators have thought; and unlike the Nicomachean argument, makes the highest good definitionally independent of the human function.

In this paper, I argue that Plotinus’s critique of divine deliberation in Ennead 6.7 does not seek to banish teleology altogether from his philosophy of nature. Rather, his critique aims to situate teleology within his own metaphysical system so as to reconcile it with the basic principles governing the intelligible universe. In this sense, Plotinus does not propose that we expunge all reference to notions of utility and benefit from our natural explanations; he merely wishes to render those notions coherent (...) with an ontology in which the intelligible always takes precedence over sensible reality. To this end, Plotinus introduces, first, what I call a vertical teleology, where the different animal species create the necessary conditions for the maintenance of higher forms of intelligible life, such as genera. Second, Plotinus advances what I call a horizontal teleology, where the various animal organs serve to provide a minimal coefficient of noetic content to each species in its respective ontic level. Plotinus thus sketches the outlines of a properly ‘noetic’ teleology in Ennead 6.7. (shrink)

For Aristotle, demonstrative knowledge is the result of what he calls ‘intellectual learning’, a process in which the knowledge of a conclusion depends on previous knowledge of the premises. Since demonstrations are ultimately based on indemonstrable principles (the knowledge of which is called ‘νοῦς’), Aristotle is often described as advancing a foundationalist doctrine. Without disputing the nomenclature, I shall attempt to show that Aristotle’s ‘foundationalism’ should not be taken as a rationalist theory of epistemic justification, as if the first principles (...) of science could be known as such independently of their explanatory connections to demonstrable propositions. I shall argue that knowing first principles as such involves knowing them as explanatory of other scientific propositions. I shall then explain in which way noetic and demonstrative knowledge are in a sense interdependent cognitive states – even though νοῦς remains distinct from (and, in Aristotle’s words, more ‘accurate’ than) demonstrative knowledge. (shrink)

According to the early Yogācāra, following non-conceptual awareness, the advanced bodhisattva is said to attain a state characterized by a "subsequent awareness". Yogācāra thinkers identify this state with ultimate knowledge of causality and view it as involving a unique kind of conceptual activity and propositional attitudes, which are very different, however, from ordinary conceptual awareness insofar as they do not involve vikalpa. Translated back into the terms of some version of the contemporary debate between conceptualists and nonconceptualists, this would amount (...) to something like the claim that we can use concepts in a non-conceptual way. But how can we make sense... (shrink)

The ability to solve problems is a prerequisite in preparing mathematics preservice teachers. This study assessed preservice teachers’ problem-solving difficulties and performance, particularly in worded problems on number sense, measurement, geometry, algebra, and probability. Also, academic profile differences in the preservice teacher’s problem-solving performance and common errors were determined. A descriptive-comparative research design was employed with 158 random respondents. Data were gathered face-to-face during the first semester of the school year 2022-2023, and data were analyzed with the aid of jamovi (...) software, ensuring ethical measures. Overall findings revealed that the preservice teachers experienced average difficulty in solving problems. The low performance of the preservice teachers on the given problems was also demonstrated. Further analysis revealed a significant difference between the preservice teachers’ problem-solving performance based on their subject preference and program. Moreover, the error analysis revealed that the preservice teachers incurred comprehension errors in misrepresentation, misinterpretation, and miscalculation. These results will serve as a measure for policymakers and curriculum developers of the teacher education institution concerned to make relevant enhancements to the math courses offered in the elementary and secondary education programs. (shrink)

In this paper, we define projection and bidirectional projection measures between interval rough neutrosophic sets and prove their basic properties. Then two new multi attribute decision making strategies are proposed based on interval rough neutrosophic projection and bidirectional projection measures respectively. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.

Competitive negotiators frequently use tactics which others view as "unethical", in that these tactics either violate standards of truth telling or violate the perceived rules of negotiation. This paper sought to determine how business students viewed a number of marginally ethical negotiating tactics, and to determine the underlying factor structure of these tactics. The factor analysis of these tactics revealed five clear factors which were highly similar across the two samples, and which parallel (to a moderate degree) categories of tactics (...) proposed by earlier theory. Data from one sample also permitted comparisons of the appropriateness of certain tactics across gender, nationality, ethnic origin and perception of one's negotiating style. (shrink)

Coleridge rarely mentions Hegel in his philosophical writings and seems to have read very little of Hegel's work. Yet I argue that Coleridge's criticisms of Schelling's philosophy—as recorded in letters and marginalia—betray remarkable intellectual affinities with his nearly exact contemporary Hegel, particularly in their shared doubts about Schelling's foundationalist intuitionism. With this background in place, I seek to demonstrate that volume one of Coleridge's Biographia Literaria is a radically self-undermining text: its philosophical argument, far from slavishly recapitulating Schelling's philosophy, remains (...) haunted by a quasi-Hegelian skepticism toward intuition even as it advances intuition as the foundation of its theoretical edifice. (shrink)

This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of theoretical economics. This analysis is substantially expanded through a dynamic approach, where the truth of a valuation results in an updated interpretation or changes in the agent's subjective belief regarding the effectiveness of the selected action as well as the objective reality of the effectiveness of all other (...) possible actions (i.e. consequence realization). Complications arise when the economic agent is presented with a set of actions that render ambiguous preference, or when the effectiveness of an action cannot be perceived upon its selection, thereby necessitating a different theory of choice and consequence realization. (shrink)

Conditional independence tests have received special attention lately in machine learning and computational intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of probabilistic graphical models, which includes Bayesian network models, conditional independence tests are especially important for the task of learning the probabilistic graphical model structure from data. In this paper, we propose the full Bayesian significance test for tests of conditional independence for discrete datasets. The full Bayesian (...) significance test is a powerful Bayesian test for precise hypothesis, as an alternative to the frequentist’s significance tests (characterized by the calculation of the p-value). (shrink)

In this paper, I explore two possible readings of Republic IV, 439c2-d8, and of Plato’s claim that the just soul is governed by its rational element. My aim is to argue against a “desiderative” interpretation of the passage, according to which the motivational strength of rational desires depends on a set of desires given in advance and produced independently of reason. As an alternative, I advance a “cognitivist” reading according to which the rational desires of the just soul have as (...) its ultimate source a knowledge about the nature of goodness and happiness, with its own motivational force. Finally, I argue for a reinterpretation of 439a4-b1, a passage that, at first sight, seems to contradict my analysis of 439c2-d8. (shrink)

During the Winter of 2011 I visited SADAF and gave a series of talks based on the central chapters of my manuscript on the Yablo paradox. The following year, I visited again, and was pleased and honored to find out that Eduardo Barrio and six of his students had written ‘responses’ that addressed the claims and arguments found in the manuscript, as well as explored new directions in which to take the ideas and themes found there. These comments reflect my (...) thoughts on these responses (also collected in this issue), as well as my thoughts on further issues that arose during the symposium that was based on the papers and during the many hours I spent talking and working with Eduardo and his students. Durante el invierno de 2011, visité SADAF y dí una serie de conferencias sobre los capítulos centrales de mi manuscrito sobre la paradoja de Yablo. El año siguiente, visité Buenos aires nuevamente y tuve el placer y el honor de descubrir que Eduardo Barrio y seis de sus estudiantes habían escrito respuestas que abordan las afirmaciones y argumentos de mi manuscrito, además de explorar nuevas direcciones en las cuales considerar las ideas y temas encontrados allí. El presente trabajo refleja mis pensamientos sobre estas respuestas (también incluidas en este volumen), así como mis ideas sobre otras cuestiones que surgieron durante el simposio en el que se presentaron los artículos y en las muchas horas que nosotros discutimos y trabajamos con Eduardo y sus estudiantes. (shrink)

In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion . We propose (...) a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony. The construction is based on a classification of I-rules, and constitute an implementation to Gentzen’s (and Pawitz’) remark, that E-rules can be “read off” I-rules. (shrink)

Comics comprise a hybrid art form descended from printmaking and mostly made using print technologies. But comics are an art form in their own right and do not belong to the art form of printmaking. We explore some features art comics and fine art prints do and do not have in common. Although most fine art prints and comics are multiple artworks, it is not obvious whether the multiple instances of comics and prints are artworks in their own right. The (...) comparison of comics and fine art prints provides a promising test for assessing how hybrid art forms develop more generally, and for assessing how they differ from closely related nonhybrid cousins. (shrink)

The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type interpretation (in arbitrary Henkin models). The domains (...) of derivations are collections of derivations in the associated “dedicated” natural-deduction proof-system, and functions therein (with no appeal to models, truth-values and elements of a domain). The compositionality of the semantics is analyzed. (shrink)

Immanuel Kant promised, ‘as Your Majesty's loyal subject’, to abstain from all public lectures about religion. All past commentators agree this phrase permitted Kant to return to the topic after the King died. But it is not part of the ‘at-issue content’. Consequently, ‘as Your Majesty's loyal subject’ is no more an escape clause than the corresponding phrase in ‘I guarantee, as your devoted fan, that these guitar strings will not break’. Just as the guarantee stands regardless of whether the (...) guarantor ceases to be your devoted fan, the compliance conditions of Kant's promise are not affected by Kant's ceasing to be the king's loyal subject. For good or ill, Kant made a lying promise to King Friedrich Wilhelm II in 1794. (shrink)

Charitable interpreters of David Hume set aside his sprinkles of piety. Better to read him as lying than as clumsily inconsistent. We argue that the attribution of lies can pay dividends in historical scholarship no matter how strongly the theorist condemns lying. Accordingly, we show that our approach works even with one of the strongest condemners of lying: Immanuel Kant. We argue that Kant lied in his scholarly work and even in the first Critique. And we defend the claim that (...) this lie attribution, strange as it may sound, amounts to a kind of scholarly charity. (shrink)

Aristotle's theory of demonstration, developed in the Posterior Analytics, is not restricted to determining the formal requirements for formulating probative arguments that establish properly the results of scientific investigation. To the probative aspect of demonstration it shall be added its primarily explanatory character, orientated by theses of strong ontological and metaphysical content and involving notions like substance, essence and causation. We shall analyze the relation between those two ranges of Aristotle's philosophy of science and investigate how the formal features of (...) demonstration maintain an affinity with the metaphysical background to which scientific activity is conditioned. (shrink)

This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While (...) non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

In this essay I will defend three points, the first being that Descartes- unlike the aristotelian traditon- maintained that abstraction is not a operation in which the intellect builds the mathematical object resorting to sensible ob- jects. Secondly I will demonstrate that, according to cartesian philosophy, the faculty of understanding has the ability to instatiate- within the process of abstraction- mathematical symbols that represent the relation between quantities, whether magnitude or multitude.And finally I will advocate that the lack of onthological (...) commitment with sensible experience found in cartesian philosophy of mathematics allows for the creation of a mathematical language that regards the objects of geometry and arithmetics through a system of rules and notations, in other words, algebra. (shrink)

“Love hurts”—as the saying goes—and a certain amount of pain and difficulty in intimate relationships is unavoidable. Sometimes it may even be beneficial, since adversity can lead to personal growth, self-discovery, and a range of other components of a life well-lived. But other times, love can be downright dangerous. It may bind a spouse to her domestic abuser, draw an unscrupulous adult toward sexual involvement with a child, put someone under the insidious spell of a cult leader, and even inspire (...) jealousy-fueled homicide. How might these perilous devotions be diminished? The ancients thought that treatments such as phlebotomy, exercise, or bloodletting could “cure” an individual of love. But modern neuroscience and emerging developments in psychopharmacology open up a range of possible interventions that might actually work. These developments raise profound moral questions about the potential uses—and misuses—of such anti-love biotechnology. In this article, we describe a number of prospective love-diminishing interventions, and offer a preliminary ethical framework for dealing with them responsibly should they arise. (shrink)

Notions such as Sunyata, Catuskoti, and Indra's Net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nagarjuna considered two levels of reality: one called conventional reality and the other ultimate reality. Within this framework, Sunyata refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuskoti refers to the claim (...) that four truth values, along with contradiction, are admissible in reasoning. Indra's Net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions which are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of Sunyata. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of Catuskoti. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's Net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

According to Essentialism, an object’s properties divide into those that are essential and those that are accidental. While being human is commonly thought to be essential to Socrates, being a philosopher plausibly is not. We can motivate the distinction by appealing—as we just did—to examples. However, it is not obvious how best to characterize the notion of essential property, nor is it easy to give conclusive arguments for the essentiality of a given property. In this paper, I elaborate on these (...) issues and explore the way in which essential properties behave in relation to other related properties, like sufficient-for-existence properties and individual essences. (shrink)

We define consciousness as the category of all conscious experiences. This immediately raises the question: What is the essence in which every conscious experience in the category of conscious experiences partakes? We consider various abstract essences of conscious experiences as theories of consciousness. They are: (i) conscious experience is an action of memory on sensation, (ii) conscious experience is experiencing a particular as an exemplar of a general, (iii) conscious experience is an interpretation of sensation, (iv) conscious experience is referring (...) sensation to an object as its cause, and (v) conscious experience is a model of stimulus. Corresponding to each one of these theories we obtain a category of models of conscious experiences: (i) category of actions, (ii) category of idempotents, (iii) category of two sequential maps, (iv) category of brain-generalized figures, and (v) functor categories with intuition as base and conceptual repertoire as exponent, respectively. For each theory of consciousness we also calculate its truth value object and characterize the objective logic intrinsic to the corresponding category of models of consciousness experiences. (shrink)