This book is about experiential content: what it is; what kind of account can be given of it. I am concerned with identifying and attacking one main view - I call it the inferentialist proposal. This account is central to the philosophy of mind, epistemology and philosophy of science and perception. I claim, however, that it needs to be recast into something far more subtle and enriched, and I attempt to provide a better alternative in these pages. The inferentialist proposal (...) holds that experiential content is necessarily under¬pinned by sophisticated cognitive influences. My alternative, the continuum theory, holds that these influences are relevant to experience only at certain levels of organisation and that at other levels there are contents which such features do not capture at all. Central to my account is that there are degrees to which cognitive influences affect experiential content; indeed, for the most part, experience is an amalgam of both inferential and non-inferential features. I claim that the inferentialist proposal is fundamentally flawed and deserves replacement, and I argue that my alternative fills the hollow that remains. The book is divided into four sections. In Part I, Chapter 1, I introduce two traditionally rival views of experiential content. In Chapter 2, I develop my continuum alternative. Chapter 3 assesses the relationship between experience and language, while Chapter 4 explores the relationship between beliefs and experience. The overall argument is that it has been a mistake to understand experience simply in inferential or non-inferential terms. In Part II, I examine the structure of mental content. Chapter 5 is concerned with the kinds of experiences which escape the inferentialist analysis. Chapter 6 considers Kant’s metaphysic of experience counterpointed to Lorenz’s reading of his work in the light of evolutionary biology. Chapter 7 treats animal experience in relation to the continuum view I am developing, while Chapter 8 reviews Fodor’s contribution to perceptual psychology. It is argued that the view of experiential content being developed is both consistent with empirical data on informationally local perceptual sub-systems, but also accords well with evolutionary theory and a naturalist interpretation of Kant’s taxonomy. Part III deals with inferentialism in the philosophy of science. In Chapter 9, I assess the theory dependence of observation thesis as it is advanced by Paul Feyerabend. I bring out of his account a subtle confusion concerning the importance of inference in the context of scientific inquiry. Part IV deals with the issue of experience in the philosophy of mind. In Chapter 10, I look at Wilfred Sellars’s attack on sense data theories. Chapter 11 confronts Paul Churchland’s treatment of ‘folk psychology’ while Chapter 12 isolates the issue of experiential qualia and the position of property dualism. I offer a critical review of Thomas Nagel’s work in this chapter and claim that his position can be read in a way which is consistent with the continuum account I am developing. I conclude the book in the usual fashion with a summary of the central claims. (shrink)

This thesis is about experiential content: what it is; what kind of account can be given of it. I am concerned with identifying and attacking one main view - I call it the inferentialist proposal. This account is central to the philosophy of mind, epistemology and philosophy of science and perception. I claim, however, that it needs to be recast into something far more subtle and enriched, and I attempt to provide a better alternative in these pages. The inferentialist proposal (...) holds that experiential content is necessarily under¬pinned by sophisticated cognitive influences. My alternative, the continuum theory, holds that these influences are relevant to experience only at certain levels of organisation and that at other levels there are contents which such features do not capture at all. Central to my account is that there are degrees to which cognitive influences affect experiential content; indeed, for the most part, experience is an amalgam of both inferential and non-inferential features. I claim that the inferentialist proposal is fundamentally flawed and deserves replacement, and I argue that my alternative fills the hollow that remains. The thesis is divided into four sections. In Part I, Chapter 1, I introduce two traditionally rival views of experiential content. In Chapter 2, I develop my continuum alternative. Chapter 3 assesses the relationship between experience and language, while Chapter 4 explores the relationship between beliefs and experience. The overall argument is that it has been a mistake to understand experience simply in inferential or non-inferential terms. In Part II, I examine the structure of mental content. Chapter 5 is concerned with the kinds of experiences which escape the inferentialist analysis. Chapter 6 considers Kant’s metaphysic of experience counterpointed to Lorenz’s reading of his work in the light of evolutionary biology. Chapter 7 treats animal experience in relation to the continuum view I am developing, while Chapter 8 reviews Fodor’s contribution to perceptual psychology. It is argued that the view of experiential content being developed is both consistent with empirical data on informationally local perceptual sub-systems, but also accords well with evolutionary theory and a naturalist interpretation of Kant’s taxonomy. Part III deals with inferentialism in the philosophy of science. In Chapter 9, I assess the theory dependence of observation thesis as it is advanced by Paul Feyerabend. I bring out of his account a subtle confusion concerning the importance of inference in the context of scientific inquiry. Part IV deals with the issue of experience in the philosophy of mind. In Chapter 10, I look at Wilfred Sellars’s attack on sense data theories. Chapter 11 confronts Paul Churchland’s treatment of ‘folk psychology’ while Chapter 12 isolates the issue of experiential qualia and the position of property dualism. I offer a critical review of Thomas Nagel’s work in this chapter and claim that his position can be read in a way which is consistent with the continuum account I am developing. I conclude the thesis in the usual fashion with a summary of the central claims. (shrink)

This paper is on Aristotle's conception of the continuum. It is argued that although Aristotle did not have the modern conception of real numbers, his account of the continuum does mirror the topology of the real number continuum in modern mathematics especially as seen in the work of Georg Cantor. Some differences are noted, particularly as regards Aristotle's conception of number and the modern conception of real numbers. The issue of whether Aristotle had the notion of open (...) versus closed intervals is discussed. Finally, it is suggested that one reason there is a common structure between Aristotle's account of the continuum and that found in Cantor's definition of the real number continuum is that our intuitions about the continuum have their source in the experience of the real spatiotemporal world. A plea is made to consider Aristotle's abstractionist philosophy of mathematics anew. (shrink)

Although Peirce frequently insisted that continuity was a core component of his philosophical thought, his conception of it evolved considerably during his lifetime, culminating in a theory grounded primarily in topical geometry. Two manuscripts, one of which has never before been published, reveal that his formulation of this approach was both earlier and more thorough than most scholars seem to have realized. Combining these and other relevant texts with the better-known passages highlights a key ontological distinction: a collection is (...) bottom-up, such that the parts are real and the whole is an ens rationis, while a continuum is top-down, such that the whole is real and the parts are entia rationis. Accordingly, five properties are jointly necessary and sufficient for Peirce’s topical continuum: rationality, divisibility, homogeneity, contiguity, and inexhaustibility. (shrink)

A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both “time” and “world” are considered as mutually independent modes of existence. The theory combines elements of (...) Bohmian mechanics and of Everett’s many-worlds interpretation; it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett’s approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random “collapse of the wavefunction” caused by the measurement, while still being an objectively deterministic theory. (shrink)

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly (...) pick out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. (shrink)

It is often argued that the indispensability of continuum models comes from their empirical adequacy despite their decoupling from the microscopic details of the modelled physical system. There is thus a commonly held misconception that temperature varying across a region of space or time can always be accurately represented as a continuous function. We discuss three inter-related cases of temperature modelling — in phase transitions, thermal boundary resistance and slip flows — and show that the continuum view is (...) fallacious on the ground that the microscopic details of a physical system are not necessarily decoupled from continuum models. We show how temperature discontinuities are present in both data (experiments and simulations) and phenomena (theory and models) and how discontinuum models of temperature variation may have greater empirical adequacy and explanatory power. The conclusions of our paper are: a) continuum idealisations are not indispensable to modelling physical phenomena and both continuous and discontinuous representations of phenomena work depending on the context; b) temperature is not necessarily a continuously defined function in our best scientific representations of the world; and c) that its continuity, where applicable, is a contingent matter. We also raise a question as to whether discontinuous representations should be considered truly de-idealised descriptions of physical phenomena. (shrink)

ABSTRACT In previous work I explored how Integral Theory can be applied as a metatheoretical and transdisciplinary framework, in an attempt to arrive at an integrally informed metatheory of addiction. There was an overemphasis on Integral Methodological Pluralism in that thread of research, without clarifying the ontological pluralism of addiction as a multiple object enacted by various methodologies. To arrive at a comprehensive integral metatheory and integral ontology of addiction, I believe it is necessary to include the conception of (...) Integral Pluralism and Integral Enactment Theory as posited by Sean Esbjörn-Hargens. Integral Enactment Theory highlights the phenomenon of addiction as a multiple and dynamic object arising along a continuum of ontological complexity; it adeptly points out how etiological models “co-arise” in relation to methodology (methodological pluralism) to enact a particular reality of addiction (ontological pluralism) while being mediated by the worldview of the subject (epistemological pluralism) applying the method. This article briefly explores the significance of including Integral Pluralism and Integral Enactment Theory in the quest of an integral metatheory and integral ontology of addiction. (shrink)

What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the transfinite deadlock (...) of higher set theory the jewel of mathematical Continuum -- this genuine, even if mostly forgotten today raison d'etre of all set-theoretical enterprises to Infinity and beyond, from Georg Cantor to W. Hugh Woodin to Buzz Lightyear, by simultaneously exhibiting the limits and pitfalls of all old and new reductionist foundational approaches to mathematical truth: be it Cantor's or post-Cantorian Idealism, Brouwer's or post-Brouwerian Constructivism, Hilbert's or post-Hilbertian Formalism, Goedel's or post-Goedelian Platonism. -/- In the spirit of Zeno's paradoxes, but with the enormous historical advantage of hindsight, we claim that Cantor's set-theoretical methodology, powerful and reach in proof-theoretic and similar applications as it might be, is inherently limited by its epistemological framework of transfinite local causality, and neither can be held accountable for the properties of the Continuum already acquired through geometrical, analytical, and arithmetical studies, nor can it be used for an adequate, conceptually sensible, operationally workable, and axiomatically sustainable re-creation of the Continuum. -/- From a strictly mathematical point of view, this intrinsic limitation of the constative and explicative power of higher set theory finds its explanation in the identified in this study ultimate phenomenological obstacle to Cantor's transfinite construction, similar to topological obstacles in homotopy theory and theoretical physics: the entanglement capacity of the mathematical Continuum. (shrink)

In this paper I reconstruct and discuss Antonio Rubio (1546-1615)’s theory of the composition of the continuum, as set out in his Tractatus de compositione continui, a part of his influential commentary on Aristotle’s Physics, published in 1605 but rewritten in 1606. Here I attempt especially to show that Rubio’s is a significant case of Scholastic overlapping between Aristotle’s theory of infinitely divisible parts and indivisibilism or ‘Zenonism’, i.e. the theory that allows for indivisibles, extensionless points, (...) lines, and surfaces, which are supposed to take part in the composition of the continuum. Even if such a syncretic tendency was, in many different ways, already developing in the medieval period and then at the end of the sixteenth century, Rubio’s position is indeed peculiar. He maintains that indivisibles are real and actual, infinite in act, really distinct from each other, and that, although they indwell in substance, indivisibles do not contribute directly to the constitution of the continuum. In this reconstruction I emphasize notably Rubio’s usage of mereological notions like those of part, whole, completeness and incompleteness. (shrink)

In Cybernetics (1961 Edition), Professor Norbert Wiener noted that “The role of information and the technique of measuring and transmitting information constitute a whole discipline for the engineer, for the neuroscientist, for the psychologist, and for the sociologist”. Sociology aside, the neuroscientists and the psychologists inferred “information transmitted” using the discrete summations from Shannon Information Theory. The present author has since scrutinized the psychologists’ approach in depth, and found it wrong. The neuroscientists’ approach is highly related, but remains unexamined. (...) Neuroscientists quantified “the ability of [physiological sensory] receptors (or other signal-processing elements) to transmit information about stimulus parameters”. Such parameters could vary along a single continuum (e.g., intensity), or along multiple dimensions that altogether provide a Gestalt – such as a face. Here, unprecedented scrutiny is given to how 23 neuroscience papers computed “information transmitted” in terms of stimulus parameters and the evoked neuronal spikes. The computations relied upon Shannon’s “confusion matrix”, which quantifies the fidelity of a “general communication system”. Shannon’s matrix is square, with the same labels for columns and for rows. Nonetheless, neuroscientists labelled the columns by “stimulus category” and the rows by “spike-count category”. The resulting “information transmitted” is spurious, unless the evoked spike-counts are worked backwards to infer the hypothetical evoking stimuli. The latter task is probabilistic and, regardless, requires that the confusion matrix be square. Was it? For these 23 significant papers, the answer is No. (shrink)

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s (...) theory of rest and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises. (shrink)

We aim to show that Kant’s theory of time is consistent by providing axioms whose models validate all synthetic a priori principles for time proposed in the Critique of Pure Reason. In this paper we focus on the distinction between time as form of intuition and time as formal intuition, for which Kant’s own explanations are all too brief. We provide axioms that allow us to construct ‘time as formal intuition’ as a pair of continua, corresponding to time as (...) ‘inner sense’ and the external representation of time as a line Both continua are replete with infinitesimals, which we use to elucidate an enigmatic discussion of ‘rest’ in the Metaphysical foundations of natural science. Our main formal tools are Alexandroff topologies, inverse systems and the ring of dual numbers. (shrink)

Noise and silence as social phenomena with certain depths in terms of their cultural value, when viewed through the lens of the mindsponge theory, become very interesting and often contain many underlying educational implications.

What happens to the inner light of consciousness with the death of the individual body and brain? Reductive materialism assumes it simply fades to black. Others think of consciousness as indicating a continuation of self, a transformation, an awakening or even alternatives based on the quality of life experience. In this issue, speculation drawn from theoretic research are presented. -/- Table of Contents Epigraph: From “The Immortal”, Jorge Luis Borges iii Editor’s Introduction: I Killed a Squirrel the Other Day, Gregory (...) M. Nixon iv-xi Research Essays The Tilde Fallacy and Reincarnation: Variations on a "Skeptical" Argument Teed Rockwell 862-881 Death, Consciousness, and Phenomenology, Steve Bindeman 882-899 The Idealist View of Consciousness After Death, Bernardo Kastrup 900-909 Consciousness, a Cosmic Phenomenon—A Hypothesis, Eva Déli 910-930 The Theory of a Natural Afterlife: A Newfound, Real Possibility for What Awaits Us at Death, Bryon K. Ehlmann 931-950 Near-Death Cases Desegregating Non-Locality/Disembodiment via Quantum Mediated Consciousness: An Extended Version of the Cell-Soul Pathway, Contzen Pereira & J Shashi Kiran Reddy 951-968 On the Possible Existence of Quantum Consciousness After Brain Death, Massimo Pregnolato & Alfredo Pereira Jr. 969-991 Science and Postmortem Survival, Edward F. Kelly 992-1011 Explorations ISS Theory: Cosmic Consciousness, Self, and Life Beyond Death in a Hyperdimensional Physics, Chris H. Hardy 1012-1035 Does the Consciousness End, Remain Awake, or Transform After Death? Radivoj Stankovich (with Micho Durdevich) 1036-1050 Big Bang Spirituality, Life, and Death, Ken Bausch 1051-1063 Death, Consciousness and the Quantum Paradigm, Ronald Peter Glasberg 1064-1077 Living With Limits: The Continuum of Consciousness, Donald Brackett 1078-1098 Mysticism, Consciousness, Death, Mike Sosteric 1099-1118 What Dies? Eternalism and the Afterlife in William James, Jonathan Bricklin 1119-1140 Theories of Consciousness and Death: Does Consciousness End, Continue, Awaken, or Transform When the Body Dies? Roger Cook 1141-1153 It’s the Other Way Around: Matter is a Form of Consciousness and Death is the End of the Illusion of Life in the World, James P. Kowall & Pradeep B. Deshpande 1154-1208 Statements A Feminine Vision for the World Consciousness, & a New Outrageous Ontology, Lorna Green 1209-1217 The Mask of Eternity: The Quest for Immortality and the Afterlife, Iona Miller 1218-1228 Are We Really “such stuff as dreams are made on”? Chris Nunn 1229-1225 Is the Afterlife a Non-Question? (Let's Hope Not), Deepak Chopra 1226-1230 Life After Death? An Improbable Essay, Stuart Kauffman 1231-1236. (shrink)

The original purpose of the present study, 2011, started with a preprint «On the Probable Failure of the Uncountable Power Set Axiom», 1988, is to save from the transfinite deadlock of higher set theory the jewel of mathematical Continuum — this genuine, even if mostly forgotten today raison d’être of all traditional set-theoretical enterprises to Infinity and beyond, from Georg Cantor to David Hilbert to Kurt Gödel to W. Hugh Woodin to Buzz Lightyear.

According to Brentano's theory of boundaries, no boundary can exist without being connected with a continuum. But there is no specifiable part of the continuum, and no point, which is such that we may say that it is the existence of that part or of that point which conditions the boundary. - An adequate theory of the continuum must now recognize that boundaries be boundaries only in certain directions and not in others. This leads to (...) consequences in other areas, too. (shrink)

A methodological model of origin and settlement of theory-choice situations (previously tried on the theories of Einstein and Lorentz in electrodynamics) is applied to modern Theory of Gravity. The process of origin and growth of empirically-equivalent relativistic theories of gravitation is theoretically reproduced. It is argued that all of them are proposed within the two rival research programmes – (1) metric (A. Einstein et al.) and (2) nonmetric (H. Poincare et al.). Each programme aims at elimination of the (...) cross-contradiction between the special theory of relativity and Newton’s theory of gravitation. New arguments in favor of Einstein’s programme are given. Nevertheless, this does not imply the necessity to rule out all the nonmetric theories, since Einstein’s and Poincare’s programmes are alternative only as different tools of the cross-contradiction elimination. In the other respects these programmes are complementary: description, explanation and prediction of gravitational experimental data entails the usage of the languages of nonmetric theories as well as of metric ones. The part of the present investigation elucidating the necessity of nonmetric theories is an implementation of the ideas of A.Z. Petrov, the founder of Kazan University Relativity Department. Late Alexei Zinovievich had frequently punctuated that the notion of Riemann space-time continuum common for all metric theories obfuscates all the gravitational notions considerably and hampers the analogies with other physical theories at hand. Since the ambiguity is a hallmark of all the general relativism notions, approach to their definitions “should be determined not by analogies and contingent facts, but by general considerations linked the physical measurements theory… No matter how far the events lie out of the frames of classical physical explanations, all the experimental data should be described by classical notions” (Petrov, 1965,pp. 59,66). Key words: Kip S. Thorne, A.P. Lightman, Stepin, theory of gravity . (shrink)

DEFINING OUR TERMS A “paradox" is an argumentation that appears to deduce a conclusion believed to be false from premises believed to be true. An “inconsistency proof for a theory" is an argumentation that actually deduces a negation of a theorem of the theory from premises that are all theorems of the theory. An “indirect proof of the negation of a hypothesis" is an argumentation that actually deduces a conclusion known to be false from the hypothesis alone (...) or, more commonly, from the hypothesis augmented by a set of premises known to be true. A “direct proof of a hypothesis" is an argumentation that actually deduces the hypothesis itself from premises known to be true. Since `appears', `believes' and `knows' all make elliptical reference to a participant, it is clear that `paradox', `indirect proof' and `direct proof' are all participant-relative. PARTICIPANT RELATIVITY In normal mathematical writing the participant is presumed to be “the community of mathematicians" or some more or less well-defined subcommunity and, therefore, omission of explicit reference to the participant is often warranted. However, in historical, critical, or philosophical writing focused on emerging branches of mathematics such omission often invites confusion. One and the same argumentation has been a paradox for one mathematician, an inconsistency proof for another, and an indirect proof to a third. One and the same argumentation-text can appear to one mathematician to express an indirect proof while appearing to another mathematician to express a direct proof. WHAT IS A PARADOX’S SOLUTION? Of the above four sorts of argumentation only the paradox invites “solution" or “resolution", and ordinarily this is to be accomplished either by discovering a logical fallacy in the “reasoning" of the argumentation or by discovering that the conclusion is not really false or by discovering that one of the premises is not really true. Resolution of a paradox by a participant amounts to reclassifying a formerly paradoxical argumentation either as a “fallacy", as a direct proof of its conclusion, as an indirect proof of the negation of one of its premises, as an inconsistency proof, or as something else depending on the participant's state of knowledge or belief. This illustrates why an argumentation which is a paradox to a given mathematician at a given time may well not be a paradox to the same mathematician at a later time. -/- The present article considers several set-theoretic argumentations that appeared in the period 1903-1908. The year 1903 saw the publication of B. Russell's Principles of mathematics, [Cambridge Univ. Press, Cambridge, 1903; Jbuch 34, 62]. The year 1908 saw the publication of Russell's article on type theory as well as Ernst Zermelo's two watershed articles on the axiom of choice and the foundations of set theory. The argumentations discussed concern “the largest cardinal", “the largest ordinal", the well-ordering principle, “the well-ordering of the continuum", denumerability of ordinals and denumerability of reals. The article shows that these argumentations were variously classified by various mathematicians and that the surrounding atmosphere was one of confusion and misunderstanding, partly as a result of failure to make or to heed distinctions similar to those made above. The article implies that historians have made the situation worse by not observing or not analysing the nature of the confusion. -/- RECOMMENDATION This well-written and well-documented article exemplifies the fact that clarification of history can be achieved through articulation of distinctions that had not been articulated (or were not being heeded) at the time. The article presupposes extensive knowledge of the history of mathematics, of mathematics itself (especially set theory) and of philosophy. It is therefore not to be recommended for casual reading. AFTERWORD: This review was written at the same time Corcoran was writing his signature “Argumentations and logic”[249] that covers much of the same ground in much more detail. https://www.academia.edu/14089432/Argumentations_and_Logic . (shrink)

This paper presents a comparative evaluation of constructivist and error theoretic accounts of moral claims. It is argued that constructivism has distinct advantages over error theory.

How to account for metaphor has long been a contentious issue within pragmatics. Revisiting this debate, Wilson & Carston (2019) analyse Grice’s oft-discussed exclusion of metaphor as an empirically unjustified use of cut-off points on the empirical continuum of language and link it a tension between his underlying focus on formalisation contrary to their aim of maximising pragmatics’ empirical scope. In spite of the latter, Relevance Theory’s various own models fail to account for essential characteristics of metaphor caused (...) by certain non-propositional effects eluding its grasp and subsequently excluded. Rather than solving this with new tools, as Wilson & Carston propose, this paper seeks to examine the aforementioned tension and its link to the use of cut-off points they criticised. I will argue that Relevance Theory, too, uses cut-off points, highlighting their nature as the effect of a shared approach vis-à-vis formalisation rather than an individual flaw of Grice’s: Both exclude certain empirical effects of language in pursuance of a unified theory of communication organised around the notion of intention and grounded in teleological assumptions external to language. Drawing on Derrida’s analogous critique of Austin’s pragmatics, I will illustrate the paradoxical nature of such cut-off points and possible ways forward. (shrink)

African jurisprudence, like African philosophy, continues to be hotly debated. This article contends that the debate straddles the uniqueness claim which either emphasises the existence or possibility of a peculiar legal framework on the continent, and a historical co-extensional position reiterating that African jurisprudence is a continuum of other legal traditions. The article argues that there is no uniquely African jurisprudence, and that what obtains within the structures of jurisprudence on the continent also exists within various legal traditions elsewhere, (...) and as such can at best be described as ‘jurisprudence in Africa’ rather than ‘African jurisprudence’. It defends this thesis through analytic and comparative explications of the content of natural law theory and legal positivism as experienced on the continent. It concedes that relics of the colonial legal experience create contestations that inform scholars’ calls for a return to traditional legal systems. It concludes that a reconstructive jurisprudence in Africa must take cognisance of the continent’s historical and evolutionary legal experiences, but that a unified or monolithic theory may not be sufficient to address the choice of functional jurisprudence. Keywords African jurisprudence, jurisprudence in Africa, African legal evolution, diffused legal theories. (shrink)

In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of the (...) concept of ‘denumerability’ as it is presented in set theory as well as his philosophic refutation of Cantor’s Diagonal Argument and the implications of such a refutation onto the problems of the Continuum Hypothesis and Cantor’s Theorem. Throughout, the discussion will be placed within the historical and philosophical framework of the Grundlagenkrise der Mathematik and Hilbert’s problems. (shrink)

The philosophy of mathematics has been accused of paying insufficient attention to mathematical practice: one way to cope with the problem, the one we will follow in this paper on extensive magnitudes, is to combine the `history of ideas' and the `philosophy of models' in a logical and epistemological perspective. The history of ideas allows the reconstruction of the theory of extensive magnitudes as a theory of ordered algebraic structures; the philosophy of models allows an investigation into the (...) way epistemology might affect relevant mathematical notions. The article takes two historical examples as a starting point for the investigation of the role of numerical models in the construction of a system of non-Archimedean magnitudes. A brief exposition of the theories developed by Giuseppe Veronese and by Rodolfo Bettazzi at the end of the 19th century will throw new light on the role played by magnitudes and numbers in the development of the concept of a non-Archimedean order. Different ways of introducing non-Archimedean models will be compared and the influence of epistemological models will be evaluated. Particular attention will be devoted to the comparison between the models that oriented Veronese's and Bettazzi's works and the mathematical theories they developed, but also to the analysis of the way epistemological beliefs affected the concepts of continuity and measurement. (shrink)

I look at the distinction between between realist and antirealist views of the quantum state. I argue that this binary classification should be reconceived as a continuum of different views about which properties of the quantum state are representationally significant. What's more, the extreme cases -- all or none --- are simply absurd, and should be rejected by all parties. In other words, no sane person should advocate extreme realism or antirealism about the quantum state. And if we focus (...) on the reasonable views, it's no longer clear who counts as a realist, and who counts as an antirealist. Among those taking a more reasonable intermediate view, we find figures such as Bohr and Carnap -- in stark opposition to the stories we've been told. (shrink)

At the turn of the seventeenth century, Bruno and Cavalieri independently developed two theories, central to which was the concept of the geometrical indivisible. The introduction of indivisibles had significant implications for geometry – especially in the case of Cavalieri, for whom indivisibles provided a forerunner of the calculus. But how did this event occur? What can we learn from the fact that two theories of indivisibles arose at about the same time? These are the questions addressed in this paper. (...) Relying on the methodology of “historical epistemology”, this paper asserts that the similarities and differences between the theories of Bruno and Cavalieri can be explained in terms of “shared knowledge”. The paper shows that the idea – on which both Bruno and Cavalieri build – that geometrical objects are generated by motion was part of the mathematical culture of the time. Tracing this idea back to its Pythagorean origins thus sheds light on the relationship between motion and continuum in mathematics. (shrink)

The main subject of this paper is the two significant problems of environmental ethics which are ecofascism and speciesism. This scrutiny offers an evaluative perspective on the main problems of environmental ethics and is conducted with this aim. Most of the environmental philosophers, all the difficulties notwithstanding, try to find a middle way in the ecofascism-speciesism continuum and their theories get closer to one or the other edge of this continuum. John Baird Callicott is one of the environmental (...) philosophers who struggle with this issue when his theory indicates one of the problems or gets closer to one of the edges, he tries to find a new way to go. There are six turns in Callicott's philosophy starting with strong holism due to accepting Leopold's land ethic as a basis. Then, he constructed a theory that pushes him closer to the speciesist edge, and finally, he found a way out from these fatal consequences. However, all the environmental philosophers face the same problems in their journey although they are either holists or individualists in the end. In constructing a holistic environmental ethical theory, for instance, they may be in ecofascism difficulty because holism requires man to be an ordinary member of the biotic community as seen in the first turn. Or, establishing a special place for humankind to ditch the ecofascism crisis may cause another equally important crisis, namely, speciesism (see the third turn). Some philosophers prefer to be closer to one of the edges always being on guard against the other. Some others, like Callicott, try to find a middle way equally far from the edges. However, this choice is no easier. Selecting to be a member of both the human community and biotic community brings different problems, such as ranking problems between the duties and obligations toward the communities and their members, i.e. a challenge to decision-making processes. For such problems, they come up with some principles or rules like second-order principles (SOPs) as Callicott did (in the fifth turn). But, these rules or principles are not sufficient enough to solve the ranking problems of setting priorities among our duties to members of both communities, either. Thus, either there is a need for more regulations and rules, or these two communities should be separated in a different dimension and gathered at another level. The second choice is preferred by Callicott and used as a solution to the main problem: constructing an environmental ethical theory that involves whole nature with its members and which is free from two essential problems (see the sixth turn). As a final point, Callicott's last theory seems to point to the conclusion that an environmental ethical theory is possible without falling into the ecofascism and speciesism traps, i.e. his last stand can facilitate the attainment of the main subject of this essay. (shrink)

Information flow in a system is a core cybernetics concept. It has been used frequently in Sensory Psychology since 1951. There, Shannon Information Theory was used to calculate "information transmitted" in "absolute identification" experiments involving human subjects. Originally, in Shannon's "system", any symbol received ("outcome") is among the symbols sent ("events"). Not all symbols are received as transmitted, hence an indirect noise measure is calculated, "information transmitted", which requires knowing the confusion matrix, its columns labeled by "event" and its (...) rows labeled by "outcome". Each matrix entry is dependent upon the frequency with which a particular outcome corresponds to a particular event. However, for the sensory psychologist, stimulus intensities are "events"; the experimenter partitions the intensity continuum into ranges called "stimulus categories" and "response categories", such that each confusion-matrix entry represents the frequency with which a stimulus from a stimulus category falls within a particular response category. Of course, a stimulus evokes a sensation, and the subject's immediate memory of it is compared to the memories of sensations learned during practice, to make a categorization. Categorizing thus introduces "false noise", which is only removed if categorizations can be converted back to their hypothetical evoking stimuli. But sensations and categorizations are both statistically distributed, and the stimulus that corresponds to a given mean categorization cannot be known from only the latter; the relation of intensity to mean sensation, and of mean sensation to mean categorization, are needed. Neither, however, are presently knowable. This is a quandary, which arose because sensory psychologists ignored an ubiquitous component of Shannon's "system", the uninvolved observer, who calculates "information transmitted". Human sensory systems, however, are within de facto observers, making "false noise" inevitable. (shrink)

Space-time intervals are the fundamental components of conscious experience, gravity, and a Theory of Everything. Space-time intervals are relationships that arise naturally between events. They have a general covariance (independence of coordinate systems, scale invariance), a physical constancy, that encompasses all frames of reference. There are three basic types of space-time intervals (light-like, time-like, space-like) which interact to create space-time and its properties. Human conscious experience is a four-dimensional space-time continuum created through the processing of space-time intervals by (...) the brain; space-time intervals are the source of conscious experience (observed physical reality). Human conscious experience is modeled by Einstein’s special theory of relativity, a theory designed specifically from the general covariance of space-time intervals (for inertial frames of reference). General relativity is our most accurate description of gravity. In general relativity, the general covariance of space-time intervals is extended to all frames of reference (inertial and non-inertial), including gravitational reference frames; space-time intervals are the source of gravity in general relativity. The general covariance of space-time intervals is further extended to quantum mechanics; space-time intervals are the source of quantum gravity. The general covariance of space-time intervals seamlessly merges general relativity with quantum field theory (the two grand theories of the universe). Space-time intervals consequently are the basis of a Theory of Everything (a single all-encompassing coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe). This theoretical framework encompasses our observed physical reality (conscious experience) as well; space-time intervals link observed physical reality to actual physical reality. This provides an accurate and reliable match between observed physical reality and the physical universe by which we can carry on our activity. The Minkowski metric, which defines generally covariant space-time intervals, may be considered an axiom (premise, postulate) for the Theory of Everything. (shrink)

The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the relativity of mathematical languages used to describe the Turing machines. A deep investigation is performed on the interrelations between mechanical computations and their mathematical descriptions emerging when a human (the researcher) starts to describe a Turing machine (the object of the study) by (...) different mathematical languages (the instruments of investigation). Together with traditional mathematical languages using such concepts as ‘enumerable sets’ and ‘continuum’ a new computational methodology allowing one to measure the number of elements of different infinite sets is used in this paper. It is shown how mathematical languages used to describe the machines limit our possibilities to observe them. In particular, notions of observable deterministic and non-deterministic Turing machines are introduced and conditions ensuring that the latter can be simulated by the former are established. (shrink)

Our understanding of ourselves and the world as historical has drastically changed since the postwar period, yet this emerging historical sensibility has not been appropriately explained in a coherent theory of history. In this book, Zoltán Simon argues that instead of seeing the past, the present and the future together on a temporal continuum as history, we now expect unprecedented change to happen in the future and we look at the past by assuming that such changes have already (...) happened. This radical theory of history challenges narrative conceptualizations of history which assume a past potential of humanity unfolding over time to reach future fulfillment and seeks new ways of conceptualizing the altered socio-cultural concerns Western societies are currently facing. By creating a novel set of concepts to make sense of our altered historical condition regarding both history understood as the course of human affairs and historical writing, History in Times of Unprecedented Change offers a highly original and engaging take on the state of history and historical theory in the present and beyond. (shrink)

This paper reveals errors within Norwich et al.’s Entropy Theory of Perception, errors that have broad implications for our understanding of perception. What Norwich and coauthors dubbed their “informational theory of neural coding” is based on cybernetics, that is, control and communication in man and machine. The Entropy Theory uses information theory to interpret human performance in absolute judgments. There, the continuum of the intensity of a sensory stimulus is cut into categories and the subject (...) is shown exemplar stimuli of each category. The subject must then identify individual exemplars by category. The identifications are recorded in the Garner-Hake version of the Shannon “confusion matrix”. The matrix yields “H”, the entropy (degree of uncertainty) about what stimulus was presented. Hypothetically, uncertainty drops as a stimulus lengthens, i.e. a plot of H vs. stimulus duration should fall monotonically. Such “adaptation” is known for both sensation and firing rate. Hence, because “the physiological adaptation curve has the same general shape as the psychophysical adaptation curve”, Norwich et al. assumed that both have the same time course; sensation and firing rate were thus both declared proportional to H. However, a closer look reveals insurmountable contradictions. First, the peripheral neuron hypothetically cannot fire in response to a stimulus of a given intensity until after somehow computing H from its responses to stimuli of various intensities. Thus no sensation occurs until firing rate adapts, i.e. attains its spontaneous rate. But hypothetically, once adaptation is complete, certainty is reached and perception ends. Altogether, then, perception cannot occur until perception is over. Secondly, sensations, firing rates, and H’s are empirically not synchronous, contrary to assumption. In sum, the core concept of the cybernetics-based Entropy Theory of Perception, that is, that uncertainty reduction is the basis for perception, is irrational. (shrink)

An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the `width' of the set theoretic universe, such as Cantor's continuum hypothesis. Within a higher-order framework I show that contingency about (...) the width of the set-theoretic universe refutes two orthodoxies concerning the structure of modal reality: the view that the broadest necessity has a logic of S5, and the "Leibniz biconditionals" stating that what is possible, in the broadest sense of possible, is what is true in some possible world. Nonetheless, I suggest that the underlying picture of modal set-theory is coherent and has attractions. (shrink)

Set-theoretic pluralism is an increasingly influential position in the philosophy of set theory (Balaguer [1998], Linksy and Zalta [1995], Hamkins [2012]). There is considerable room for debate about how best to formulate set-theoretic pluralism, and even about whether the view is coherent. But there is widespread agreement as to what there is to recommend the view (given that it can be formulated coherently). Unlike set-theoretic universalism, set-theoretic pluralism affords an answer to Benacerraf’s epistemological challenge. The purpose of this paper (...) is to determine what Benacerraf’s challenge could be such that this view is warranted. I argue that it could not be any of the challenges with which it has been traditionally identified by its advocates, like of Benacerraf and Field. Not only are none of the challenges easier for the pluralist to meet. None satisfies a key constraint that has been placed on Benacerraf’s challenge. However, I argue that Benacerraf’s challenge could be the challenge to show that our set-theoretic beliefs are safe – i.e., to show that we could not have easily had false ones. Whether the pluralist is, in fact, better positioned to show that our set-theoretic beliefs are safe turns on a broadly empirical conjecture which is outstanding. If this conjecture proves to be false, then it is unclear what the epistemological argument for set-theoretic pluralism is supposed to be. (shrink)

A number of general theories of physics provide a model for the fundamental rules that govern our universe, becoming a structural framework to which the new discoveries must conform. The theory of relativity is such a general theory. The theory of relativity is a complex theoretical framework that facilitates the understanding of the universal laws of physics. It is based on the curved space-time continuum fabric abstract concept, and it is well suited for interpreting cosmic events. (...) More so, a general theory based on abstract concepts and imagination facilitates the emergence of countless new extravagant theories. A new simplified theory of the natural world is necessary, a simple theory that provides a verifiable framework on which new discoveries can be integrated. The paper describes a view of the abstract time/space concept, and also a very simple model of our ever-changing universe. Views of physicists, mathematicians, chemists, engineers and of course philosophers have to be all in harmony with such a theory. We leave in a beautiful, uniform, and logical world. We live in a world where everything probable is possible. Contact email: [email protected] . (shrink)

It is traditionally thought that metaphorical utterances constitute a special— nonliteral—kind of departure from lexical constraints on meaning. Dan Sperber and Deirdre Wilson have been forcefully arguing against this: according to them, relevance theory’s comprehension/interpretation procedure for metaphorical utterances does not require details specifi c to metaphor (or nonliteral discourse); instead, the same type of comprehension procedure as that in place for literal utterances covers metaphors as well. One of Sperber and Wilson’s central reasons for holding this is that (...) metaphorical utterances occupy one end of a continuum that includes literal, loose and hyperbolic utterances with no sharp boundaries in between them. Call this the continuum argument about interpreting metaphors. My aim is to show that this continuum argument doesn’t work. For if it were to work, it would have an unwanted consequence: it could be converted into a continuum argument about interpreting linguistic errors, including slips of the tongue, of which malaprops are a special case. In particular, based on the premise that the literal–loose–metaphorical continuum extends to malaprops also, we could conclude that the relevance-theoretic comprehension procedure for malaprops does not require details specifi c to linguistic errors, that is, details beyond those already in place for interpreting literal utterances. Given that we have good reason to reject this conclusion, we also have good reason to rethink the conclusion of the continuum argument about interpreting metaphors and consider what additional (metaphor-specifi c) details—about the role of constraints due to what is lexically encoded by the words used—might be added to relevance-theoretic comprehension procedures. (shrink)

This paper offers an overview of various alternative formulations for Analysis, the theory of Integral and Differential Calculus, and its diverging conceptions of the topological structure of the continuum. We pay particularly attention to Smooth Analysis, a proposal created by William Lawvere and Anders Kock based on Grothendieck’s work on a categorical algebraic geometry. The role of Heyting’s logic, common to all these alternatives is emphasized.

This report reviews what quantum physics and information theory have to tell us about the age-old question, How come existence? No escape is evident from four conclusions: (1) The world cannot be a giant machine, ruled by any preestablished continuum physical law. (2) There is no such thing at the microscopic level as space or time or spacetime continuum. (3) The familiar probability function or functional, and wave equation or functional wave equation, of standard quantum theory (...) provide mere continuum idealizations and by reason of this circumstance conceal the information-theoretic source from which they derive. (4) No element in the description of physics shows itself as closer to primordial than the elementary quantum phenomenon, that is, the elementary device-intermediated act of posing a yes-no physical question and eliciting an answer or, in brief, the elementary act of observer-participancy. Otherwise stated, every physical quantity, every it, derives its ultimate significance from bits, binary yes-or-no indications, a conclusion which we epitomize in the phrase, it from bit. (shrink)

In this paper I reconstruct and discuss Antonio Rubio (1546-1615)’s theory of the composition of the continuum, as set out in his Tractatus de compositione continui, a part of his influential commentary on Aristotle’s Physics, published in 1605 but rewritten in 1606. Here I attempt especially to show that Rubio’s is a significant case of Scholastic overlapping between Aristotle’s theory of infinitely divisible parts and indivisibilism or ‘Zenonism’, i.e. the theory that allows for indivisibles, extensionless points, (...) lines, and surfaces, which are supposed to take part in the composition of the continuum. Even if such a syncretic tendency was, in many different ways, already developing in the medieval period and then at the end of the sixteenth century, Rubio’s position is indeed peculiar. He maintains that indivisibles are real and actual, infinite in act, really distinct from each other, and that, although they indwell in substance, indivisibles do not contribute directly to the constitution of the continuum. In this reconstruction, I emphasize notably Rubio’s usage of mereological notions like those of part, whole, completeness and incompleteness. (shrink)

It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is (...) countable and that the continuum is a proper class. We examine several principles based on maximality considerations in this framework, and show how some (namely Ordinal Inner Model Hypotheses) enable us to incorporate standard set theories (including ZFC with large cardinals added). We conclude that the systems considered raise questions concerning the foundational purposes of set theory. (shrink)

In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.

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)

In a previous paper we outlined a series of historical touchpoints between classical aether theories and modern theoretical physics which showed a shared conceptual lineage for the modern tools and methods of the most common interpretations and fluid based “Hydrodynamic” treatments of an electromagnetic medium. It was proposed that, though the weight of modern experimentation leaves an extremely narrow and convoluted window for even a reconceptualization of a medium, all of modern physics recognizes a plethora of behaviors and attributes for (...) free space and these physics are interchangeable with modern methods for treating superfluid-like continuums. Thus the mathematical equivalence of the methods do not comprise alternative physics but an alternative interpretation of the same physics. Though many individual components describing a “neo-aether” or “quintessence” are available, an overarching structural outline of how these tools can work together to provide an alternative working overview of modern physics has remained undefined. This paper will propose a set of introductory concepts in the first outline of a toy model which will later connect the alternative tools and conceptualizations with their modern counterparts. This introductory paper provides the simpler “100-miles out” overview of the whole of physics from this perspective, in an easily comprehensible, familiar and intuitive, informal dialog fashion. While this paper grants the largest and loosest introductory overview, subsequent papers in this series will address the finite connections between modern physics and this hydrodynamic view. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

On September 11, 2001, many of us experienced life as what it is not: we lived an extreme instance of the spectacle, of the sublime outside the realm of ethics. Starting with a few compelling questions that the media representations of the attack on the New York World Trade Center inevitably raise, this paper explores a series of similarities, continuums, and extrapolations of the aesthetic in different types of discourse from Friedrich Schiller to Guy Debord. My assessment of the individual‘s (...) dissolution in the ritual (former dissident and present Czech President Václav Havel‘s phrase) rejects the bleak Marxist theories of manipulation, without overlooking, at the same time, the potential dangers of unfreedom that the process of surrendering to the spectacle implies. Living life as show time may ultimately, and oxymoronically, prove to be the only option toward an infinitude of choices. (shrink)

This article establishes grounds on which attributions of information and encoding in animal signals are warranted. As common interest increases between evolutionary agents, the theoretical approach best suited to describing their interaction shifts from evolutionary game theory to communication theory, which warrants informational language. The take-home positive message is that in cooperative settings, signals can appropriately be described as transmitting encoded information, regardless of the cognitive powers of signalers. The canonical example is the honeybee waggle dance, which is (...) discussed extensively in the second and third sections. The take-home negative message is that signals are not always a consequence of coadaptation. The communication theory approach is just one end of a continuum explored more thoroughly by evolutionary game theory. The fourth and fifth sections explore this wider framework, as well as overturning some widely held misconceptions about information theory. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

In the field theories in physics, any particular region of the presumed space-time continuum and all interactions between elementary objects therein can be objectively measured and/or accounted for mathematically. Since this does not apply to any of thefield theories, or any other neural theory, of consciousness, their explanatory power is limited. As discussed in detail herein, the matter is complicated further by the facts than any scientifically operational definition of consciousness is inevitably partial, and that the phenomenon has (...) no spatial dimensionality. Under the light of insights from research on meditation and expanded consciousness, chronic pain syndrome, healthy aging, and eudaimonic well being, we may conceive consciousness as a source of potential energy that has no clearly defined spatial dimensionality, but can produce significant changes in others and in the world, observable in terms of changes in time. It is argued that consciousness may have evolved to enable the human species to generate such changes in order to cope with unprecedented and/or unpredictable adversity. Such coping could, ultimately, include the conscious planning of our own extinction when survival on the planet is no longer an acceptable option. (shrink)

In the Critique of Pure Reason, Kant defends the mathematically deterministic world of physics by arguing that its essential features arise necessarily from innate forms of intuition and rules of understanding through combinatory acts of imagination. Knowing is active: it constructs the unity of nature by combining appearances in certain mandatory ways. What is mandated is that sensible awareness provide objects that conform to the structure of ostensive judgment: “This (S) is P.” -/- Sensibility alone provides no such objects, so (...) the imagination compensates by combining passing point-data into “pure” referents for the subject-position, predicate-position, and copula. The result is a cognitive encounter with a generic physical object whose characteristics—magnitude, substance, property, quality, and causality—are abstracted as the Kantian categories. Each characteristic is a product of “sensible synthesis” that has been “determined” by a “function of unity” in judgment. -/- Understanding the possibility of such determination by judgment is the chief difficulty for any rehabilitative reconstruction of Kant’s theory. I will show that Kant conceives of figurative synthesis as an act of line-drawing, and of the functions of unity as rules for attending to this act. The subject-position refers to substance, identified as the objective time-continuum; the predicate-position, to quality, identified as the continuum of property values (constituting the second-order type named by the predicate concept). The upshot is that both positions refer to continuous magnitudes, related so that one (time-value) is the condition of the other (property-value). -/- Kant’s theory of physically constructive grammar is thus equivalent to the analytic-geometric formalism at work in the practice of mathematical physics, which schematizes time and state as lines related by an algebraic formula. Kant theorizes the subject–predicate relation in ostensive judgment as an algebraic time–state function. When aimed towards sensibility, “S is P” functions as the algebraic relation “t → ƒ(t).”. (shrink)