According to the iterative conception of set, sets are formed in stages. According to the purely iterative conception of set, sets are formed by iterated application of a set-of operation. The cumulative hierarchy is a mathematical realization of the iterative conception of set. A mathematical realization of the purely iterative conception can be found in Peter Aczel’s type-theoretic model of constructive set theory. I will explain Aczel’s model construction in a way that (...) presupposes no previous familiarity with the theories on which it is based. (shrink)

According to the iterative conception of set, each set is a collection of sets formed prior to it. The notion of priority here plays an essential role in explanations of why contradiction-inducing sets, such as the Russell set, do not exist. Consequently, these explanations are successful only to the extent that a satisfactory priority relation is made out. I argue that attempts to do this have fallen short: understanding priority in a straightforwardly constructivist sense threatens the coherence of (...) the empty set and raises serious epistemological concerns; but the leading realist interpretations---ontological and modal interpretations of priority---are deeply problematic as well. I conclude that the purported explanatory virtues of the iterative conception are, at present, unfounded. (shrink)

Hilary Putnam once suggested that “the actual existence of sets as ‘intangible objects’ suffers… from a generalization of a problem first pointed out by Paul Benacerraf… are sets a kind of function or are functions a sort of set?” Sadly, he did not elaborate; my aim, here, is to do so on his behalf. There are well-known methods for treating sets as functions and functions as sets. But these do not raise any obvious philosophical or foundational puzzles. For that, we (...) first need to provide a full-fledged function theory. I supply such a theory: it axiomatizes the iterative notion of function in exactly the same sense that ZF axiomatizes the iterative notion of set. Indeed, this function theory is synonymous with ZF. It might seem that set theory and function theory present us with rival foundations for mathematics, since they postulate different ontologies. But appearances are deceptive. Set theory and function theory provide the very same judicial foundation for mathematics. They do not supply rival metaphysical foundations; indeed, if they supply metaphysical foundations at all, then they supply the very same metaphysical foundations. (shrink)

The iterative conception of set is typically considered to provide the intuitive underpinnings for ZFCU (ZFC+Urelements). It is an easy theorem of ZFCU that all sets have a definite cardinality. But the iterative conception seems to be entirely consistent with the existence of “wide” sets, sets (of, in particular, urelements) that are larger than any cardinal. This paper diagnoses the source of the apparent disconnect here and proposes modifications of the Replacement and Powerset axioms so as (...) to allow for the existence of wide sets. Drawing upon Cantor’s notion of the absolute infinite, the paper argues that the modifications are warranted and preserve a robust iterative conception of set. The resulting theory is proved consistent relative to ZFC + “there exists an inaccessible cardinal number.”. (shrink)

Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands). -/- By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any (...) loosely constructive way of fleshing out this idea is synonymous with a ZF-like theory. -/- This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974). (shrink)

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...) on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. -/- I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected. (shrink)

This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.

Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended (...) in particular ways) face complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology. (shrink)

The Hyperuniverse Programme, introduced in Arrigoni and Friedman (2013), fosters the search for new set-theoretic axioms. In this paper, we present the procedure envisaged by the programme to find new axioms and the conceptual framework behind it. The procedure comes in several steps. Intrinsically motivated axioms are those statements which are suggested by the standard concept of set, i.e. the `maximal iterative concept', and the programme identi fies higher-order statements motivated by the maximal iterative concept. The satisfaction of (...) these statements (H-axioms) in countable transitive models, the collection of which constitutes the `hyperuniverse' (H), has remarkable 1st-order consequences, some of which we review in section 5. (shrink)

The Forrest-Armstrong argument, as reconfigured by David Lewis, is a reductio against an unrestricted principle of recombination. There is a gap in the argument which Lewis thought could be bridged by an appeal to recombination. After presenting the argument, I show that no plausible principle of recombination can bridge the gap. But other plausible principles of plenitude can bridge the gap, both principles of plenitude for world contents and principles of plenitude for world structures. I conclude that the Forrest-Armstrong argument, (...) when fortified in one of these ways, demands that unrestricted recombination be rejected. The appropriate restriction comes from a consideration of what world structures are possible. I argue that, although there are too many worlds to form a set, for any world, the individuals at that world do form a set. To defend it I invoke a principle of Limitation of Size together with an iterative conception of structure. (shrink)

In the late 1940s and early 1950s Lorenzen developed his operative logic and mathematics, a form of constructive mathematics. Nowadays this is mostly seen as the precursor to the more well-known dialogical logic and one could assumed that the same philosophical motivations were present in both works. However we want to show that this is not always the case. In particular, we claim, that Lorenzen’s well-known rejection of the actual infinite as stated in Lorenzen (1957) was not a major motivation (...) for operative logic and mathematics. In this article, we claim that this is in fact not the case. Rather, we argue for a shift that happened in Lorenzen’s treatment of the infinite from the early to the late 1950s. His early motivation for the development of operativism is concerned with a critique of the Cantorian notion of set and related questions about the notion of countability and uncountability; only later, his motivation switches to focusing on the concept of infinity and the debate about actual and potential infinity. (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)

Inductively defined structures are ubiquitous in mathematics; their specification is unambiguous and their properties are powerful. All fields of mathematical logic feature these structures prominently: the formula of a language, the set of theorems, the natural numbers, the primitive recursive functions, the constructive number classes and segments of the cumulative hierarchy of sets. -/- This dissertation gives a mathematical characterization of a species of inductively defined structures, called accessible domains, which include all of the above examples except the set of (...) theorems. The concept of an accessible domain comes from Wilfried Sieg's analysis of proof-theoretic practices, starting with his dissertation. In particular, he noticed the special epistemological character of elements of an accessible domain: they can always be uniquely identified with their build-up. Generally, the unique build-up of elements justifies the principles of induction and recursion. -/- I use category theory to give an abstract characterization of accessible domains. I claim that accessible domains are all instances of initial algebras for endofunctors. Grounded in the historical roots of Sieg's discussions, this dissertation shows how the properties of initial algebras for endofunctors and accessible domains coincide in a satisfying and natural way. -/- Filling out this characterization, I show how important examples of accessible domains fit into this broad characterization. I first characterize some accessible domains by relatively simple functors (e.g. finite, polynomial, those that preserve certain colimits) where we can see how iterating the functor can produce the accessible domain. Then I describe accessible domains that result from more involved specifications (e.g. ordinals and segments of the cumulative hierarchies associated with CZF, IZF, and ZF) by relying heavily on algebraic set theory. I end with a discussion of some of the methodological features of category theory in particular that helped characterize accessible domains. (shrink)

Individuals with high self-concept will likely have high life satisfaction, they easily get adjusted to life, and they communicate their feeling more appropriately. However, it was not certain whether self-concept would decline or improve as individuals age, or whether self-concept would vary between genders and ethnic groups. To prove, a study was carried out to compare the self-concept of college students in an Asian context. The inquiry utilized the cross-sectional design in finding out significant differences in the self-concept of participants (...) in terms of age, gender, and ethnicity. A 22-item questionnaire was adapted and administered to 222 Bachelor of Public Administration and Bachelor of Science in Business Administration students from the satellite campus of Bukidnon State University in the Philippines. Initially, a sample was randomly drawn from the population. During the actual data collection, the researchers had difficulty getting the responses from the randomly selected individuals due to internet connection and it was done amidst a pandemic. Instead, it took all responses from those who were available, have access to the internet, and could accomplish the google forms. The data were analyzed using Mean, Standard Deviation, T-test for independent sample, ANOVA and Post Hoc test. The results revealed that college students at the locale have a high level of self-concept in self-fulfilment, emotional adjustment, and honesty. Yet, they only had a moderate level of self-concept in autonomy. Further, there were significant differences in college students’ autonomy and honesty in terms of age and gender. Furthermore, there were significant differences in their emotional adjustment and self-fulfilment as to their ethnicity. The results have implications for instruction, administration, guidance services, and future research. (shrink)

continent. 1.1 : 3-13. / 0/ – Introduction I want to propose, as a trajectory into the philosophically weird, an absurd theoretical claim and pursue it, or perhaps more accurately, construct it as I point to it, collecting the ground work behind me like the Perpetual Train from China Mieville's Iron Council which puts down track as it moves reclaiming it along the way. The strange trajectory is the following: Kant's critical philosophy and much of continental philosophy which has followed, (...) has been a defense against horror and madness. Kant's prohibition on speculative metaphysics such as dogmatic metaphysics and transcendental realism, on thinking beyond the imposition of transcendental and moral constraints, has been challenged by numerous figures proceeding him. One of the more interesting critiques of Kant comes from the mad black Deleuzianism of Nick Land stating, “Kant’s critical philosophy is the most elaborate fit of panic in the history of the Earth.” And while Alain Badiou would certainly be opposed to the libidinal investments of Land's Deleuzo-Guattarian thought, he is likewise critical of Kant's normative thought-bureaucracies: Kant is the one author for whom I cannot feel any kinship. Everything in him exasperates me, above all his legalism—always asking Quid Juris? Or ‘Haven’t you crossed the limit?’—combined, as in today’s United States, with a religiosity that is all the more dismal in that it is both omnipresent and vague. The critical machinery he set up has enduringly poisoned philosophy, while giving great succour to the academy, which loves nothing more than to rap the knuckles of the overambitious [….] That is how I understand the truth of Monique David-Menard’s reflections on the properly psychotic origins of Kantianism. I am persuaded that the whole of the critical enterprise is set up to to shield against the tempting symptom represented by the seer Swedenborg, or against ‘diseases of the head’, as Kant puts it. An entire nexus of the limits of reason and philosophy are set up here, namely that the critical philosophy not only defends thought from madness, philosophy from madness, and philosophy from itself, but that philosophy following the advent of the critical enterprise philosophy becomes auto-vampiric; feeding on itself to support the academy. Following Francois Laruelle's non-philosophical indictment of philosophy, we could go one step further and say that philosophy operates on the material of what is philosophizable and not the material of the external world. [1] Beyond this, the Kantian scheme of nestling human thinking between our limited empirical powers and transcendental guarantees of categorical coherence, forms of thinking which stretch beyond either appear illegitimate, thereby liquefying both pre-critical metaphysics and the ravings of the mad in the same critical acid. In rejecting the Kantian apparatus we are left with two entities – an unsure relation of thought to reality where thought is susceptible to internal and external breakdown and a reality with an uncertain sense of stability. These two strands will be pursued, against the sane-seal of post-Kantian philosophy by engaging the work of weird fiction authors H.P. Lovecraft and Thomas Ligotti. The absolute inhumanism of the formers universe will be used to describe a Shoggothic Materialism while the dream worlds of the latter will articulate the mad speculation of a Ventriloquil Idealism. But first we must address the relation of philosophy to madness as well as philosophy to weird fiction. /1/ – Philosophy and Madness There is nothing that the madness of men invents which is not either nature made manifest or nature restored. Michel Foucault. Madness and Civilization. The moment I doubt whether an event that I recall actually took place, I bring the suspicion of madness upon myself: unless I am uncertain as to whether it was not a mere dream. Arthur Schopenhauer. The World as Will and Idea, Vol. 3. Madness is commonly thought of as moving through several well known cultural-historical shifts from madness as a demonic or otherwise theological force, to rationalization, to medicalization psychiatric and otherwise. Foucault's Madness and Civilization is well known for orientating madness as a form of exclusionary social control which operated by demarcating madness from reason. Yet Foucault points to the possibility of madness as the necessity of nature at least prior to the crushing weight of the church. Kant’s philosophy as a response to madness is grounded by his humanizing of madness itself. As Adrian Johnston points out in the early pages of Time Driven pre-Kantian madness meant humans were seized by demonic or angelic forces whereas Kantian madness became one of being too human. Madness becomes internalized, the external demonic forces become flaws of the individual mind. Foucault argues that, while madness is de-demonized it is also dehumanized during the Renaissance, as madmen become creatures neither diabolic nor totally human reduced to the zero degree of humanity. It is immediately clear why for Kant, speculative metaphysics must be curbed – with the problem of internal madness and without the external safeguards of transcendental conditions, there is nothing to formally separate the speculative capacities for metaphysical diagnosis from the mad ramblings of the insane mind – both equally fall outside the realm of practicality and quotidian experience. David-Menard's work is particularly useful in diagnosing the relation of thought and madness in Kant's texts. David-Menard argues that in Kant's relatively unknown “An Essay on the Maladies of the Mind” as well as his later discussion of the Seer of Swedenborg, that Kant formulates madness primarily in terms of sensory upheaval or other hallucinatory theaters. She writes: “madness is an organization of thought. It is made possible by the ambiguity of the normal relation between the imaginary and the perceived, whether this pertains to the order of sensation or to the relations between our ideas” Kant's fascination with the Seer forces Kant between the pincers of “aesthetic reconciliation” – namely melancholic withdrawal – and “a philosophical invention” – namely the critical project. Deleuze and Guattari's schizoanalysis is a combination and reversal of Kant's split, where an aesthetic over engagement with the world entails prolific conceptual invention. Their embrace of madness, however, is of course itself conceptual despite all their rhizomatic maneuvers. Though they move with the energy of madness, Deleuze and Guattari save the capacity of thought from the fangs of insanity by imbuing materiality itself with the capacity for thought. Or, as Ray Brassier puts it, “Deleuze insists, it is necessary to absolutize the immanence of this world in such a way as to dissolve the transcendent disjunction between things as we know them and as they are in themselves”. That is, whereas Kant relied on the faculty of judgment to divide representation from objectivity Deleuze attempts to flatten the whole economy beneath the juggernaut of ontological univocity. Speculation, as a particularly useful form of madness, might fall close to Deleuze and Guattari’s shaping of philosophy into a concept producing machine but is different in that it is potentially self destructive – less reliant on the stability of its own concepts and more adherent to exposing a particular horrifying swath of reality. Speculative madness is always a potential disaster in that it acknowledges little more than its own speculative power with the hope that the gibbering of at least a handful of hysterical brains will be useful. Pre-critical metaphysics amounts to madness, though this may be because the world itself is mad while new attempts at speculative metaphysics, at post-Kantian pre-critical metaphysics, are well aware of our own madness. Without the sobriety of the principle of sufficient reason we have a world of neon madness: “we would have to conceive what our life would be if all the movements of the earth, all the noises of the earth, all the smells, the tastes, all the light – of the earth and elsewhere, came to us in a moment, in an instant – like an atrocious screaming tumult of things”. Speculative thought may be participatory in the screaming tumult of the world or, worse yet, may produce its spectral double. Against theology or reason or simply commonsense, the speculative becomes heretical. Speculation, as the cognitive extension of the horrorific sublime should be met with melancholic detachment. Whereas Kant's theoretical invention, or productivity of thought, is self -sabotaging, since the advent of the critical project is a productivity of thought which then delimits the engine of thought at large either in dogmatic gestures or non-systematizable empirical wondrousness. The former is celebrated by the fiction of Thomas Ligotti whereas the latter is espoused by the tales of H.P. Lovecraft. /2/ – Weird Fiction and Philosophy. Supernatural horror, in all its eerie constructions, enables a reader to taste treats inconsistent with his personal welfare. Thomas Ligotti Songs of a Dead Dreamer. I choose weird stories because they suit my inclination best—one of my strongest and most persistent wishes being to achieve,momentarily, the illusion of some strange suspension or violation of the galling limitations of time, space, and natural law which forever imprison us and frustrate our curiosity about the infinite cosmic spaces beyond the radius of our sight and analysis H.P. Lovecraft. “Notes on Writing Weird Fiction” Lovecraft states that his creation of a story is to suspend natural law yet, at the same time, he indexes the tenuousness of such laws, suggesting the vast possibilities of the cosmic. The tension that Lovecraft sets up between his own fictions and the universe or nature is reproduced within his fictions in the common theme of the unreliable narrator; unreliable precisely because they are either mad or what they have witnessed questions the bounds of material reality. In “The Call of Cthulhu” Lovecraft writes: The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age. Despite Lovecraft's invocations of illusion, he is not claiming that his fantastic creations such as the Old Ones are supernatural but, following Joshi, are only ever supernormal. One can immediately see that instead of nullifying realism Lovecraft in fact opens up the real to an unbearable degree. In various letters and non-fictional statements Lovecraft espoused strictly materialist tenets, ones which he borrowed from Hugh Elliot namely the uniformity of law, the denial of teleology and the denial of non-material existence. Lovecraft seeks to explore the possibilities of such a universe by piling horror upon horror until the fragile brain which attempts to grasp it fractures. This may be why philosophy has largely ignored weird fiction – while Deleuze and Guattari mark the turn towards weird fiction and Lovecraft in particular, with the precursors to speculative realism as well as contemporary related thinkers have begun to view Lovecraft as making philosophical contributions. Lovecraft's own relation to philosophy is largely critical while celebrating Nietzsche and Schopenhauer. This relationship of Lovecraft to philosophy and philosophy to Lovecraft is coupled with Lovecraft's habit of mercilessly destroying the philosopher and the figure of the academic more generally in his work, a destruction which is both an epistemological destruction and an ontological destruction. Thomas Ligotti's weird fiction which he has designated as a kind of “confrontational escapism” might be best described in the following quote from one of his shortstories, “The human phenomenon is but the sum of densely coiled layers of illusion each of which winds itself on the supreme insanity. That there are persons of any kind when all there can be is mindless mirrors laughing and screaming as they parade about in an endless dream”. Whereas Lovecraft's weirdness draws predominantly from the abyssal depths of the uncharted universe, Ligotti's existential horror focuses on the awful proliferation of meaningless surfaces that is, the banal and every day function of representation. In an interview, Ligotti states: We don't even know what the world is like except through our sense organs, which are provably inadequate. It's no less the case with our brains. Our whole lives are motored along by forces we cannot know and perceptions that are faulty. We sometimes hear people say that they're not feeling themselves. Well, who or what do they feel like then? This is not to say that Ligotti sees nothing beneath the surface but that there is only darkness or blackness behind it, whether that surface is on the cosmological level or the personal. By addressing the implicit and explicit philosophical issues in Ligotti's work we will see that his nightmarish take on reality is a form of malevolent idealism, an idealism which is grounded in a real, albeit dark and obscure materiality. If Ligotti's horrors ultimately circle around mad perceptions which degrade the subject, it takes aim at the vast majority of the focus of continental philosophy. While Lovecraft's acidic materialism clearly assaults any romantic concept of being from the outside, Ligotti attacks consciousness from the inside: Just a little doubt slipped into the mind, a little trickle of suspicion in the bloodstream, and all those eyes of ours, one by one, open up to the world and see its horror [...] Not even the solar brilliance of a summer day will harbor you from horror. For horror eats the light and digests it into darkness. Clearly, the weird fiction of Lovecraft and Ligotti amount to a anti-anthrocentric onslaught against the ramparts of correlationist continental philosophy. /3/ – Shoggothic Materialism or the Formless Formless protoplasm able to mock and reflect all forms and organs and processes—viscous agglutinations of bubbling cells—rubbery fifteen-foot spheroids infinitely plastic and ductile—slaves of suggestion, builders of cities—more and more sullen, more and more intelligent, more and more amphibious, more and more imitative—Great God! What madness made even those blasphemous Old Ones willing to use and to carve such things? H.P. Lovecraft. “At the Mountains of Madness” On the other hand, affirming that the universe resembles nothing and is only formless amounts to saying that the universe is something like a spider or spit. Georges Bataille. “Formless”. The Shoggoths feature most prominently in H.P. Lovecraft's shortstory “At the Mountains of Madness” where they are described in the following manner: It was a terrible, indescribable thing vaster than any subway train – a shapeless congeries of protoplasmic bubbles, faintly self -luminous, and with myriads of temporary eyes forming and un-forming as pustules of greenish light all over the tunnel-filling front that bore down upon us, crushing the frantic penguins and slithering over the glistening floor that it and its kind had swept so evilly free of all litter. The term is a litmus test for materialism itself as the Shoggoth is an amorphous creature. The Shoggoths were living digging machines bio engineered by the Elder Things, and their protoplasmic bodies being formed into various tools by their hypnotic powers. The Shoggoths eventually became self aware and rose up against their masters in an ultimately failed rebellion. After the Elder Ones retreated into the oceans leaving the Shoggoths to roam the frozen wastes of the Antarctic. The onto-genesis of the Shoggoths and their gross materiality, index the horrifyingly deep time of the earth a concept near and dear to Lovecraft's formulation of horror as well as the fear of intelligences far beyond, and far before, the ascent of humankind on earth and elsewhere. The sickly amorphous nature of the Shoggoths invade materialism at large, where while materiality is unmistakably real ie not discursive, psychological, or otherwise overly subjectivist, it questions the relation of materialism to life. As Eugene Thacker writes: The Shoggoths or Elder Things do not even share the same reality with the human beings who encounter them—and yet this encounter takes place, though in a strange no-place that is neither quite that of the phenomenal world of the human subject or the noumenal world of an external reality. Amorphous yet definitively material beings are a constant in Lovecraft's tales. In his tale “The Dream-Quest of Unknown Kadatth” Lovecraft describes Azathoth as, “that shocking final peril which gibbers unmentionably outside the ordered universe,” that, “last amorphous blight of nethermost confusion which blashphemes and bubbles at the centre of all infinity,” who, “gnaws hungrily in inconceivable, unlighted chambers beyond time”. Azathoth's name may have multiple origins but the most striking is the alchemy term azoth which is both a cohesive agent and a acidic creation pointing back to the generative and the decayed. The indistinction of generation and degradation materially mirrors the blur between the natural and the unnatural as well as life and non-life. Lovecraft speaks of the tension between the natural and the unnatural is his short story “The Unnameable.” He writes, “if the psychic emanations of human creatures be grotesque distortions, what coherent representation could express or portray so gibbous and infamous a nebulousity as the spectre of a malign, chaotic perversion, itself a morbid blasphemy against Nature?”. Lovecraft explores exactly the tension outlined at the beginning of this chapter, between life and thought. At the end of his short tale Lovecraft compounds the problem as the unnameable is described as “a gelatin—a slime—yet it had shapes, a thousand shapes of horror beyond all memory”. Deleuze suggests that becoming-animal is operative throughout Lovecraft's work, where narrators feel themselves reeling at their becoming non-human or of being the anomalous or of becoming atomized. Following Eugene Thacker however, it may be far more accurate to say that Lovecraft's tales exhibit not a becoming-animal but a becoming-creature. Where the monstrous breaks the purportedly fixed laws of nature, the creature is far more ontologically ambiguous. The nameless thing is an altogether different horizon for thought. The creature is either less than animal or more than animal – its becoming is too strange for animal categories and indexes the slow march of thought towards the bizarre. This strangeness is, as aways, some indefinite swirling in the category of immanence and becoming. Bataille begins “The Labyrinth” with the assertion that being, to continue to be, is becoming. More becoming means more being hence the assertion that Bataille's barking dog is more than the sponge. This would mean that the Shoggotth is altogether too much being, too much material in the materialism. Bataille suggests that there is an immanence between the eater and the eaten, across the species and never within them. That is, despite the chaotic storm of immanence there must remain some capacity to distinguish the gradients of becoming without reliance upon, or at least total dependence upon, the powers of intellection to parse the universe into recognizable bits, properly digestible factoids. That is, if we undo Deleuze's aforementioned valorization of sense which, for his variation of materialism, performed the work of the transcendental, but refuse to reinstate Kant's transcendental disjunction between thing and appearance, then it must be a quality of becoming-as-being itself which can account for the discernible nature of things by sense. In an interview with Peter Gratton, Jane Bennett formulates the problem thusly: What is this strange systematicity proper to a world of Becoming? What, for example, initiates this congealing that will undo itself? Is it possible to identify phases within this formativity, plateaus of differentiation? If so, do the phases/plateaus follow a temporal sequence? Or, does the process of formation inside Becoming require us to theorize a non-chronological kind of time? I think that your student’s question: “How can we account for something like iterable structures in an assemblage theory?” is exactly the right question. Philosophy has erred too far on the side of the subject in the subject-object relation and has furthermore, lost the very weirdness of the non-human. Beyond this, the madness of thought need not override. /4/ - Ventriloquial Idealism or the Externality of Thought My aim is the opposite of Lovecraft's. He had an appreciation for natural scenery on earth and wanted to reach beyond the visible in the universe. I have no appreciation for natural scenery and want the objective universe to be a reflection of a character. Thomas Ligotti. “Devotees of Decay and Desolation.” Unless life is a dream, nothing makes sense. For as a reality, it is a rank failure [….] Horror is more real than we are. Thomas Ligotti. “Professor Nobody's Little Lectures on Supernatural Horror”. Thomas Ligotti's tales are rife with mannequins, puppets, and other brainless entities which of replace the valorized subject of philosophy – that of the free thinking human being. His tales such as “The Dream of the Manikin” aim to destroy the rootedness of consciousness. James Trafford has connected the anti-egoism of Ligotti to Thomas Metzinger – where the self is at best an illusion and we plead desperately for someone else to acknowledge that we are real. Trafford has stated it thus, “Life is played out as an inescapable puppet show, an endless dream in which the puppets are generally unaware that they are trapped within a mesmeric dance of whose mechanisms they know nothing and over which they have no control”. An absolute materialism, for Ligotti, implies an alienation of the idea which leads to a ventriloquil idealism. As Ligotti notes in an interview, “the fiasco and nightmare of existence, the particular fiasco and nightmare of human existence, the sense that people are puppets of powers they cannot comprehend, etc.” And then further elaborates that,“[a]ssuming that anything has to exist, my perfect world would be one in which everyone has experienced the annulment of his or her ego. That is, our consciousness of ourselves as unique individuals would entirely disappear”. The externality of the idea leads to the unfortunate consequence of consciousness eating at itself through horror which, for Ligotti, is more real than reality and goes beyond horror-as-affect. Beyond this, taking together with the unreality of life and the ventriloquizing of subjectivity, Ligotti's thought becomes an idealism in which thought itself is alien and ultimately horrifying. The role of human thought and the relation of non-relation of horror to thought is not completely clear in Ligotti's The Conspiracy Against the Human Race. Ligotti argues in his The Conspiracy Against the Human Race,that the advent of thought is a mistake of nature and that horror is being in the sense that horror results from knowing too much. Yet, at the same time, Ligotti seems to suggest that thought separates us from nature whereas, for Lovecraft, thought is far less privileged – mind is just another manifestation of the vital principal, it is just another materialization of energy. In his brilliant “Prospects for Post-Copernican Dogmatism” Iain Grant rallies against the negative definition of dogmatism and the transcendental, and suggests that negatively defining both over-focuses on conditions of access and subjectivism at the expense of the real or nature. With Schelling, who is Grant's champion against the subjectivist bastions of both Fichte and Kant, Ligotti's idealism could be taken as a transcendental realism following from an ontological realism. Yet the transcendental status of Ligotti's thought move towards a treatment of the transcendental which may threaten to leave beyond its realist ground. Ligotti states: Belief in the supernatural is only superstition. That said, a sense of the supernatural, as Conrad evidenced in Heart of Darkness, must be admitted if one's inclination is to go to the limits of horror. It is the sense of what should not be- the sense of being ravaged by the impossible. Phenomenally speaking, the super-natural may be regarded as the metaphysical counterpart of insanity, a transcendental correlative of a mind that has been driven mad. Again, Ligotti equates madness with thought, qualifying both as supernatural while remaining less emphatic about the metaphysical dimensions of horror. The question becomes one of how exactly the hallucinatory realm of the ideal relates to the black churning matter of Lovecraft's chaos of elementary particles. In his tale “I Have a Special Plan for This World” Ligotti formulates thus: A: There is no grand scheme of things. B: If there were a grand scheme of things, the fact – the fact – that we are not equipped to perceive it, either by natural or supernatural means, is a nightmarish obscenity. C: The very notion of a grand scheme of things is a nightmarish obscenity. Here Ligotti is not discounting metaphysics but implying that if it does exist the fact that we are phenomenologically ill-equipped to perceive that it is nightmarish. For Ligotti, nightmare and horror occur within the circuit of consciousness whereas for Lovecraft the relation between reality and mind is less productive on the side of mind. It is easier to ascertain how the Kantian philosophy is a defense against the diseases of the head as Kant armors his critical enterprise from too much of the world and too much of the mind. The weird fiction of both Lovecraft and Ligotti demonstrates that there is too much of both feeding into one another in a way that corrodes the Kantian schema throughly, breaking it down into a dead but still ontologically potentiated nigredo. The haunting, terrifying fact of Ligotti's idealism is that the transcendental motion which brought thought to matter, while throughly material and naturalized, brings with it the horror that thought cannot be undone without ending the material that bears it either locally or completely. Thought comes from an elsewhere and an elsewhen being-in-thought. The unthinkable outside thought is as maddening as the unthought engine of thought itself within thought which doesn't exist except for the mind, the rotting décor of the brain. /5/ - Hyperstitional Transcendental Paranoia or Self -Expelled Thought Weird fiction has been given some direct treatment in philosophy in the mad black Deleuzianism of Nick Land. Nick Land along with others in the 1990s created the Cyber Culture Research Unit as well as the research group Hyperstition. The now defunct hyperstitional website, an outgrowth of the Cyber Culture Research Unit, defined hyperstition in the following fourfold: 1-Element of effective culture that makes itself real. 2-Fictional quantity functional as a time-traveling device. 3-Coincidence intensifier. 4-Call to the Old Ones. The distinctively Lovecraftian character of hyperstition is hard to miss as is its Deleuzo-Guattarian roots. In the opening pages of A Thousand Plateaus Deleuze and Guattari write, “We have been criticized for over-quoting literary authors. But when one writes, the only question is which other machine the literary machine can be plugged into”. The indisinction of literature and philosophy mirrors the mess of being and knowing as post-correlationist philosophy, where philosophy tries to make itself real where literature, especially the weird, aims itself at the brain-circuit of horror. The texts of both Lovecraft and Ligotti work through horror as epistemological plasticity meeting with proximity as well as the deep time of Lovecraft and the glacially slow time of paranoia in Ligotti. Against Deleuze, and following Brassier, we cannot allow the time of consciousness, the Bergsonian time of the duree, to override natural time, but instead acknowledge that it is an unfortunate fact of existence as a thinking being. Horror-time, the time of consciousness, with all its punctuated moments and drawn out terrors, cannot compare to the deep time of non-existence both in the unreachable past and the unknown future. The crystalline cogs of Kant's account of experience as the leading light for the possibility of metaphysics must be throughly obliterated. His gloss of experience in Prolegomena to any Future Metaphysics could not be more sterile: Experience consists of intuitions, which belong to the sensibility, and of judgments, which are entirely a work of the understanding. But the judgments which the understanding makes entirely out of sensuous intuitions are far from being judgments of experience. For in the one case the judgment connects only the perceptions as they are given in sensuous intuition [....] Experience consists in the synthetic connection of appearances in consciousness, so far as this connection is necessary. Here it is difficult to dismiss the queasiness that Kant's legalism induces upon sight for both Badiou and David-Menard. Kant's thought becomes, as Foucault says when reflecting on Sade's text in relation to nature, “the savage abolition of itself”. For Badiou, Kant's philosophy simply closes off too much of the outside, freezing the world of thought in an all too limited formalism. Critical philosophy is simply the systematized quarantine on future thinking, on thinking which would threaten the formalism which artificially grants thought its own coherency in the face of madness. Even the becoming-mad of Deleuze, while escaping the rumbling ground, makes grounds for itself, mad grounds but grounds which are thinkable in their affect. The field of effects allows for Deleuze's aesthetic and radical empiricism, in which effects and/or occasions make up the material of the world to be thought as a chaosmosis of simulacra. Given a critique of an empiricism of aesthetics, of the image, it may be difficult to justify an attack on Kantian formalism with the madness of literature, which does not aim to make itself real but which we may attempt to make real. That is, how do Lovecraft's and Ligotti's materials, as materials for philosophy to work on, differ from either the operative formalisms of Kant or the implicitly formalized images of Deleuzian empiricism? It is simply that such texts do not aim to make themselves real, and make claims to the real which are more alien to us than familiar, which is why their horror is immediately more trustworthy. This is the madness which Blanchot discusses in The Infinite Conversation through Cervantes and his knight – the madness of book-life, of the perverse unity of literature and life a discussion which culminates in the discussion of one of the weird's masters, that of Kafka. The text is the knowing of madness, since madness, in its moment of becoming-more-mad, cannot be frozen in place but by the solidifications of externalizing production. This is why Foucault ends his famous study with works of art. Furthermore extilligence, the ability to export the products of our maligned brains, is the companion of the attempts to export, or discover the possibility of intelligences outside of our heads, in order for philosophy to survive the solar catastrophe. To borrow again from Deleuze, writing is inseparable from becoming. The mistake is to believe that madness is reabsorbed by extilligence, by great works, or that it could be exorcised by the expelling of thought into the inorganic or differently organic. Going out of our heads does not guarantee we will no longer mean we cannot still go out of our minds. This is simply because of the outside, of matter, or force, or energy, or thing-in-itself, or Schopenhauerian Will. In Lovecraft’s “The Music of Erich Zahn” an “impoverished student of metaphysics” becomes intrigued by strange viol music coming from above his room. After meeting the musician the student discovers that each night he plays frantic music at a window in order to keep some horridness at bay, some “impenetrable darkness with chaos and pandemonium”. The aesthetic defenses provided by the well trained brain can bear the hex of matter for so long, the specter of unalterability within it which too many minds obliterate, collapsing everything before the thought of thought as thinkable or at least noetically mutable on our own terms. Transcendental paranoia is the concurrent nightmare and promise of Paul Humphrey's work, of being literally out of our minds. It is the gothic counterpart of thinking non-conceptually but also of thinking never belonging to any instance of purportedly solid being. As Bataille stated, “At the boundary of that which escapes cohesion, he who reflects within cohesion realizes there is no longer any room for him” Thought is immaterial only to the degree that it is inhuman, it is a power that tries, always with failure, to ascertain its own genesis. Philosophy, if it can truly return to the great outdoors, if it can leave behind the dead loop of the human skull, must recognize not only the non-priority of human thought, but that thought never belongs to the brain that thinks it, thought comes from somewhere else. To return to the train image from the beginning “a locomotive rolling on the surface of the earth is the image of continuous metamorphosis” this is the problem of thought, and of thinking thought, of being no longer able to isolate thought, with only a thought-formed structure. [1] One of the central tenets of Francois Laruelle's non-philosophy is that philosophy has traditionally operated on material already presupposed as thinkable instead of trying to think the real in itself. Philosophy, according to Laruelle, remains fixated on transcendental synthesis which shatters immanence into an empirical datum and an a prori factum which are then fused by a third thing such as the ego. For a critical account of Laruelle's non-philosophy see Ray Brassier's Nihil Unbound. (shrink)

From The Cone of Perception, volume one of my collected works, you will remember that one of the main topics in that work was V-Curvature, also called, "phenomenological velocity." In that work, although a solution to the v - curvature variable was provided as well as many graphs that yielded numerous jewels of spiral formulations in exquisite 3D color formations, that method by which the solution was found was not iterated. This chapter begins by showing how it is possible to (...) solve for something that ideally ought cancel out with itself and how, although commutation between square roots is valid, there may be room here for an alternate route of accessing a hidden dimension - that dimension we call V-Curvature, or, "Phenomenological Velocity." Herein is provided the pathway for solving for V-Curvature in terms of Csc, which can be translated into Sin and Cos functionality. Furthermore, the processing these equations through WolframAlpha yielded other insights into limits, roots, and series that logically follow. How did the solutions to the, "velocity," v - variable curvature in the Lorentz coefficient, "manifest," when the Lorentz coefficient ought cancel out with itself? The step - by - step solution below illustrates the algebraic process by which a specific solution for something that ought cancel out with itself can be found. The Sphere of Realization is a groundbreaking work of philosophical and mathematical theory. The first volume of this epic collection examines the concept of V-Curvature, or Phenomenological Velocity, using algebraic equations to explain how this phenomenon can be solved. This book goes on to explore the implications of these equations, such as limits, roots, series, and introspection into infinity, providing an alternate route for accessing a 'hidden dimension' that connects physical laws with abstract philosophical ideas. By utilizing this understanding, the author creates a platform for introspection into life and nature, and considers the philosophical implications of this perception, from the exploration of the infinity of angles to theions of time, velocity, the emergence of real numbers, and the meanings of eternity, forever, infinity, and never ending. This landmark work of mathematical exploration and philosophical discovery will challenge and expand our understanding of the universe, and invite us into a journey of introspection and understanding. An exploration of the esoteric terms therein, and the pathways they provide to access new modes of thought, will give the reader the ability to gain a greater insight into the intricacies of reality. The Sphere of Realization provides a unique and comprehensive approach to a difficult concept. Through a blend of philosophical and mathematical exploration, the author delves into the concept of V-Curvature, or Phenomenological Velocity to unlock the mysteries of "hidden dimensions" within our reality. These equations and theories allow the reader to explore angles, time, velocity, roots, series, and other related concepts. In so doing, the book offers an exciting journey into the esoteric. The author also provides insights into the emergence of real numbers from infinity, introducing concepts such as eternity, forever, and never ending in the process. A comprehensive discussion of the applicable equations and transformations, immune to the construct of time, serves as a powerful tool for unlocking a meaningful understanding of the universe. The Sphere of Realization is an opportunity to gain a deeper appreciation of the reality of our world. (shrink)

Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the (...) lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the notions of disjunction and iterated conditioning and we show that the usual probabilistic properties still hold. (shrink)

In this thesis, I develop a nonreductive and general conception of potentiality, and explore the prospects of a realist account of possibility based on this account of potentiality. Potentialities are properties of individual objects; they include dispositions such as fragility and abilities such as the ability to play the piano. Potentialities are individuated by their manifestation alone. In order to provide a unified account of potentialities, I argue in chapter 2 that dispositions, contrary to philosophical orthodoxy, are best understood (...) in terms only of their manifestations (as disposi- tions to ...), rather than in terms of a stimulus and a manifestation condition (as dispositions to ... if ...). Chapter 3 provides some preliminary motivation for a nonreductive and gen- eral account of potentiality, and chapter 4 develops such an account. The guiding question is how far the notion of potentiality can be extended from the initial ex- amples of familiar dispositions and abilities, and it is argued that it can be extended very far. Various features of potentialities are explored, among them extrinsicality, iterations of potentiality, and the behaviour of potentiality with regard to logical equivalence. In chapter 5, the account is set to work in providing the outlines and a defense of a potentiality-based account of possibility. The basic idea of such an account is that it is possible that p just in case some thing has a potentiality for p. The account is defended against the objection that there may not be enough potential- ities to ground all the possibilities that there are. Finally, in chapter 6, a logic of potentiality is formulated and the logic of possibility derived from it, showing that the potentiality-based account of possibility is formally adequate: it provides pos- sibility with the formal features that modal logicians have studied. I conclude that the proposed account of possibility is a promising research programme. (shrink)

Groove, as a musical quality, is an important part of jazz and pop music appreciative practices. Groove talk is widespread among musicians and audiences, and considerable importance is placed on generating and appreciating grooves in music. However, musicians, musicologists, and audiences use groove attributions in a variety of ways that do not track one consistent underlying concept. I argue that that there are at least two distinct concepts of groove. On one account, groove is ‘the feel of the music’ and, (...) on the other, groove is the psychological feeling (induced by music) of wanting to move one’s body. Further, I argue that recent work in music psychology shows that these two concepts do not converge on a unified set of musical features. Finally, I also argue that these two concepts play different functional roles in the appreciative practices of jazz and popular music. This should cause us to further consider the mediating role genre plays for aesthetic concepts and provides us with reason for adopting a more communitarian approach to aesthetics which is attentive to the ways in which aesthetic discourse serves the practices of different audiences. (shrink)

This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent conceptions of harmony through category (...) theory. This categorical harmony is stated in terms of adjoints and says that any concept definable by iterated adjoints from general categorical operations is harmonious. Moreover, it has been shown that identity in a categorical setting is determined by an adjoint in the relevant way. Furthermore, path induction as a rule comes from this definition. Thus we arrive at an account of how path induction, as a rule of inference governing identity, can be justified on mathematically motivated grounds. (shrink)

The concept of formal transcendentalism is utilized. The fundamental and definitive property of the totality suggests for “the totality to be all”, thus, its externality (unlike any other entity) is contained within it. This generates a fundamental (or philosophical) “doubling” of anything being referred to the totality, i.e. considered philosophically. Thus, that doubling as well as transcendentalism underlying it can be interpreted formally as an elementary choice such as a bit of information and a quantity corresponding to the number of (...) elementary choices to be defined. This is the quantity of information defined both transcendentally and formally and thus, philosophically and mathematically. If one defines information specifically, as an elementary choice between finiteness (or mathematically, as any natural number of Peano arithmetic) and infinity (i.e. an actually infinite set in the meaning of set theory), the quantity of quantum information is defined. One can demonstrate that the so-defined quantum information and quantum information standardly defined by quantum mechanics are equivalent to each other. The equivalence of the axiom of choice and the well-ordering “theorem” is involved. It can be justified transcendentally as well, in virtue of transcendental equivalence implied by the totality. Thus, all can be considered as temporal as far anything possesses such a temporal counterpart necessarily. Formally defined, the frontier of time is the current choice now, a bit of information, furthermore interpretable as a qubit of quantum information. (shrink)

In his "Two concepts of possible worlds", Peter Van Inwagen explores two kinds of views about the nature of possible worlds : abstractionism and concretism. The latter is the view defended by David Lewis who claims that possible worlds are concrete spatio-temporal universes, very much like our own, causally and spatio-temporally disconnected from each other. The former is the view of the majority who claims that possible worlds are some kind of abstract objects – such as propositions, properties, states of (...) affairs, or sets of numbers. In this paper, I will develop this view in an 'extreme abstractionist' way, appealing to a 'modal bundle theory', and I will try to show that it is preferable to the standard abstractionist ones. Finally, I will compare this kind of abstractionism to concretism, only to find that the difference between the two is minimal. (shrink)

What is absolutely unrestricted quantification? We distinguish two theoretical roles and identify two conceptions of absolute generality: maximally strong generality and maximally inclusive generality. We also distinguish two corresponding kinds of absolute domain. A maximally strong domain contains every potential counterexample to a generalisation. A maximally inclusive domain is such that no domain extends it. We argue that both conceptions of absolute generality are legitimate and investigate the relations between them. Although these conceptions coincide in standard settings, we show how (...) they diverge under more complex assumptions about the structure of meaningful predication, such as cumulative type theory. We conclude by arguing that maximally strong generality is the more theoretically valuable conception. (shrink)

There is no uniquely standard concept of an effectively decidable set of real numbers or real n-tuples. Here we consider three notions: decidability up to measure zero [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382], which we abbreviate d.m.z.; recursive approximability [or r.a.; K.-I. Ko, Complexity Theory of Real Functions, Birkhäuser, Boston, 1991]; and decidability ignoring boundaries [d.i.b.; W.C. Myrvold, The decision problem for entanglement, in: R.S. (...) Cohen et al. (Eds.), Potentiality, Entanglement, and Passion-at-a-Distance: Quantum Mechanical Studies fo Abner Shimony, Vol. 2, Kluwer Academic Publishers, Great Britain, 1997, pp. 177–190]. Unlike some others in the literature, these notions apply not only to certain nice sets, but to general sets in Rn and other appropriate spaces. We consider some motivations for these concepts and the logical relations between them. It has been argued that d.m.z. is especially appropriate for physical applications, and on Rn with the standard measure, it is strictly stronger than r.a. [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382]. Here we show that this is the only implication that holds among our three decidabilities in that setting. Under arbitrary measures, even this implication fails. Yet for intervals of non-zero length, and more generally, convex sets of non-zero measure, the three concepts are equivalent. (shrink)

On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surreal numbers; and a (...) natural extension of BLT is definitionally equivalent with ZF. (shrink)

An essay on Kant's theory of justification, where by “justification” is meant the evaluative concept that specifies conditions under which a propositional attitude is rationally acceptable with a moderate-to-high degree of confidence. Kant employs both epistemic and non-epistemic concepts of justification: an epistemic concept of justification sets out conditions under which a propositional attitude is rationally acceptable with a moderate-to-high degree of confidence and a candidate (if true and Gettier-immune) for knowledge. A non-epistemic concept of justification, by contrast, sets out (...) conditions under which attitudes are rationally acceptable with a moderate-to-high degree of confidence but not candidates for knowledge (even if true). The latter conditions will typically be “pragmatic” or “practical,” and thus license acceptance from a “practical” point of view. For Kant, only broadly-speaking practical reasons can provide adequate motivation for adopting a positive attitude towards a proposition (rather than suspending judgment) in the absence of sufficient epistemic grounds. -/- . (shrink)

German Lutheran scholar Johann Friedrich Weitenkampf (d.1758) sets out to explain and refute the Turkish concept of fate, dividing his dissertation into two sections: the first outlining the Turkish-Muslim view of fate; and the second seeking to prove the invalidity of the Muslim concept of fate with philosophical argumentation. He begins with some brief notes on the historical origin of the Turks, turning then to the backstory of the Qur’an, which he claims can be divided into six sections or topics, (...) the last of which concerns its teachings on fate. According to Weitenkampf, in mainstream Islamic thought, fate is predetermined and immutable. Weitenkampf categorizes most Turks as Jabrites who believe that God is the source of all evil and that men do not have free will. Therefore, men are compelled to do evil or good through God’s omnipotence. He offers examples of how this belief is manifested in the actions and values of the Turks. According to Weitenkampf, since Turks believe in predestination, they do not flee plague-ridden cities or shun contact with those infected. They do not fear death. If they suffer, they believe fate decreed it. In battle, this makes them brave to the point of foolhardy. Weitenkampf also paraphrases an exhortation from the Qur’an in which Muslims are told not to avoid danger, as God has already determined their fate. . . . Weitenkampf’s dissertatio is a symptom of the struggle between the weakened Lutheran orthodoxy and the rise of Pietism and rationalism in the wake of the Enlightenment in the eighteenth century. Unlike other Lutheran authors, he analyzes Islamic thought through systematic philosophical argumentation, deeply influenced by his logic and metaphysics teacher Knutzen, who tried to combine Wolffan Enlightenment rationalism with pietistic spirituality. (shrink)

There is no single Jewish philosophical conception of God, and the array of competing conceptions does not lend itself to easy systemization. Nonetheless, it is the aim of this chapter to provide an overview of this unruly theological terrain. It does this by setting out ‘maps’ of the range of positions which Jewish philosophers have taken regarding key aspects of the God-idea. These conceptual maps will cover: (i) how Jewish philosophers have thought of the role and status of conceiving (...) of God in the first place; (ii) what Jewish philosophers have understood to be definitive of God or Divinity; (iii) Jewish philosophical conceptions of God’s oneness; (iv) Jewish philosophical conceptions of God’s transcendence or immanence; (v) Jewish philosophical conceptions of God’s personhood or lack thereof; (vi) Jewish philosophical understandings of why God created (or caused) a world; and (vii) Jewish philosophical understandings of God’s relationship to the Jewish people. Jointly, these seven conceptual maps outline the broad range of vying conceptions of God that have been held by Jewish philosophers over the centuries, while also enabling the reader a bird’s-eye-view of how these multiple conceptions relate to one another. The chapter concludes by touching on what Jewish philosophers have made of this immense diversity of theological conceptions included within the tradition. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more definite (...) states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

One of the ideas that characterises the enactive approach to cognition is that life and mind are deeply continuous, which means that both phenomena share the same basic set of organisational and phenomenological properties. The appeal to phenomenology to address life and basic cognition is controversial. It has been argued that, because of its reliance on phenomenological categories, enactivism may implicitly subscribe to a form of anthropomorphism incompatible with the modern scientific framework. These worries are a result of a lack (...) of clarity concerning the role that phenomenology can play in relation to biology and our understanding of non-human organisms. In this paper, I examine whether phenomenology can be validly incorporated into the enactive conception of mind and life. I argue that enactivists must rely on phenomenology when addressing life and mind so that they can properly conceptualise minimal living systems as cognitive, as well as argue for an enactive conception of biology in line with their call for a non-objectivist science. To sustain these claims, I suggest that enactivism must be further phenomenologised by not only drawing from Hans Jonas’s phenomenology of the organism (as enactivists often do) but also from Edmund Husserl’s thoughts on the connection between transcendental phenomenology and biology. Additionally, phenomenology must be considered capable of providing explanatory accounts of phenomena. (shrink)

It has become popular of late to identify the phenomenon of thinking a singular thought with that of thinking with a mental file. Proponents of the mental files conception of singular thought claim that one thinks a singular thought about an object o iff one employs a mental file to think about o. I argue that this is false by arguing that there are what I call descriptive mental files, so some file-based thought is not singular thought. Descriptive mental (...) files are mental files for which descriptive information plays four roles: determines which object the file is about, if any, it sets limits on possible mistakes that fall within the scope of successful reference for the file, it acts as a ‘gatekeeper’ for the file, and it determines persistence conditions for the file. Contrary to popular assumption, a description playing these roles is consistent with the file-theoretic framework. Recognising this allows us to distinguish the notion of singular thought from that of file-thinking and better understand the nature and role of both. (shrink)

Cooperation is rife in the microbial world, yet our best current theories of the evolution of cooperation were developed with multicellular animals in mind. Hamilton’s theory of inclusive fitness is an important case in point: applying the theory in a microbial setting is far from straightforward, as social evolution in microbes has a number of distinctive features that the theory was never intended to capture. In this article, I focus on the conceptual challenges posed by the project of extending Hamilton’s (...) theory to accommodate the effects of gene mobility. I begin by outlining the basics of the theory of inclusive fitness, emphasizing the role that the concept of relatedness is intended to play. I then provide a brief history of this concept, showing how, over the past fifty years, it has departed from the intuitive notion of genealogical kinship to encompass a range of generalized measures of genetic similarity. I proceed to argue that gene mobility forces a further revision of the concept. The reason in short is that, when the genes implicated in producing social behaviour are mobile, we cannot talk of an organism’s genotype simpliciter; we can talk only of an organism’s genotype at a particular stage in its life cycle. We must therefore ask: with respect to which stage(s) in the life cycle should relatedness be evaluated? For instance: is it genetic similarity at the time of social interaction that matters to the evolution of social behaviour, or is it genetic similarity at the time of reproduction? I argue that, strictly speaking, it is neither of these: what really matters to the evolution of social behaviour is diachronic genetic similarity between the producers of fitness benefits at the time they produce them and the recipients of those benefits at the end of their life-cycle. I close by discussing the implications of this result. The main payoff is that it makes room for a possible new mechanism for the evolution of altruism in microbes that does not require correlated interaction among bearers of the genes for altruism. The importance of this mechanism in nature remains an open empirical question. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s (...) Induction-Axiom Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

In this chapter, we philosophically reflect on the concept of innovation. To this end, we distinguish between the innovation process and outcome dimension, and between the ontic and ontological dimension of innovation. The ontic dimension of innovation concerns beings like new artefacts, and the ontological dimension concerns the being of these beings. These distinctions lead to four characteristics of our understanding of innovation with several implications for the object of innovation and its novelty, as well as for the temporality and (...) human involvement in innovation practices. It will turn out that innovation concerns the ontogenetic process in which primarily a world is constituted - i.e. the digital world - in which the invention of new artefacts - i.e. blockchain technology - is embedded. This ontogenetic process doesn’t follow a chronological temporal order, but is constituted by a temporal iterative process. Human creativity is involved in this ontogenetic process as co-creative capacity. In section three, we show the advantage of our conceptualization of innovation and its implications for contemporary and future alternative theories of innovation. (shrink)

On the standard interpretation of Metaphysics IX, Aristotle proceeds from the original sense of δύναμις and ἐνέργεια to an ontological conception of these terms. This should raise the question of what is not ontological about the former and what is ontological about the latter. To address these questions I discuss the commentaries by Heidegger and Menn, which alone come close to addressing these issues. But their readings cannot neatly distinguish between the two senses of δύναμις and ἐνέργεια that we (...) find in the Aristotelian text, thus compelling us to seek a better way of clarifying the standard interpretation, which I argue can be more precisely understood in the following way: δύναμις and ἐνέργεια in their customary meaning cannot be considered ontological in the sense that they have a particular locus among the categories, which is what sets them apart from their newer, ontological meaning. I conclude therefore that the text of Metaphysics IX can be understood as proceeding from an intracategorial conception of δύναμις and ἐνέργεια toward a transcategorial conception of these terms. (shrink)

This chapter sets out John Rawls’s conception of autonomy and considers the role that it plays in his thought across A Theory of Justice and Political Liberalism. I suggest that one distinctive but overlooked feature of this conception is that it takes seriously the threat to autonomy that arises from how individuals are shaped by their social and political institutions. After setting out this conception and tracing its connections to wider discussions of autonomy, I argue for two (...) main conclusions. First, that despite appearances to the contrary, Rawls’s autonomy-based commitments are broadly speaking consistent across his two main works. Second, that these autonomy-based commitments are not in fact disbarred from playing a grounding role in Political Liberalism. On the contrary, I suggest that Rawls’s conception of autonomy motivates his aim of finding principles of justice that can be stable, and that this in turn illuminates his later commitment to a political liberalism. (shrink)

Igal Kvart A Coding Conception in Action-Directed-Pragmatics -/- I present formal Pragmatics for a domain in Pragmatics that I call Action-Directed Pragmatics, which focuses on the Pragmatic riddle of how implicit contents are conveyed and understood, by adopting a coding model, in which the speaker and addressee simulate each other iteratively in a deliberative context (an ‘action-pregnant’ one). The implicit content, conveyed by a speaker and decoded by her addressee, in such cases, consists in the specified steered-to action, plus (...) modulations on the action-polarity (pro or con) and the degree of the so-called Steering Thrust that accompanies such assertions and is conveyed by verbal locutions, intonation, and/or bodily and facial gestures. There are two main tasks to model (in a given setup and conversational context): First, how is the speaker, with a steered-to action in mind (and Steering Thrust), to select an assertion so as to (say) optimize the successful transmission and decoding of its implicit pragmatic content by her and her addressee? Second, how does the addressee, given an assertion by the speaker, decipher the implicit pragmatic content conveyed via it? Both will invoke pertinent information they have about each other and the setup/context in order to best encode and best decode the implicit pragmatic content. (This coding mechanism proposed here is not offered for the ubiquitous ‘frozen’, ‘trivial’ or ‘routinized’ pragmatic messages.) A prelude to this formal Pragmatics is a general formal Pragmatic account of Assertibility in contexts that are multi-normative (which is the common case). I focus here only on Epistemic/Semantic and Instrumental Norms. A linear representation of degrees of Overall Assertibility (i.e., taking into account various operative norms) will be an n-dimensional qualitative vector space with a function that computes them given different degrees of sub-normative Assertibility on each axis. (shrink)

Although the fact that Merleau-Ponty has a dialectical approach in Phenomenology of Perception has been discussed in recent Anglophone readings, there has not been an explicit clarification as to how his varying usages of the term hang together. Given his repeated references to Hegel and to dialectics, coupled with the fact that dialectics are not part of the Husserlian phenomenology or Heideggerean existentialism from which Merleau-Ponty draws so much, the question of just what he does with the idea of dialectics (...) presents itself. In this paper I argue that, in Phenomenology of Perception, Merleau- Ponty saw Hegel as providing a model for the conception of rationality and meaning that must underpin the existentialist response to the problems bequeathed him by Husserlian phenomenology: namely, the problems of embodiment, perception and the constitution of the world. In connection with this, I suggest an interpretation of Merleau-Ponty’s “existential dialectics” that focuses on his three principal uses of the term: 1) a “dialectic of objective thought,” 2) a set of existential-dialectical categories intended to capture the ontological structure of the “body-subject” as “being-in-the-world,” and 3) a dialectic at the cultural level concerning others and history. (shrink)

It is illegitimate to read any ontology about "race" off of biological theory or data. Indeed, the technical meaning of "genetic variation" is fluid, and there is no single theoretical agreed-upon criterion for defining and distinguishing populations (or groups or clusters) given a particular set of genetic variation data. Thus, by analyzing three formal senses of "genetic variation"—diversity, differentiation, and heterozygosity—we argue that the use of biological theory for making epistemic claims about "race" can only seem plausible when it relies (...) on the user’s own assumptions about race; the move from biological measures to claims about “race” inevitably amounts to a pernicious reification. We also excavate assumptions in the history of the technical discourse over the concept of "race" (e.g., Livingstone's and Dobzhansky's 1962 exchange, Edwards' 2003 response to Lewontin 1972, as well as contemporary discussions of cladistic "race", and "races" as clusters). We show that claims about the existence (or non-existence) of "race" are underdetermined by biological facts, methods, and theories. Biological theory does not force the concept of "race" upon us; our social discourse, social ontology, and social expectations do. We become prisoners of our abstractions at our own hands, and at our own expense. (shrink)

This article presents Franz Rosenzweig’s concept of redemption as a vehicle for raising some important questions for confronting the contemporary movement of Transhumanism. The upshot of our discussion is located in the existential questions asked, following a philosophical comparison of Rosenzweig’s religious and philosophical commitment to human life in its most robust form, with Transhumanism’s scientistic vision. To do so, the article first discusses some techno-scientistic assumptions of Transhumanism, showing that it presumes what was once a core principle of German (...) Idealism, the identity of reason and being, against which Rosenzweig rebelled. Then, the article turns to examine Rosenzweig’s humanistic redemptive vision and its emphasis on the corporeal, the temporal, and the worldly. The conclusion makes explicit the ways in which Rosenzweig’s redemptive vision provides a contrasting model to the one set forth by Transhumanism. (shrink)

This paper begins the last instalment of a six-part project correlating the key aspects of Kant’s architectonic conception of philosophy with a special version of the Chinese Book of Changes that I call the “Compound Yijing”, which arranges the 64 hexagrams (gua) into both fourfold and threefold sets. I begin by briefly summarizing the foregoing articles: although Kant and the Yijing employ different types of architectonic reasoning, the two systems can both be described in terms of three “levels” of (...) elements. Starting at an unnumbered level devoid of any element (the tao or thing in itself), the system proceeds by elaborating a key fourfold distinction (or “quaternity”) on the first level, a twelvefold distinction on the second level, and twelve quaternities (grouped in four quadrants, each with a set of three quaternities) on the third level. Each set of three quaternities (i.e., each quadrant) on the third level corresponds to one of the four “faculties” of the university, as elaborated in Kant’s book, The Conflict of the Faculties. Previous papers have examined the correlations between three key quaternities that Kant defends in relation to each of three faculties (philosophy, theology, and law) and the 12 gua that correspond to that faculty in the Compound Yijing. The final step is to explore the fourth quaternity on the third level, the 12 gua corresponding to the medical faculty. The “idea of reason” in Kant’s metaphysics that guides this wing of the comparative analysis is freedom, and the ultimate purpose of this faculty of the university is to train doctors to care for people’s physical well-being, as free agents imbedded in nature. But this paper will focus only on the four gua that correspond to four basic concepts in Kant’s theory of medicine. The two quaternities in the “yin-yang” (medical) quadrant of the Compound Yijing that will be skipped here are as follows. First, Kant’s account of the idea of freedom itself, which gives rise to the area of traditional metaphysics known as rational cosmology, comes in the first Critique’s Dialectic, in the section on the Antinomy of Reason (CPR A405-567/B432- 595). There he examines four irresolvable issues: whether the world has a beginning in time; whether composite substances consist of simple parts; whether a causality of freedom operates in the natural world; and whether an absolutely necessary being exists. Later I will argue that these correspond to the quaternity consisting of gua 15, 22, 36, and 52. (shrink)

The endeavor of this proposal seeks to engage the intellect in a new perspective of Moral along those characteristic operations of human nature/faculties elucidated to periodically delineate -in accordance with a theoretical framework-, the evolutional outcome of four distinct sets of free willed actions capable of denoting the gradual advancement of conduct, herein deemed as the universal path to moral conduct. In addition, the distinctive particularities defining the singularities of their outcome were perceived to duly sustain the moral guidance that (...) the course of humanity has so far proved to so direly need. (shrink)

The Question of Iterated Grounding (QIG) asks what grounds the grounding facts. Although the question received a lot of attention in the past few years, it is usually discussed independently of another important issue: the connection between metaphysical explanation and the relation or relations that supposedly “back” it. I will show that once we get clear on the distinction between metaphysical explanation and the relation(s) backing it, we can distinguish no fewer than four questions lumped under QIG. I will also (...) argue that given some plausible assumptions about what it would take for a relation to back metaphysical explanation, many salient views about grounding allow us to give “easy” answers to these questions—easy in the sense that we can straightforwardly derive them from the respective conception of grounding without getting into the sorts of complexities that typically inform answers to QIG. The paper's main upshot is that we cannot expect to make much progress on QIG without first addressing the difficult issue of how exactly grounding is related to metaphysical explanation. (shrink)

In this article, I will focus on the notion of supervenience introduced and deployed by Armstrong. The aim is to settle the issue of whether it has any fruitful applications. My conclusions are negative. Armstrong gives to his notion of supervenience a major explanatory role of telling why one need not consider certain beings as a genuine ontic expansion, if one already assumes a certain meagre set of more basic entities. On closer inspection, however, Armstrong’s notion does not clarify such (...) intuitions any further. The legitimate uses of the notion for the above purpose turn out to be redundant: the concepts of identity and partial identity can be employed instead. (shrink)

This essay offers a novel interpretation of Michel Foucault’s original and often misunderstood conception of philosophy as a critical activity. While it is well known that Foucault’s critique undertakes to disclose contingent limits of thought that appear necessary in the present, the nature of the obstacle whose overcoming critique is meant to facilitate remains poorly understood. I argue that this obstacle, “the present limits of the necessary,” resides on the unconscious level of thought Foucault identified as the object of (...) analysis for an archaeology of knowledge. Therefore, Foucault’s conception of a critique can be grasped only against the background of the distinctive conception of thought that informs his archaeological analyses of discursive practices. According to that view, thinking is always shaped by some historically specific system of unconscious norms that define the contingent set of conceptual possibilities subjects are able to recognize in the present. Drawing on Foucault’s largely neglected remarks on the obvious and the habitual, I argue that these unconscious norms of thought are enacted habitually in a discursive practice, which endows them with an appearance of obviousness. In this way, I explain how something contingent appears in the guise of necessity and begins to function as part of the present limits of the necessary. Finally, I argue that the task of a critique to expand the scope of conceptual possibility by disclosing these unconscious limits of thought is motivated by Foucault’s commitment to the ideal of autonomy understood as subject’s self-determination. (shrink)

Expression is the central concept in Wittgenstein’s philosophy of mind, and our experiences are reflected in our bodily expressions or gestures, facial expressions, behaviors and linguistic expressions. It seems true that we have no access of other people’s experiences but we can know or talk about them in so far as they are the common experiences of all. This inaccessibility of other’s experiences may create a genuine thinking that one’s experiences are private and the first person present tense psychological utterances (...) are not descriptive at all. They are understood solely as expressive and expression is the outer concept of a mental phenomenon. In this paper, an attempt will be made on the basis of Wittgenstein’s critique of the relationship between the concepts of experience and expression we shall argue that certain uses of the dichotomy between the inner and the outer are mistakes. According to Wittgenstein, the inner is not a set of experiences which are or are not expressed by our immediate (primitive) expressions or linguistic expressions rather it is the capacity of the subject to express himself genuinely. (shrink)

Gallagher is right in pointing out that scientific realism is an implicit background assumption of BNO, and that I did not give an independent argument for it. He is also right in saying that science does not _demonstrate_ the existence of certain entities, but that it assumes those entities in a process of explanation and theory formation. However, it is not true that science, as Gallagher writes (p.2), “simply” assumes the reality of certain things: such assumptions are embedded in the (...) context of an attempt to find the_ minimal _ set of ontological assumptions one has to make relative to a set of explanatory goals and relative to a specific data set in a certain domain. This parsimonious spirit is also the <blockquote> PSYCHE: http://psyche.cs.monash.edu.au/ </blockquote> spirit of SMT, which can be seen as a search for the minimal conditions under which a phenomenal self and a consciously experienced first-person perspective can emerge. (shrink)

The programmatic statement put forward in von Wright's last works on deontic logic introduces the perspective of logical pragmatics, which has been formally explicated here and extended so to include the role of norm-recipient as well as the role of norm-giver. Using the translation function from the language of deontic logic to the language of set-theoretical approach, the connection has been established between the deontic postulates, on one side, and the perfection properties of the norm-set and the counter-set, on the (...) other side. In the study of conditions of rational norm-related activities it has been shown that diverse dynamic second-order norms related to the concept of the consistency norm-system hold: -- the norm-giver ought to restore ``classical'' consistency by revising an inconsistent system, -- the norm-recipient ought to preserve an inconsistent system by revision of its logic so that inconsistency does not imply destruction of the system. Dialetheic deontic logic of Priest is a suitable logic for the purpose since it preserves other perfection properties of the system. (shrink)

Frege discussed Mill’s empiricist ideas and Kant’s rationalist ideas about the nature of mathematics, and employed Set Theory and logico-philosophical notions to develop a new concept for the natural numbers. All this is objectively exposed by this paper.