The incompleteness of set theory ZFC leads one to look for natural extensions of ZFC in which one can prove statements independent of ZFC which appear to be "true". One approach has been to add large cardinal axioms. Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski- Grothendieck set theory TG [1]-[3] It is a non-conservative extension of ZFC and is obtaineed from other axiomatic set theories by the inclusion of Tarski's axiom which implies (...) the existence of inaccessible cardinals [1].Non-conservative extension of ZFC based on an generalized quantifiers considered in [4]. In this paper we look at a set theory NC_{∞^{#}}^{#},based on bivalent gyper infinitary logic with restricted Modus Ponens Rule [5]-[8]. In this paper we deal with set theory NC_{∞^{#}}^{#} based on gyper infinitary logic with Restricted Modus Ponens Rule. Set theory NC_{∞^{}}^{} contains Aczel's anti-foundation axiom [9]. We present a new approach to the invariant subspace problem for Hilbert spaces. Our main result will be that: if T is a bounded linear operator on an infinite-dimensional complex separable Hilbert space H,it follow that T has a non-trivial closed invariant subspace. Non-conservative extension based on set theory NC_{∞}^{#} of the model theoretical nonstandard analysis [10]-[12] also is considered. (shrink)

This paper examines the conservative point of view about distributive justice. The first section explains the methodology used to develop this point of view. The second section describes one conservative point of view and briefly provides empirical evidence that it reflects the viewpoint of many ordinary conservatives. The third section explains how this conservative view can ground objections to social safety net programs, using as examples the recent health reform legislation and more extensive proposals for a true (...) national health system. The fourth section sketches ways that non-conservative philosophers might try to refute those objections. Examining a conservative point of view leads to several important conclusions. One is that the conservative point of view is not properly represented in contemporary philosophical discussions. Another is that the conservative point of view cannot be refuted by appealing to existing egalitarian writings. A third is that if progressive philosophers such as myself want to address the conservative point of view, we must expand the range of issues that we discuss in contemporary political philosophy. Doing so is a vital task, because otherwise we ignore the political views held by as much as half the American population. (shrink)

This paper deals with Peirce’s understanding of perceptual judgment, relating it to the conditions for the use of language defined by Michael Dummett. Namely, drawing on Dummett’s requirement for harmony between descriptive and evaluative aspects of our linguistic practice, we will try to give an interpretation of Peirce’s view of perception that implies rejecting the idea that the formation of a perceptual judgment has an inferential structure. On the other hand, since it is, in Peirce’s opinion, the structure of abductive (...) inference, this approach should enable us to draw some conclusions related to abduction in general. (shrink)

We study the representation of sets of desirable gambles by sets of probability mass functions. Sets of desirable gambles are a very general uncertainty model, that may be non-Archimedean, and therefore not representable by a set of probability mass functions. Recently, Cozman (2018) has shown that imposing the additional requirement of even convexity on sets of desirable gambles guarantees that they are representable by a set of probability mass functions. Already more that 20 years earlier, Seidenfeld et al. (1995) gave (...) an axiomatisation of binary preferences—on horse lotteries, rather than on gambles—that also leads to a unique representation in terms of sets of probability mass functions. To reach this goal, they use two devices, which we will call ‘SSK–Archimedeanity’ and ‘SSK–extension’. In this paper, we will make the arguments of Seidenfeld et al. (1995) explicit in the language of gambles, and show how their ideas imply even convexity and allow for conservative reasoning with evenly convex sets of desirable gambles, by deriving an equivalence between the SSK–Archimedean natural extension, the SSK–extension, and the evenly convex natural extension. (shrink)

In this paper we present a solution to Saul Kripke’s Puzzle About Belief Meaning and use, Dordrecht, 1979) based on Kaplan’s metaphysical picture of words. Although it is widely accepted that providing such a solution was one of the main incentives for the development of Kaplan’s theory, it was never presented by Kaplan in a systematic manner and was regarded by many as unsatisfactory. We agree with these critiques, and develop an extension of Kaplan’s theory by introducing the notion (...) of “conservative” word uses, as well as arguing for the restriction of Kripke’s Disquotational Principle only to such uses. This restriction allows us to solve Kripke’s Puzzle by arguing that the assent of the puzzle’s protagonist does not allow disquotation and ascription of corresponding inconsistent belief, as it contains the non-conservative use of a proper name. At the end of the paper, we defend two of Kaplan’s theses that we find essential for our argument to work: that individuation of word tokens involves taking into account the intention of the speaker, and that different uniquely referring proper names of the same shape should be regarded as different homonymous words. (shrink)

An application of diagrams for separating modes of theory development.

We present an overview of typed and untyped disquotational truth theories with the emphasis on their (non)conservativity over the base theory of syntax. Two types of conservativity are discussed: syntactic and semantic. We observe in particular that TB—one of the most basic disquotational theories—is not semantically conservative over its base; we show also that an untyped disquotational theory PTB is a syntactically conservative extension of Peano Arithmetic.

Fine (2017) proposes a new logic of vagueness, CL, that promises to provide both a solution to the sorites paradox and a way to avoid the impossibility result from Fine (2008). The present paper presents a challenge to his new theory of vagueness. I argue that the possibility theorem stated in Fine (2017), as well as his solution to the sorites paradox, fail in certain reasonable extensions of the language of CL. More specifically, I show that if we extend the (...) language with any negation operator that obeys reductio ad absurdum, we can prove a new impossibility result that makes the kind of indeterminacy that Fine takes to be a hallmark of vagueness impossible. I show that such negation operators can be conservatively added to CL and examine some of the philosophical consequences of this result. Moreover, I demonstrate that we can define a particular negation operator that behaves exactly like intuitionistic negation in a natural and unobjectionable propositionally quantified extension of CL. Since intuitionistic negation obeys reductio, the new impossibility result holds in this propositionally quantified extension of CL. In addition, the sorites paradox resurfaces for the new negation. (shrink)

We study the conservation of energy, or lack thereof, when measurements are performed in quantum mechanics. The expectation value of the Hamiltonian of a system changes when wave functions collapse in accordance with the standard textbook treatment of quantum measurement, but one might imagine that the change in energy is compensated by the measuring apparatus or environment. We show that this is not true; the change in the energy of a state after measurement can be arbitrarily large, independent of the (...) physical measurement process. In Everettian quantum theory, while the expectation value of the Hamiltonian is conserved for the wave function of the universe, it is not constant within individual worlds. It should therefore be possible to experimentally measure violations of conservation of energy, and we suggest an experimental protocol for doing so. (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)

In this paper, we look at applying the techniques from analyzing superintuitionistic logics to extensions of the cointuitionistic Priest-da Costa logic daC (introduced by Graham Priest as “da Costa logic”). The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc-logics. A sequence of strengthenings of Priest-da Costa logic is examined and employed to pinpoint (...) the maximal non-classical extension of both daC and Heyting-Brouwer logic HB . Finally, the relationship between daC and Logics of Formal Inconsistency is examined. (shrink)

In this paper, I argue that one of the arguments usually put forward in defence of universism is in tension with current set theoretic practice. According to universism, there is only one set theoretic universe, V, and when applying the method of forcing we are not producing new universes, but only simulating them inside V. Since the usual interpretation of set generic forcing is used to produce a “simulation” of an extension of V from a countable set inside V (...) itself, the above argument is credited to be a strong defence of universism. However, I claim, such an argument does not take into account current mathematical practice. Indeed, it is possible to find theorems that are available to the multiversists but that the advocate of universism cannot prove. For example, it is possible to prove results on infinite games in non-well-founded set-theories plus the axiom of determinacy (such as ZF + AFA + PD) that are not available in ZFC + PD. These results, I contend, are philosophically problematic on a strict universist approach to forcing. I suggest that the best way to avoid the difficulty is to adopt a pluralist conception of set theory and embrace a set theoretic multiverse. Consequently, the current practice of set generic forcing better supports a multiverse conception of set theory. (shrink)

This paper attempts to resolve the puzzle associated with the non-spatiality of monads by investigating the possibility that Leibniz employed a version of the extension of power doctrine, a Scholastic concept that explains the relationship between immaterial and material beings. As will be demonstrated, not only does the extension of power doctrine lead to a better understanding of Leibniz’ reasons for claiming that monads are non-spatial, but it also supports those interpretations of Leibniz’ metaphysics that accepts the real (...) extension of bodies. (shrink)

The incompleteness of set theory ZF C leads one to look for natural nonconservative extensions of ZF C in which one can prove statements independent of ZF C which appear to be “true”. One approach has been to add large cardinal axioms.Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski-Grothendieck set theory T G or It is a nonconservative extension of ZF C and is obtained from other axiomatic set theories by the inclusion of Tarski’s (...) axiom which implies the existence of inaccessible cardinals. See also related set theory with a filter quantifier ZF (aa). In this paper we look at a set theory NC# ∞# , based on bivalent gyper infinitary logic with restricted Modus Ponens Rule In this paper we deal with set theory NC# ∞# based on bivalent gyper infinitary logic with Restricted Modus Ponens Rule. Nonconservative extensions of the canonical internal set theories IST and HST are proposed. (shrink)

The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the -fragment of the logics of nonsense, such as the ones due to Bochvar and Halldén, among others. Here, we extend these logics with classical negations, and we furthermore show that some of these extended systems can be properly regarded as logics of formal inconsistency and logics of formal undeterminedness.

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 search for the extensions of sentences can be guided by Frege’s “principle of compositionality of extension”, according to which the extension of a composed expression depends only on its logical form and the extensions of its parts capable of having extensions. By means of this principle, a strict criterion for the admissibility of objects as extensions of sentences can be derived: every object is admissible as the extension of a sentence that is preserved under the substitution (...) of co-extensional expressions. The question is: what are the extensions of elementary sentences containing empty singular terms, like ‘Vulcan rotates’. It can be demonstrated that in such sentences, states of affairs as structured objects (but not truth-values) are preserved under the substitution of co-extensional expressions. Hence, such states of affairs are admissible (while truth-values are not) as extensions of elementary sentences containing empty singular terms. (shrink)

In 1980 F. Wattenberg constructed the Dedekind completion

d of the Robinson non-archimedean field

and established basic algebraic properties of

d [6]. In 1985 H. Gonshor established further fundamental properties of

d [7].In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completion

d in transcendental number theory were considered. We dealing using set theory ZFC
(
-model of ZFC).Given (...) an class of analytic functions of one complex variable f  

z, we investigate the arithmetic nature of the values of fz at transcendental points en, n  .Main results are: (i) the both numbers e
 and e   are irrational, (ii) number ee is transcendental. Nontrivial generalization of the Lindemann- Weierstrass theorem is obtained. (shrink)

In this paper, I raise a novel objection to David Lewis’s Humean account of laws. The objection is that non-universal laws are metaphysically possible, but Lewis’s account cannot accommodate them. I then propose and defend an extension of Lewis’s view that gives us an account of Humean non-universal laws.

The purpose of this paper is discuss an application of non-Marxian historical materalism to explanation of non-European societies. Until now this theory has been limited to interpretation of European societies. In order to grasp development of non-European societies (e.gr. Mexico) the extension of typology of societies is proposed which constitutes a new scientific programme based on this theory of historical development.

This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke resource models (...) extended with a neighbourhood function: modal Kripke resource models. We propose a Hilbert-style axiomatisation and a Gentzen-style sequent calculus. We show that the proof theories are sound and complete with respect to the class of modal Kripke resource models. We show that the sequent calculus admits cut elimination and that proof-search is in PSPACE. We then show how to extend the results when non-commutative connectives are added to the language. Finally, we put the l.. (shrink)

Whether nature is valuable on its own (intrinsic values) or because of the benefits it provides to humans (instrumental values) has been a long-standing debate. The concept of relational values has been proposed as a solution to this supposed dichotomy, but the empirical validation of its intuitiveness remains limited. We experimentally assessed whether intrinsic/relational values of sentient beings/non-sentient beings/ecosystems better explain people’s sense of moral duty towards global nature conservation for the future. Participants from a representative sample of the population (...) of Singapore (n = 1508) were randomly allocated to two “the last human” scenarios. We found that the best predictor of such a sense of moral duty for future nature conservation is the recognition of the intrinsic values of sentient beings. Our results suggest that the concern for animal welfare may enhance rather than compete with the sense of moral duty towards nature conservation. (shrink)

This paper brings together several strands of thought from both the analytic and phenomenological traditions in order to critically examine accounts of cognitive enhancement that rely on the idea of cognitive extension. First, I explain the idea of cognitive extension, the metaphysics of mind on which it depends, and how it has figured in recent discussions of cognitive enhancement. Then, I develop ideas from Husserl that emphasize the agential character of thought and the distinctive way that conscious thoughts (...) are related to one another. I argue that these considerations are necessary for understanding why forms of cognitive extension may diminish our cognitive lives in different ways. This does not lead to a categorical rejection of cognitive enhancement as unethical or bad for human flourishing, but does warrant a conservative approach to the design and implementation of cognitive artifacts. (shrink)

Ecological economics is an interdisciplinary science that is primarily concerned with developing interventions to achieve sustainable ecological and economic systems. While ecological economists have, over the last few decades, made various empirical, theoretical, and conceptual advancements, there is one concept in particular that remains subject to confusion: critical natural capital. While critical natural capital denotes parts of the environment that are essential for the continued existence of our species, the meaning of terms commonly associated with this concept, such as ‘non-substitutable’ (...) and ‘impossible to substitute,’ require a clearer formulation then they tend to receive. With the help of equations and graphs, this article develops new definite account of critical natural capital that makes explicit what it means for objective environmental conditions to be essential for continued existence. The second main part of this article turns to the question of formally modeling the priority of conserving critical natural capital. While some ecological economists have maintained that, beyond a certain threshold, critical natural capital possesses absolute infinite value, absolute infinite utility models encounter significant problems. This article shows that a relative infinite utility model provides a better way to model the priority of conserving critical natural capital. (shrink)

We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...) reflection in contrast to the usual height reflection of the Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed \Pi_2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles. (shrink)

We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information (...) and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems. (shrink)

The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, end Einstein. The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects can (...) be represented by corresponding oppositions. These are: macroscopic – microscopic; elements – states; relational – non-relational; and observable – theoretical. They can be interpreted as axes of independent qualities constituting a common qualitative reference frame shared by those theories. Each of them can be situated in this reference frame occupying a different place. This reference frame can be interpreted as an additional selection of reality within Carnot’s initial selection describable as macroscopic and both observable and theoretical. The deduced reference frame refers implicitly to many scientific theories independent of their subject therefore defining a general and common space or subspace for scientific theories (not for all). The immediate conclusion is: The examples of a few statistical thermodynamic theories demonstrate that the concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another. Still a few more general suggestions referring the scientific realism debate can be added: One can admit that reality in scientific theories is some partially shared common qualitative space or subspace describable by relevant oppositions and rather independent of their subject quite different in general. Many or maybe all theories can be situated in that space of reality, which should develop adding new dimensions in it for still newer and newer theories. Its division of independent subspaces can represent the many-realities conception. The subject of a theory determines some relevant subspace of reality. This represents a selection within reality, relevant to the theory in question. The success of that theory correlates essentially with the selection within reality, relevant to its subject. (shrink)

This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that (...) the theory is a proof-theoretically conservative extension of the theory PT of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground. (shrink)

There is hardly anything more central to our universe than conservation. Many scientific fields and disciplines view the law of conservation as one of the most fundamental universal laws. The Darwinian model pivots the process of evolution on variability, reproduction, and natural selection. Conservation plays a marginal role in this model and is not really universal, as the model allows exceptions to conservation, i.e. non-conservation, to play an equally important role in evolution. This anomalous role of conservation in the Darwinian (...) model raises questions: What is the reason for this anomaly? Is conservation really universal, as we tend to believe or is it not, as the Darwinian model suggests? This contribution proposes a new model of evolution that focuses on levels of organization, rather than of species, organisms, or populations. It argues that conservation is central to evolution. Not only does this new model restores the universal status of conservation but it also makes possible to resolve some outstanding problems and controversies that continue to plague the Darwinian model. The article tries to advance the broad Darwinian project that seeks to explain the process of evolution as a product of the spontaneous processes in nature. (shrink)

Given that one-million species are currently threatened with extinction and that humans are undermining the entire natural infrastructure on which our modern world depends (IPBES, 2019), this dissertation will show that there is a need to provide an alternative approach to wildlife conservation, one that avoids anthropocentrism and wildlife valuation on an instrumental basis to provide meaningful and tangible success for both wildlife conservation and human well-being in an inclusive way. In this sense, The Value of Being Wild will showcase (...) the concept of eco-phenomenology as an important non-anthropocentric alternative to the current approach to wildlife conservation, namely sustainable development. The problem with this dominant paradigm, as Chapter Two will reveal, is that sustainable development has not only failed to provide humans and future generations of humans with their own needs but, as per the latest IPBES report, failed in arresting the freefall decline of wild species. The situation currently requires a radical overhaul of the current system. As emerged from the later work of French phenomenologist, Maurice Merleau-Ponty (1908-1961), eco-phenomenology is particularly well-suited as a practical alternative to sustainable development. The core reason is that eco-phenomenology moves away from a human-centred framework toward a far more inclusive approach that embraces the conservation of wild animals as well the wild environment they dwell in, beyond any human needs (although humans are embraced within the approach too). Merleau-Ponty helps us to move away from anthropocentrism to a more inclusive approach in conserving wildlife, since his phenomenology does not consider the human animal’s relationship in the world as exclusive (to use and exploit wild animals solely for their benefit), but inclusive (as an interconnected biological component in a broad ecological system). The strength of Merleau-Ponty’s concept of phenomenology is that it facilitates an understanding of all living and even non-living entities, such as air, water and soil, as interconnected and interrelated within a broad biosphere. While Merleau-Ponty did not address the concept of wild animals or the biosphere directly, his later work points to the fact that human animals cannot exist outside a world that provides life-giving force to all living beings. Phenomenology, as developed by Merleau-Ponty, is a concept that recognises the axiological qualities of the natural world are inherent and ineliminable from the discipline of traditional phenomenology, hence the term ‘eco-phenomenology’, developed in one reception of his thinking. Eco-phenomenology offers a return to a world that humans have tried hard to alienate themselves from, in that it approaches the natural environment and wild animals, not as a complex set of objects and objective processes, but rather as they are experienced and lived from within by the attentive animal who is entirely a part of the world that he or she experiences. Merleau-Pontian eco-phenomenology thus emphasises a holistic dialogue within a more-than-human world (Abram, 1996: 65). Eco-phenomenology is a concept that points toward an applied strategy but so far this has not been attempted in earnest. This is specifically true when it comes to wildlife conservation. The Value of Being Wild, therefore, sets out to employ the concept of eco-phenomenology in order to provide a new practical wildlife conservation approach that challenges, and potentially replaces, the current prevailing policies as employed by global governmental and inter-governmental agencies. In particular, this alternative frame is posed as a replacement for the failing anthropocentric conservation practices currently in place in South Africa. This dissertation will therefore conclude by exploring strategies where conservation of wildlife is not taken as instrumentally-valued, or even intrinsically-valued, but rather as wild-valued in that the existence of wild animals as wild is conserved within a broader, more inclusive overall ecology that supports the survival and flourishing of all living beings that include plants, wild animals and human beings. (shrink)

Blame is multifarious. It can be passionate or dispassionate. It can be expressed or kept private. We blame both the living and the dead. And we blame ourselves as well as others. What’s more, we blame ourselves, not only for our moral failings, but also for our non-moral failings: for our aesthetic bad taste, gustatory self-indulgence, or poor athletic performance. And we blame ourselves both for things over which we exerted agential control (e.g., our voluntary acts) and for things over (...) which we lacked such control (e.g., our desires, beliefs, and intentions). I argue that, despite this manifest diversity in our blaming practices, it’s possible to provide comprehensive account of blame. Indeed, I propose a set of necessary and sufficient conditions that aims to specify blame’s extension in terms of its constitution as opposed to its function. And I argue that this proposal has a number of advantages beyond accounting for blame in all its disparate forms. For one, it can account for the fact that one’s having had control over whether one was to φ is a necessary condition for one’s being fittingly blamed for having φ-ed. For another, it can account for why, unlike fitting shame, fitting blame is always deserved, which in turn explains why there is something morally problematic about ridding oneself of one’s fitting self-blame (e.g., one’s fitting guilt). (shrink)

It is widely believed that a conservative moral outlook is opposed to biomedical forms of human enhancement. In this paper, I argue that this widespread belief is incorrect. Using Cohen’s evaluative conservatism as my starting point, I argue that there are strong conservative reasons to prioritise the development of biomedical enhancements. In particular, I suggest that biomedical enhancement may be essential if we are to maintain our current evaluative equilibrium (i.e. the set of values that undergird and permeate (...) our current political, economic, and personal lives) against the threats to that equilibrium posed by external, non-biomedical forms of enhancement. I defend this view against modest conservatives who insist that biomedical enhancements pose a greater risk to our current evaluative equilibrium, and against those who see no principled distinction between the forms of human enhancement. (shrink)

This essay explores various problematical aspects of Descartes' conservation principle for the quantity of motion (size times speed), particularly its largely neglected "dual role" as a measure of both durational motion and instantaneous "tendencies towards motion". Overall, an underlying non-local, or "holistic", element of quantity of motion (largely derived from his statics) will be revealed as central to a full understanding of the conservation principle's conceptual development and intended operation; and this insight can be of use in responding to some (...) of the recent and traditional criticisms of Descartes' physics. (shrink)

The principle of energy conservation is widely taken to be a se- rious difficulty for interactionist dualism (whether property or sub- stance). Interactionists often have therefore tried to make it satisfy energy conservation. This paper examines several such attempts, especially including E. J. Lowe’s varying constants proposal, show- ing how they all miss their goal due to lack of engagement with the physico-mathematical roots of energy conservation physics: the first Noether theorem (that symmetries imply conservation laws), its converse (that conservation (...) laws imply symmetries), and the locality of continuum/field physics. Thus the “conditionality re- sponse”, which sees conservation as (bi)conditional upon symme- tries and simply accepts energy non-conservation as an aspect of interactionist dualism, is seen to be, perhaps surprisingly, the one most in accord with contemporary physics (apart from quantum mechanics) by not conflicting with mathematical theorems basic to physics. A decent objection to interactionism should be a posteri- ori, based on empirically studying the brain. (shrink)

Predictive Processing (PP) framework construes perception and action (and perhaps other cognitive phenomena) as a matter of minimizing prediction error, i.e. the mismatch between the sensory input and sensory predictions generated by a hierarchically organized statistical model. There is a question of how PP fits into the debate between traditional, neurocentric and representation-heavy approaches in cognitive science and those approaches that see cognition as embodied, environmentally embedded, extended and (largely) representation-free. In the present paper, I aim to investigate and clarify (...) the cognitivist or ‘conservative’ reading of PP. I argue that the conservative commitments of PP can be divided into three distinct categories: (1) representationalism, (2) inferentialism, and (3) internalism. I show how these commitments and their relations should be understood and argue for an interpretation of each that is both non-trivial and largely ecumenical towards the 4E literature. Conservative PP is as progressive as conservatism gets. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous attempts (...) all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

Neo-Fregean logicists claim that Hume’s Principle (HP) may be taken as an implicit definition of cardinal number, true simply by fiat. A long-standing problem for neo-Fregean logicism is that HP is not deductively conservative over pure axiomatic second-order logic. This seems to preclude HP from being true by fiat. In this paper, we study Richard Kimberly Heck’s Two-Sorted Frege Arithmetic (2FA), a variation on HP which has been thought to be deductively conservative over second-order logic. We show that (...) it isn’t. In fact, 2FA is not conservative over n-th order logic, for all $n \geq 2$. It follows that in the usual one-sorted setting, HP is not deductively Field-conservative over second- or higher-order logic. (shrink)

This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our theory is (...) a proof-theoretically conservative extension of the ramified theory of positive truth up to. (shrink)

Hybridization by introgression (“hybridization”) is a complex topic in conservation. Many conservation decision-makers are concerned about hybridization by introgression because it may threaten species persistence or local phenotypes, among other potential long-term problems. While attitudes have changed towards hybridization as a conservation threat, there are still concerns about hybridization as a problem, particularly if the hybridization was anthropogenically mediated. I propose that these concerns are overblown and that it is misguided to focus on whether hybridization is unintentionally human-mediated. I argue (...) that practitioners should still consider the effects of hybridization on conservation, but the reasons should concern the long-term environmental consequences, such as ecological function and social and cultural that hybridization has, rather than whether humans “caused” the hybrid. I propose a series of steps to think differently about these cases. (shrink)

John Rawls’s use of the “fully cooperating assumption” has been criticized for hindering attempts to address the needs of disabled individuals, or non-cooperators. In response, philosophers sympathetic to Rawls’s project have extended his theory. I assess one such extension by Cynthia Stark, that proposes dropping Rawls’s assumption in the constitutional stage (of his four-stage sequence), and address the needs of non-cooperators via the social minimum. I defend Stark’s proposal against criticisms by Sophia Wong, Christie Hartley, and Elizabeth Edenberg and (...) Marilyn Friedman. Nevertheless, I argue that Stark’s proposal is crucially incomplete. Her formulation of the social minimum lacks accompanying criteria with which the adequacy of the provisions for non-cooperators may be assessed. Despite initial appearances, Stark’s proposal does not fully address the needs of non-cooperators. I conclude by considering two payoffs of identifying this lack of criteria. (shrink)

Social norms – rules governing which behaviours are deemed appropriate or inappropriate within a given community – are typically taken to be uniquely human. Recently, this position has been challenged by a number of philosophers, cognitive scientists, and ethologists, who have suggested that social norms may also be found in certain non-human animal communities. Such claims have elicited considerable scepticism from norm cognition researchers, who doubt that any non-human animals possess the psychological capacities necessary for normative cognition. However, there is (...) little agreement among these researchers about what these psychological prerequisites are. This makes empirical study of animal social norms difficult, since it is not clear what we are looking for and thus what should count as behavioural evidence for the presence (or absence) of social norms in animals. To break this impasse, we offer an approach that moves beyond contested psychological criteria for social norms. This approach is inspired by the animal culture research program, which has made a similar shift away from heavily psychological definitions of ‘culture’ and to become organized around a cluster of more empirically tractable concepts of culture. Here, we propose an analogous set of constructs built around the core notion of a normative regularity, which we define as a socially maintained pattern of behavioural conformity within a community. We suggest methods for studying potential normative regularities in wild and captive primates. We also discuss the broader scientific and philosophical implications of this research program with respect to questions of human uniqueness, animal welfare and conservation. (shrink)

Non-well-founded set theories allow set-theoretic exotica that standard ZFC will not allow, such as a set that has itself as its sole member. We can distinguish plenitudinous non-well-founded set theories, such as Boffa set theory, that allow infinitely many such sets, from restrictive theories, such as Finsler-Aczel or AFA, that allow exactly one. Plenitudinous non-well-founded set theories face a puzzle: nothing seems to explain the identity or distinctness of various of the sets they countenance. In this paper I aim to (...) sharpen this puzzle, make clear who it does and does not apply to and, ultimately, to argue in favor of a plenitudinous theory like Boffa. (shrink)

Inventing novel knowledge to solve problems is a crucial, creative, mechanism employed by humans, to extend their range of action. In this paper, we present TCL (typicality-based compositional logic): a probabilistic, non monotonic extension of standard Description Logics of typicality, and will show how this framework is able to endow artificial systems of a human-like, commonsense based, concept composition procedure that allows its employment in a number of applications (ranging from computational creativity to goal-based reasoning to recommender systems and (...) affective computing). -/- The framework relies on 3 main ingredients: a non monotonic extension of standard Description Logics (allowing to reason on exceptions to inheritance in standard knowledge bases) a probabilistic extension coming from the field of logic programming (the DISPONTE semantics) a cognitive heuristics known ad HEAD-Modifier determining preference rules for the inheritance mechanisms of the novel concepts to be generated via commonsense rules. -/- We report the obtained results and the lessons learned of this research path in the context of model-based AI applications. -/- . (shrink)

Environmental historian Kevin Armitage’s new book offers welcome relief to readers grown weary of anthropocentrism versus nonanthropecentrism debates and Muir-Pinchot-Leopold “third way” arguments. It will also find a receptive audience among those who have maintained all along that education is the key to addressing our environmental woes. In the United States, environmental education has a vibrant history. During the late nineteenth and early twentieth century, a critical mass of policy makers, educators, scientists, and philosophers shared the belief that a curriculum (...) based on the careful observation and study of nature should be taught in primary and secondary school classrooms. The “nature study movement,” as it was called, advanced an ambitious agenda for education reform based on a simple theory: children who develop a deep and abiding interest in the natural world mature into environmentally conscious adults and good citizens. Organized thematically, Armitage’s book lays out the meaning of nature study as well as its scientific and sentimental interpretations (introduction and chap. 1), the influence of progressive education on nature study (chap. 2), the connection between recapitulation theory and nature study (chap. 3), nature study and bird conservation (chap. 4), school gardening as an extension of nature study (chap. 5), the growth of nature photography in tandem with nature study (chap. 6), and finally nature study’s role in promoting agricultural reform (chap. 7). In case the significance of this progressive-era movement is still in doubt, the movement’s legacy can still be felt, Armitage contends, in the ideas of perhaps two of the most influential environmental thinkers of the past century: Aldo Leopold and Rachel Carson (conclusion). (shrink)

Hartry Field argues that conservative rather than true mathematical sentences facilitate deductions in nominalist (i.e., abstracta-free) science without prejudging its empirical outcomes. In this paper, I identify one branch of mathematics as nonconservative, for its indispensable role in enabling nominalist language about a fundamental scientific property, in a fictional scientific community. The fundamental property is electromagnetic reflectance, and the mathematics is Fourier analysis, which renders reflectance ascribable, and nominalist reflectance claims utterable, by this community. Using a recent characterization of (...) conservativeness by Kenneth Boyce, I argue that infinitudes can be rendered inherently mathematical and non-nominalizable in the fictional community, and that rendering infinitudes inherently mathematical for all real communities would yield a convincing counterexample to Fieldian conservativeness. (shrink)

An increasing number of scholars at the intersection of feminist philosophy and critical disability studies have turned to Merleau-Ponty to develop phenomenologies of disability or of what, following Rosemarie Garland-Thomson, I call "non-normate" embodiment. These studies buck the historical trend of philosophers employing disability as an example of deficiency or harm, a mere litmus test for normative theories, or an umbrella term for aphenotypical bodily variation. While a Merleau-Pontian-inspired phenomenology is a promising starting point for thinking about embodied experiences of (...) all sorts, I here draw a cautionary tale about how ableist assumptions can easily undermine accounts of non-normate experience. I first argue that the omission or misguided treatment of disability within the history of philosophy in general and the phenomenological tradition in particular is due to the inheritance of what I call “the ableist conflation” of disability with pain, suffering, and disadvantage. I then show that Merleau-Ponty’s famous reading of the blind man’s cane is problematic insofar as it omits the social dimensions of disabled experiences, misconstrues the radicality of blindness as a world-creating disability, and operates via an able-bodied simulation that confuses object annexation or extension with incorporation. In closing, I contend that if phenomenology is to overcome the errors of traditional philosophy, as Merleau-Ponty once hoped, it must heed the insights of “crip” or non-normate phenomenology, which takes the lived experience of disability as its point of departure. [French translation forthcoming in Pour une phénoménologie critique, ed. Donald A. Landes, Quebec City, Les Presses de l'Université Laval/Paris, J.Vrin]. (shrink)

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...) for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (shrink)

The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping (...) theories of semantics, the usual account for the possibility of non intentional semantics, doesn’t seem able to account for the indefinitely extensible productivity of natural language. (shrink)

Quasi-Nelson logic (QNL) was recently introduced as a common generalisation of intuitionistic logic and Nelson's constructive logic with strong negation. Viewed as a substructural logic, QNL is the axiomatic extension of the Full Lambek Calculus with Exchange and Weakening by the Nelson axiom, and its algebraic counterpart is a variety of residuated lattices called quasi-Nelson algebras. Nelson's logic, in turn, may be obtained as the axiomatic extension of QNL by the double negation (or involutivity) axiom, and intuitionistic logic (...) as the extension of QNL by the contraction axiom. A recent series of papers by the author and collaborators initiated the study of fragments of QNL, which correspond to subreducts of quasi-Nelson algebras. In the present paper we focus on fragments that contain the connectives forming a residuated pair (the monoid conjunction and the so-called strong Nelson implication), these being the most interesting ones from a substructural logic perspective. We provide quasi-equational (whenever possible, equational) axiomatisations for the corresponding classes of algebras, obtain twist representations for them, study their congruence properties and take a look at a few notable subvarieties. Our results specialise to the involutive case, yielding characterisations of the corresponding fragments of Nelson's logic and their algebraic counterparts. (shrink)

James Sterba describes the egoist as thinking only egoist reasons decide the rationality of choices of action, the altruist, only altruistic reasons, that each in effect begs the question of what reasons there are against the other, and that the only non-question-begging and therefore rationally defensible position in this controversy is the middle-ground position that high-ranking egoistic reasons should trump low ranking-altruistic considerations and vice versa, this position being co-extensive with morality. Therefore it is rationally obligatory choose morally. I object (...) that the mere fact that a position is intermediate between two extremes does not mean it isn’t question-begging; that Sterba’s style of argument could be used to prove anything and therefore proves nothing; that it can be used to prove obvious falsehoods and therefore doesn’t necessarily track the truth; that it can be used to prove the truth of contingent, empirically obvious falsehoods when, since it is necessary a prior that one ought to be moral, something can be a good argument for the rationality of morality only if the argument’s style would entail only truths necessary a priori; that Sterba’s argument cannot inherit plausibility from what Sterba describes as the decision theoretic idea that when choosing among options where we have no evidence that one is more appropriate than the other, we must treat them as equally choice-worthy, since there is no such idea in decision theory, and shouldn’t be (for when, for example, there is no evidence that x exists and no evidence that x does not exist, one should believe that x does not exist; one should not chose as if x’s existence and non-existence were equally likely); that Sterba’s argument style is not analogous to the compromise strategies recommended in bargaining theory, nor in negotiating situations (although it would profit Sterba to consider David Gauthier’s approach in seeking to demonstrate that morality is both a middle ground between egoism and altruism, and is rationally obligatory); that it is problematic to see egoistic and altruistic reasons as commensurable and therefore admitting of a middle ground, especially a unique middle ground; that in any case, egoistic and altruistic reasons are not exhaustive of the reasons there could be; that the only sense in which moving to middle ground results in the parties not begging the question against each other is that it means they would be agreeing with each other and therefore not holding positions against each other, whether question-beggingly or otherwise, a fact which offers neither any rationally compelling reason to move her position closer to that of the other (for how can the mere fact that if we agreed we wouldn’t be begging the question against each other be a reason to agree?); and that even if morality is both rationally obligatory and a middle ground between egoism and altruism, it won’t be in any interesting sense true that this holds because the alternative would be question-begging, which means that analyzing the basis of the rationality of morality as being found in this principle of argumentation theory misconceives the nature of morality. (shrink)