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 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)

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)

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.

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 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)

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.

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)

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)

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)

Architecture and Deconstruction Case of Peter Eisenman and Bernard Tschumi -/- Introduction Towards deconstruction in architecture Intensive relations between philosophical deconstruction and architecture, which were present in the late 1980s and early 1990s, belong to the past and therefore may be described from a greater than before distance. Within these relations three basic variations can be distinguished: the first one, in which philosophy of deconstruction deals with architectural terms but does not interfere with real architecture, the second one, in which (...) a collaboration between Jacques Derrida and a group of architects interested in his concepts is commenced, and the third one, in which completed or only designed objects or new concepts of deconstruction created by architects gain their supremacy over philosophy. The following book analyses these three possible ways, first of all with the reference to Peter Eisenman and Bernard Tschumi. -/- Peter Eisenman -/- Misreading… and Other Errors -/- The issue of relations between Peter Eisenman’s work and philosophy of deconstruction may be referred to his activity more than ten years preceding his direct collaboration with Jacques Derrida (in 1985) and organisation of the exhibition Deconstructivist Architecture at Museum of Modern Art in New York (in 1988). As soon as at the stage of designing the first houses (House I-III, 1967-1970), which almost entirely inscribed in formalistic aesthetics of Modernism, the architect analysed the problem of architecture dependence on its assumptions. All his later designs may be treated as consequence of this initial interest in relations between practice and theory, and at the same time as an introduction to manipulations later on led at the level of metaphysics of architecture. Beginning with the issue of presence, considered in comments to House VI (1972), the number of ideas having their analogies in philosophy of deconstruction increased. The text entitled The End of the Classical: The End of the Beginning, The End of the End (1984), in which Eisenman criticised questions of representation in architecture, its delusive strive for truth and comparably unattainable attempts at ultimate definition of elementary rules, should be acclaimed the breaking point. This attitude was extended by numerous strategies disturbing architecture rules defined at metaphysical level in an essay Moving Arrows, Eros, and Other Errors: an Architecture of Absence (1986). The issue of Eisenman’s passage from formalism to deconstruction has already been much discussed in the literature (Rosalind Krauss, Thomas Patin among others), still it should be mentioned that the threads similar to Derrida’s concept included in Eisenman’s writing reveal untranslatability of architecture and philosophy. -/- Choral Works or Separate tricks -/- In 1985-1986 a series of seven disputes between Jacques Derrida and Peter Eisenman took place. The pretext for them were designs concerning Parc de la Villette in Paris. The situation of many months of collaboration between a notable philosopher of the second half of the 20th c. and an architect that already had a huge theoretical oeuvre, ended up with a publication of a large volume entitled Chora L Works and it became at the same time a vast study area for historians of contemporary architecture and philosophers. Derrida’s contribution to concept works were his considerations over the idea of chôra, the properties related to this concept were about to be reflected in shapes of the park. Therefore, Chora L Works became an example of the abilities of contemporary art, both in its capability of translation from philosophical ideas to artistic forms and its resistance to tradition of representing in architecture some phenomena and values originating outside this discipline. In the final period of their collaboration both interlocutors started to polemicise with each other more decidedly, what became a separate part of their thought exchange. The exchange of letters between Derrida and Eisenman at the turn of 1989 ended up the period of their direct contacts, nevertheless, at this time precisely a large group of experts in issues of deconstruction joined the discussion and extended the revealed in the former dispute problems into more than ten years of further considerations and publications. Except for a long text by Jeffrey Kipnis, who had participated in the meetings of the philosopher and the architect, there appeared also comments of researchers of artistic theories (K. Michael Hays, Thomas Patin), philosophers (Andrew Benjamin), and even experts in Greek literature (Maria Theodorou or Ann Bergren). Following these debates a contemporary reflection on architecture has saturated with indeed numerous concepts originating in philosophy of deconstruction. -/- Architecture which imitates mute philosophy -/- The series of Jacques Derrida and Peter Eisenman meetings, which took place in the period of 1985-1987, induced many authors to make comments. Some of them (Jeffrey Kipnis, Ann Bergren, Maria Theodorou) developed the subject of chôra which was introduced to the discussion by Derrida. The problem that was about to be solved was the question of tying up the concept of chôra with architecture, including Eisenman’s architecture and the series of meetings within frames of Chora L Works project. Kipnis on this occasion paid attention to chôra and its character of anachronia which infects any being created within chôra. In other words any event has its counterpart (analogon) in another, earlier event. He demonstrated the similarity of structure of many events and statements from the times of Derrida and Eisenman’s meetings to the almost identical behaviour of figures in Plato’s dialogue Timaeus. The loss of beginning present in this phenomenon was appropriate to both features of chôra and the effects of typical analyses of philosophy of deconstruction. Bergren’s analyses focused on accentuating gender of chôra, which, according to this author, had been neglected hitherto in discussions. She collated chôra descriptions with characteristics of women in myths, early Greek epic and philosophy and she arrived at a conclusion that chôra has features of a single woman and a married one at the same time. And yet Theodorou’s studies showed that in the Homeric epics chôra is not treated as an idea but is related with single things and events. The other part of the comments (represented by Andrew Benjamin and K. Michael Hays’ utterances) concerns Eisenman’s attitude to tradition which was treated as a variety of iteration understood philosophically. Benjamin commenced his considerations at the point of closeness between a definition of tradition and a concept of chôra understood as perpetuation (placement). A problematic issue was for him Eisenman’s complex relation to tradition based on its contest and affirmation at the same time. Overcoming the simple subordination to tradition – according to Benjamin – was based on awareness of the role of repetition in culture not known before. Hays made an attempt to explain the pleasure and torment of repetition with the support of Sigmund Freud and Roland Barthes’ concepts. According to Hays repetitions are attempts of a single being to a certain primal state perceived as free of any tension. In a similar way Rosalind Krauss explained a motif of a grate present in Modernistic art and also exceptionally frequent in Eisenman’s work. -/- Annex Architecture is still writing Balzac novels. Peter Eisenman and literature -/- Architecture’s approach to writing, script or literature, present within Peter Eisenman’s work, is an exceptional phenomenon, furthermore a complex one. The article considers four possible relations. The first one relates to Eisenman’s characteristics as a person extremely gifted with the ability to wordplay, which very ‘play’ reveals skills to create architectural images. In the second approach the attention has been paid to Eisenman’s interests – in the first period of his oeuvre – in linguistic works by Noam Chomsky and his transformational-generative grammar. The third kind of relations applied to overcoming the need for autonomy of architecture (and of modernist aesthetics at the same time) and renew interests in questions of meaning in architecture. The fourth sort of relations occurred when Eisenman started to create reflections of historic or literary narrations in architecture – ‘stone stories’ and architectural fictions of their kind. -/- Bernard Tschumi -/- From perversion to deconstruction In Bernard Tschumi’s writings from the 1970s and 1980s we can find a transposition of important threads of post-structuralist ideas deriving from Georges Bataille, Roland Barthes and Jacques Derrida’s works. The analysis of the architect’s writings also shows roots in Phillippe Sollers, Michel Foucault and Denis Hollier’s works. The analysis of borrowed elements from the beginnings of Tschumi’s theoretical activity may be helpful in explaining the contents of his later writings motre inspired by philosophy of deconstruction. The set of his earliest views was inspired by Marxism, Neo Marxism and French Structuralism, mainly by the writings of Henri Levebre and Guy Debord. From the thought of Levebre Tschumi took interest for city as not only a question of urbanistics but also a political issue. From Debord’s concepts he borrowed a conviction about the role of situational violation for changes in the society structure. Some of these beliefs were preserved in his own concepts of architecture as an event. From this period derived also his will to change conservative elements of social structure not by means of political revolution but of theoretical and creative activity. Tschumi acknowledged that the effective way of the proceedings towards achieving his aims would be accepting the role of both a critical intellectualist and architecture expert who would not hide away his left-wing orientation. The speculations defined by the architect as ‘revolting analyses’ were about to characterise contradictions which tear the society apart, penetrate architecture and constitute the basis of culture. Spreading away of the conscience of false assumptions hidden away in various disciplines could have weakened cohesion of a conservative society and influence the will to change among the elites. This way the beginnings of political revolution were rooted in philosophy of architecture. In 1977 Tschumi published his text entitled The Pleasure of Architecture inspired by Roland Barthes’s The Pleasure of the Text, it also included some concepts derived from Georges Bataille and Jacques Derrida. First of all the author used Barthes’s concept which made an assumption that literary activity is pervaded by the spirit of resistance towards social rules, and Tschudi transferred this remark onto architecture. From the ideas of Bataille, acquainted via Holier’s work, he derived his belief that two concepts of space, a conceptual one (defined as Pyramid) and a sensual one (defined as Labirynth), not losing their distinct features, they join in the concept of experienced space which exceeds contradictions. The exceeding itself was defined as the basic rule of architecture and it was referred to situations in which architecture not only negates social needs, but also disavows its own tradition. Crossing the borders applies not only to political issues or permanent rules of the very discipline but also interfering with other fields (especially literature and film). The fact that architecture is associated with organising events turned Tschumi’s attention to questions of violence that result from upsetting architectural order of a given building by its users and the one hand, and on the other from forcing the users to specific acts imposed by this very order. The analysis of the concepts used by Tschumi in his early writings indicates that they are close to definitions that would occur in his reflection in the following years influenced by philosophy of deconstruction. -/- Approaching deconstruction Tschumi in his theories developed in the 1980s presumed that the current social world had undergone a deep process of decay, and the reaction against which ought to be based on ordering-up actions, and also preserving the main outline of disintegration of the whole and its elements in the state of conflict. The statements concerning the nature of the contemporary to Tschumi social relations were applied by him to the world of architecture, this led him to coming up with designing strategies that took into consideration the destabilised character of conditions in which works of architecture were created. New ways of conduct invented by Tschumi drew their inspiration from literature and research on literature, psychoanalysis, structural linguistics, structuralism and post structuralism, and eventually also deconstruction philosophy. The proposed methods were opposed by their author both to functionalism continuity trends and postmodern architecture. Tschumi’s proposals contradicted any forms of conservatism or traditionalism in political sphere as well as in reference to tendencies in architecture. They were not simple contradictions of social or architectural rules, they intrude them from the inside, weaken or escalate the already existing incongruities, they move the boundaries between the areas. Revolutionary illusions about the possibility of radical changes were replaced with strategies which completed, tainted or test former rules in the series of formal games of permutation and combination. Quite different from avant-garde formalism Tschumi’s games were not about maintaining the autonomy of a given area, but on the contrary – polluting it with other areas’ influences. Tschumi enjoyed demonstrating illusions of architecture concerning simple relations between form and function, or between form and meaning. Making use of Freud, Lacan and Foucault’s research he introduced a category of “madness” into architecture allowing an observation that the recognised norms are nothing but merely ones of many possible principles of behaviour, and their recognised status resulted from unjustified hindering innovativeness which is crucial for architecture. To reborn architecture’s capability of changing Tschumi also made use of Barthes’s discoveries concerning rules of narration and works by writers who applied in their writing knowledge on linguistics. Making a work’s author unclear by various mechanical transformations of its elements was however apparent only, and formal rigours imposed on the process of designing liberated possibilities difficult to obtain in more traditional creative action. Another mode of acting introduced by Tschumi was combining his work of elements deriving from outside architecture; joining space records with notation of motion and events accompanying architectural objects among others. These architectural and extra-architectural elements were not unified, on the contrary their heterogenous and conflictual character was stressed. This is how shock, anxiety and instability, typical for live in great metropolises, infiltrated architecture. Taking some ideas of deconstruction philosophy as a pattern Tschumi also took into critical consideration in his essays traditional in architecture oppositions between form and figuration, or theory and practice. By combining various inspirations he eventually worked out an idea of architectural event, which he understood as a series of actions contesting its own field, redefining its sources, principles and elements. An event, understood in this way, was not so much producing works as rather creating conditions of their production and at the same time designing the society different from a hierarchic one. -/- Park of deconstruction Among numerous philosophical strategies of deconstruction most frequently used was questioning the practice of strong opposition of two reasons. In many cases Bernard Tschumi’s writings just consider functioning of the conflict juxtaposition of the ideas of structure and ornament or theory and practice in history of architecture. Violation of traditional relations between terms of this kind, both old and modern, raised Jacques Derrida’s objections, when he was induced for the first time to co-operate with architects’ milieu. During this long lasting thought exchange the philosopher eventually acknowledged Bernard Tschumi’s arguments for reasoning the encroachment of architecture’s fundamental rules. Deconstruction applied in architecture was not a simple transposition or analogy of practices that had been applied by philosophy of deconstruction. We may even say that considering architectural terms became an important formula of deconstruction. Architecture understood in philosophical way became something beyond the practice and theory of its own discipline, a sort of metaphysics of both philosophy and architecture. The deliberate encroachment of simplicity of dividing architecture into theory and practice, for the first time became a clear aim for Tschumi in his drawings and texts entitled The Manhattan Transcripts. The contents of this series of works was a record of characteristic features of this New York district in such a way that not only objects were the subject of the record but also relations between objects, people and events. The record was about to take into consideration a conflict character of elements of this representation and at the same time to avoid applying to them the rule of mimetism. The record became a form of reflection over the very record by an increased control over the ways of representation. Architecture which was considered in the The Manhattan Transcripts was not directed to fulfill the needs of inhabitation or production, it was rather related with hitherto usually marginalised liminal situations: building ostentatiously big monuments, religious cult, war etc. Architecture operating in these relations focused also the attention on the included in it continuous tendency to overpass its own restrictions, the role of violence as its not recognised factor, or the meaning of excess and shock in its operation. Architecture moving from reason towards madness became even more visible in the design of Parisian Parc de la Villette, whose pavilions were defined as folies (in French it means both small park buildings and follies). The park was supposed to be on the one hand a reflection of traditional society disintegration while on the other it questioned basic rules of producing a work of architecture. The traditional rules of designing, based on ordering up, were replaced with the strategies of dysfunction and dissociation. In Tschumi’s opinion methods of this kind may be equivalent of what Derrida named différance. Instead of aiming at mergence, any diversity, plays or variations were strengthen. Tschumi’s texts, in which he explained his attitude, were completed by Derrida’s extent statement entitled Point de folie – Maintenant l’architecture. Derrida’s article is the most significant of all his statements on architecture as a form of thinking and activity. According to the philosopher, architecture should divide space (in French defined as espacement), what enables both thinking and action – it arranges the space of an event. Tschumi’s buildings, defined as folies, in an essential way destabilise any created order, and at the same time they refresh it. Derrida’s statement suggests that architecture may become both metaphor of an order merging a language or a society but also of inner forces which deconstruct and reconstruct it. Therefore architecture is at the same time a construction, a deconstruction and a reconstruction. Parc de la Villette stands out in this system with its attempt to step beyond the scheme of an easy repetition and its heading for chances of achieving more radical otherness. -/- Conclusion Destruction as construction. Paradoxes of deconstruction in architecture -/- Scepticism about persistence and common importance of fundamental values of human culture evinced in philosophers and writers’ works as early as in Greek antiquity, nevertheless it was not expressed so strongly as in the second half of the 20th century. Especially in Heidegger’s work Being and Time (although originated in 1927, still influential in all later philosophy) the following states were characterised: the state of losing the ground (Abgrund), of being out of sight (Unheimlichkeit) and of being out of dwelling (Un-zuhause-sein) – as the basis of self-confidence of conscious being there (Dasein). The entire criticism of philosophy of home and dwelling draws the inspiration from this early writing of the German philosopher, it combines crisis of basic terms of metaphysics with social conditions which are dictated by living in large metropolis. The crisis of both metaphysical foundation and home appears to be similar to the situation of weakening the relations between a man and his dwelling in extensively expanding cities. Whereas philosophy, as well as many disciplines of social sciences, have diagnosed for a long time the destabilisation of fundamental ideas of Western culture and crucial changes in the ways of dwelling, architecture itself occurred to be “the last fortress of metaphysics” (J. Derrida). Among contemporary architects, Peter Eisenman and Bernard Tschumi were the ones who engaged most decidedly in the issues of critical analysis of architecture foundation and its social role. Both the architects noticed new formulas of contemporary social and individual existence, tremendously different from the entire history, and at the same time they affirmed lack of adequacy of architecture concepts to new situations. Both Eisenman and Tschumi used to describe the existing architecture as a tool for consolidation of highly integrated and hierarchised societies, and also as a discipline extremely uncoincidental with the current character of social life based on ideas of freedom and diversity. The means to transform architecture and make a factor of further social changes out of it, was a concept that accentuated revealing the inner contradictions of this discipline, and considering them in designing strategies. Eisenman’s activity, in regard of what has just been noticed, was focused on questioning the basic rules of traditionally comprehended architecture, especially the rule of purpose. The American architect noticed that the concept of architecture as fulfilment the need of location, hides away the fact that the location has to be constantly reconsidered, and hence it is overtaken by change (dislocation). Therefore new concept of architecture propounded architectural activity to translocate the concept of location – more than before – but also to change its status perpetually. Such comprehended architecture should claim, as its main purpose, the constant revision of this purpose and create itself anew permanently. Even Eisenman’s earliest designs of houses nos. I-IV broke with such values as the sense of safety, closeness and familiarity, and just on the contrary they accentuated senses of strangeness, homelessness and loss of confidence. The contradictions within architecture noticed by Tschumi referred to combination of intellectual and sensual values in architecture, when their non-appropriation was defeated by an additional condition, namely the way of experience based on pleasure of excess, marked by insanity. The features of folly were especially visible in his designs of gardens, where the order of planning was mixed with sensual experience introduced by particular elements (both the ones created by nature, and the buildings defined as folies). Parc de la Villette designed by the French architect in Paris put in question not only the common understanding of purpose in architecture but also the ideas of order and integrity, as its plan was based on the combination of independent layers with records of grids of points, various lines and planes. The architecture that collides inadequate elements with each other was supposed to be a kind of an event with no beginning and no end. The architecture treated as an event became a form of a space weakened articulation that maintains its diversity and lack of accordance of the elements building it up. The analyses of Eisenman and Tschumi’s theoretical writings indicate how much the aims of architecture have actually changed; instead of supporting social persistence, the architecture is rather intensifying contradictions, and instead of providing people with the sense of safety, it sublimes danger. From simple acts of defamiliarisation, increasing the distance to itself and enhancing the role of theory, through discomfort, anxiety, not feeling someone at home, weirdness, excess, shock and violence, architecture reached the edge of stability and uncertainty, only to make an attempt at penetrating what is impossible and unutterable, and recording what cannot become the subject of any records. -/- . (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)

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 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)

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)

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)

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)

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)

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.

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)

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)

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)

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)

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)

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)

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)

At the beginning of 2020, the world was experiencing the Covid-19 pandemic, and Indonesia was no exception. The occurrence of this affects the learning system in Indonesia, the learning system that was originally face-to-face was forced to online form, in this case the teachers are required to provide a creative, efficient and optimal learning system for students. So the purpose of this study is to find out the difference in the average learning result of elementary school students during the (...) pandemic. The method used in this study is quantitative with a posttest-only control group design. The population in this study were grade 4 elementary school students in Majalengka district, Indonesia. There were 64 samples and was taken by purposive sampling. The results of this study are that there are differences in the average student learning results where students who study with the hybrid learning system are higher than the face-to-face learning system. The hybrid learning system is very reliable in the 4.0 era as well as learning during the Covid-19 pandemic. However, for the record, it is necessary to look at the facilities and infrastructure considering that this system relies on technology, it is necessary to understand and be able to control the learning media for both teachers and students so that learning outcomes can be optimal and minimize the occurrence of obstacles. The present study revealed the implementation of 21st century learning. (shrink)

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

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)

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)

The well-definedness of particles of any kind depends on the limits, approximations, or other conditions that may or may not be involved, for example, whether there are interactions and whether ostensibly related energy is localizable. In particular, their theoretical status differs between its non-relativistic and relativistic versions: One can properly define interacting elementary particles in single-system non-relativistic quantum mechanics, at least in the case of non-zero mass systems; by contrast, one is severely challenged to define even these properly in (...) the relativistic quantum field theories that now underlie the study of particle physics. Here, the impact of localizability on this status is reviewed in relation to the work of Paul Busch on positive operator valued measures that significantly probes the relevance of quantum unsharpness to it. (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)

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)

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)

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)

In this paper, we show that for each forcing notion P in a transitive model M of ZFC, if P satisfies some conditions, there is an elementary embedding from M into a generic ultrapower contains a P-generic set. And, we also introduce the result that if we assume the existence of some large cardinals, the above generic ultrapower can be well-founded. Using this result, we prove some theorems on the problems of regularity properties of definable sets of reals.

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)