Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This equality is motivated by generality of deductions. Characterizations are given for pairs of isomorphic formulae, which lead to decision procedures for this isomorphism.

This paper explores two questions central to understanding the nature of formulaic sequences: (1) What are they for? and (2) What determines how many there are? The “Communicative Impact” model draws into a single account how language is shaped by cognitive processing on the one hand and socio-interactional function on the other: Formulaic sequences play a range of coordinated roles in neutralizing unanticipated perturbations in the cognitive management of language, so the speaker's socio-interactional goals can still be achieved. One role (...) involves compensatory actions to sustain fluency. However, these actions are themselves context-sensitive, so the balance of types of formulaic sequence will vary according to situation. The model applies equally to temporary cognitive pressure and chronic problems such as dementia and limited linguistic competency in a foreign language. (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)

Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics (B-eS). This semantics is given by a relation called support, explaining the meaning of the logical constants, which is parameterized by systems of rules called bases that provide the semantics of atomic propositions. In this paper, we interpret bases as collections of definite formulae and use (...) the operational view of them as provided by uniform proof-search—the proof-theoretic foundation of logic programming (LP)—to establish the completeness of IPL for the B-eS. This perspective allows negation, a subtle issue in P-tS, to be understood in terms of the negation-as-failure protocol in LP. Specifically, while the denial of a proposition is traditionally understood as the assertion of its negation, in B-eS we may understand the denial of a proposition as the failure to find a proof of it. In this way, assertion and denial are both prime concepts in P-tS. (shrink)

Breastfeeding is analogous to pregnancy as an experience, in its exclusiveness to women, and in its cost and the effects it has on equitable share of labor. Therefore, the history of formula feeding provides useful insights into the future of full ectogenesis, which could evolve into a more severe version of what formula feeding is today: simplify life for some women and provide couples with a more equitable share of work at the cost of stigma, guilt and a (...) daily diet of studies purporting to show the benefits of natural pregnancy. Making pregnancy an optional route to motherhood would make women's life trajectory more similar to men's and thus put pressure on women to compete with men on the ground shaped by men's preferences. Despite being a treasured experience of many women today, bearing children could become the luxury of the few, the province of the very poor and a choice working women will pay a high price for as women who choose pregnancy become stigmatized as self-indulgent or unprofessional and penalized for it in the workplace. At the same time, scarce societal resources that could be used to support pregnant women and working mothers would instead be directed toward proving to women or even forcing them to gestate children "the right way." While not necessarily threatening on its own, when added to formula feeding, IVF, stem-cell produced ova and sex robots, full ectogenesis could diminish men's stake in women's wellbeing and even existence. (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)

This paper provides a methodologically original construction of Kant’s “Formula of Universal Law” . A formal structure consisting of possible worlds and games—a “game frame”—is used to implement Kant’s concept of a maxim and to define the two tests FUL comprises: the “contradiction in conception” and “contradiction in the will” tests. The paper makes two contributions. Firstly, the model provides a formal account of the variables that are built into FUL: agents, maxims, intentions, actions, and outcomes. This establishes a (...) clear benchmark for understanding how the mechanics of FUL actually work. Secondly, the analysis of the resulting framework sheds new light on discussions about the implications of FUL. On the basis of this, we suggest a move to “comprehensive Kantianism’, which is the application of FUL to systems of maxims rather than to isolated maxims. (shrink)

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)

Ritualistic formulae and acts pervade the political, legal, societal and religious life of the ancient world. In many instances there are striking similarities between the formulae of the Greco-Roman world and those of the Near East. Often illumination exists from one to the other. Here I wish to notice a few passages in Greek drama where I think such illumination is possible.

A Fórmula Porchat — ou seja, a intuição de um conflito das filosofias de caráter indecidível – possui papel tanto propedêutico quanto compulsório para um tratamento não dogmático da história dos sistemas filosóficos. Ao mesmo tempo em que reconhece tal papel, o presente artigo pretende indicar o caráter problemático da correspondência entre “conflito das filosofias” e “indecidibilidade filosófica”. Para tal, sustenta que o sentimento de indecidibilidade filosófica tem como referência impensada uma nostalgia da decidibilidade. O artigo sugere, ainda, o abandono (...) do tema da indecidibilidade, como um falso problema filosófico, e sustenta a necessidade de considerar os efeitos da prática filosófica sobre a configuração da vida comum e de tomar tais efeitos como formas de decidibilidade. Para tal é necessário considerar a atividade filosófica como inscrita no campo maior da manufatura da experiência humana. (shrink)

Kantians are increasingly deserting the universal law formula in favor of the humanity formula. The former, they argue, is open to various decisive objections; the two are not equivalent; and it is only by appealing to the humanity formula that Kant can reliably generate substantive implications from his theory of an acceptable sort. These assessments of the universal law formula, which clash starkly with Kant's own assessment of it, are based on various widely accepted interpretative assumptions. (...) These assumptions, it is argued in this article, depend on misleading translations of key terms; selective attention to Kant's concrete examples; not taking seriously Kant's theoretical claims about the relations among his various ideas; and a failure to take into account Kant's idiosyncratic definitions of key concepts. The article seeks to right these interpretative wrongs, and finds that the universal law formula is not open to many of the standard objections. (shrink)

Ancient Greek mathematics developed the original feature of being deductive mathematics. This article attempts to give a explanation f or this achievement. The focus is on the use of a fixed system of linguistic formulae in Greek mathematical texts. It is shown that the structure of this system was especially adapted for the easy computation of operations of substitution on such formulae, that is, of replacing one element in a fixed formula by another, and it is further argued that (...) such operations of substitution were the main logical tool required by Greek mathematical deduction. The conclusion explains why, assuming the validity of the description above, this historical level is the best explanatory level for the phenomenon of Greek mathematical deduction. (shrink)

The formula of universal law (FUL) is a natural starting point for philosophers interested in a Kantian perspective on the morality of abortion. I argue, however, that FUL does not yield much in the way of promising or substantive conclusions regarding the morality of abortion. I first reveal how two philosophers' (Hare's and Gensler's) attempts to use Kantian considerations of universality and prescriptivity fail to provide analyses of abortion that are either compelling or true to Kant=s understanding of FUL. (...) I then turn to some recent interpretations of Kant=s FUL contradiction in conception (CC) and contradiction in will (CW) tests. I argue that none of the interpretations of the CC testBincluding the practical interpretation favored by KorsgaardBdoes much to reveal moral problems with maxims of abortion. The CW test (as developed by Herman) is more helpful. Nevertheless, I argue that neither by considering abortion maxims as a subset of maxims of convenience killing, nor by considering such maxims as maxims of refusing to aid, can the CW test generate a general prohibition of abortion. At best, the CW test illuminates the abortion issue because by forcing us to think about how killing a fetus differs from killing other human beings, what attitudes we may reasonably have toward a fetus, and whether Kant's moral theory must be amended to do justice to the problem of abortion. But to pursue these questions, we must look beyond FUL; Kant’s formula of humanity and doctrine of virtue may well have more to offer. (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)

This is a survey article in which I explore some important recent work on the topic in question, Kant’s formula of the end in itself (or “formula of humanity”). I first provide an overview of the formulation, including what the formula seems roughly to be saying, and what Kant’s main argument for it seems to be. I then call the reader’s attention to a variety of questions one might have about the import of and argument for this (...) formula, alluding to some of the works in which philosophers have recently raised or tried to answer these questions. Then, for the bulk of the paper, I focus my discussion on two issues of contention: the identity of the “end in itself” that the formula refers to, and the relation between the value of the end in itself and the value of other ends. I do not attempt to argue for a particular position of my own regarding these issues. Instead, I explain a number of the more interesting or influential recent attempts to answer these questions, compare these approaches in various ways, draw implications from them, and raise concerns about some of them. I also suggest that an important link connects the question about the identity of the end in itself and the question about the relation between the value of the end in itself in relation to the value of other ends: How one answers these questions commits one to a position on the thorny issue of whether, how, and how fully, autonomy is manifested through empirical (not simply pure) practical reason. (shrink)

In The Formula, Luke Dormehl takes readers inside the world of numbers, asking how we came to believe in the all-conquering power of algorithms; introducing the mathematicians, artificial intelligence experts and Silicon Valley entrepreneurs who are shaping this brave new world, and ultimately asking how we survive in an era where numbers can sometimes seem to create as many problems as they solve.

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)

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)

Tomada desde Artaud por Deleuze ya desde la redacción de Lógica del sentido, la expresión de cuerpo sin órganos no deja de causar al menos perplejidad. En su enunciación se traman puntos cruciales de la filosofía de Deleuze desde su teoría del acontecimiento y de la diferencia, pasando por una definición y una analítica del deseo, hasta una determinada noción de vida que articularía el proceso de su generación. Sin desestimar lo anterior y los profusos usos y determinaciones actuales que (...) ha cobrado esta noción, nuestro propósito es vincular al CsO con la concepción de vida, que según nuestra lectura, se halla en la base de su formulación. Esto permanece en el texto como subyacente, y nuestra propuesta se inscribe en determinar el grado de influjo que posee el vitalismo de Bergson en la concepción de esta fórmula: desde este punto de vista es plausible sostener que el CsO es una operación que se funda de modo crucial en una lectura atenta al élan vital de bergsoniano. En suma, si el CsO es una involución creadora por definición de su proceso, no es sino porque su puesta en marcha significa y se efectúa en una constante y radical lucha que implica cada vez el desmontaje o desmembramiento de la idea de organismo.Taken from Artaud by Deleuze and from the writing of Logic of Sense, the expression of a body without organs continues to cause at least perplexity. In his statement plots crucial points in the philosophy of Deleuze from his theory of the event and the difference, to an analytical definition and the desire, to a certain concept of life that would articulate the process of their conception. Without underestimating the above and the profuse use and current measurements that has claimed this, our aim is to link the BwO with the conception of life, which according to our reading, is at the source of their formulation. This remains the underlying text, and our proposal settle on to determine the degree of influence that has the vitalism of Bergson in the design of this formula: From this point of view is plausible that the CSO is an operation that is based on crucially on a careful reading of the bergsonian élan vital. In brief, if the BwO is an involution of their creative process by definition, is merely because their start-up means and takes place in a constant struggle and radical increasingly involves the subtraction or dismantling of the idea of organism. (shrink)

While both humor and prosody in interaction have received scholarly attention in recent years, the prosody of humor has not been extensively explored. This study begins to fill this gap by investigating whether prosodic cues can be identified for riddles told in interaction, focusing on wh-questions in riddles versus ordinary conversation. The analysis demonstrates that in comparison to conversational wh-questions, riddles have less pitch variation both within the utterance and at the syllable level. It is argued that riddles do not (...) contain such wide pitch excursions because they do not require contextual disambiguation. While this study provides no evidence that riddles must be prosodically packaged in a specific way, the analysis suggests that the pitch of riddles is constrained due to interactional context. This constrained pitch is argued to work in conjunction with the formulaic syntax and content of riddle questions to signal to hearers that a joke is being told. (shrink)

Gandhi’s writings on moral issues propose an easiest formula to the world to establish harmony and peace in the global society. In a world where people are confronting a psychological fear of sudden terror and violence, the Gandhian formula of ‘non-violence (ahimsa) as a means’ to form a perfect harmonious world is getting strong attention of the world-community. Truth and non-violence are the two most valuable ingredients of Gandhian moral thoughts. For him, Truth or God is the end (...) and non-violence is the mean and the two can not be separated. They are more effective in life when they are used in their united form. This unity can be actualized only through the motive of ‘love to humanity’ without separating one person from another on any ground. He argues that the unity of truth and non-violence is a better way to have a moral and harmonious life. In this paper, I will focus upon the Gandhian formula in wider perspective, which reflects in his political activities and his writings as well, with the contention that it is highly applicable to normalize the violence rooted in different parts of the world at both the levels of religious and political. I will contend that Gandhian notion of truth and non-violence in terms of ends and means may play a medicinal role to harmonize the world suffering from extremism and terrorism. (shrink)

O processo de conversão ao Cristianismo, em sua versão ortodoxa, dos povos bárbaros assentados em território do Antigo Império Romano, durante os séculos V e VIl, evidencia o empenho das autoridades religiosas capazes de forjar variadas estratégias na busca do seu intento. Nesse sentido, destaca-se a atuação de Martinho de Braga pelo seu sistemático trabalho de evangelização, do que fez parte a redação de variadas obras. Entre estas desejamos sublinhar De Formula Vitae Honestae, obra de caráter político e moral (...) dirigida aos príncipes do referido reino, reproduzida inúmeras vezes na Idade Média a partir do século XII e inserida no conjunto de escritos conhecidos como espelho dos príncipes. (shrink)

En esta nota discutimos una forma generaldel Teorema de Deducción (TD) para sistemas modales de primer orden, la cual permite derivar varias otras formulaciones del mismoque aparecen en la literatura, así como su relación con la Fórmula de Barcan.

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 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)

Speakers routinely rely on a vast store of fixed and semi-fixed institutionalized utterances. In our mother tongue, we know how to combine pre-patterned phrases, complete semi-fixed expressions, and produce deviant versions for humorous effect. There are analogies with the way traditional folk musicians embellish tunes with a largely fixed structure, and the way jazz musicians improvise, and also with oral traditions in which poets composed or improvised tales during performance by using fixed formulas and formulaic phrases (though without the metrical (...) requirements of Homeric poetry). In written literature, the use of ready-made language was long disparaged as the opposite of creativity, but Barthes describes both speech and literature in general as consisting entirely of transformations of words that have already been set in order, and describes individual style as essentially a citational process, and the transformation of earlier formulae. Formulaic language can be shown to underlie much linguistic creativity. (shrink)

The marketing of infant formula in third-world countries in the 1970s by Nestlé S.A. gave rise to a consumer boycott that came to be a widely taught case study in the field of Business Ethics. This article extends that case study by identifying three specific individuals who were associated with managing Nestlé’s response to that boycott. It reveals their subsequent direct involvement in a number of additional “classic” 1980s business scandals (some of which ended with major criminal trials and (...) the imprisonment of eminent business figures)—and describes tangential linkages to other business scandals of the time. The article discloses a behind-the-scenes pattern of business villainy, adding both depth and breadth to previous accounts of these scandals. The article offers a conceptual framework that goes beyond personal greed as an explanatory factor for such unethical behavior in the business world, suggesting the presence of personal and organizational networks of intrigue and opportunity. The linkages between the scandals suggest an epidemiological process with the plotters acting as “virus” carriers contaminating various corporate cultures. (shrink)

Este artículo demuestra de un modo fáctico la utilidad del test de proporcionalidad y la fórmula del peso del profesor Robert Alexy en la práctica de los tribunales constitucionales y de otros altos tribunales. Para ello se aplica detenidamente este modelo a la Decisión del Tribunal Constitucional alemán de 2015 en el que se falla a favor de la compatibilidad del uso del velo por profesoras funcionarias que trabajan en la enseñanza pública con la neutralidad del Estado. Se examinan los (...) tres pasos de la ponderación el principio de adecuación o idoneidad, el principio de necesidad y la proporcionalidad en sentido estricto, concluyendo que esta nueva decisión del primer senado del Tribunal Constitucional federal alemán de 2015 aplica correctamente el principio de la proporcionalidad estricta. Primero porque establece adecuadamente que el grado de insatisfacción de la paz escolar o de los derechos de los padres debe medirse y calificarse a la vista de conflictos reales. Segundo porque al examinar la importancia de satisfacer el derecho de libertad religiosa de las profesoras y las consecuencias negativas de la ley prohibitiva del Land juzga que ello supone una lesión grave y que es una medida desproporcionada e innecesaria. Una Ley prohibitiva general basada en un peligro abstracto es contraria a la LF y una injerencia desmedida en un DF porque no permite la ponderación del caso concreto. Por ello, en el tercer paso se concluye que la importancia de satisfacer los derechos de las profesoras justifica que ceda la libertad negativa religiosa de los alumnos y que prevalezca la liberta religiosa positiva. Con la excepción de casos en los que haya conflictos reales. En estos últimos, ponderadas las circunstancias cabría ciertas prohibiciones temporales transitorias del uso del velo en lugares concretos, un extremo que por nuestra parte no hemos considerado adecuado. (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 \emph{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 \emph{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 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)

Kantian socialists at the turn of the twentieth century, as well as contemporary authors seeking a principle with which to condemn capitalism, have turned to Kant’s Formula of the End in Itself. This article assesses the arguments from FEI against capitalism from the perspective of the issues that arise in interpreting and applying Kant’s formula. There are various strategies with which a Kantian might use FEI to condemn conduct that Kant did not use FEI to condemn. The article (...) asks whether any of the existing arguments from FEI employ plausible versions of these strategies to derive a strict duty from that formula’s Never Merely as a Means principle that condemns capitalism. (shrink)

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)

This chapter contains sections titled: What Should We Treat as an End in Itself? Value and Ends The Argument for the Humanity Formulation How Particular Duties Follow Final Thoughts Bibliography.

En los debates recientes sobre la fórmula de la humanidad del imperativo categórico se intenta comprender los insumos conceptuales de dicha fórmula a partir de obras kantianas que no son propiamente la Fundamentación de la metafísica de las costumbres. Este proceder se ampara en la falsa suposición de que en la GMS no hay un significado claro o concreto de lo que encarnarían términos como humanidad (Mensch) o fin en sí mismo (Zweck an sich selbst). En virtud de lo anterior, (...) en este artículo buscaré analizar acuciosa y detalladamente qué es lo que tiene que decir Kant concretamente en GMS AA IV 42719-42833, puesto que ahí sí hay una argumentación que se construye progresivamente desde la noción de fin hasta la equivalencia de la naturaleza racional como fin en sí mismo, lo cual considero que es central para una comprensión adecuada de la fórmula de la humanidad presentada posteriormente. (shrink)

It is shown that the well-known disparity in classical electrodynamics between the power losses calculated from the radiation reaction and that from Larmor’s formula, is succinctly understood when a proper distinction is made between quantities expressed in terms of a “real time” and those expressed in terms of a retarded time. It is explicitly shown that an accelerated charge, taken to be a sphere of vanishingly small radius \, experiences at any time a self-force proportional to the acceleration it (...) had at a time \ earlier, while the rate of work done on the charge is obtained by a scalar product of the self-force with the instantaneous value of its velocity. Now if the retarded value of acceleration is expressed in terms of the present values of acceleration, then we get the rate of work done according to the radiation reaction equation, however if we instead express the present value of velocity in terms of its time-retarded value, then we get back the familiar Larmor’s radiation formula. From this simple relation between the two we show that they differ because Larmor’s formula, in contrast with the radiation reaction, is written not in terms of the real-time values of quantities specifying the charge motion but is instead expressed in terms of the time-retarded values. Moreover, it is explicitly shown that the difference in the two formulas for radiative power loss exactly matches the difference in the temporal rate of the change of energy in the self-fields between the retarded and real times. From this it becomes obvious that the ad hoc introduction of an acceleration-dependent energy term, usually referred to in the prevalent literature as Schott-term, in order to make the two formulas comply with each other, is redundant. (shrink)

The study examined the development of Chinese as a second language learners’ formulaic knowledge through comparing the processing of Chinese idioms versus non-idiomatic formulaic sequences (FSs) by advanced-level learners (ALs), super-advanced learners (SLs), and native speakers (NSs). Using two phrase acceptability judgment tasks with and without think-aloud protocols, we collected data on participants’ processing accuracy, processing speed, and processing strategies of reading the two types of FSs. Four processing patterns emerged from the analyses of the datasets. First, learners’ processing accuracy (...) and speed increased along with their proficiency. Second, learners’ idiom processing ability was generally lower than that of non-idiom processing ability, but they demonstrated an improving trend as their proficiency level increased. Third, learners’ use of processing strategies did not change much as proficiency rose and demonstrated a categorical difference from NSs. Fourth, all three groups exhibited poorer productive idiom knowledge than productive non-idiom knowledge. The overall findings denote that second language learners’ formulaic knowledge can evolve beyond the lexical plateau as learners move from the advanced to a higher proficiency level, but the productive idiom knowledge can be a long-term problem. The findings provide implications for measuring and teaching Chinese formulaic knowledge at the higher-than-advanced stage. (shrink)

Pauline Kleingeld’s “Contradiction and Kant’s Formula of Universal Law”, published in this journal in 2017, presents a powerful challenge to what has become the standard reconstruction of the categorical imperative. In this response to Kleingeld, I argue that she is right to emphasise the ‘simultaneity requirement’ - that we must be able to will a proposed maxim and ‘simulataneously’, ‘also’ or ‘at the same time’ the maxim in its universalised form - but I deny that this removes the categorical (...) imperative test from the world of universalisation because the agent must be understood as part of that world. There are two distinct types of conflict: a contradiction that results from non-universalisability and Kleingeld’s ‘volitional’ conflict, located within the will of the immoral agent. The standard ‘practical’ reconstruction of the categorical imperative remains largely intact. (shrink)

This paper is concerned with the normative content of Kant's formula of humanity (FH). More specifically, does FH, as some seem to think, imply the specific and rigid prescriptions in 'standard' deontological theories? To this latter question, I argue, the answer is 'no'. I propose reading FH largely through the formula of autonomy and the formula of the kingdom of ends, where I understand FA to describe the nature of the capacity of humanity-a capacity for self-governance. The (...) latter, I suggest, is akin to the capacity for planning and intentional action described in Michael Bratman's work. A significant part of what FH requires, I then propose, is that we exercise these capacities for planning in such a way that we accommodate and coordinate with the (permissible) plans and intentions of others. Kant himself, as do many commentators, emphasizes the idea that our human capacities give us a distinctive kind of value. On my interpretation, by contrast, what is fundamentally important is not the value of the capacities but rather what they make possible: distinctive ways of mistreating (using) persons, but also a distinctive kind of morally desirable relationship. CiteULike Connotea Del.icio.us What's this? (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.

The formula "being of beginning " is employed by Hegel to name the immediate non- determined being from which the beginning of science must take place. Beginning come together in it. Being and doing of beginning are one. To Hegel, this means that being is the only and factic response to the question about beginning. The being of beginning neither is nor represents itself by means of any principle, it is pure "determinetness". To Hegel, the task of depuration and (...) action of beginning constitutes the moment of consummation of philosophy. "Being", as a concept in itself, is set as pure sign void of signification. But in this lack of signification lies the "demand of signs". "Being of beginning" expresses being as pure sign. Lack and significance, considered up to now as negation and position of the being of beginning, are both consummated simultaneously and at the same time. Consummation of scepticism also carries nominalism with it. All words and representations may be emptied of significance and set to work in view of pure signification. But pure being may be considered, in the context of the Doctrine of Being, as the irreductible result of the proof of semiotic resistance carried out in the beginning. Scepticism consummates itself in beginning. "Being" is the only sign that signifies, even empty of significations; it is the only signifier in itself.La fórmula "ser del comienzo" es utilizada por Hegel para denominar al ser inmediato indeterminado a partir del cual debe ser hecho el comienzo de la ciencia. En ella convergen comienzo y ser. El ser y el hacer del comienzo son uno. Esto significa para Hegel que el ser es la única y fáctica respuesta a la pregunta por el comienzo. El ser del comienzo no es ni se representa mediante ningún principio, él es pura determinidad . La tarea de depuración y acción del comienzo constituye para Hegel el momento de consumación de la filosofía. "Ser" en tanto concepto en sí es puesto como signo puro vaciado de significación. Pero en esta carencia de significación radica la "demanda de signos". "Ser del comienzo" expresa al ser en tanto signo puro. Carencia y significación, considerados hasta aquí como negación y posición del ser del comienzo, se consuman ambos simultánea y conjuntamente. La consumación del escepticismo conlleva también del nominalismo. Todas las palabras o representaciones pueden ser vaciadas de significado y puestas en función de la pura significación. Pero el ser puro puede ser considerado, en el contexto de la Doctrina del ser, como el resultado irreductible de la prueba de resistencia semiótica efectuada por el comienzo. El escepticismo se consuma en el comienzo. "Ser" es el único signo que significa aún vacío de significados, es el único signo significante en sí. (shrink)

A (normal) system of propositional modal logic is said to be complete iff it is characterized by a class of (Kripke) frames. When we move to modal predicate logic the question of completeness can again be raised. It is not hard to prove that if a predicate modal logic is complete then it is characterized by the class of all frames for the propositional logic on which it is based. Nor is it hard to prove that if a propositional modal (...) logic is incomplete then so is the predicate logic based on it. But the interesting question is whether a complete propositional modal logic can have an incomplete extension. In 1967 Kripke announced the incompleteness of a predicate extension of S4. The purpose of the present article is to present several such systems. In the first group it is the systems with the Barcan Formula which are incomplete, while those without are complete. In the second group it is those without the Barcan formula which are incomplete, while those with the Barcan Formula are complete. But all these are based on propositional systems which are characterized by frames satisfying in each case a single first-order sentence. (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)

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)

I criticize the widely accepted “practical” interpretation of the universality test contained in Kant’s first formula of the categorical imperative in the Groundwork of the Metaphysics of Morals – the formula of the universal law of nature. I argue that this interpretation does not work for contradictions in conception because it wrongly takes contradictions in the will as the model for them and, as a consequence, cannot establish a clear distinction between the two kinds of contradiction. This interpretation (...) also assumes an understanding of universality that departs from Kant’s own and, cannot, for this reason, capture the kind of contradiction that he explicitly claims to establish. I provide an alternative interpretation, which I call revised logical interpretation, that allows us to account for contradictions in conception, including those examples that the practical interpretation cannot handle, as well as to establish a clear distinction between the two kinds of contradiction. (shrink)

Kant offers the following argument for the formula of humanity (FH): Each rational agent necessarily conceives of her own rational nature as an end in itself and does so on the same grounds as every other rational agent, so all rational agents must conceive of one another's rational nature as an end in itself. As it stands, the argument appears to be question-begging and fallacious. Drawing on resources from the formula of universal law (FUL) and Kant's claims about (...) the primacy of duties to oneself, I propose a contractualist reconstruction of this puzzling line of reasoning. (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)