In this paper, I consider the use of mathematical results in philosophical arguments arriving at conclusions with non-mathematical content, with the view that in general such usage requires additional justification. As a cautionary example, I examine Kreisel’s arguments that the Continuum Hypothesis is determined by the axioms of Zermelo-Fraenkel set theory, and interpret Weston’s 1976 reply as showing that Kreisel fails to provide sufficient justification for the use of his main technical result. If we take the perspective that mathematical results (...) are used in the context of a modelling of something not necessarily mathematical, then the situation is clarified somewhat, and the procedure for arriving at justification for the use of such results becomes clear. I give an example of a particularly strong form this justification might take, using the idea of formalism independence due to Gödel and Kennedy. (shrink)

A re-evaluation of the notion of vacuum in quantum electrodynamics is presented, focusing on the vacuum of the quantized electromagnetic field. In contrast to the ‘nothingness’ associated to the idea of classical vacuum, subtle aspects are found in relation to the vacuum of the quantized electromagnetic field both at theoretical and experimental levels. These are not the usually called vacuum effects. The view defended here is that the so-called vacuum effects are not due to the ground state of the quantized (...) electromagnetic field. Nevertheless it is possible to maintain an empirically demonstrable notion of vacuum state that is consistent with the interpretation of the formalism of the theory. (shrink)

The proposed theoretical motivation for legal fictionalism begins by focusing upon the seemingly supernatural powers of creation and control that mere mortals exercise over legal things, as a subclass of socially constructed things. This focus brings to the fore a dilemma of uncharitableness concerning the ontological commitments expressed in the discourse of whole societies about such things. Either, there is widespread equivocation as to the fundamental concept expressed by terms such as ‘existence’ or our claims about legal and other institutional (...) things are never really true. When stated as a dilemma, rather than assuming either horn from the outset, our broader social practice of fiction-telling yields a reason to prefer the fictionalist horn. -/- I differentiate three grades of legal fictionalism and contrast strong legal fictionalism with Horacio Spector’s weak form. Only the stronger form has it that engagement in a fictional discourse of law can provide reasons for legal decision-making independent of moral opinions or policy considerations. This stance relies on the claim that maintaining a fictional discourse with respect for its integrity justifies inferences to conclusions about a fictional domain beyond what is described in existing expressions of the discourse. Focusing on ontology allows an analogy between a fictional discourse of law and literary or popular fiction, in which context such inferences are more obviously persuasive. I argue that this notion of respect for the integrity of such a discourse saves legal formalist jurisprudence from the indeterminacy objections of legal realists. (shrink)

The mathematical formalism of quantum theory has been established for nearly a century, yet its physical foundations remain elusive. In recent decades, connections between quantum theory and information theory have garnered increasing attention. This study presents a physical derivation of the mathematical formalism quantum theory based on information-theoretic considerations in physical systems. We postulate that quantum systems are characterized by single independent adjustable variables. Utilizing this physical postulate along with the conservation of total probability, we derive the standard (...) Hilbert space formalism of quantum theory, including the Born probability rule. This comprehensive derivation of quantum theory offers a clear and concise physical foundation for the mathematical formalism of quantum mechanics. (shrink)

The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems that have only one adjustable property cannot carry more than a single message at a time. We demonstrate this is the case for the single photons in the double-slit experiment, and the root of the fundamental limit on measuring the complementary aspect of the photons. Next, we analyze the other ‘quantal’ behavior of the systems with a single adjustable (...) property, such as noncommutativity and no-cloning. Finally, we formulate a mathematical theory to describe the dynamics of such systems and derive the standard Hilbert-space formalism of quantum mechanics. Our derivation demonstrates the physical foundation of the quantum theory. (shrink)

The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to our diverse purposes (...) and pragmatic goals. Hence there is no independent or uniform fact to the matter, and I advance the ‘anti-realist’ conclusion that computational descriptions of physical systems are not founded upon deep ontological distinctions, but rather upon interest-relative human conventions. Hence physical computation is a ‘conventional’ rather than a ‘natural’ kind. (shrink)

The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No other premises (besides the above only mathematical (...) equivalence) are necessary to explain how the probabilistic causation of quantum mechanics refers to the unambiguous determinism of classical physics. The same equivalence underlies the mathematical formalism of quantum mechanics. It merged the well-ordered components of the vectors of Heisenberg’s matrix mechanics and the non-ordered members of the wave functions of Schrödinger’s undulatory mechanics. The mathematical condition of that merging is just the equivalence of the axiom of choice and the well-ordering theorem implying in turn Max Born’s probabilistic interpretation of quantum mechanics. Particularly, energy conservation is justified differently than classical physics. It is due to the equivalence at issue rather than to the principle of least action. One may involve two forms of energy conservation corresponding whether to the smooth changes of classical physics or to the discrete changes of quantum mechanics. Further both kinds of changes can be equated to each other under the unified energy conservation as well as the conditions for the violation of energy conservation to be investigated therefore directing to a certain generalization of energy conservation. (shrink)

In this work, we derive the standard formalism of quantum theory by analyzing the behavior of single-variable systems under measurements. These systems, with minimal information capacity, exhibit indeterministic behavior in independent measurements while yielding probabilistically predictable outcomes in dependent measurements. Enforcing probability conservation in the probability transformations leads to the derivation of the Born rule, which subsequently gives rise to the Hilbert space structure and the Schrödinger equation. Additionally, we show that preparing physical systems in coherent states —crucial for (...) observing quantum phenomena— effectively reduces the number of independent variables to one. This first-principles derivation of quantum theory from probability conservation in single-variable systems offers new insights into the physical meaning of quantum theory and clarifies its domain of applicability. (shrink)

In the present paper I argue that the formalism of Newtonian mechanics stems directly from the general principle to be called the principle of microlevel reducibility which physical systems obey in the realm of classical physics. This principle assumes, first, that all the properties of physical systems must be determined by their states at the current moment of time, in a slogan form it is ``only the present matters to physics.'' Second, it postulates that any physical system is nothing (...) but an ensemble of structureless particles arranged in some whose interaction obeys the superposition principle. I substantiate this statement and demonstrate directly how the formalism of differential equations, the notion of forces in Newtonian mechanics, the concept of phase space and initial conditions, the principle of least actions, etc. result from the principle of microlevel reducibility. The philosophical concept of thick presentism and the introduction of two dimensional time-physical time and meta-time that are mutually independent on infinitesimal scales-are the the pivot points in these constructions. (shrink)

The Aristotelian origins of formal systems are outlined, together with Aristotle's use of causal terms in describing syllogisms. The precision and exactness of a formalism, based on the projection of logical forms into perceptive signs, is contrasted with foundational, abstract concepts, independent of any formalism, which are presupposed for the understanding of a formal language. The definition of a formal system by means of a Turing machine is put in the context of Wittgenstein's general considerations of a machine (...) understood as a sign. A modification of Łukasiewicz's logic Ł3 with the inclusion of justification terms is proposed in order to formally analyse some features of formalistic reasoning as a mechanical, causal affair within a wider context of "indeterminacy". (shrink)

Simultaneous observation of the wave-like and particle-like aspects of the photon in the double-slit experiment is unallowed. The underlying reason behind this limitation is not understood. In this paper, we explain this unique behavior by considering the communicational properties of the photons. Photons have three independently adjustable properties (energy, direction, and spin) that can be used to communicate messages. The double-slit experiment setup fixes two of these properties and confines the single photon’s capacity for conveying messages to no more than (...) one message. With such a low communication capacity, information theory dictates that measurements associated only with one proposition can obtain consistent results, and a second measurement associated with an independent proposition must necessarily lead to randomness. In the double-slit example, these are the wave or particle properties of the photon. The interpretation we offer is based on the formalism of information theory and does not make use of Heisenberg’s uncertainty relation in any form. (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)

The scientific study of consciousness, also referred to as consciousness science, is a young scientific field devoted to understanding how conscious experiences and the brain relate. It comprises a host of theories, experiments, and analyses that aim to investigate the problem of consciousness empirically, theoretically, and conceptually. This thesis addresses some of the questions that arise in these investigations from a formal and mathematical perspective. These questions concern theories of consciousness, experimental paradigms, methodology, and artificial consciousness. -/- Regarding theories of (...) consciousness, the thesis contributes to the understanding of the mathematical structure that some of the formal theories in the field propose. The work presented here targets the theory of consciousness known as Integrated Information Theory (IIT) and the neuroscientific theory known as Predictive Processing Theory or Free Energy Principle in its Active Inference form (AI-PP). The thesis provides axiomatic definitions of the mathematical structures that constitute these theories, and uses these definitions to address some of the open questions surrounding the theories. For AI-PP, this includes a rigorous derivation of the formula for Active Inference via Free Energy minimisation and a proof of compositionality of Free Energy. For IIT, this includes resolutions of some of the criticisms of IIT's formal scope and applications, but also the identification of new issues that concern the formalism and its derivation. When possible, the definitions are provided in the mathematical framework of category theory. -/- Regarding experiments, the thesis addresses the main paradigm for testing and falsifying theories of consciousness currently applied in the field. This paradigm consists of comparing the conscious experience that a theory predicts with the conscious experience that is inferred from behavioural data or report by use of measures of consciousness. The thesis provides a formal model of this paradigm and shows that under a certain condition—if inference and prediction are independent—, any minimally informative theory of consciousness can always be falsified. This is deeply problematic since the field’s reliance on report or behaviour to infer conscious experiences, in conjunction with the general structure of most contemporary theories of consciousness, implies such independence. This observation provides the exact formal underpinning of the well-known unfolding argument. The thesis analyses the origin of the problem and identifies precisely which changes are required to avoid this problem in future research. The thesis furthermore shows that the problem of falsifying theories of consciousness, and of empirical comparisons of theories of consciousness more generally, follows from a pervasive closure paradigm in consciousness science, that consists of taking a neuroscientific account of the brain as input to a theory of consciousness, so as to explain what consciousness is, without allowing for modifications or adaptations of the neuroscientific account that would accommodate consciousness as part of the brain's functioning. As is shown in the thesis, this paradigm has implications that point to a fundamental need of revision. -/- Regarding methodological and conceptual questions, the thesis contributes to the foundations of structural research in consciousness science. Structural research aims to use mathematical structures or mathematical spaces, instead of verbal descriptions or simple categorisations, to represent conscious experiences scientifically, for example when building theories of consciousness, or when exploring new empirical avenues to measure consciousness. Despite considerable advances in this realm, there was, prior to this thesis, no explicit definition of what a mathematical structure of conscious experience should be; that is, how the attribution of mathematical structure to conscious experiences should be systematically understood. Perhaps the most important contribution of this thesis to the field is to propose such a definition. The definition, a structural concept, extends existing approaches wherever available, and provides a basis for developing a common formal language to study consciousness, bridging developments as far apart as psychophysics and phenomenology. In addition, and independently of this proposal, the thesis offers a critical analysis of which metaphysical premises need to be presumed in structural research, whether the use of particular formal tools (such as structure-preserving mappings or homomorphisms) is justified, and how structural theories of consciousness could otherwise be built in the first place. An attempt to expand the results from consciousness to more general problems in philosophy of science is made in the context of the well-known Newman problem. -/- Regarding the question of artificial consciousness—can AI feel?—, the thesis contributes two results that take the form of no-go theorems, as known from physics. The first no-go theorem shows that if consciousness is relevant for the temporal evolution of a system's states—if it is dynamically relevant—, then contemporary AI systems cannot be conscious. That is because AI systems run on CPUs, GPUs, TPUs or other processors which have been designed and verified to adhere to computational dynamics that systematically preclude or suppress deviations. The second no-go theorem is situated in the context of computational functionalism, a view which posits that consciousness is a computation. The theorem shows that if computational functionalism holds true, consciousness cannot be a Turing computation. Rather, it must be a novel type of computation that has recently been proposed by Geoffrey Hinton, called mortal computation. -/- This thesis is part of a global effort to pioneer a mathematical perspective in consciousness science, now called Mathematical Consciousness Science. The hope behind the research carried out in this PhD is to illustrate the power and usefulness of mathematical approaches in different areas of consciousness science, and in doing so, to lay the foundations for future mathematical work that complements and supports empirical and theoretical work in the further development of this exciting field. (shrink)

We develop an approach to temporal logic that replaces the traditional objective, agent- and event-independent notion of time with a constructive, event-dependent notion of time. We show how to make this event-dependent time entropic and hence well-defined. We use sheaf-theoretic techniques to render event-dependent time functorial and to construct memories as sequences of observed and constructed events with well-defined limits that maximize the consistency of categorizations assigned to objects appearing in memories. We then develop a condensed formalism that represents (...) memories as pure constructs from single events. We formulate an empirical hypothesis that human episodic memory implements a particular constructive functor. (shrink)

If episodic memory is constructive, experienced time is also a construct. We develop an event-based formalism that replaces the traditional objective, agent-independent notion of time with a constructive, agent-dependent notion of time. We show how to make this agent-dependent time entropic and hence well-defined. We use sheaf-theoretic techniques to render agent-dependent time functorial and to construct episodic memories as sequences of observed and constructed events with well-defined limits that maximize the consistency of categorizations assigned to objects appearing in memories. (...) We then develop a condensed formalism that represents episodic memories as pure constructs from single events. We formulate an empirical hypothesis that human episodic memory implements a particular time-symmetric constructive functor, and discuss possible experimental tests. (shrink)

Triadic (systemical) logic can provide an interpretive paradigm for understanding how quantum indeterminacy is a consequence of the formal nature of light in relativity theory. This interpretive paradigm is coherent and constitutionally open to ethical and theological interests. -/- In this statement: -/- (1) Triadic logic refers to a formal pattern that describes systemic (collaborative) processes involving signs that mediate between interiority (individuation) and exteriority (generalized worldview or Umwelt). It is also called systemical logic or the logic of relatives. The (...) term "triadic logic" emphasizes that this logic involves mediation of dualities through an irreducibly triadic formalism. The term "systemical logic" emphasizes that this logic applies to systems in contrast to traditional binary logic which applies to classes. The term "logic of relatives" emphasizes that this logic is background independent (in the sense discussed by Smolin ). -/- (2) An interpretive paradigm refers to a way of thinking that generates an understanding through concepts, their inter-relationships and their connections with experience. -/- (3) Coherence refers to holistic integrity or continuity in the meaning of concepts that form an interpretation or understanding. -/- (4) Constitutionally open refers to an inherent dependence in principle of an interpretation or understanding on something outside of a specific discipline's discourse or domain of inquiry (epistemic system). Interpretations that are constitutionally open are incomplete in themselves and open to responsive, interdisciplinary discourse and collaborative learning. (shrink)

Mathematical formalism is the the view that numbers are "signs" and that arithmetic is like a game played with such signs. Frege's colleague Thomae defended formalism using an analogy with chess, and Frege's critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. (...) I argue that for Thomae, the formal standpoint is an _algebraic perspective_ on a domain of objects, and a "sign" is not a linguistic expression or mark, but a representation of an object within that perspective. Thomae exploits a shift into this perspective to give a purely algebraic construction of the real numbers from the rational numbers. I suggest that Thomae's chess analogy is intended to provide a model for such shifts in perspective. (shrink)

This paper objectively defines the three main contemporary philosophies of mathematics: formalism, logicism, and intuitionism. Being the three leading scientists of each: Hilbert (formalist), Frege (logicist), and Poincaré (intuitionist).

Legal decisions and theories are frequently condemned as formalistic, yet little discussion has occurred regarding exactly what the term "'formalism" means. In this Article, Professor Schauer examines divergent uses of the term to elucidate its descriptive content. Conceptions offormalism, he argues, involve the notion that rules constrict the choice of the decisionmaker. Our aversion to formalism stems from denial that the language of rules either can or should constrict choice in this way. Yet Professor Schauer argues that this (...) aversion to formalism should be rethought: At times language both can and should restrict decisionmakers. Consequently, the term "'formalistic" should not be used as a blanket condemnation of a decisionmaking process; instead the debate regarding decision according to rules should be confronted on its own terms. (shrink)

We often get evidence that bears on the reliability of some of our own first-order reasoning. The rational response to such “higher-order” evidence would seem to depend on a rational assessment of how reliable we can expect that reasoning to be, in light of the higher-order evidence. “Independence” principles are intended to constrain this reliability-assessment, so as to prevent question-begging reliance on the very reasoning being assessed. However, extant formulations of Independence principles tend to be vague or ambiguous, (...) and coming up with a tolerably precise formulation turns out to be tricky. This paper aims to make some progress toward developing a more precise Independence principle, and also to highlight some of the difficulties the project entails. The hope is to take a step toward understanding how rational belief is informed by evidence bearing on agents’ cognitive reliability. (shrink)

This essay presents the Aestheticism of the 19th century as the foundational movement of modernist-formalist aesthetics of the 20th century. The main principle of this movement is what I denominate “productive opacity”. Aestheticism has not been recognized as a philosophical aesthetic theory. However, its definition of artwork as an exclusive kind of form—a deep, opaque form—is among the most precise ever given in the discipline. This essay offers an interpretation of aestheticism as a formalist theory, referred to here as “deep (...) formalism”, focusing on the thinking of leading aestheticists, Walter Pater, Oscar Wilde, and James Whistler. These three thinkers defined artwork as a form saturated with an inextricable content, viz. opaque form. (shrink)

Discussions of political obligation and political authority have long focused on the idea that the commands of genuine authorities constitute content-independent reasons. Despite its centrality in these debates, the notion of content-independence is unclear and controversial, with some claiming that it is incoherent, useless, or increasingly irrelevant. I clarify content-independence by focusing on how reasons can depend on features of their source or container. I then solve the long-standing puzzle of whether the fact that laws can constitute content-independent (...) reasons is consistent with the fact that some laws must fail to bind due to their egregiously unjust content. Finally I defend my understanding of content-independence against challenges and show why it retains a place of special importance for questions about the law and political obligation. Content-independence highlights that it is some feature of the law or law-making process in general that is supposed to generate moral obligations for citizens, not the merits of particular laws. (shrink)

Frege says, at the end of a discussion of formalism in the Foundations of Arithmetic, that his own foundational program “could be called formal” but is “completely different” from the view he has just criticized. This essay examines Frege’s relationship to Hermann Hankel, his main formalist interlocutor in the Foundations, in order to make sense of these claims. The investigation reveals a surprising result: Frege’s foundational program actually has quite a lot in common with Hankel’s. This undercuts Frege’s claim (...) that his own view is completely different from Hankel’s formalism, and motivates a closer examination of where the differences lie. On the interpretation offered here, Frege shares important parts of the formalist perspective, but differs in recognizing a kind of content for arithmetical terms which can only be made available via proof from prior postulates. (shrink)

A current focus of legal debate is the proper role of the courts in the interpretation of statutes and the Constitution. Are judges to look solely to the naked language of an enactment, then logically deduce its application in simple syllogistic fashion, as legal formalists had purported to do? Or may the inquiry into meaning be informed by perhaps unbridled and unaccountable judicial notions of public policy, using legal realism to best promote the general welfare? Judge Posner considers the concepts (...) of formalism and realism to be meaningful and useful in common law reasoning but in interpretation to be useless and, worse, forbidden. He analogizes unclear "orders" from a legislature to garbled battlefield communications, and argues that the duty of the recipient of those orders (the judge) is to advance as best he can the enterprise set on foot by the superiors. Case studies elaborate this thesis. Judicial decisions interpreting fixed texts, Judge Posner concludes, can be neither logically correct or incorrect, philosophically sound or unsound, until the ultimate jurist, time, has adjudged their results. (shrink)

In a recent paper in this Journal San Pedro I formulated a conjecture relating Measurement Independence and Parameter Independence, in the context of common cause explanations of EPR correlations. My conjecture suggested that a violation of Measurement Independence would entail a violation of Parameter Independence as well. Leszek Wroński has shown that conjecture to be false. In this note, I review Wroński’s arguments and agree with him on the fate of the conjecture. I argue that what (...) is interesting about the conjecture, however, is not whether it is true or false in itself, but the reasons for the actual verdict, and their implications regarding locality. (shrink)

Background independence begins life as an informal property that a physical theory might have, often glossed as 'doesn't posit a fixed spacetime background'. Interest in trying to offer a precise account of background independence has been sparked by the pronouncements of several theorists working on quantum gravity that background independence embodies in some sense an essential discovery of the General Theory of Relativity, and a feature we should strive to carry forward to future physical theories. This paper (...) has two goals. The first is to investigate what a world must be like in order to be truly described by a background independent theory given extant accounts of background independence. The second is to argue that there are no non-empirical reasons to be more confident in theories that satisfy extant accounts of background independence than in theories that don't. The paper concludes by drawing a general moral about a way in which focussing primarily on mathematical formulations of our physical theories can adversely affect debates in the metaphysics of physics. (shrink)

Moderate formalism is the view that all artworks which have aesthetic properties have formal aesthetic properties, and some but not all of those works also have non-formal aesthetic properties. Nick Zangwill develops this view in his Metaphysics of Beauty after having argued against its alternatives – extreme formalism and anti-formalism. This article reviews his arguments against the rivals of moderate formalism, and argues that the rejection of anti-formalism is unjustified. Zangwill does not succeed in proving (...) that the broadly determined (context-determined) properties of artworks are in some cases irrelevant to their aesthetic properties – and following that, interpretation and assessment. A historical argument presented here shows how aesthetic properties of every work must partly supervene on this work’s contextual properties. In particular, this disproves Zangwill’s claim that epistemological matters are unessential in determining the artwork’s properties, and exposes some problems his account has with explaining relations between nonaesthetic and aesthetic properties. (shrink)

Two recent and influential papers, van Rooij 2007 and Lassiter 2012, propose solutions to the proviso problem that make central use of related notions of independence—qualitative in the first case, probabilistic in the second. We argue here that, if these solutions are to work, they must incorporate an implicit assumption about presupposition accommodation, namely that accommodation does not interfere with existing qualitative or probabilistic independencies. We show, however, that this assumption is implausible, as updating beliefs with conditional information does (...) not in general preserve independencies. We conclude that the approach taken by van Rooij and Lassiter does not succeed in resolving the proviso problem. (shrink)

I develop Schopenhauerian musical formalism. First, I present a Schopenhauerian account of music with a background of his metaphysical framework. Then, I define meaningfulness as an analog to a Kantian notion of purposiveness and argue that, in light of Schopenhauer, music is meaningful as a direct manifestation of the universal will. Given the ineffable nature of what music points to, its form lacks any representation of meaning. Music is therefore the mere form of meaningfulness, and it is precisely this (...) mere form that gives rise to the infinite possibilities to ascribe it with a variety of musical meaning. (shrink)

Intuitively, a classical field theory is background-in- dependent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an (...) interpretation if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails. (shrink)

An important principle in the epistemology of disagreement is Independence, which states, “In evaluating the epistemic credentials of another’s expressed belief about P, in order to determine how (or whether) to modify my own belief about P, I should do so in a way that doesn’t rely on the reasoning behind my initial belief about P” (Christensen 2011, 1-2). I present a series of new counterexamples to both Independence and also a revised, more widely applicable, version of it. (...) I then formulate and endorse a third version of Independence that avoids those counterexamples. Lastly, I show how this third version of Independence reveals two new ways one may remain steadfast in the face of two real life disagreements: one about God’s existence and one about moral realism. (shrink)

In the face of an impossibility result, some assumption must be relaxed. The Mere Addition Paradox is an impossibility result in population ethics. Here, I explore substantially weakening the decision-theoretic assumptions involved. The central finding is that the Mere Addition Paradox persists even in the general framework of choice functions when we assume Path Independence as a minimal decision-theoretic constraint. Choice functions can be thought of either as generalizing the standard axiological assumption of a binary “betterness” relation, or as (...) providing a general framework for a normative (rather than axiological) theory of population ethics. Path Independence, a weaker assumption than typically (implicitly) made in population ethics, expresses the idea that, in making a choice from a set of alternatives, the order in which options are assessed or considered is ethically arbitrary and should not affect the final choice. Since the result establishes a conflict between the relevant ethical principles and even very weak decision-theoretic principles, we have more reason to doubt the ethical principles. (shrink)

In spite of its everyday connotations, the term independence as republicans understand it is not a celebration of individualism or self-reliance but embodies an acknowledgement of the importance of personal and social relationships in people’s lives. It reflects our connectedness rather than separateness and is in this regard a relational ideal. Properly understood, independence is a useful concept in addressing a fundamental problem in social philosophy that has preoccupied theorists of relational autonomy, namely how to reconcile the idea (...) of individual human agency with the inevitable and necessary influence of other people, both directly and indirectly. I derive my account from the work of Mary Wollstonecraft and Catharine Macaulay, whose contributions have remained largely overlooked by current republican theorists. I have three purposes in this chapter. First, I set out the relational character of independence. Secondly, I outline a republican approach to the problem of structural social threats to agency. Finally, I hope to establish the basis for a fruitful dialogue between republicans and relational autonomy theorists on the requirements and dynamics of individual agency and freedom in oppressive social situations. I identify three distinctive features of the internal logic of freedom as independence that give it a relational character: it always locates the person within a community; there is a mediating role played by the notion of arbitrariness in connecting individual and collective perspectives; a causal relationship exists linking each person’s freedom as independence such that that the dependence of one class of persons jeopardizes the independence of the whole community. (shrink)

The paper deals with the formalistic view on music presented in Eduard Hanslick’s treatise On the Musically Beautiful, which is taken to be the foundingwork of the aesthtetics of music. In the paper I propose an interpretation of Hanslick’s treatise which differs on many points from the interpretations displayed in the works of several most influential contemporary aestheticians of music. My main thesis is that Hanslick’s treatise is misunderstood and incorrectly presented by these authors. I try to demonstrate this thesis (...) by referring to Hanslick’s original formulations in the German edition and by showing that my interpretation renders Hanslick’s view far more coherent and his arguments successful in showing his main conclusions. Accepting this alternative interpretation should have further implications on many contemporary theories in the aesthetics of music that reckon on the failure of Hanslick’s arguments as presented by usual interpretations. (shrink)

The article presents Hanslick’s aesthetic formalism as the starting point of the contemporary aesthetics of music. His book, written in the 19th century, is considered contemporary because it still proves to be influential and fruitful in the contemporary theoretical circles, especially in the modern analytic aesthetics of music, where it is widely cited and discussed. The article positions Hanslick’s book in relation to his nearest predecessors Kant and Herbart, and to the neighbouring area where the formalistic view appeared, namely (...) in Fidler’s visual formalism in fine arts. It is shown that by being the first piece of writing to attempt to systematically and comprehensively determine the essence and the content of music, and the criteria for evaluation of musical worth, Hanslick’s book sets the foundation for a rigorous examination of the aesthetics of music, and also breaks off with the widely ingrained preconceptions of music, which were in themselves an obstacle to establishing the aesthetics of music as a scientific discipline. (shrink)

Bilateralism is a theory of meaning according to which assertion and denial are independent speech acts. Bilateralism also proposes two coordination principles for assertion and denial. I argue that if assertion and denial are independent speech acts, they cannot be coordinated by the bilateralist principles.

There have been many attempts to determine what makes a natural kind real, chief among them is the criterion according to which natural kinds must be mind-independent. But it is difficult to specify this criterion: many supposed natural kinds have an element of mind-dependence. I will argue that the mind-independence criterion is nevertheless a good one, if correctly understood: the mind-independence criterion concerns the unification principles for natural kinds. Unification principles determine how natural kinds unify their properties, and (...) only those natural kinds that have a mind-independent unification principle should be considered real. (shrink)

In cognitive science, the concept of dissociation has been central to the functional individuation and decomposition of cognitive systems. Setting aside debates about the legitimacy of inferring the existence of dissociable systems from ‘behavioural’ dissociation data, the main idea behind the dissociation approach is that two cognitive systems are dissociable, and thus viewed as distinct, if each can be damaged, or impaired, without affecting the other system’s functions. In this article, I propose a notion of functional independence that does (...) not require dissociability, and describe an approach to the functional decomposition and modelling of cognitive systems that complements the dissociation approach. I show that highly integrated cognitive and neurocognitive systems can be decomposed into non-dissociable but functionally independent components, and argue that this approach can provide a general account of cognitive specialization in terms of a stable structure–function relationship. 1 Introduction2 Functional Independence without Dissociability3 FI Systems and Cognitive Architecture4 FI Systems and Cognitive Specialization. (shrink)

Robustness arguments hold that hypotheses are more likely to be true when they are confirmed by diverse kinds of evidence. Robustness arguments require the confirming evidence to be independent. We identify two kinds of independence appealed to in robustness arguments: ontic independence —when the multiple lines of evidence depend on different materials, assumptions, or theories—and probabilistic independence. Many assume that OI is sufficient for a robustness argument to be warranted. However, we argue that, as typically construed, OI (...) is not a sufficient independence condition for warranting robustness arguments. We show that OI evidence can collectively confirm a hypothesis to a lower degree than individual lines of evidence, contrary to the standard assumption undergirding usual robustness arguments. We employ Bayesian networks to represent the ideal empirical scenario for a robustness argument and a variety of ways in which empirical scenarios can fall short of this ideal. (shrink)

In the latter half of the twentieth century, philosophers of science have argued (implicitly and explicitly) that epistemically rational individuals might compose epistemically irrational groups and that, conversely, epistemically rational groups might be composed of epistemically irrational individuals. We call the conjunction of these two claims the Independence Thesis, as they together imply that methodological prescriptions for scientific communities and those for individual scientists might be logically independent of one another. We develop a formal model of scientific inquiry, define (...) four criteria for individual and group epistemic rationality, and then prove that the four definitions diverge, in the sense that individuals will be judged rational when groups are not and vice versa. We conclude by explaining implications of the inconsistency thesis for (i) descriptive history and sociology of science and (ii) normative prescriptions for scientific communities. (shrink)

It seems necessary to introduce the basic concepts used in this article i.e. formalism, anti-formalism and moderate formalism. Formalists believe that the aesthetic appreciation of an art work generally involves an attentive awareness of its sensory or conceptual qualities and does not require knowledge about its non-perceptual properties. Anti-formalists on the hand hold that noon of the aesthetic properties in the work of art are formal. A number of philosophers have recently advocated a more moderate formalism. (...) According to this view although not all aesthetic properties are formal, many are, and some artworks possess only formal aesthetic qualities. The quarrel among these three rival views concerns what sort of knowledge, if any, is required for appropriate aesthetic appreciation of an art work. In what follows, we will give a brief exposition of these three view points. Subsequently we will give our preferred position with regard to these views. (shrink)

This paper introduces the axiom of Negative Dominance, stating that if a lottery f is strictly preferred to a lottery g, then some outcome in the support of f is strictly preferred to some outcome in the support of g. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this setting, Negative (...) Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent. (shrink)

Democratic decision-making is often defended on grounds of the ‘wisdom of crowds’: decisions are more likely to be correct if they are based on many independent opinions, so a typical argument in social epistemology. But what does it mean to have independent opinions? Opinions can be probabilistically dependent even if individuals form their opinion in causal isolation from each other. We distinguish four probabilistic notions of opinion independence. Which of them holds depends on how individuals are causally affected by (...) environmental factors such as commonly perceived evidence. In a general theorem, we identify causal conditions guaranteeing each kind of opinion independence. These results have implications for whether and how ‘wisdom of crowds’ arguments are possible, and how truth-conducive institutions can be designed. (shrink)

The value of optimality modeling has long been a source of contention amongst population biologists. Here I present a view of the optimality approach as at once playing a crucial explanatory role and yet also depending on external sources of confirmation. Optimality models are not alone in facing this tension between their explanatory value and their dependence on other approaches; I suspect that the scenario is quite common in science. This investigation of the optimality approach thus serves as a case (...) study, on the basis of which I suggest that there is a widely felt tension in science between explanatory independence and broad epistemic interdependence, and that this tension influences scientific methodology. (shrink)

We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are (...) aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less informative imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [22], which De Bock and De Cooman [1] have called S-independence. We show that neither is more general than the other. (shrink)

This paper represents a philosophical experiment inspired by the formalist philosophy of mathematics. In the formalist picture of cognition, the principal act of knowledge generation is represented as tentative postulation – as introduction of a new knowledge construct followed by exploration of the consequences that can be derived from it. Depending on the result, the new construct may be accepted as normative, rejected, modified etc. Languages and means of reasoning are generated and selected in a similar process. In the formalist (...) picture, all kinds of “truth” are detected intra-theoretically. Some knowledge construct may be considered as “true”, if it is accepted in a particular normative knowledge system. Some knowledge construct may be considered as persistently true, if it remains invariant during the evolution of some knowledge system for a sufficiently long time. And, if you wish, you may consider some knowledge construct as absolutely true, if you do not intend abandoning it in your knowledge system. And finally, in the formalist picture, all kinds of ontologies generated by humans can be demystified by reconstructing them within the basic solipsist ontology simply as hypothetical branches of it. (shrink)

This article defends a formalist interpretation of Wittgenstein’s later thought on music by comparing it with Eduard Hanslick’s musical formalism. In doing so, it returns to a disagreement I have had with Bela Szabados who, in his book Wittgenstein as a Philosophical Tone-Poet, claims that the attribution of formalism obscures the role that music played in the development of Wittgenstein’s thought. The paper scrutinizes the four arguments Szabados presents to defend his claim, pertaining to alleged differences between Wittgenstein (...) and Hanslick on their accounts of theory, beauty, rules, and the broader significance of music. I will argue that in each case the similarities between Wittgenstein’s and Hanslick’s respective views outshine possible differences. Ultimately, I will argue that instead of rendering music a marginal phenomenon suited for mere entertainment, formalism –as presented by Hanslick and Wittgenstein, whom I read as influenced by Kant’s aesthetics– underscores music’s ability to show fundamental features of reality and our relation to it. Music does this precisely by being treated as a sensuous yet structured medium that is irreducible to any conceptually determined domain. (shrink)

Much of the literature on the relationship between belief and credence has focused on the reduction question: that is, whether either belief or credence reduces to the other. This debate, while important, only scratches the surface of the belief-credence connection. Even on the anti-reductive dualist view, belief and credence could still be very tightly connected. Here, I explore questions about the belief-credence connection that go beyond reduction. This paper is dedicated to what I call the independence question: just how (...) independent are belief and credence? I look at this question from two angles: a descriptive one (as a psychological matter, how much can belief and credence come apart?) and a normative one (for a rational person, how closely connected are belief and credence?) Ultimately, I suggest that the two attitudes are more independent than one might think. (shrink)

Orthodox semantics for natural language modals give rise to two puzzles for their interactions with disjunction: Ross’s puzzle and the puzzle of free choice permission. It is widely assumed that each puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from the truth of a possibility or necessity modal with an embedded disjunction, hearers infer that each disjunct is compatible with the relevant set of worlds. I argue that Diversity inferences are too weak to explain the full (...) range of data. Instead, I argue, modals with embedded disjunctions license ‘Independence’ inferences: from the truth of a modal with an embedded disjunction, hearers infer that each disjunct is an independent alternative among the relevant set of worlds. I then develop a bilateral inquisitive semantics for modals that predicts the validity of these Independence inferences. My account vindicates common intuitions about both Ross’s puzzle and the puzzle of free choice permission, and explains the full range of data. (shrink)

In this paper, I consider particular attempts by E. J. Lowe and Michael Gorman at providing an independence criterion of substancehood and argue that the stipulative exclusion of non-particulars and proper parts (or constituents) from such accounts raises difficult issues for their proponents. The results of the present discussion seem to indicate that, at least for the case of composite entities, a unity criterion of substancehood might have at least as much, and perhaps more, to offer than an (...) class='Hi'>independence criterion and therefore ought to be explored further by neo-Aristotelians in search of a defensible notion of substancehood. I indicated briefly how such a unity criterion might be used by neo-Aristotelians to support the inclusion of hylomorphic compounds in the category of substance, given the traditional role of form as the principle of unity within the compound. (shrink)