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)

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)

The Universal Formula for Eliminating Government Corruption: A Natural Law-Based Approach -/- Introduction -/- Government corruption is one of the most persistent obstacles to societal progress, leading to economic decline, weakened institutions, and widespread inequality. Traditional anti-corruption measures—such as stricter laws, transparency initiatives, and public awareness campaigns—have failed to fully eliminate corruption because they do not address the problem at a systemic and scientific level. -/- By applying the universal formula, which is based on the universal law of balance in (...) nature, we can understand corruption as a systemic defect—a violation of natural equilibrium that causes inefficiency and societal suffering. This essay will provide a comprehensive scientific explanation of corruption, supported by research, and propose a complete solution that integrates education, institutional reforms, AGI-driven governance, cultural adaptation, and strategic implementation. -/- 1. The Science Behind Corruption: A Systemic Imbalance -/- A. Psychological and Biological Causes → Internal Homeostasis -/- Scientific research suggests that corruption is rooted in human psychology and biology, particularly in: -/- Evolutionary survival instincts – Studies indicate that self-preservation and resource hoarding behaviors evolved to ensure survival but can also lead to greed and corruption in modern societies. (Reference: Trivers, 1971 – Evolutionary theory of reciprocity) -/- Cognitive biases – Research in behavioral psychology shows that self-justification, moral disengagement, and in-group favoritism make individuals rationalize corrupt behavior. (Reference: Bandura, 1999 – Moral disengagement theory) -/- Neurological reward systems – Studies using fMRI scans reveal that bribery activates brain regions associated with pleasure, reinforcing corrupt behaviors. (Reference: Ariely & Loewenstein, 2006 – Neurological basis of unethical behavior) -/- Universal Formula Solution: -/- Educational reprogramming is needed to counteract these internal imbalances. -/- Schools should instill ethical reasoning, self-regulation, and critical thinking from an early age. -/- Leaders must be trained to recognize that corruption leads to long-term systemic instability, disrupting both individual and societal balance. -/- B. Economic Incentives and Systemic Defects → Structural Homeostasis -/- Economists have long observed that corruption is often a rational response to flawed systems where: -/- Low salaries and financial insecurity create incentives for bribery. (Reference: Becker & Stigler, 1974 – Economics of crime and punishment) -/- Weak regulatory oversight allows corruption to persist with minimal consequences. -/- Lack of transparency in financial systems enables embezzlement and fraud. -/- Universal Formula Solution: -/- The economic system must be free of defects—governments should: -/- Ensure fair wages for public officials to reduce bribery incentives. -/- Use blockchain-based transparency systems to track public spending. -/- Implement AI-driven financial audits to detect corruption in real time. -/- C. Political and Institutional Weakness → Governance Homeostasis -/- Corruption thrives when institutions fail to enforce accountability and transparency. -/- The Principal-Agent Problem: Public officials (agents) may act in their own interests rather than serving the public (principals). (Reference: Rose-Ackerman, 1978 – Corruption and governance theory) -/- Legal Loopholes: Weak anti-corruption laws allow elites to manipulate the system. -/- Lack of Whistleblower Protections: Fear of retaliation prevents corruption from being exposed. -/- Universal Formula Solution: -/- Governments must function like biological systems, with constant monitoring and correction mechanisms: -/- Real-time transparency tools (AI-driven monitoring of government transactions). -/- Independent anti-corruption agencies with full enforcement powers. -/- Legal frameworks based on the principle of natural balance, where punishments restore equilibrium rather than being arbitrary. -/- D. Cultural Normalization of Corruption → Collective Homeostasis -/- In some societies, corruption is seen as an accepted norm due to: -/- Patronage networks and nepotism embedded in political cultures. -/- Religious and social justifications for bribery (“gifts” given in exchange for favors). -/- Distrust in the justice system, leading to reliance on informal corruption-based solutions. -/- Universal Formula Solution: -/- A holistic education system must be implemented to reprogram societal attitudes toward corruption. -/- Schools should teach: -/- The universal law of balance and its ethical implications. -/- The cause-and-effect nature of corruption—how even small acts of dishonesty contribute to systemic collapse. -/- Critical thinking skills to challenge corrupt norms and misinformation. -/- 2. Case Studies: Applying the Universal Formula to Real-World Corruption -/- Case Study 1: Singapore’s Zero-Tolerance Approach -/- Singapore successfully reduced corruption by: -/- Increasing public sector salaries to remove bribery incentives. -/- Strict enforcement of anti-corruption laws, ensuring accountability. -/- Cultural reprogramming through education and public campaigns. -/- Universal Formula Connection: Singapore’s model aligns with systemic homeostasis, ensuring a balance between economic incentives, strong institutions, and ethical education. -/- Case Study 2: Scandinavian Countries – Transparency and Trust -/- Nordic countries (Denmark, Sweden, Norway) maintain low corruption levels through: -/- Public trust in institutions based on long-term systemic balance. -/- High transparency in government spending. -/- Strong legal frameworks with immediate corrective feedback mechanisms. -/- Universal Formula Connection: These countries maintain governance homeostasis, preventing corruption through self-correcting institutional designs. -/- 3. Implementing the Universal Formula to Eliminate Corruption -/- A. Education Reform: The Foundation of Ethical Governance -/- Integrate the universal law of balance into curricula from elementary to higher education. -/- Teach cause-and-effect relationships in governance (e.g., how small bribes lead to systemic collapse). -/- Develop leadership training programs that emphasize ethical decision-making based on natural balance. -/- B. Institutional Reforms: Creating a Self-Correcting System -/- Implement blockchain-based transparency systems for public finance. -/- Strengthen whistleblower protections to ensure safe reporting of corruption. -/- Decentralize power to reduce opportunities for monopolistic corruption. -/- C. AGI-Driven Ethical Governance -/- Artificial General Intelligence (AGI) can be programmed with the universal formula to: -/- Monitor government transactions and detect corruption patterns. -/- Ensure transparent decision-making based on systemic balance. -/- Remove human cognitive biases from governance. -/- D. Cultural Adaptation: Tailoring Solutions to Different Societies -/- In high-corruption societies, initial reforms should focus on education and small wins to shift cultural attitudes. -/- In developing countries, AGI-driven transparency tools can bypass weak institutions. -/- In democratic nations, citizen engagement should be emphasized to create self-regulating governance. -/- --- -/- 4. Addressing Challenges and Counterarguments -/- Objection: “Corruption is inevitable in human nature.” Response: Human nature includes both corruption and ethical reasoning—education determines which dominates. -/- Objection: “Elites will resist systemic reforms.” Response: AGI-driven transparency tools and mass education campaigns can reduce elite control. -/- Objection: “Implementing these changes is unrealistic.” Response: Small-scale pilots in cities or institutions can demonstrate success before national adoption. -/- --- -/- Conclusion: The Universal Formula as the Ultimate Solution to Corruption -/- Corruption is a systemic defect—a violation of the universal law of balance in nature. By applying scientific principles of homeostasis, cause and effect, and feedback regulation, we can create a corruption-free governance model. The universal formula offers the only complete solution, integrating education, institutional reform, AGI-driven oversight, and cultural adaptation. -/- If implemented, this model could lead to a world where governance functions as a perfectly balanced system—free of defects, ethical, and in harmony with natural law. -/- . (shrink)

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)

In the first section of this paper we show that i Π1 ≡ W⌝⌝lΠ1 and that a Kripke model which decides bounded formulas forces iΠ1 if and only if the union of the worlds in any path in it satisflies IΠ1. In particular, the union of the worlds in any path of a Kripke model of HA models IΠ1. In the second section of the paper, we show that for equivalence of forcing and satisfaction of Πm-formulas in a linear Kripke (...) model deciding Δ0-formulas it is necessary and sufficient that the model be Σm-elementary. This implies that if a linear Kripke model forces PEMprenex, then it forces PEM. We also show that, for each n ≥ 1, iΦn does not prove ℋ(IΠn's are Burr's fragments of HA. (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.

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)

My first aim in this paper is to use time diagrams in the style of Brentano to analyze constructions in Brouwer's separable mathematics more precisely. I argue that constructions must involve not only pairing and projecting as basic operations guaranteed by the intuition of twoity, as sometimes assumed in the literature, but also a recalling operation. My second aim is to argue that Brouwer's views on the intuition of twoity and arithmetic lead to an ontological explosion. Redeveloping the constructions of (...) natural numbers and systems sketched in an appendix to Brouwer's Cambridge lectures, I observe that the only plausible way he can make some elementary arithmetic in his separable mathematics is by allowing for the same canonical number to be determined by multiple separable entities, resulting in an overabundant mathematical ontology. (shrink)

The objective of this paper is to develop neutrosophic quadruple algebraic hyperstructures. Specifically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them.

The aim of this article is to address the problem of what is usually called “self-consciousness” by studying Charles S. Peirce’s semeiotic treatment of self-referential statements. Peirce believes that an adequate study of the mind requires “to reduce all mental action,” including “self-consciousness,” “to the formula of valid reasoning” (W 2:214, EP 1:30, 5:267, 1868) and its semeiotic nature. While Peirce makes frequent use of the notion of “consciousness,” he is at the same time distant from the understanding of the (...) “conscious mind” that Descartes invented and made canonical (e.g., W 1:491, 1866), and which from the modern epoch stretches out to the contemporary discussion on, as David Chalmers put it, the “hard problem” of the mind. In what follows, I argue that Peirce puts forth a powerful theory of self-consciousness based on his semeiotic understanding of self-reference and indexicality. To the question, “How can we elucidate the phenomenon of self-consciousness?”, we should answer, with Peirce, “What we call self-consciousness corresponds to the practice of narratives and descriptions ultimately based on indexical self-referential statements, which are in turn rooted in very specific dimensions of human experience.” It is also important to underscore from the outset that the problem of indexical self-reference cannot be separated from Peirce’s concept of experience, which is one of the most interesting insights of Peirce’s philosophy and classical American pragmatism. In particular, it will be essential to see what are the experiential-perceptual conditions under which indexical self-referential statements can work as such. (shrink)

We give a new and elementary construction of primitive positive decomposition of higher arity relations into binary relations on finite domains. Such decompositions come up in applications to constraint satisfaction problems, clone theory and relational databases. The construction exploits functional completeness of 2-input functions in many-valued logic by interpreting relations as graphs of partially defined multivalued ‘functions’. The ‘functions’ are then composed from ordinary functions in the usual sense. The construction is computationally effective and relies on well-developed methods of (...) functional decomposition, but reduces relations only to ternary relations. An additional construction then decomposes ternary into binary relations, also effectively, by converting certain disjunctions into existential quantifications. The result gives a uniform proof of Peirce’s reduction thesis on finite domains, and shows that the graph of any Sheffer function composes all relations there. (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)

This paper develops a new class of justification logic, the logic of epistemic entitlement. The logic of epistemic entitlement invokes the notion of epistemic entitlement in epistemology, and interprets a justification formula in the form of???? ∶???? as follows: the warrant???? entitles the agent to believe????. In the logic of epistemic entitlement, the formula???? ∶???? is true if and only if???? is true in all possible worlds entitled to be conceived by????. In contrast to the standard epistemic semantics of justification (...) logic, the formula???? ∶???? in Fitting’s model is true if and only if???? is true in all possible worlds that can be conceived of and satisfies the evidential condition: the epistemic state???? ∈ ℰ(????,????) that the epistemic agent is in. Thus, if???? is not a dead point in the model, the point model of???? cannot satisfy both formulas of the form???? ∶???? and????′∶ ¬????. Thus standard justification logic cannot characterize the conflicting beliefs of agents for different warrants. Instead, the logic of epistemic entitlement solves this problem by entitling agents to believe???? and ¬???? on two disjoint sets of possible worlds on????,???? and????′, respectively. ℳ,???? ⊩???? ∶???? if and only if ℳ,???? ⊩???? for every???? ∈????????????(????,????) with????????????. Such an epistemic entitlement in the paper is axiomatized into the logic J_???????????? and the validity of its axioms is verified. And a canonical model of J_???????????? is established to prove its completeness. Finally, extensions of J_???????????? are attempted to explore the logic of entitlement of belief J_EntD4 and logic of entitlement of knowledge J_EntT4. (shrink)

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)

The present study aims to carry out an analysis of the relation between the Bibles of Samuil Micu and Andrei Șaguna from an isagogic perspective, with a particular focus on the canon and canonicity of the books of the Holy Scripture. We believe that, through such an analysis, we can observe what they have in common, but also what differentiates the two Transylvanian editions of the Holy Scripture so that we can help those interested in understanding the reasons behind the (...) current controversies as to the relation between them. Although these controversies refer to the biblical text of the two Scriptural editions, the fact that the attitude towards it was caused by denominational factors, whose doctrinal background is represented by two different traditions of understanding the biblical canon, has been overlooked. This is why we find that the evaluation of how the two Romanian editions of the Holy Scripture (the Bible of Samuil Micu, 1795, and the Bible of Andrei Șaguna, 1856-1858) relate to the canonical tradition of each Church and cultivate their isagogics is fundamental for the establishment and understanding of the relation between them. (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)

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)

Schrödinger discusses what an elementary particle is. This essay originally appeared in the journal Endeavour.

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)

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)

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 elementary particles of relativistic quantum field theory are not simple field quanta, as has long been assumed. Rather, they supplement quantum fields, on which they depend but to which they are not reducible, as shown here with particles defined instead as a unified collection of properties that appear in both physical symmetry group representations and field propagators. This notion of particle provides consistency between the practice of particle physics and its basis in quantum field theory.

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)

We have previously argued that historical cases must be rendered canonical before they can plausibly serve as evidence for philosophical claims, where canonicity is established through a process of negotiation among historians and philosophers of science (Bolinska and Martin, 2020). Here, we extend this proposal by exploring how that negotiation might take place in practice. The working stock of historical examples that philosophers tend to employ has long been established informally, and, as a result, somewhat haphazardly. The composition of (...) the historical canon of philosophy of science is therefore path dependent, and cases often become stock examples for reasons tangential to their appropriateness for the purposes at hand. We show how the lack of rigor around the canonization of case studies has muddied the waters in selected philosophical debates. This, in turn, lays the groundwork for proposing ways in which they can be improved. (shrink)

Lo personal es político. Revisito la potente frase de Carol Hanish (1970) que sigue resonando en las luchas y discursos feministas desde que se hiciera pública a comienzos de 1970. Me permito reversionarla, con gran libertad, para marcar el pulso de este texto y contar, a partir de mi relación con la filosofía, cómo lo personal pasó a ser político en el interés por conocer las filósofas modernas e interpelar y rearmar el canon filosófico. Con ello, los y las invito (...) a reflexionar sobre la perspectiva de género en la historiografía filosófica, las formas de construcción del canon y sus repercusiones en la enseñanza de la filosofía. (shrink)

Parental environmental education in early childhood is vital for nurturing environmental awareness and ecological protection. This study investigates how parents’ nature engagement methods influence children’s environmental awareness and participation in protection activities. Using the Bayesian Mindsponge Framework with data from 516 children and their primary caregivers across 23 elementary summer schools in five urban Chinese cities, the findings reveal varying impacts of parental engagement methods. Raising animals and plants is positively associated with environmental awareness (moderate reliability) and protection activities (...) (high reliability). Visiting museums about endangered and extinct species enhances children’s environmental awareness, while learning about insects and their habits improves their participation in protection activities (both high reliability). However, outdoor learning experiences and playing in natural environments (e.g., parks and forests) show ambiguous effects. These results underscore the value of family-centered environmental education, emphasizing the crucial roles of direct nature interactions and providing actionable insights for child-focused environmental policies. (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)

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)

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)

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.

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 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)

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)

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)

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)

Dispositional Essentialism is a unified anti-Humean account of the metaphysics of low-level physical properties and laws of nature. In this paper, I articulate the view that I label Canonical Dispositional Essentialism, which comprises a structuralist metaphysics of properties and an account of laws as relations in the property structure. I then present an alternative anti-Humean account of properties and laws. This account rejects CDE’s structuralist metaphysics of properties in favour of a view of properties as qualitative grounds of dispositions (...) and it rejects CDE’s view of laws as relations in favour of a view of laws as features of an efficient description of possible property distributions. I then defend this view over CDE on the grounds that it can overcome an explanatory shortcoming of CDE and that it achieves a level of continuity with science that CDE fails to achieve. The upshot of this paper is a significant narrowing of the range of possibilities in which the absolutely best unified account of laws and properties resides. (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)

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)