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 elementarycanonicalformulae 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 elementarycanonical 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 elementarycanonicalformulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames. (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)
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.
What does it mean to ‘give’ the value of a variable in an algebraic context, and how does giving the value of a variable differ from merely describing it? I argue that to answer this question, we need to examine the role that giving the value of a variable plays in problem-solving practice. I argue that four different features are required for a statement to count as giving the value of a variable in the context of solving an elementary (...) algebra problem: the variable must be in the scope opened by the problem statement; the values given must be in the range of the variable, which is determined by the problem; the statement giving the values must represent a complete solution; and it must be in a canonical form. This account helps us better understand elementary algebra itself, as well as the use of algebraic tools to analyze phenomena in natural language. (shrink)
The previously introduced algorithm \sqema\ computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend \sqema\ with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of modal formulae in the extension of first-order logic with monadic least fixed-points \mffo. This computation operates by transforming input formulae into locally frame equivalent ones in the pure fragment of the hybrid mu-calculus. In particular, (...) we prove that the recursive extension of \sqema\ succeeds on the class of `recursive formulae'. We also show that a certain version of this algorithm guarantees the canonicity of the formulae on which it succeeds. (shrink)
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)
Immanuel Kant (1724-1804), the German philosopher, is considered as the father of modern ethics and one of the great philosophers in the history of philosophy. He wanted to establish a firm foundation for moral philosophy. He contributed something new to modern ethics which was not attempted by earlier ethicists. He wanted to show by using reason that morality is based on a single supreme universal principle, which is binding to all rational beings. Precisely, Kant wanted to establish the first principle (...) of morality which neglects all consideration of self-interest and even particular human problems. In the Groundwork of the Metaphysics of Morals, Kant claimed that his intention is to seek out and establish the supreme principle of morality, and that supreme principle is the categorical imperative. He puts the supreme principle of morality or the categorical imperative in at least five ways. These are formula of universal law (FUL), formula of universal law (FLN), formula of humanity (FH), formula of humanity (FA), and formula of realm of ends (FRE). However, Kant affirms that there is one canonical and general formulation of the categorical imperative and it is the FUL. For him, the other formulas are not distinct ethical principles; rather they are the reformulations or variant formulations of the single categorical imperative. Kant put this position in his works, The Groundwork of the Metaphysics of Morals. So, in this paper, I will mainly concentrate on the fundamental doctrine of the Groundwork of the Metaphysics of Morals. As I have tried to make clear before, Kant’s aim in the Groundwork of the Metaphysics of Morals is to search for and establish the supreme principle of morality (i.e., categorical imperative). He attempted to do this at the end of the Groundwork of the Metaphysics of Morals. But, to me, the way he attempted to justify the categorical imperative is problematic. Thus, in this paper, I argue that Kant did not put the categorical imperative or morality on a solid ground. (shrink)
In reflecting on the relation between early empiricist conceptions of the mind and more experimentally motivated materialist philosophies of mind in the mid-eighteenth century, I suggest that we take seriously the existence of what I shall call ‘phantom philosophical projects’. A canonical empiricist like Locke goes out of his way to state that their project to investigate and articulate the ‘logic of ideas’ is not a scientific project: “I shall not at present meddle with the Physical consideration of the (...) Mind” (Essay, I.i.2). An equally prominent thinker, Immanuel Kant, seems to make an elementary mistake, given such a clear statement, when he claims that Locke’s project was a “physiology of the understanding,” in the Preface to the A edition of the first Critique). A first question, then, would be: what is this physiology of the understanding, if it was not Locke’s project? Did anyone undertake such a project? If not, what would it have resembled? My second and related case comes out of a remark the Hieronymus Gaub makes in a letter to Charles Bonnet of 1761: criticizing materialist accounts of mind and mind-body relations such as La Mettrie’s, Gaub suggests that what is needed is a thorough study of the “mechanics of the soul,” and that Bonnet could write such a study. What is the mechanics of the soul, especially given that it is presented as a non-materialist project? To what extent does it resemble the purported “physiology of the understanding”? And more generally, what do both of these phantom projects have to do with a process we might describe as a ‘naturalization of the soul’? (shrink)
We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities. En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways game identities into modal formulae. The completeness proof is based on reduction of game terms to (...) a certain 'minimal canonical form', by using only the axiomatic identities, and on showing that the equivalence of two minimal canonical terms can be established from these identities. (shrink)
It is quite well-known from Kurt G¨odel’s (1931) ground-breaking Incompleteness Theorem that rudimentary relations (i.e., those definable by bounded formulae) are primitive recursive, and that primitive recursive functions are representable in sufficiently strong arithmetical theories. It is also known, though perhaps not as well-known as the former one, that some primitive recursive relations are not rudimentary. We present a simple and elementary proof of this fact in the first part of the paper. In the second part, we review (...) some possible notions of representability of functions studied in the literature, and give a new proof of the equivalence of the weak representability with the (strong) representability of functions in sufficiently strong arithmetical theories. (shrink)
How should we determine the distribution of psychological traits—such as Theory of Mind, episodic memory, and metacognition—throughout the Animal kingdom? Researchers have long worried about the distorting effects of anthropomorphic bias on this comparative project. A purported corrective against this bias was offered as a cornerstone of comparative psychology by C. Lloyd Morgan in his famous “Canon”. Also dangerous, however, is a distinct bias that loads the deck against animal mentality: our tendency to tie the competence criteria for cognitive capacities (...) to an exaggerated sense of typical human performance. I dub this error “anthropofabulation”, since it combines anthropocentrism with confabulation about our own prowess. Anthropofabulation has long distorted the debate about animal minds, but it is a bias that has been little discussed and against which the Canon provides no protection. Luckily, there is a venerable corrective against anthropofabulation: a principle offered long ago by David Hume, which I call “Hume’s Dictum”. In this paper, I argue that Hume’s Dictum deserves a privileged place next to Morgan’s Canon in the methodology of comparative psychology, illustrating my point through a discussion of the debate over Theory of Mind in nonhuman animals. (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)
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)
En la consideración de numerosos asuntos y respecto de muy variadas exposiciones, el uso de expresiones como "filosófica" sugiere que debemos remitirnos a procederes, preguntas o exigencias especiales. Rabossi propone un modo de caracterizar el sentido con que usamos esas expresiones y, sobre esa base, concluye que la filosofía tal como se la practica desde hace doscientos años pretende ser una disciplina profesional pero no puede serlo debido a la índole de la preceptiva que la constituye. En este artículo se (...) examinan sus argumentos y se sostiene que, aunque no parecen suficientes para la conclusión a la que apuntan, hay razones para modificarlos de cierto modo que conducen a ese resultado. Whenever expressions like "X is philosophical" appear in different questions and assorted statements, the reference to special kinds of actions, questions or demands are suggested by these uses. Rabossi propounds a way for characterizing the sense of our using such expressions and, based on it, he states that philosophy, as it is accomplished from the last two centuries up to now, pretends to be a professional discipline but she cannot to be as such because the nature of its precepts. Rabossi's arguments are examined and it is maintained that although they do not seem to be sufficient for the pursued conclusion, there are reasons to modify them such a way to come to that conclusion. (shrink)
This paper addresses a fundamental line of research in neuroscience: the identification of a putative neural processing core of the cerebral cortex, often claimed to be “canonical”. This “canonical” core would be shared by the entire cortex, and would explain why it is so powerful and diversified in tasks and functions, yet so uniform in architecture. The purpose of this paper is to analyze the search for canonical explanations over the past 40 years, discussing the theoretical frameworks (...) informing this research. It will highlight a bias that, in my opinion, has limited the success of this research project, that of overlooking the dimension of cortical development. The earliest explanation of the cerebral cortex as canonical was attempted by David Marr, deriving putative cortical circuits from general mathematical laws, loosely following a deductive-nomological account. Although Marr’s theory turned out to be incorrect, one of its merits was to have put the issue of cortical circuit development at the top of his agenda. This aspect has been largely neglected in much of the research on canonical models that has followed. Models proposed in the 1980s were conceived as mechanistic. They identified a small number of components that interacted as a basic circuit, with each component defined as a function. More recent models have been presented as idealized canonical computations, distinct from mechanistic explanations, due to the lack of identifiable cortical components. Currently, the entire enterprise of coming up with a single canonical explanation has been criticized as being misguided, and the premise of the uniformity of the cortex has been strongly challenged. This debate is analyzed here. The legacy of the canonical circuit concept is reflected in both positive and negative ways in recent large-scale brain projects, such as the Human Brain Project. One positive aspect is that these projects might achieve the aim of producing detailed simulations of cortical electrical activity, a negative one regards whether they will be able to find ways of simulating how circuits actually develop. (shrink)
Elementary patterns of resemblance notate ordinals up to the ordinal of Pi^1_1-CA_0. We provide ordinal multiplication and exponentiation algorithms using these notations.
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)
Conwy Lloyd Morgan (1852–1936) is widely regarded as the father of modern comparative psychology. Yet, Morgan initially had significant doubts about whether a genuine science of comparative psychology was even possible, only later becoming more optimistic about our ability to make reliable inferences about the mental capacities of non-human animals. There has been a fair amount of disagreement amongst scholars of Morgan’s work about the nature, timing, and causes of this shift in Morgan’s thinking. We argue that Morgan underwent two (...) quite different shifts of attitude towards the proper practice of comparative psychology. The first was a qualified acceptance of the Romanesian approach to comparative psychology that he had initially criticized. The second was a shift away from Romanes’ reliance on systematizing anecdotal evidence of animal intelligence towards an experimental approach, focused on studying the development of behaviour. We emphasize the role of Morgan’s evolving epistemological views in bringing about the first shift – in particular, his philosophy of science. We emphasize the role of an intriguing but overlooked figure in the history of comparative psychology in explaining the second shift, T. Mann Jones, whose correspondence with Morgan provided an important catalyst for Morgan’s experimental turn, particularly the special focus on development. We also shed light on the intended function of Morgan’s Canon, the methodological principle for which Morgan is now mostly known. The Canon can only be properly understood by seeing it in the context of Morgan’s own unique experimental vision for comparative psychology. (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.
The purpose of this paper is to show that the Elementary Process Theory (EPT) agrees with the knowledge of the physical world obtained from the successful predictions of Special Relativity (SR). For that matter, a recently developed method is applied: a categorical model of the EPT that incorporates SR is fully specified. Ultimate constituents of the universe of the EPT are modeled as point-particles, gamma-rays, or time-like strings, all represented by integrable hyperreal functions on Minkowski space. This proves that (...) the EPT agrees with SR. (shrink)
In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the (...) Weyl’s system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (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)
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)
Andrew Wiles' analytic proof of Fermat's Last Theorem FLT, which appeals to geometrical properties of real and complex numbers, leaves two questions unanswered: (i) What technique might Fermat have used that led him to, even if only briefly, believe he had `a truly marvellous demonstration' of FLT? (ii) Why is x^n+y^n=z^n solvable only for n<3? In this inter-disciplinary perspective, we offer insight into, and answers to, both queries; yielding a pre-formal proof of why FLT can be treated as a true (...) arithmetical proposition (one which, moreover, might not be provable formally in the first-order Peano Arithmetic PA), where we admit only elementary (i.e., number-theoretic) reasoning, without appeal to analytic properties of real and complex numbers. We cogently argue, further, that any formal proof of FLT needs---as is implicitly suggested by Wiles' proof---to appeal essentially to formal geometrical properties of formal arithmetical propositions. (shrink)
The historiographical narrative describing early modern European philosophy as the confrontation between rationalism and empiricism and its overcoming through the Kantian synthesis had a huge spread in Argentina. This article investigates the genesis of this traditional account in the universities of Córdoba, Buenos Aires and La Plata between 1780 and 1920. It offers an introduction concerning the formation of this narrative in Europe and a survey of the teaching of early modern philosophy in Argentina during that period. It concludes that, (...) although some of its components are found during the nineteenth century, it was only in the second decade of the twentieth century that the traditional narrative was formulated in its entirety, in parallel with the introduction of Kantianism in Argentine. However, the construction of this narrative is not merely explained by this fact but also by the weight that the history of philosophy gained in the syllabus as part of the demands involved in the shaping of the academic philosophical field. Finally, this paper suggests ways to reconfigure and renew the canon. (shrink)
Categorical foundations and set-theoretical foundations are sometimes presented as alternative foundational schemes. So far, the literature has mostly focused on the weaknesses of the categorical foundations. We want here to concentrate on what we take to be one of its strengths: the explicit identification of so-called canonical maps and their role in mathematics. Canonical maps play a central role in contemporary mathematics and although some are easily defined by set-theoretical tools, they all appear systematically in a categorical framework. (...) The key element here is the systematic nature of these maps in a categorical framework and I suggest that, from that point of view, one can see an architectonic of mathematics emerging clearly. Moreover, they force us to reconsider the nature of mathematical knowledge itself. Thus, to understand certain fundamental aspects of mathematics, category theory is necessary (at least, in the present state of mathematics). (shrink)
Decision makers of the art world usually ignore the existence and evolution of this oversupply of artists that work without imaging the actual mechanism that governs the system of selection and exclusion as well as the nature of the matrix, and are occasionally encouraged to forget their national identity, history, and culture. Although repeating warning on the birth of an artificial canon seems to be useless, renewed efforts for recovering, at least, a rational system of work flow would be acknowledged (...) by contemporary artists. Framing a theory that recognizes those works that cause pleasure to humans may be the foundation for building a canon for discerning what acknowledge as art. (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.
In the interpretation of canonical quantum gravity (CQG), gravity appears as a geometric pseudoforce, is reduced to spacetime geometry and becomes a simple effect of spacetime curvature. The scale at which quantum gravitational effects occur is determined by the different physical constants of fundamental physics: h, c and G, which characterize quantum, relativistic and gravitational phenomena. By combining these constants, we obtain the Planck constants at which the effects of quantum gravity must manifest. Loop quantum gravity attempts to unify (...) gravity with the other three fundamental forces starting with relativity and adding quantum traits. DOI: 10.13140/RG.2.2.10368.58889 . (shrink)
The concept of the highest good is an important but hardly uncontroversial piece of Kant’s moral philosophy. In the considerable literature on the topic, challenges are raised concerning its apparently heteronomous role in moral motivation, whether there is a distinct duty to promote it, and more broadly whether it is ultimately to be construed as a theological or merely secular ideal. Yet comparatively little attention has been paid to the context of a doctrine that had enjoyed a place of prominence (...) in the ethical systems of the ancients, where these systems provided a key critical foil for the development of Kant’s own conception of the highest good in terms of “happiness distributed in exact proportion to morality” (cf. 5:110). Indeed, these ethical systems prove important for Kant not only in his initial presentation of his account in the Canon of Pure Reason in the first Critique, where he sought to redress the errors of the Epicurean and Stoic conception in particular, but also and importantly in the course of his development towards the second Critique. As I argue in this paper, Christian Garve’s defense of a revised but recognizably Stoic conception of the highest good in his translation of and commentary on Cicero’s De officiis (On Duties), helps to account for Kant’s renewed attention to that doctrine, and specifically to the errors attending the Stoic version, in the Dialectic of Pure Practical Reason. (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)
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)
This paper investigates the crucial notion of a "canonical ascription statement" in Bruno Mölder's /Mind Ascribed/, and argues that the reasons given for preferring the book's approach of canonicallity to a more common understanding of canonicallity in terms of the ascriptions we would "ideally" make are not only unpersuasive, but also leave the interpretivist position more open to skeptical worries than it should be. The paper further argues that the resources for a more compelling justification of Mölder's conception of (...) canonicality are already in Mölder's book itself. (shrink)
I take issue with an argument to the effect that because contractualism proves--both practically and theoretically--the philosophically superior moral theory, we have the result that nonhuman animals can have no, nor ought be extended any, moral standing. The combined argument belongs to Peter Carruthers, and appears in his The Animals Issue. My response involves demonstration that on careful analysis contractualism fares even less well than the two theories against which Carruthers compares it--rights and utilitarian. Furthermore, I offer a sketch of (...) a theory which does not fall for reliance on a singularly problematic premise--a premise which plays pivotally in traditional contractualist, rights and utilitarian accounts. The upshot is that this "alternative rights theory" fares best in reflective equilibrium analysis as against not only those theories Carruthers decries, but contractualism as well. We are, it appears, drawn back to the nagging question of whether and how things nonhuman may matter morally. For, Carruthers conclusion is disallowed. That the alternative rights theory offers novel yet satisfactory means by which to account for moral motivation and knowledge, as well as differences in moral respect due morally relevant beings, is explored. That the theory avoids the troublesome pitfalls of intuitionism and supervenience further secures its frontrunning position--which, again, begins to indicate that and how more than solely humans are of moral relevance. (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)
Abstract: This essay traces the relationship between Hegel and some common portrayals of modern philosophy in the nineteenth century. I explain much of the rationale behind the neo-Kantian narrative of modern philosophy, and argue that the common division of modern philosophers into rationalists and empiricists executed a principally anti-Hegelian agenda. I then trace some failed attempts by anglophone philosophers to reconcile Hegel with the neo-Kantian history, in the interest of explaining Hegel’s subsequent unpopularity in England and America. Finally, I argue (...) that recent attempts to read Hegel in Kantian terms often rest on a misguided appropriation of an anti-Hegelian historical narrative. (shrink)
I describe two prejudices that can obstruct efforts to diversify philosophical curricula that I call neophilia and xenophilia. Individually and collectively they feed a sort of metaphilosophical myopia: a narrow vision that fails or refuses to see the richness and value of the philosophical enterprise in its many forms as manifested in different times and cultures. The discussion focuses on neophilia and xenophilia among undergraduate students.
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)
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)
The Elementary Process Theory (EPT) is a collection of seven elementary process-physical principles that describe the individual processes by which interactions have to take place for repulsive gravity to exist. One of the two main problems of the EPT is that there is no proof that the four fundamental interactions (gravitational, electromagnetic, strong, and weak) as we know them can take place in the elementary processes described by the EPT. This paper sets forth the method by which (...) it can be proven that the EPT agrees with the knowledge that derives from the successful predictions of a modern interaction theory T. This determines a fundamentally new research program in theoretical physics. (shrink)
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