The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets. Several counting systems are taken into consideration. It is emphasized in the paper that different mathematical languages can describe mathematical objects (in particular, sets and the number of their (...) elements) with different accuracies. The traditional and the new approaches are compared and discussed. (shrink)

This paper aims to show that Frege’s and Hilbert’s mutual disagreement results from different notions of Anschauung and their relation to axioms. In the first section of the paper, evidence is provided to support that Frege and Hilbert were influenced by the same developments of 19th-century geometry, in particular the work of Gauss, Plücker, and von Staudt. The second section of the paper shows that Frege and Hilbert take different approaches to deal with the problems that (...) the developments in 19th-century geometry posed for the traditional Kantian philosophy of mathematics. Frege maintains that Anschauung is a source of knowledge by which we acknowledge geometrical axioms as true. For Hilbert, in contrast, axioms provide one of several correct “pictures” of reality. Hilbert’s position is thereby deeply influenced by epistemological ideas from Hertz and Helmholtz, and, in turn, influenced the neo-Kantian Cassirer. (shrink)

This dissertation examines several of the problems that Hilbert discovered in the foundations of mathematics, from a metalogical perspective. The problems manifest themselves in four different aspects of Hilbert’s views: (i) Hilbert’s axiomatic approach to the foundations of mathematics; (ii) His response to criticisms of set theory; (iii) His response to intuitionist criticisms of classical mathematics; (iv) Hilbert’s contribution to the specification of the role of logical inference in mathematical reasoning. This dissertation argues that Hilbert’s (...) axiomatic approach was guided primarily by model theoretical concerns. Accordingly, the ultimate aim of his consistency program was to prove the model-theoretical consistency of mathematical theories. It turns out that for the purpose of carrying out such consistency proofs, a suitable modification of the ordinary first-order logic is needed. To effect this modification, independence-friendly logic is needed as the appropriate conceptual framework. It is then shown how the model theoretical consistency of arithmetic can be proved by using IF logic as its basic logic. Hilbert’s other problems, manifesting themselves as aspects (ii), (iii), and (iv)—most notably the problem of the status of the axiom of choice, the problem of the role of the law of excluded middle, and the problem of giving an elementary account of quantification—can likewise be approached by using the resources of IF logic. It is shown that by means of IF logic one can carry out Hilbertian solutions to all these problems. The two major results concerning aspects (ii), (iii) and (iv) are the following: (a) The axiom of choice is a logical principle; (b) The law of excluded middle divides metamathematical methods into elementary and non-elementary ones. It is argued that these results show that IF logic helps to vindicate Hilbert’s nominalist philosophy of mathematics. On the basis of an elementary approach to logic, which enriches the expressive resources of ordinary first-order logic, this dissertation shows how the different problems that Hilbert discovered in the foundations of mathematics can be solved. (shrink)

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of (...) Hilbert mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions. (shrink)

The central motivating idea behind the development of this work is the concept of prespace, a hypothetical structure that is postulated by some physicists to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the rest of reality as we know it, and the implications of the existence of this structure for quantum theory. Understanding how this structure could relate to space and to the rest of reality requires, I (...) believe, that we consider how space itself relates to reality, and how other so-called "spaces" used in physics relate to reality. In chapter 2, I compare space and space-time to other spaces used in physics, such as configuration space, phase space and Hilbert space. I support what is known as the "property view" of space, opposing both the traditional views of space and space-time, substantivalism and relationism. I argue that all these spaces are property spaces. After examining the relationships of these spaces to causality, I argue that configuration space has, due to its role in quantum mechanics, a special status in the microscopic world similar to the status of position space in the macroscopic world. In chapter 3, prespace itself is considered. One way of approaching this structure is through the comparison of the prespace structure with a computational system, in particular to a cellular automaton, in which space or space-time and all other physical quantities are broken down into discrete units. I suggest that one way open for a prespace metaphysics can be found if physics is made fully discrete in this way. I suggest as a heuristic principle that the physical laws of our world are such that the computational cost of implementing those laws on an arbitrary computational system is minimized, adapting a heuristic principle of this type proposed by Feynman. In chapter 4, some of the ideas of the previous chapters are applied in an examination of the physics and metaphysics of quantum theory. I first discuss the "measurement problem" of quantum mechanics: this problem and its proposed solution are the primary subjects of chapter 4. It turns out that considering how quantum theory could be made fully discrete leads naturally to a suggestion of how standard linear quantum mechanics could be modified to give rise to a solution to the measurement problem. The computational heuristic principle reinforces the same solution. I call the modified quantum mechanics Critical Complexity Quantum Mechanics (CCQM). I compare CCQM with some of the other proposed solutions to the measurement problem, in particular the spontaneous localization model of Ghirardi, Rimini and Weber. Finally, in chapters 5 and 6, I argue that the measure of complexity of quantum mechanical states I introduce in CCQM also provides a new definition of entropy for quantum mechanics, and suggests a solution to the problem of providing an objective foundation for statistical mechanics, thermodynamics, and the arrow of time. (shrink)

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

We consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary evidence-based definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways: (1) in terms of classical algorithmic verifiabilty; and (2) in terms of finitary algorithmic computability. We then show that the two definitions correspond to two distinctly different assignments of satisfaction and (...) truth to the compound formulas of PA over N---I_PA(N; SV ) and I_PA(N; SC). We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both I_PA(N; SV ) and I_PA(N; SC). We then show: (a) that if we assume the satisfaction and truth of the compound formulas of PA are always non-finitarily decidable under I_PA(N; SV ), then this assignment corresponds to the classical non-finitary putative standard interpretation I_PA(N; S) of PA over the domain N; and (b) that the satisfaction and truth of the compound formulas of PA are always finitarily decidable under the assignment I_PA(N; SC), from which we may finitarily conclude that PA is consistent. We further conclude that the appropriate inference to be drawn from Goedel's 1931 paper on undecidable arithmetical propositions is that we can define PA formulas which---under interpretation---are algorithmically verifiable as always true over N, but not algorithmically computable as always true over N. We conclude from this that Lucas' Goedelian argument is validated if the assignment I_PA(N; SV ) can be treated as circumscribing the ambit of human reasoning about `true' arithmetical propositions, and the assignment I_PA(N; SC) as circumscribing the ambit of mechanistic reasoning about `true' arithmetical propositions. (shrink)

We present a new approach to the invariant subspace problem for complex Hilbert spaces.This approach based on nonconservative Extension of the Model Theoretical NSA. Our main result will be that: if T is a bounded linear operator on an infinite-dimensional complex separable Hilbert space H,it follow that T has a non-trivial closed invariant subspace.

This paper critically examines color relationalism and color relativism, two theories of color that are allegedly supported by variation in normal human color vision. We mostly discuss color relationalism, defended at length in Jonathan Cohen's The Red and the Real, and argue that the theory has insuperable problems.

Panpsychism, the view that consciousness is present everywhere at the fundamental level of reality, has established itself as an increasingly popular option in the philosophy of mind. Situated between substance dualism and reductive physicalism, panpsychism aims to capture the intuitions behind both, integrating consciousness into the physical world without explaining it in terms of purely physical facts. In this thesis, I offer a defence of panpsychism. -/- First, I examine influential arguments against physicalism, such as Thomas Nagel’s (1974, 1979) (...) perspective-based proposal, Frank Jackson’s (1982) knowledge argument, David Chalmers’ (1996, 2010) conceivability argument, as well as vagueness arguments (Antony 2006a; Tye 1996). I argue that none of them offers a knockdown case against physicalism, particularly because of the threat presented by the phenomenal concept strategy (Chalmers 2007; Papineau 2007a), though they suggest panpsychism as a promising alternative that avoids many common objections. -/- Second, I discuss independent arguments for panpsychism, including the Russellian monist view (Goff 2017; Russell 1927/1992), the intrinsic nature argument (Seager 2006; Strawson 2006), recent developments in the literature as presented by Hedda Hassel Mørch (2018, 2020) and Luca Dondoni (2022), Tye’s (2021b) representational panpsychism based on the vagueness argument, as well as cosmopsychism (Nagasawa & Wager 2016; Shani 2015) – an alternative to panpsychism that shares its aims whilst claiming to avoid its shortcomings. -/- Third, I address the most pressing objection to panpsychism: the combination problem or the question of how fundamental consciousness can combine to lead to complex consciousness (James 1890). Focusing especially on the subject-summing version of the combination problem or the issue of how small subjects can combine to form complex subjects, I go over various proposals for either solving or avoiding it, such as Philip Goff’s (2016) phenomenal bonding relation and William Seager’s (2010) combinatorial infusion proposal, arguing against both and agreeing at the end with Sam Coleman (2014), who advocates that subject-summing is demonstrably incoherent. -/- However, as I argue in the fourth and final chapter, the panpsychist still has an option that avoids the subject-summing problem, while also circumventing the objections faced by the alternative view of cosmopsychism. Inspired though not reliant on the philosophy of Gottfried Wilhelm Leibniz (1902/2005), I introduce what I call monadic panpsychism, the view that the phenomenal character of any given consciousness-bearing physical ultimate is determined by its relations to other such ultimates featuring in the relevant causal structure. -/- The theory consists of two key claims. The first is that phenomenal qualities are relational rather than intrinsic. This view has precedent in literature on the philosophy of mind, such as in Rudolf Carnap (1928), Gottlob Frege (1956), Moritz Schlick (1959), as well as more recently in David Hilbert and Mark Kalderon (2000) and Austen Clark (2000), though not in the context of panpsychism. -/- The second claim is that physical ultimates only possess a very basic form of consciousness necessary for experiencing as such. There are many ways to conceptualise this basic consciousness: non-relational or intrinsic, rudimentary and non-specific, a point of view without experiences, the minimal subject, a mere conduit for experience, phenomenal space, etc. Russellian panpsychists offer a more detailed proposal in which every physical ultimate has an appropriate associated type of experience. For example, all quarks have the same quark-type of experience, assuming for the sake of discussion that quarks are ultimates. Still, arguing for a more minimal notion, as I do, requires making less claims and should not be controversial to any panpsychist. -/- So, what follows from these two claims? I propose that the relational constitution of phenomenal qualities has its endpoint at the fundamental level rather than at the level of a combined complex or emergent subject. Put simply, physical ultimates guarantee the basic consciousness or the point of view that I occupy, while the relational structure constitutes my rich and full human experience. So to speak, relationally constituted phenomenal qualities ‘anchor’ themselves in physical ultimates. As long as these relations result in a phenomenally unified experience, which is an uncontroversial thesis, then no matter where that process reaches the end of its causal chain, it will necessarily be experienced from a subjective point of view. -/- Since only qualities but not subjects need to combine, my proposal avoids the subject-summing version of the combination problem, which is arguably an insurmountable challenge to other forms of panpsychism. Because of this, I conclude that my theory contributes to the field, serving as a good starting point for further developments of neither combinatory nor emergent panpsychism with regard to subjects. (shrink)

The moral belief problem is that of reconciling expressivism in ethics with both minimalism in the philosophy of language and the syntactic discipline of moral sentences. It is argued that the problem can be solved by distinguishing minimal and robust senses of belief, where a minimal belief is any state of mind expressed by sincere assertoric use of a syntactically disciplined sentence and a robust belief is a minimal belief with some additional property R. Two attempts to specify (...) R are discussed, both based on the thought that beliefs are states that aim at truth. According to the first, robust beliefs are criticisable to the extent that their content fails to match the state of the world. This sense fails to distinguish robust beliefs from minimal beliefs. According to the second, robust beliefs function to have their content match the state of the world. This sense succeeds in distinguishing robust beliefs from minimal beliefs. The conclusion is that the debate concerning the cognitive status of moral convictions needs to address the issue of the function of moral convictions. Evolutionary theorising may be relevant, but will not be decisive, in answering this question. (shrink)

The aim of this paper is to discuss a seemingly straightforward argument against physicalism which, despite being implicit in much of the philosophical debate about consciousness, has not received the attention it deserves (compared to other, better-known “epistemic”, “modal”, and “conceivability” arguments). This is the argument from the non-supervenience of the first-personal (and indexical) facts on the third-personal (and non-indexical) ones. This non-supervenience, together with the assumption that the physical facts (as conventionally understood) are third-personal, entails that some facts (...) – namely, first-personal, phenomenal ones – do not supervene on the physical facts. Unlike other arguments against physicalism, the first-personal argument, if successful, refutes not only physicalism but also other third-personal metaphysical pictures, including standard versions of dualism. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted (...) rather a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

One puzzling feature of Plato’s Republic is the First City or ‘city of pigs’. Socrates praises the First City as a “true”, “healthy” city, yet Plato abandons it with little explanation. I argue that the problem is not a political failing, as most previous readings have proposed: the First City is a viable political arrangement, where one can live a deeply Socratic lifestyle. But the First City has a psychological corollary, that the soul is simple (...) rather than tripartite. Plato sees this ‘First Soul’ as an inaccurate model of moral psychology, and so rejects it, along with its political analogue. (shrink)

The many-property problem has traditionally been taken to show that the adverbial theory of perception is untenable. This paper first shows that several widely accepted views concerning the nature of perception---including both representational and non-representational views---likewise face the many-property problem. It then presents a solution to the many-property problem for these views, but goes on to show how this solution can be adapted to provide a novel, fully compositional solution to the many-property problem for adverbialism. (...) Thus, with respect to the many-property problem, adverbialism and several widely accepted views in the philosophy of perception are on a par, and the problem is solved. (shrink)

ABSTRACT: Abilify MyCite was granted regulatory approval in 2017, becoming the world’s first “smart pill” that could digitally track whether patients had taken their medication. The new technology was introduced as one that had gained the support of patients and ethicists alike, and could contribute to solving the widespread and costly problem of patient nonadherence. Here, we offer an in-depth exploration of this narrative, through an examination of the origins and development of Abilify, the drug that would later (...) become MyCite. This history illuminates how an antipsychotic can become a top-selling drug and maintain its blockbuster status for more than a decade. It also provides a detailed case study for how knowledge is constructed within the logic of biomedical capitalism, providing impetus to reexamine claims regarding how MyCite addresses patient nonadherence, engenders patient support, and is ethicist-approved. (shrink)

An important part of the mind-brain problem arises because sentience and consciousness seem inherently resistant to scientific explanation and understanding. The solution to this dilemma is to recognize, first, that scientific explanation can only render comprehensible a selected aspect of what there is, and second, that there is a mode of explanation and understanding, the personalistic, quite different from, but just as viable as, scientific explanation. In order to understand the mental aspect of brain processes - that aspect (...) we know about as a result of having relevant neurological processes occur in our own brain - we need to avail ourselves of personalistic explanation, irreducible to scientific explanation. The problem of explaining and understanding why experiential or mental aspects of brain processes or things should be correlated with certain physical processes, things or states of affairs is a non-problem because there is no kind of explanation possible in terms of which an explanation could be couched. A physical theory, amplified to include the experiential, might be predictive but would, necessarily, cease to be explanatory; and an amplified personalistic explanation could not succeed either. There is, in short, an explanation as to why there cannot be an explanation of correlations between physical and mental aspects of processes going on inside our heads. (shrink)

The hypothesis that God supernaturally raised Jesus from the dead is argued by William Lane Craig to be the best explanation for the empty tomb and postmortem appearances of Jesus because it satisfies seven criteria of adequacy better than rival naturalistic hypotheses. We identify problems with Craig’s criteria-based approach and show, most significantly, that the Resurrection hypothesis fails to fulfill any but the first of his criteria—especially explanatory scope and plausibility.

In this paper, I argue for a version of panpsychist idealism on first-person experiential grounds. As things always appear in my field of consciousness, there is prima facie empirical support for idealism. Furthermore, by assuming that all things correspond to a conscious perspective or perspectives (i.e., panpsychism), realism about the world is arguably safeguarded without the need to appeal to God (as per Berkeley’s idealism). Panpsychist idealism also has a phenomenological advantage over traditional panpsychist views as it does not (...) commit perceptual experience to massive error by denying that perceived colours are properties of things. Finally, I argue that the subject combination problem for panpsychism has been motivated by the problematic assumption that consciousness is in things. Thinking about subject combination from the first-person perspective is fruitful for reframing the subject combination problem and for seeing how subjects could potentially combine for the idealist. (shrink)

My primary aim in this chapter is to explain in what the traditional mind–body problem consists, what its possible solutions are, and what obstacles lie in the way of a resolution. The discussion will develop in two phases. The first phase, sections 1.2–1.4, will be concerned to get clearer about the import of our initial question as a precondition of developing an account of possible responses to it. The second phase, sections 1.5–1.6, explains how a problem arises (...) in our attempts to answer the question we have characterized, and surveys the various solutions that can be and have been offered. More specifically, sections 1.2–1.4 are concerned with how to understand the basic elements of our initial question – how we should identify the mental, on the one hand, and the physical, on the other – and with what sorts of relations between them we are concerned. Section 1.2 identifies and explains the two traditional marks of the mental, consciousness and intentionality, and discusses how they are related. Section 1.3 gives an account of how we should understand ‘physical’ in our initial question so as not to foreclose any of the traditional positions on the mind–body problem. Section 1.4 then addresses the third element in our initial question, mapping out the basic sorts of relations that may hold between mental and physical phenomena, and identifying some for special attention. Sections 1.5–1.6 are concerned with explaining the source of the difficulty in answering our initial question, and the kinds of solutions that have been offered to it. Section 1.5 explains why our initial question gives rise to a problem, and gives a precise form to the mind–body problem, which is presented as a set of four propositions, each of which, when presented independently, seems compelling, but which are jointly inconsistent. Section 1.6 classifies responses to the mind–body problem on the basis of which of the propositions in our inconsistent set they reject, and provides a brief overview of the main varieties in each category, together with some of the difficulties that arise for each. Section 1.7 is a brief conclusion about the source of our difficulties in understanding the place of mind in the natural world. (shrink)

In this paper I begin to develop an account of the acquaintance that each of us has with our own conscious states and processes. The account is a speculative proposal about human mental architecture and specifically about the nature of the concepts via which we think in first personish ways about our qualia. In a certain sense my account is neutral between physicalist and dualist accounts of consciousness. As will be clear, a dualist could adopt the account I will (...) offer while maintaining that qualia themselves are non-physical properties. In this case the non-physical nature of qualia may play no role in accounting for the features of acquaintance. But although the account could be used by a dualist, its existence provides support for physicalism. (shrink)

In this survey, a recent computational methodology paying a special attention to the separation of mathematical objects from numeral systems involved in their representation is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the Euclid’s Common Notion no. 5 “The whole is greater than the (...) part” applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The methodology uses a computational device called the Infinity Computer (patented in USA and EU) working numerically (recall that traditional theories work with infinities and infinitesimals only symbolically) with infinite and infinitesimal numbers that can be written in a positional numeral system with an infinite radix. It is argued that numeral systems involved in computations limit our capabilities to compute and lead to ambiguities in theoretical assertions, as well. The introduced methodology gives the possibility to use the same numeral system for measuring infinite sets, working with divergent series, probability, fractals, optimization problems, numerical differentiation, ODEs, etc. (recall that traditionally different numerals lemniscate; Aleph zero, etc. are used in different situations related to infinity). Numerous numerical examples and theoretical illustrations are given. The accuracy of the achieved results is continuously compared with those obtained by traditional tools used to work with infinities and infinitesimals. In particular, it is shown that the new approach allows one to observe mathematical objects involved in the Hypotheses of Continuum and the Riemann zeta function with a higher accuracy than it is done by traditional tools. It is stressed that the hardness of both problems is not related to their nature but is a consequence of the weakness of traditional numeral systems used to study them. It is shown that the introduced methodology and numeral system change our perception of the mathematical objects studied in the two problems. (shrink)

In the first part of this investigation we highlight two, seemingly irreconcilable, beliefs that suggest an impending crisis in the teaching, research, and practice of—primarily state-supported—mathematics: (a) the belief, with increasing, essentially faith-based, conviction and authority amongst academics that first-order Set Theory can be treated as the lingua franca of mathematics, since its theorems—even if unfalsifiable—can be treated as ‘knowledge’ because they are finite proof sequences which are entailed finitarily by self-evidently Justified True Beliefs; and (b) the slowly (...) emerging, but powerfully rooted in economic imperatives, belief that only those Justified True Beliefs can be treated as ‘knowledge’ which are, further, categorically communicable as Factually Grounded Beliefs—hence as comprehensible pre-formal ‘mathematical truths’—by any intelligence that lays claims to a mathematical lingua franca. We argue that this seeming irreconcilability merely reflects a widening chasm between an increasing under-estimation of the value to society of ‘semantic arithmetical truth’, and an increasing over-estimation of the value to society of ‘syntactic set-theoretical provability’; a chasm which must be narrowed and bridged explicitly. We thus proffer a Complementarity Thesis which seeks to recognize that mathematical ‘provability’ and mathematical ‘truth’ need to be interdependent and complementary, ‘evidence-based’, assignments-by-convention to the formulas of a formal mathematical language; where (a) the goal of mathematical ‘proofs’ may be viewed as seeking to ensure that any mathematical language intended to formally represent our pre-formal conceptual metaphors and their inter-relatedness is unambiguous, and free from contradiction; whilst (b) the goal of mathematical ‘truths’ must be viewed as seeking to ensure that any such representation does, indeed, uniquely identify and adequately represent such metaphors and their inter-relatedness. Our thesis is that, by universally ignoring the need to introduce goal (b) in our curriculum, the teaching of, and research in, mathematics at the post-graduate level cannnot justify its value to society beyond the mere intellectual stimulation of individual minds. In the second part we appeal to some recent—and hitherto unsuspected—unarguably constructive Tarskian interpretations, of the first-order Peano Arithmetic PA, which establish PA as both finitarily consistent, and categorical. Since we also show that the second order subsystem ACA0 of Peano Arithmetic and PA cannot both be assumed provably consistent, we conclude that there can be no mathematical, or meta-mathematical, proof of consistency for Set Theory. Hence the theorems of any Set Theory are not sufficient for distinguishing between (i) what we can believe to be a ‘mathematical truth’; (ii) what we can evidence as a ‘mathematical truth’; and (iii) what we ought not to believe is a ‘mathematical truth’; whilst the theorems of the first-order Peano Arithmetic PA are sufficient for distinguishing between (i), (ii) and (iii). We conclude from this that the holy grail of mathematics ought to be ‘arithmetical truth’, not ‘set-theoretical proof’. (shrink)

Mobile Edge Computing (MEC) is an emerging technology that enables computing directly at the edge of the cloud computing network. Therefore, it is important that MEC is applied with reliable transmission. The problem of reaching consensus in the distributed system is one of the most important issues in designing a reliable transmission network. However, all previous protocols for the consensus problem are not suitable for an MEC paradigm. It is the first time an optimal protocol of reaching (...) consensus is pro- posed for MEC paradigm. The protocol makes all fault-free nodes communicate with each other and collect the exchanged messages to decide a common value. Based on the common value, the protocol ensures all fault-free nodes reach consensus without the influence of unreliable transmission. Finally, we proved theoretically that the proposed protocol can tolerate the maximum number of faulty components and using only two rounds of message exchanges. (shrink)

The objective of this paper is twofold. First, I present a framework called historical coherentism (Chang, 2004; Tal, 2016; Van fraassen 2008) and argue that it is the best epistemological framework available to tackle the problem of coordination, an epistemic conundrum that arises with every attempt to provide empirical content to scientific theories, models or statements. Second, I argue that the problem of coordination, which has so far been theorized only in the context of measurement practices (Reichenbach, (...) 1927; Chang, 2001; Tal, 2012; Van fraassen 2008), can be generalized beyond the philosophy of measurement. Specifically, it will be shown that the problem is embodied in classificatory practices and that, consequently, historical coherentism is well suited to analyze these practices as well as metrological ones. As a case study, I look at a contemporary debate in phylogenetics, regarding the evolutionary origin of a newly identified archaeal phylum called Methanonatronarchaeia. Exploring this debate through the lens of historical coherentism provides a detailed understanding of the dynamics of the field and a foothold for critical analyses of the standard rationale used by practitioners. (shrink)

The basic idea of quantum mechanics is that the property of any system can be in a state of superposition of various possibilities. This state of superposition is also known as wave function and it evolves linearly with time in a deterministic way in accordance with the Schrodinger equation. However, when a measurement is carried out on the system to determine the value of that property, the system instantaneously transforms to one of the eigen states and thus we get only (...) a single value as outcome of the measurement. Quantum measurement problem seeks to find the cause and exact mechanism governing this transformation. In an attempt to solve the above problem, in this paper, we will first define what the wave function represents in real world and will identify the root cause behind the stochastic nature of events. Then, we will develop a model to explain the mechanism of collapse of the quantum mechanical wave function in response to a measurement. In the process of development of model, we will explain Schrodinger cat paradox and will show how Born’s rule for probability becomes a natural consequence of measurement process. (shrink)

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with (...) other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems). (shrink)

The first article of the cycle “The role of skeptical evidence in the First and Second ‘Meditations’” compares the Cartesian and Sextus Empiricus’ concepts of doubt in, respectively, “Metaphysical meditations” and “Outlines of Pyrrhonism”. The article starts with the current state of the problem “Descartes and skepticism” and admits the existence of consensus about Cartesian perception of skeptical tradition: Cartesius (1) was influenced by all skeptical movements, known in his time, and (2) created a generalized notion that (...) contains elements of both Academic and Pyrrhonian origin. This consensus is the source of many contemporary studies on how different skeptical doctrines influenced certain parts of Cartesian philosophy. This article attempts to analyze possible Descartes’ use of Sextus Empiricus’ notion of phenomenon. Sextus clearly states in “Outlines of Pyrrhonism” that one cannot doubt phenomenon as something perceived directly. The article proves that (a) Sextus’ thesis about the “sensory” nature of phenomenon is metaphorical, so far as it includes (without distinction) both sensuality and the experience of thinking; (b) the phenomenon is realized through a wide range of passive states of mind that all have irresistible force of influence; (c) the impact of phenomena is always mediated by our self, because all skeptical phrases are strictly correlated with the first person singular. Some researchers distinguish Sextus’ isostenia, as one of such insurmountable states, from Cartesian doubt at the First Meditation, which is allegedly based on a purely volitional decision. The article proved that this argument is artificial, since Descartes’ volitional decision is caused by initial inability to take the dubious as if it were certain. Thus, Cartesian approach can be considered a specific kind of isostenia. Such parallelism is a reason to assume a key role of Sextus’ understanding of insurmountable power of phenomena in Cartesian anti-sceptical argumentation. This assumption will be tested in the following articles of the cycle. (shrink)

There are many controversial theses about intrinsicness and duplication. The first aim of this paper is to introduce a puzzle that shows that two of the uncontroversial sounding ones can’t both be true. The second aim is to suggest that the best way out of the puzzle requires sharpening some distinctions that are too frequently blurred, and adopting a fairly radical reconception of the ways things are.

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 main topic of this paper is the mind-body problem. The author analyzes it in the context of Hus- serlian phenomenology. The key texts for the analysis and interpretation are Descartes’ magnum opus “Meditations on the First Philosophy” and Husserl’ last work “The Crisis of European Sciences and Transcendental Phenomenology”. The author claims that already in Descartes’ text instead of one mind-body problem, one can find two: the ontological mind-body problem (mind-brain relation) and conceptual one (“mind” (...) and “body” as concepts). In Descartes’ “Meditations”, the ontological level is explicit, while the conceptual level is implicit. In Husserl’s “Crisis”, on the other hand, the situation is different: the conceptual level of the problem (as the opposition between transcendental phenomenology and natural sciences) is explicit, while the ontological level is implicit. Nevertheless, it seems that Husserl has answers to both the “traditional” as well as the “conceptual” mind-body problems. (shrink)

The main topic of this paper is the mind-body problem. The author analyzes it in the context of Hus- serlian phenomenology. The key texts for the analysis and interpretation are Descartes’ magnum opus “Meditations on the First Philosophy” and Husserl’ last work “The Crisis of European Sciences and Transcendental Phenomenology”. The author claims that already in Descartes’ text instead of one mind-body problem, one can find two: the ontological mind-body problem (mind-brain relation) and conceptual one (“mind” (...) and “body” as concepts). In Descartes’ “Meditations”, the ontological level is explicit, while the conceptual level is implicit. In Husserl’s “Crisis”, on the other hand, the situation is different: the conceptual level of the problem (as the opposition between transcendental phenom- enology and natural sciences) is explicit, while the ontological level is implicit. Nevertheless, it seems that Husserl has answers to both the “traditional” as well as the “conceptual” mind-body problems. (shrink)

Despite its many advantages as a metaethical theory, moral expressivism faces difficulties as a semantic theory of the meaning of moral claims, an issue underscored by the notorious Frege-Geach problem. I consider a distinct metaethical view, inferentialism, which like expressivism rejects a representational account of meaning, but unlike expressivism explains meaning in terms of inferential role instead of expressive function. Drawing on Michael Williams’ recent work on inferential theories of meaning, I argue that an appropriate understanding of the pragmatic (...) role of moral discourse—the facilitation of coordinated social behavior—suggests the kind of inferences we should expect terms with this function to license. I offer a sketch of the inferential roles the moral ‘ought’ plays, and argue that if we accept that the relevant inferential roles are meaning-constitutive, we will be in a position to solve the Frege-Geach problem. Such an inferentialist solution has advantages over those forwarded by expressivists such as Blackburn and Gibbard. First, it offers a more straightforward explanation of the meaning of moral terms. It also gives simple answers to at least two semantic worries that have vexed contemporary expressivists—the “problem of permissions” and the commitment to “mentalism”, both of which I argue are problems that don’t get traction with an inferentialist approach. I conclude by considering ways in which this approach can be expanded into a more robust semantic account. (shrink)

Peter Baumann uses the Monty Hall game to demonstrate that probabilities cannot be meaningfully applied to individual games. Baumann draws from this first conclusion a second: in a single game, it is not necessarily rational to switch from the door that I have initially chosen to the door that Monty Hall did not open. After challenging Baumann's particular arguments for these conclusions, I argue that there is a deeper problem with his position: it rests on the false assumption (...) that what justifies the switching strategy is its leading me to win a greater percentage of the time. In fact, what justifies the switching strategy is not any statistical result over the long run but rather the "causal structure" intrinsic to each individual game itself. Finally, I argue that an argument by Hilary Putnam will not help to save Baumann's second conclusion above. (shrink)

The brain is composed of electrically excitable neuronal networks regulated by the activity of voltage-gated ion channels. Further portraying the molecular composition of the brain, however, will not reveal anything remotely reminiscent of a feeling, a sensation or a conscious experience. In classical physics, addressing the mind–brain problem is a formidable task because no physical mechanism is able to explain how the brain generates the unobservable, inner psychological world of conscious experiences and how in turn those conscious experiences steer (...) the underlying brain processes toward desired behavior. Yet, this setback does not establish that consciousness is non-physical. Modern quantum physics affirms the interplay between two types of physical entities in Hilbert space: unobservable quantum states, which are vectors describing what exists in the physical world, and quantum observables, which are operators describing what can be observed in quantum measurements. Quantum no-go theorems further provide a framework for studying quantum brain dynamics, which has to be governed by a physically admissible Hamiltonian. Comprising consciousness of unobservable quantum information integrated in quantum brain states explains the origin of the inner privacy of conscious experiences and revisits the dynamic timescale of conscious processes to picosecond conformational transitions of neural biomolecules. The observable brain is then an objective construction created from classical bits of information, which are bound by Holevo’s theorem, and obtained through the measurement of quantum brain observables. Thus, quantum information theory clarifies the distinction between the unobservable mind and the observable brain, and supports a solid physical foundation for consciousness research. (shrink)

Growing concern with the panpsychist's ostensive inability to solve the ‘combination problem’ has led some authors to adopt a view titled ‘Cosmopsychism’. This position turns panpsychism on its head: rather than many tiny atomic minds, there is instead one cosmos-sized mind. It is supposed that this view voids the combination problem, however I argue that it does not. I argue that there is a ‘de-combination problem’ facing the cosmopsychist, which is equivalent to the combination problem as (...) they are both concerned with subjects being proper parts of other subjects. I then propose two methods for both theorists to avoid the problem of subject-subject proper parthood relations: a distinction between absolute and relative phenomenal unity, and a modification of the essential nature of subjects. Of these two options, I find the latter option wanting and propose that the first should be adopted. (shrink)

Arthur Clark and Michael Kube–McDowell (“The Triger”, 2000) suggested the sci-fi idea about the direct transformation from a chemical substance to another by the action of a newly physical, “Trigger” field. Karl Brohier, a Nobel Prize winner, who is a dramatic persona in the novel, elaborates a new theory, re-reading and re-writing Pauling’s “The Nature of the Chemical Bond”; according to Brohier: “Information organizes and differentiates energy. It regularizes and stabilizes matter. Information propagates through matter-energy and mediates the interactions of (...) matter-energy.” Dr Horton, his collaborator in the novel replies: “If the universe consists of energy and information, then the Trigger somehow alters the information envelope of certain substances –“. “Alters it, scrambles it, overwhelms it, destabilizes it” Brohier adds. There is a scientific debate whether or how far chemistry is fundamentally reducible to quantum mechanics. Nevertheless, the fact that many essential chemical properties and reactions are at least partly representable in terms of quantum mechanics is doubtless. For the quantum mechanics itself has been reformulated as a theory of a special kind of information, quantum information, chemistry might be in turn interpreted in the same terms. Wave function, the fundamental concept of quantum mechanics, can be equivalently defined as a series of qubits, eventually infinite. A qubit, being defined as the normed superposition of the two orthogonal subspaces of the complex Hilbert space, can be interpreted as a generalization of the standard bit of information as to infinite sets or series. All “forces” in the Standard model, which are furthermore essential for chemical transformations, are groups [U(1),SU(2),SU(3)] of the transformations of the complex Hilbert space and thus, of series of qubits. One can suggest that any chemical substances and changes are fundamentally representable as quantum information and its transformations. If entanglement is interpreted as a physical field, though any group above seems to be unattachable to it, it might be identified as the “Triger field”. It might cause a direct transformation of any chemical substance by from a remote distance. Is this possible in principle? (shrink)

The Philosophy of Mind consists of problems concerning aspects and properties of the human mind. The most important of these problems is that of the relation between mind and body, or, more generally, between mental and physical phenomena. Usually referred to as the "mind-body problem", this has been one of the fundamental problems in Philosophy since Descartes (1596-1650) and his critics introduced it four centuries ago. The mental seems, at first glance, completely different from the physical. Physical properties (...) are public, i.e. equally observable by everyone, but mental properties are not. It can be deduced that someone feels pain by his behaviour, but only that person can feel it directly. Conscious mental events are private in the sense that the subject has privileged access to them that no one has for the physical. Conscious experiences, such as the smell of jasmine, are completely different from the configurations and movements, however complex, of particles, atoms and molecules, or the physical changes of cells and tissues. Despite this, conscious phenomena do not seem to arise out of nothing, but from physical-biological processes in the body, especially from neural processes in the brain. But how can physical-biological systems have states such as thoughts, fears and hopes? (shrink)

Introduction to mathematical logic. Part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.

The English Synopsis is after the text of the book. The book presents an original and generalizing substantive vision of the philosophy of science through the prism of a detailed analysis of the polysystem structure of scientific theories. Theories are considered, firstly, as complex specialized forms of developed scientific thinking about the realities studied by natural science, secondly, as constantly improving tools for producing new knowledge in interaction with experimental research, and thirdly, as carriers of ordered and verified knowledge. Emphasis (...) is placed on their nominal and ontic subsystems. The book develops personal and joint research of the authors (theoretical physicist and philosopher), the experience of teaching philosophy of physics at NaUKMA, philosophy of science at the Higher School of Philosophy at the H. Skovoroda Institute of Philosophy of the National Academy of Sciences of Ukraine and theoretical physics at the National Technical University "Ihor Sikorsky Kyiv Polytechnic Institute". The research is based on a significant source base covering works of modern Western researchers in natural science and philosophy of science. For students, teachers, and scientists who are interested in the problems of modern philosophy of science and have a certain amount of scientific knowledge. It will also be useful for high school students who are eager to become scientists. (shrink)

Since its proposal in 1984, Derek Parfit’s ‘Non-Identity Problem’ has significantly influenced how social choice theorists understand existential harms and benefits. The ‘problem’ raises the question of whether parents act wrongly when they choose to create a child with a life barely worth living. It suggests that if the alternatives would have either resulted in a life not worth living or non-existence, then the parents are not liable for moral criticism. This article challenges Parfit’s premise by advocating for (...) a Minimal Concern Clause that is generated through the parental relation. The Clause operates under the assumption that non-existence is not a valanced experiential state and is thus not comparable to any positive state of existence. The argument unfolds in two main steps: firstly, it disputes the premise in Same-Number Cases by proposing an alternative semantic distinction between objects of reference, particularly, the status of a merely possible person. Secondly, it contends that in Different-Number Cases, parents are obligated to exercise minimal prudence under conditions of uncertainty, and that the moral weight of the Minimal Concern Clause must be compounded to reflect the replicable nature of procreation. (shrink)

This paper is an explication of Gadamer's idea of "application." I argue that the relation between the first and third persons in application contains a viable conception of the normativity of understanding. Application includes a measure for understanding. The thing that is to be understood must be allowed to address me, and such involvement responds to the text’s meaning. While this measure is not expressible in principled rules, application is normatively accountable both to the text’s third-person claim to meaning (...) and to my first-person involvement with the text. The participation of the interpreter with the item of her understanding forms a normative standard. (shrink)

The epistemic regress problem targets our ability to provide reasons for our beliefs. If we need reasons for our beliefs, then we may also need to provide reasons for those reasons, and so on into regress. Because the epistemic regress problem is often cast as an attack on our ability to achieve justification, it is often thought that epistemic positions which do not rely on notions like justification escape without difficulty. The first goal of this dissertation is (...) to establish the generality of the epistemic regress problem, beyond all technicalities regarding the nature of justification. To do this, I propose a new minimal epistemic standard, that we should hold no bald assertions to be epistemically acceptable. I then use this epistemic standard to construct two new forms of the epistemic regress problem. The first version of the problem is reminiscent of the classical problem in that it attacks our ability to locate any such reason. The second version of the problem attacks our ability to unite any such reason to a particular claim that it is supposed to support. The second goal of this dissertation is to argue that pragmatism fails as a solution to the epistemic regress problem. The pragmatist seeks to avoid the regress by provisionally accepting their beliefs to be evaluated later. In so doing, the pragmatist seeks to have reasonable beliefs, but only after having accepted them provisionally. After eliminating other theoretical alternatives that the pragmatist may use to bolster their position, I argue that the pragmatic solution is not successful because (1) it is committed to some foundational beliefs that are necessary to facilitate the evaluation of their provisional beliefs which fall prey to the regress, and (2) the employment of these criteria of evaluation encounters the regress in its second form. I conclude by advocating for an understanding of Pyrrhonian skepticism under which we are not required to eschew our everyday beliefs that is nevertheless commensurate with the epistemic regress. (shrink)

The first two sections of the paper characterize the nineteenth century respect for the phenomenal by considering Helmholtz’s position and James’ and Russell’s move to neutral monism. The third section displays a moment’s sympathy with those who recoiled from the latter view -- but only a moment’s. The recoil overshot what was a reasonable response, and denied the reality of the phenomenal, largely in the name of the physical or the material. The final two sections of the paper develop (...) a third way, which retains a healthy respect for the mental and for the mind–body relation, does not attempt to equate objects with congeries of sensations, and does not attempt to deny the reality of the phenomenal. In fact, I will claim that on some conceptions (and not merely idealist-phenomenalist conceptions), the phenomenal is a fact of nature, and hence a part of the natural world. Some aspects of this third way are familiar in the various representational and critical realisms of the twentieth-century. But the realization -- or, more neutrally, the conception -- that the natural might include the phenomenal is less familiar. Yet this position has its predecessors too, not only among the physicists and psychologists of the nineteenth century, but among major physicists (as opposed to physicalist philosophers) and psychologists of the twentieth. [A re-edited version of this paper appears in Gary Hatfield, Perception and Cognition: Essays in the Philosophy of Psychology, Clarendon Press, 2009.]. (shrink)

At the end of the first hypothesis, Parmenides gets Aristotle to agree that being [οὐσίας] must be in time; that is, that being must partake in at least one of the temporal modes: either to have been in the past, to be in the present, or it will be in the future (140e-142a). If this is true, then “the one does not partake in being” (141e7-8), meaning temporal being—to which Aristotle agrees, saying “Apparently not” (141e9). Parmenides then gets Aristotle (...) to agree that “Therefore, ‘the one’ in no way is” (141e9-10). This, however, contradicts the very first premise that begins Parmenides’ entire gymnastic exercise, “if one is” (137c4). The problem with the previous conclusion—that to be is to be in time—is that in professing his assent to it, Aristotle, in fact, gainsays it. He performatively contradicts the very thing he wants to assert. Aristotle answers Parmenides question, “Therefore could something partake of being in any way other than in one of those ways?” (141e7-8) with a two-word answer in Greek: “οὐκ ἔστιν [It’s not possible].” We can, therefore, ask of the very claim Aristotle is making—that it is impossible for something to be and not be in time—when in time does it hold true? At what time is it “not possible [οὐκ ἔστιν]” for something to not partake of temporal being? Is it not possible only in the present moment, in the past, or in the future? If Aristotle’s assertion is to have any force it must hold always. It has the same tenselessness as mathematical propositions, like ‘1+1=2.’ Forms, like mathematical entities, must necessarily have atemporal existence. Accordingly, in atemporally maintaining that anything that is must be in time, Aristotle undermines his own assertion. He performatively contradicts the very thing that he wants to affirm. (shrink)

The problem of demarcating between what is scientific and what is pseudoscientific or merely unscientific - in other words, the problem of defining scientificity - remains open. The modern debate was firstly structured around Karl Popper's falsificationist epistemology from the 1930's, before diversifying a few decades later. His central idea is that what makes something scientific is not so much how adequate it is with data, but rather to what extent it might not have been so. Since the (...) second half of the century, and in the wake of criticisms, such as the Duhem-Quine thesis, that were raised against falsificationism(s), most approaches to the problem of scientific demarcation are now multicriteria and holistic. However, the approach presented in this paper does not follow the same guideline. The present work can be seen as an attempt to adapt Popper's (sophisticated) falsificationism to a model-based view of scientific knowledge. Using formalization and focusing on a particular epistemic unit of analysis (namely, empirical models) allows to properly define the popperian corroboration degree and to view scientificity as the maximization of this degree of corroboration over all available models and data. We eventually recover, in a natural way, well-accepted scientificity criteria: empirical adequacy, Lakatos' progressive problemshifts, balance between strength and simplicity, parsimony, and coherence as special cases of this general scientificity principle. From this viewpoint, the language dependency of our empirical knowledge no longer appears as a limitation of falsificationism but as one more reason to take it as a good epistemological framework. (shrink)

McQueen and Vaidman argue that the Many Worlds Interpretation (MWI) of quantum mechanics provides local causal explanations of the outcomes of experiments in our experience that is due to the total effect of all the worlds together. We show that although the explanation is local in one world, it requires a causal influence that travels across different worlds. We further argue that in the MWI the local nature of our experience is not derivable from the Hilbert space structure, but (...) has to be added to it as an independent postulate. This is due to what we call the factorisation-symmetry and basis-symmetry of Hilbert space. (shrink)

The topic of this paper is the question of in virtue of what first-person thoughts are about what they are about. I focus on a dilemma arising from this question. On the one hand, approaches to answering this question that promise to be satisfying seem doomed to be inconsistent with the seeming truism that first-person thought is always about the thinker of the thought. But on the other hand, ensuring consistency with that truism seems doomed to make any (...) answer to the question unsatisfying. Contrary to a careful and enticing recent effort to both sharpen and escape this dilemma by Daniel Morgan, I will argue that the dilemma remains pressing both for broadly epistemic and broadly causal-acquaintance-based accounts of the aboutness of first-person thought. (shrink)

In this chapter I examine how expected-value theory might inform responses to what I call the dual-use problem. I begin by defining that problem. I then outline a procedure, which invokes expected-value theory, for tackling it. I first illustrate the procedure with the aid of a simplified schematic example of a dual-use problem, and then describe how it might also guide responses to more complex real-world cases. I outline some attractive features of the procedure. Finally, I (...) consider whether and how the procedure might be amended to accommodate various criticisms of it. (shrink)

This paper examines an insoluble Cartesian problem for classical AI, namely, how linguistic understanding involves knowledge and awareness of u’s meaning, a cognitive process that is irreducible to algorithms. As analyzed, Descartes’ view about reason and intelligence has paradoxically encouraged certain classical AI researchers to suppose that linguistic understanding suffices for machine intelligence. Several advocates of the Turing Test, for example, assume that linguistic understanding only comprises computational processes which can be recursively decomposed into algorithmic mechanisms. Against this background, (...) in the first section, I explain Descartes’ view about language and mind. To show that Turing bites the bullet with his imitation game, in the second section I analyze this method to assess intelligence. Then, in the third section, I elaborate on Schank and Abelsons’ Script Applier Mechanism (SAM, hereby), which supposedly casts doubt on Descartes’ denial that machines can think. Finally, in the fourth section, I explore a challenge that any algorithmic decomposition of linguistic understanding faces. This challenge, I argue, is the core of the Cartesian problem: knowledge and awareness of meaning require a first-person viewpoint which is irreducible to the decomposition of algorithmic mechanisms. (shrink)