We propose a generalization of Sahlqvist formulae to polyadic modal languages by representing modal polyadic languages in a combinatorial style and thus, in particular, developing what we believe to be the right approach to Sahlqvist formulae at all. The class of polyadic Sahlqvist formulae PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.

We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and (...) Vaccaro we prove that all inductive formulae are elementary canonical and thus extend Sahlqvist’s theorem over them. In particular, we give a simple example of an inductive formula which is not frame-equivalent to any Sahlqvist formula. Then, after a deeper analysis of the inductive formulae as set-theoretic operators in descriptive and Kripke frames, we establish a somewhat stronger model-theoretic characterization of these formulae in terms of a suitable equivalence to syntactically simpler formulae in the extension of the language with reversive modalities. Lastly, we study and characterize the elementary canonical formulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames. (shrink)

We propose a generalization of Sahlqvist formulas to polyadic modal languages by representing such languages in a combinatorial PDL style and thus, in particular, developing what we believe to be the right syntactic approach to Sahlqvist formulas at all. The class of polyadic Sahlqvist formulas PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.

In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several extensions (...) of \SQEMA\ where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension \SSQEMA\ we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of \SSQEMA\ which guarantee canonicity, too. (shrink)

I think it would be fair to say that, until about 1900, philosophers were generally reluctant to admit the existence of what are nowadays called polyadic properties.1 It is important to recognize, however, that this reluctance on the part of pre-twentieth-century philosophers did not prevent them from theorizing about relations. On the contrary, philosophers from the ancient through the modern period have had much to say about both the nature and the ontological status of relations. In this paper I (...) examine the views of one such philosopher, namely, Albert the Great. (shrink)

Kant’s most prominent formulation of the Categorical Imperative, known as the Formula of Universal Law (FUL), is generally thought to demand that one act only on maxims that one can will as universal laws without this generating a contradiction. Kant's view is standardly summarized as requiring the 'universalizability' of one's maxims and described in terms of the distinction between 'contradictions in conception' and 'contradictions in the will'. Focusing on the underappreciated significance of the simultaneity condition included in the FUL, I (...) argue, by contrast, that the principle is better read as requiring that one be able to will two things simultaneously without self-contradiction, namely, that a maxim be one's own and that it be a universal law. This amounts to a new interpretation of the FUL with significant interpretive and philosophical advantages. (shrink)

In this article, we provide three generators of propositional formulae for arbitrary languages, which uniformly sample three different formulae spaces. They take the same three parameters as input, namely, a desired depth, a set of atomics and a set of logical constants (with specified arities). The first generator returns formulae of exactly the given depth, using all or some of the propositional letters. The second does the same but samples up-to the given depth. The third generator outputs (...) formulae with exactly the desired depth and all the atomics in the set. To make the generators uniform (i.e. to make them return every formula in their space with the same probability), we will prove various cardinality results about those spaces. (shrink)

Formula thinking is a kind of thinking strictly by route in which the thinker never deviates from a set course. Craft thinking involves a rough approximation to a set course but allows for deviation. The arts involve craft thinking. Repairing a machine involves formula thinking. America has become almost completely dominated by formula thinking.

Kant’s formula of universal law (FUL) is standardly understood as a test of the moral permissibility of an agent’s maxim: maxims which pass the test are morally neutral, and so permissible, while those which do not are morally impermissible. In contrast, I argue that the FUL tests whether a maxim is the cause or determining ground of an action at all. According to Kant’s general account of causality, nothing can be a cause of some effect unless there is a law-like (...) relation between the putative cause and effect. Applied to the case of action, no maxim can be the cause of an agent’s action unless there is a law-like relation between maxims of that kind and actions of that kind. The special capacity to act according to maxims as law-like causes is what Kant calls a will; the basic constitutive principle of the will is a non-normative principle I call the categorical declarative. While the actions of a perfectly good will would be described by the categorical declarative alone, human action is determined not only by the causality of the will, but also by competing causes, namely those stemming from inclination. There is thus need for a causal test for putative maxims. The test contained in the FUL is meant to determine whether an action could be grounded solely on the agent’s maxim, or whether it requires a cause external to the will. This account permits one to build eventual distinctions concerning the morality of actions on prior and independent distinctions concerning their causality. (shrink)

The Barcan formula (BF) is commonly paraphrased as the schematic conditional that if it is possible that there be a phi then something or other is possibly a phi. It is validated by the most straightforward systems of quantified modal logic. It is also widely considered to pose a threat to the commonsensical metaphysical view that there are no non-actual (or ‘merely possible’) things. I show how BF can be cleared of such a charge by construing it as a bridge (...) principle connecting modality de dicto and modality de re while retaining a Russellian robust sense of reality in modal matters. (shrink)

In two recent articles I have argued that Kant’s legal and political philosophy can shed new light on his much-contested account of moral autonomy and that important changes in his political theory help to explain why in his later work the Formula of Autonomy disappears. In the present essay, I respond to comments by Sorin Baiasu and Marie Newhouse, who argue that the changes in Kant’s political theory fail to explain the disappearance of the Formula of Autonomy, since in both (...) phases Kant held that laws are given by the people’s representatives. I offer additional support for my original argument by developing a more detailed account of Kant’s conception of the relation between the legislating representatives and the people they are taken to represent. I argue that Kant’s conception of the proper representation relation changed, and that it changed so fundamentally that the analogy at the basis of the Formula of Autonomy was no longer apt, thus providing a plausible explanation for its disappearance. I also address several related comments and propose an explanation for why Kant dropped the very idea of autonomy as a property of the will. (shrink)

Este artigo empreende uma discussão acerca da noção de fórmula discursiva nos trabalhos de Krieg-Planque e de um possível diálogo com o trabalho desenvolvido por Foucault, sobretudo, a partir do modo como o filósofo percebe o discurso, uma vez que ambos pertencem a uma tradição epistemológica francesa. Dessa forma, vamos adentrar pelo percurso de lapidação da noção de fórmula, tomando, para isso, a entrevista que Krieg-Planque concedeu a Philippe Schepens do Laboratoire de Sémio-linguistique, didatique e informatique (LASELDI) e do livro (...) A noção de fórmula em análise do discurso: quadro teórico e metodológico, trabalhos que representam para nós brasileiros uma espécie de introdução à discussão sobre a noção de fórmula proposta por Krieg-Planque no campo da Escola Francesa de Análise do Discurso (AD). Nessa discussão, vamos perceber que toda fórmula discursiva traz consigo uma densidade histórica apoiada em pré-construídos que estão voltados para as novas construções, tal qual propunha Foucault acerca das práticas e das materialidades discursivas em sua arqueologia do saber e em sua genealogia do poder. (shrink)

In this paper, we present a way to translate the metainferences of a mixed metainferential system into formulae of an extended-language system, called its associated σ-system. To do this, the σ-system will contain new operators (one for each standard), called the σ operators, which represent the notions of "belonging to a (given) standard". We first prove, in a model-theoretic way, that these translations preserve (in)validity. That is, that a metainference is valid in the base system if and only if (...) its translation is a tautology of its corresponding σ-system. We then use these results to obtain other key advantages. Most interestingly, we provide a recipe for building unlabeled sequent calculi for σ-systems. We then exemplify this with a σ-system useful for logics of the ST family, and prove soundness and completeness for it, which indirectly gives us a calculus for the metainferences of all those mixed systems. Finally, we respond to some possible objections and show how our σ-framework can shed light on the “obeying” discussion within mixed metainferential contexts. (shrink)

In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize (...) main ideas and results, and outline further research perspectives. (shrink)

In the first ever commentary on the Groundwork, one of Kant’s earliest critics, Gottlob August Tittel, argues that the categorical imperative is not a new principle of morality, but merely a new formula. This objection has been unjustly neglected in the secondary literature, despite the fact that Kant explicitly responds to it in a footnote in the second Critique. In this paper I seek to offer a thorough explanation of both Tittel’s ‘new formula’ objection and Kant’s response to it, as (...) well as illustrate its significance. I argue that the objection is in fact the third step in a line of argument that Tittel presents in his commentary, and that the objection is best understood within this context. I analyze Kant’s response in the second Critique footnote line-by-line so as to show that Kant both clarifies that it was never his aim to offer a new principle, but only ‘establish’ the principle that common human reason already implicitly employs. Furthermore, I show that Kant uses the opportunity to clarify the sense in which the categorical imperative is a ‘formula [Formel]’, namely as a representation of a complicated and abstract principle, like the moral law, in a way that is easier to understand and apply. I conclude by illustrating the fourth step in Tittel’s line of argument, which makes the overall significance of the ‘new formula’ objection clear: for Tittel, the problem is not that Kant seems to be offering merely a new formula, but that the categorical imperative lacks a foundation. (shrink)

Dialectica: Mathematica and Physica, Truth and Justice, Trick and Life. Mathematica as the Constructive Metaphysica and Ontology. Mathematica as the constructive existential method. Сonsciousness and Mathematica: Dialectica of "eidos" and "logos". Mathematica is the Total Dialectica. The basic maternal Structure - "La Structure mère". Mathematica and Physica: loss of existential certainty. Is effectiveness of Mathematica "unreasonable"? The ontological structure of space. Axiomatization of the ontological basis of knowledge: one axiom, one principle and one mathematical object. The main ideas and concepts (...) of the ontological construction/ "Point with a vector germ" and "heavenly triangle". "Ordo geometricus" and "Ordo onto-topological". Architecture of the onto-topological basis of knowledge: general framework structure, carcass and foundation. The absolute space and the absolute field. The absolute (natural) system of coordinates of Universum. Eidos of "idea of ideas", the symbol and the "formula of Justice". (shrink)

A natural extension of Heron's 2000 year old formula for the area of a triangle to the volume of a tetrahedron is presented. This gives the fourth power of the volume as a polynomial in six simple rational functions of the areas of its four faces and three medial parallelograms, which will be referred to herein as "interior faces." Geometrically, these rational functions are the areas of the triangles into which the exterior faces are divided by the points at which (...) the tetrahedron's in-sphere touches those faces. Part I presents an overview of these results and some necessary but little-known background in areal geometry. Part II derives the promised extension, and ends with a conjecture as to how the formula extends to n-dimensional simplices for all n>3. Part III explains how, for n=3, the zeros of the polynomial constitute a five-dimensional semi-algebraic variety consisting almost entirely of collinear tetrahedra with vertices separated by infinite distances, but with generically well-defined distance ratios; it further proves that these unconventional Euclidean configurations can be identified with a quotient of the Klein quadric by an action of a group of reflections isomorphic to ℤ42, wherein four-point configurations in the affine plane constitute a distinguished three-dimensional subvariety. Part IV consists of five appendices which show, among other things, that the algebraic structure of the zeros in the affine plane naturally defines the associated four-element, rank 3 chirotope, aka affine oriented matroid. (shrink)

According to the objection from positive duties, Kant's Formula of Universal Law is flawed because it cannot be used to derive any affirmative moral requirements. This paper offers a response to that objection and proposes a novel way to derive positive duties from Kant's formula. The Formula of Universal Law yields positive duties to adopt our own perfection and others’ happiness as ends because we could not rationally fail to will those ends as universal ends.

Kant’s Formula of Humanity (FH) is considered by many, Kant included, to be the most intuitively appealing formulation of the categorical imperative. FH tells us that to treat persons with dignity and respect we must always treat them as ends in themselves and never as mere means. One set of issues raised by FH revolves around how FH is to be justified or grounded and how it relates to the other formulations of the categorical imperative. This set of issues, though (...) important, is not our focus here. Instead, we shall focus on a different set of issues: how do we apply or use this formula in practice, that is, how does this principle work as a moral guide to what duties and obligations we have in particular cases? This paper will seek to answer that question by defending an interpretation and rational reconstruction of FH in terms of two subsidiary principles, the Mere Means Principle (MMP), which grounds perfect duties, and the Ends in Themselves Principle (ETP), which grounds imperfect duties. These two principles will then be applied to a number of examples to illustrate how they work. (shrink)

In this paper I defend the traditional interpretations of Kant’s Formula of a Law of Nature from recent attacks leveled by Faviola Rivera-Castro, James Furner, Ido Geiger, Pauline Kleingeld and Sven Nyholm. After a short introduction, the paper is divided into four main sections. In the first, I set out the basics of the three traditional interpretations, the Logical Contradiction Interpretation, the Practical Contradiction Interpretation and the Teleological Contradiction Interpretation. In the second, I examine the work of Geiger, Kleingeld and (...) Nyholm: these three commentators reject the traditional interpretations entirely, but I argue that this rejection is ill-founded. In the third and fourth, I take a detailed look at Furner’s work, work in which he seeks to revise (rather than reject) the traditional interpretations. I argue that, despite his more modest aims, Furner’s revision is also ill-founded. (shrink)

One of the most important difficulties facing Kant’s Formula of Universal Law (FUL) is its apparent inability to show that it is always impermissible to kill others for the sake of convenience. This difficulty has led current Kantian ethicists to de-emphasize the FUL or at least complement it with other Kantian principles when dealing with murder. The difficulty stems from the fact that the maxim of convenience killing fails to generate a ‘contradiction in conception’, producing only a ‘contradiction in the (...) will’ when subjected to the two-fold test associated with the FUL. This result is thought to imply that the FUL allows us sometimes to kill for the sake of convenience. In this essay, I argue that the very diagnosis of the problem rests on a mistake, and that if the maxim of convenience killing generates a contradiction in the will, then acting on it is never permissible. (shrink)

Kant's formulae ought to effectively produce the same result when applied to the moral validity of any particular maxim; further, no valid maxim produces contradictory results when applied against Kant's Universal Law and Humanity formulae. Where one uses all formulae in the assessment of a maxim, one gains a more complete understanding of the moral law, thereby bridging principles of reason with intuition within the agent who has undertaken to evaluate the morality of a particular action. These (...) formulae command without regard to any particular interests, but are instead unconditional; further, these formulae effectively limit choice of action and therefore give rise to duty. Kant implies that the structure of all maxims requires different formulae of the same moral law, i.e., all maxims have a ‘form’ and a ‘matter’, which prompt reconfiguring of the categorical imperative into different formulae in order to test the morality of a maxim. (shrink)

Semantic Information conveyed by daily language has been researched for many years; yet, we still need a practical formula to measure information of a simple sentence or prediction, such as “There will be heavy rain tomorrow”. For practical purpose, this paper introduces a new formula, Semantic Information Formula (SIF), which is based on L. A. Zadeh’s fuzzy set theory and P. Z. Wang’s random set falling shadow theory. It carries forward C. E. Shannon and K. Popper’s thought. The fuzzy set’s (...) probability defined by Zadeh is treated as the logical probability sought by Popper, and the membership grade is treated as the truth-value of a proposition and also as the posterior logical probability. The classical relative information formula (Information=log(Posterior probability / Prior probability) is revised into SIF by replacing the posterior probability with the membership grade and the prior probability with the fuzzy set’s probability. The SIF can be explained as “Information=Testing severity – Relative square deviation” and hence can be used as Popper's information criterion to test scientific theories or propositions. The information measure defined by the SIF also means the spared codeword length as the classical information measure. This paper introduces the set-Bayes’ formula which establishes the relationship between statistical probability and logical probability, derives Fuzzy Information Criterion (FIC) for the optimization of semantic channel, and discusses applications of SIF and FIC in areas such as linguistic communication, prediction, estimation, test, GPS, translation, and fuzzy reasoning. Particularly, through a detailed example of reasoning, it is proved that we can improve semantic channel with proper fuzziness to increase average semantic information to reach its upper limit: Shannon mutual information. (shrink)

Many Kantian scholars have debated what normative guidance the formula of the law of nature provides. There are three ways of understanding the role of FLN in Kant’s ethics. The first line of interpretation claims that FLN and FLU are logically equivalent. The second line claims that there are only subjective differences, meaning that FLN is easier to apply than the abstrct method of FUL. The third line of interpretation claims that there are objective differences between FLN and FUL in (...) the sense that each formula has an irreducible role in Kant’s ethics. In this article I will show that the first and second lines of interpretation cannot fully explain Kant’s account of FLN and I will propose a new interpretation which pertains to the third type. I will explore the schematism model to understand the role of FLN and argue that it is an intermediary principle that fills in a practical gap between the moral law and action. In the end, I will consider a possible objection against this understanding which claims that the schematism model is not applicable to practical judgment since nothing is given in experience. (shrink)

According to the standard reading of Kant's formula of universal law (FUL), positive duties can be derived from FUL. In this article, I argue that the standard reading does not work. In the first section, I articulate FUL and what I mean by a positive duty. In the second section, I set out an intuitive version of the standard reading of FUL and argue that it does not work. In the third section, I set out a more rigorous version of (...) the standard reading of FUL and argue that even this more rigorous version does not work. (shrink)

Ever since Hegel famously objected to Kant’s universalization formulations of the Categorical Imperative on the grounds that they are nothing but an empty formalism, there has been continual debate about whether he was right. In this paper I argue that Hegel got things at least half-right: I argue that even if negative duties (duties to omit actions or not to adopt maxims) can be derived from the universalization formulations, positive duties (duties to commit actions or to adopt maxims) cannot. The (...) paper is divided into three main sections. In the first, I set out the procedures generally accepted among Kantians for deriving positive duties from the universalization formulations. In the second, I set out the arguments from section 1 in more detail and explain why they do not work. In the third, I examine a strategy that might be used to supplement the arguments from section 2 and I argue that it also does not work. (shrink)

This paper explores the charge by Bruce Aune and Allen Wood that a gap exists in Kant's derivation of the Categorical Imperative. I show that properly understood, no such gap exists, and that the deduction of the Categorical Imperative is successful as it stands.

My aim in this paper is to explore different ways of understanding Kant’s Formula of Humanity as a formal principle. I believe that a formal principle for Kant is a principle that is constitutive of some domain of cognition or rational activity. It is a principle that both constitutively guides that activity and serves as its internal regulative norm. In the first section of this essay, I explain why it is desirable to find a way to understand the Formula of (...) Humanity as a formal principle in this sense. In sections II and III I discuss two interpretive approaches to Kant’s idea that rational nature or humanity is an end in itself, both of which may be construed as treating the Formula of Humanity as a formal principle. By focusing on the notion of formal principle, I hope to raise a set of issues about how to understand the idea of rational nature or humanity as an end in itself, and about the relation of the Formula of Humanity [FH] to the Formula of Universal Law [FUL]. I do not resolve the issues in this paper, though I briefly sketch some resolution at the end. (shrink)

This article investigates the original meaning of dependent arising in the Buddha’s teaching, by focussing on the imasmi" sati formula. Modern scholars such as the Rhys Davidses, K.N. Jayatilleke and Paul Williams have interpreted it as a princi- ple of causation, comparable to a scientific conception of causation. I argue instead that this formula implies that the Buddha held that causation is nothing more than the correlation of causes and effects, and that it commits the Buddha to a Humean regularity (...) thesis about causation. I draw a distinction between the Buddhist and scientific concepts of causation, and then summarise an alternative approach made by more recent scholars such as Sue Hamilton, Noa Ronkin and Eviatar Shulman, who present dependent arising in terms of conditionality in the causal structure of subjective experience. I conclude by presenting the argument that the imasmi" sati formula does not express a principle of causation but is rather a formula for the method of discovering and presenting causation as conditionality in experience. (shrink)

A scheme to help merge the ideas of quantum gravity.

The article reviews the category of ‘happiness’ along three lines: etymological discourse, ‘objective’ indicators and elements of happiness as a social/cultural phenomenon, as well as the author's proposed formula for happiness. The relevance of this study is determined by the fact that human resource is the main resource of the State, and the future of the country depends on the well-being of each individual. As a result of the etymological discourse, the following conclusions have been drawn: 1, the category of (...) ‘happiness’ is a more recent entity; 2, the ancient Greek categories of ‘good’ and ‘the highest good’ are its progenitors; 3, in the West European philosophy, good is understood inconsistently and includes the range from its utilitarian meaning to its connection with the notion of ‘value’; 4, the category of ‘happiness’ includes two aspects: one under the control of a man and another determined by external factors. Thus, in understanding happiness, most studies focus on either social/biological or social/economic components. The author proposes an integrative formula for happiness, which has the following elements: 1, ‘why’/belief system: life according to one’s own convictions; 2, ‘what’/abilities: their fulfilment in a professional/cognitive activity, i.e. the implementation of cognitive interest; 3, ‘where’/the place for fulfilling one’s life, understood as a geographical and climatic space; 4, ‘with whom’/ communication with people the person truly likes and who like him/her, while keeping a socially acceptable distance of a detached polite interaction with the rest of the social space. Therefore, happiness is the harmony of triune: the person with the Self, the Self with the world and the world with the Self. (shrink)

We analyze the properties of optimum portfolios, the price of which is considered a new quantum variable and derive a quantum analog of the Black-Scholes formula for the price of financial variables in assumption that the market dynamics can by considered as its continuous weak measurement at no-arbitrage condition.

O presente artigo deseja estudar a questão da música enquanto linguagem e como seria a sua ação linguística dentro do campo da comunicabilidade e das mediações. Para isso, utilizando as ideias da Filosofia Analítica da Linguagem (especialmente Ludwig Wittgenstein, J. L. Austin e John Searle), serão analisados dois elementos da linguagem musical de épocas distintas e antagônicas: o leitmotiv (com enfoque em O Anel do Nibelungo, de Richard Wagner) e a fórmula (com enfoque em Licht, de Karlheinz Stockhausen). A ideia (...) aqui é verificar a autonomia da linguagem musical bem como as suas possibilidades de lógica ilocucionária. Palavras-chaves: Linguagem musical; Pragmática; Ação linguística. (shrink)

O presente artigo busca analisar, no aspecto da imagem fílmica, os documentários de arquivo sobre a Fórmula 1 em seus primórdios garagistas (pré-1950 ao fim da década de 1970). Para isso, serão analisados três documentários recentes sobre grandes pilotos da categoria, a saber: Jack Brabham, Graham Hill e Juan Manuel Fangio. Utilizando a teorização de Gilles Deleuze acerca da imagem-movimento e seus aspectos semióticos, o objetivo aqui é ver que a cadeia de significação provocada pela reedição de imagens de arquivo (...) provoca a construção de um argumento que ressalta mais o lado humano dos pilotos do que os seus feitos enquanto esportistas consagrados. (shrink)

Book review of 'Means, Ends, and Persons: The Meaning and Psychological Dimensions of Kant's Humanity Formula, by Robert Audi, OUP'.

This is a two page handout, briefly summarizing late nineteenth and early twentieth century philosopher Henry Sidgwick's objections to giving all citizens a right to as much equal freedom as possible. H.L.A. Hart, who uses the material in a notable paper, also figures.

By formalizing some classical facts about provably total functions of intuitionistic primitive recursive arithmetic (iPRA), we prove that the set of decidable formulas of iPRA and of iΣ1+ (intuitionistic Σ1-induction in the language of PRA) coincides with the set of its provably ∆1-formulas and coincides with the set of its provably atomic formulas. By the same methods, we shall give another proof of a theorem of Marković and De Jongh: the decidable formulas of HA are its provably ∆1-formulas.

A concept is traditionally defined via the necessary and sufficient conditions that clearly determine its extension. By contrast, cognitive views of concepts intend to account for empirical data that show that categorisation under a concept presents typicality effects and a certain degree of indeterminacy. We propose a formal language to compactly represent concepts by leveraging on weighted logical formulas. In this way, we can model the possible synergies among the qualities that are relevant for categorising an object under a concept. (...) We show that our proposal can account for a number of views of concepts such as the prototype theory and the exemplar theory. Moreover, we show how the proposed model can overcome some limitations of cognitive views. (shrink)

This paper presents an attempt to bridge the gap between logical and cognitive treatments of strategic reasoning in games. There have been extensive formal debates about the merits of the principle of backward induction among game theorists and logicians. Experimental economists and psychologists have shown that human subjects, perhaps due to their bounded resources, do not always follow the backward induction strategy, leading to unexpected outcomes. Recently, based on an eye-tracking study, it has turned out that even human subjects who (...) produce the outwardly correct ‘backward induction answer’ use a different internal reasoning strategy to achieve it. The paper presents a formal language to represent different strategies on a finer-grained level than was possible before. The language and its semantics help to precisely distinguish different cognitive reasoning strategies, that can then be tested on the basis of computational cognitive models and experiments with human subjects. The syntactic framework of the formal system provides a generic way of constructing computational cognitive models of the participants of the Marble Drop game. (shrink)

In his debut book, The Birth of Tragedy, Nietzsche presents what he understands as a metaphysics of art or metaphysics of the artist. As it becomes clear throughout the argument developed in the work, his aim is to favor a justification of the world and of existence as an aesthetic phenomenon. The path to his metaphysics passes through the interaction with Kantian and, mostly, Schopenhauerian formulations, and through a deep dialogue with Greek culture in general and, indirectly, with Pre-Socratic thought. (...) The objective of this article is to delimit the retentions and displacements of the critical tradition in his book from 1872, and highlight the importance of the interlocution with the Greek cultural repertoire in the conformation of his metaphysics of the artist. In particular, the working hypothesis is that Nietzsche, in these approaches and appropriations of critical and archaic philosophical tradition, finds the possibility of an immanent metaphysics in the post-Kantian context, conceived as a physiology (in the antique sense) of aesthetic bias. (shrink)

Kant’s Formula of Humanity can be analyzed into two parts. One is an injunction to treat humanity always as an end. The other is a prohibition on using humanity as a mere means. The second is often referred to as the FH prohibition or the mere means prohibition. It has become popular to interpret this prohibition in terms of consent. The idea is that, if X uses Y's humanity as a means and Y does not consent to it, then X (...) uses Y's humanity as a mere means. There is then debate about the kind of consent that is relevant: possible, actual, or rational. In this paper, I argue against this interpretation. Section one sets up the consent account. Section two attacks possible and actual consent accounts on doctrinal grounds. Section three extends this doctrinal attack to rational consent accounts. Section four circles back to the original motivation for the consent interpretation. I argue that the consent account rests on a misinterpretation, and I conclude with a quick sketch of an alternative interpretation of the FH prohibition. (shrink)

The institution of the family and its importance have recently received considerable attention from political theorists. Leading views maintain that the institution’s justification is grounded, at least in part, in the non-instrumental value of the parent-child relationship itself. Such views face the challenge of identifying a specific good in the parent-child relationship that can account for how adults acquire parental rights over a particular child—as opposed to general parental rights, which need not warrant a claim to parent one’s biological progeny. (...) I develop a view that meets this challenge. This Project View identifies the pursuit of a parental project as a distinctive non-instrumentally valuable good that provides a justification for the family and whose pursuit is necessary and sufficient for the acquisition of parental rights. This view grounds moral parenthood in a normative relation as opposed to a biological one, supports polyadic forms of parenting, and provides plausible guidance in cases of assisted reproduction. (shrink)

In this paper ontological implications of the Barcan formula and its converse will be discussed at the conceptual and technical level. The thesis that will be defended is that sentential moods are not ontologically neutral since the rejection of ontological implications of Barcan formula and its converse is a condition of a possibility of the imperative mood. The paper is divided into four sections. In the first section a systematization of semantical systems of quantified modal logic is introduced for the (...) purpose of making explicit their ontological presuppositions. In this context Jadacki's ontological difference between being and existence is discussed and analyzed within the framework of hereby proposed system of quantified modal logic. The second section discusses ontological implications of the Barcan formula and its converse within the system accommodating the difference between being and existence. The third section presents a proof of incompatibility of the Barcan formula and its converse with the use of imperatives. In the concluding section, a thesis on logical pragmatics foreclosing the dilemma between necessitism and contingentism is put forward and defended against some objections. (shrink)

Kant’s Formula of Universal Law (FUL) is generally believed to require you to act only on the basis of maxims that you can will without contradiction to become universal laws. In “Contradiction and Kant’s Formula of Universal Law” (2017), I have proposed to read the FUL instead as requiring that, for any maxim on which you act, you can will two things simultaneously, without volitional self-contradiction: (1) willing the maxim as your own action principle and (2) willing that it become (...) a universal law. In the present essay, I reply to comments by Mark Timmons, Michael Walschots, Paola Romero, and Stefano Lo Re. In response to their comments concerning the application of the FUL, I expand the interpretive framework of the Volitional Self-Contradiction Interpretation. I argue that Kant also constructs the diagnostic volitional self-contradiction as a contradiction between (1) willing a tested maxim to become a universal law and (2) willing what humans, qua finite rational beings, necessarily will, namely the means to their actual and possible future ends. I also clarify how the two ways in which Kant specifies the test are related. Furthermore, I clarify the relation between the Volitional Self-Contradiction interpretation and other interpretations of the FUL, in particular the ‘Practical Contradiction’ and ‘Logical Contradiction’ interpretations, as well as its difference from the Golden Rule. I also address the objection that the volitional self-contradiction is superfluous, clarify the relation between the Formula of Universal Law and the Formula of the Law of Nature, and explain why the will of an immoral agent does not contain a volitional self-contradiction of the type at issue. (shrink)

In this volume Paul Formosa sets out a novel approach to Kantian ethics as an ethics of dignity by focusing on the Formula of Humanity as a normative principle distinct from the Formula of Universal Law. By situating the Kantian conception of dignity within the wider literature on dignity, he develops an important distinction between status dignity, which all rational agents have, and achievement dignity, which all rational agents should aspire to. He then explores constructivist and realist views on the (...) foundation of the dignity of rational agents, before developing a compelling account of who does and does not have status dignity and of what kind of achievement dignity or virtue we, as vulnerable rational agents, can and should strive for. His study will be highly valuable for those interested in Kant's ethical, moral and political philosophies. (shrink)

In this paper, I confront Parfit’s Mixed Maxims Objection. I argue that recent attempts to respond to this objection fail, and I argue that their failure is compounded by the failure of recent attempts to show how the Formula of Universal Law can be used to demarcate the category of obligatory maxims. I then set out my own response to the objection, drawing on remarks from Kant’s Metaphysics of Morals for inspiration and developing a novel account of how the Formula (...) of Universal Law can be employed to determine the deontic status of action tokens, action types, and maxims. (shrink)