Most commonly, the scientific realism debate is seen as dividing those who do and do not think that the striking empirical and practical successes of at least our best scientific theories indicate with high probability that those theories are ‘approximately true’. But I want to suggest that this characterization of the debate has far outlived its usefulness. Not only does it obscure the central differences between two profoundly different types of contemporary scientific realist, but even more importantly it serves to (...) disguise the most substantial points of actual disagreement between these two kinds of realists and those who instead think the historical record of scientific inquiry itself reveals that such realism is untenable in either form. (shrink)

We analyse the extent of possible computations following Hogarth ([2004]) conducted in Malament–Hogarth (MH) spacetimes, and Etesi and Németi ([2002]) in the special subclass containing rotating Kerr black holes. Hogarth ([1994]) had shown that any arithmetic statement could be resolved in a suitable MH spacetime. Etesi and Németi ([2002]) had shown that some relations on natural numbers that are neither universal nor co-universal, can be decided in Kerr spacetimes, and had asked specifically as to the extent of computational limits there. (...) The purpose of this note is to address this question, and further show that MH spacetimes can compute far beyond the arithmetic: effectively Borel statements (so hyperarithmetic in second-order number theory, or the structure of analysis) can likewise be resolved: Theorem A. If H is any hyperarithmetic predicate on integers, then there is an MH spacetime in which any query ? n H ? can be computed. In one sense this is best possible, as there is an upper bound to computational ability in any spacetime, which is thus a universal constant of that spacetime. Theorem C. Assuming the (modest and standard) requirement that spacetime manifolds be paracompact and Hausdorff, for any spacetime there will be a countable ordinal upper bound, , on the complexity of questions in the Borel hierarchy computable in it. Introduction 1.1 History and preliminaries Hyperarithmetic Computations in MH Spacetimes 2.1 Generalising SADn regions 2.2 The complexity of questions decidable in Kerr spacetimes An Upper Bound on Computational Complexity for Each Spacetime CiteULike Connotea Del.icio.us What's this? (shrink)

We show how in the hierarchies${F_\alpha }$of Fieldian truth sets, and Herzberger’s${H_\alpha }$revision sequence starting from any hypothesis for${F_0}$ that essentially each${H_\alpha }$ carries within it a history of the whole prior revision process.As applications we provide a precise representation for, and a calculation of the length of, possiblepath independent determinateness hierarchiesof Field’s construction with a binary conditional operator. We demonstrate the existence of generalized liar sentences, that can be considered as diagonalizing past the determinateness hierarchies definable in Field’s recent (...) models. The ‘defectiveness’ of such diagonal sentences necessarily cannot be classified by any of the determinateness predicates of the model. They are ‘ineffable liars’. We may consider them a response to the claim of Field that ‘the conditional can be used to show that the theory is not subject to “revenge problems”.’. (shrink)

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.

We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of $\Sum_{3}^{0}$.

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

We locate winning strategies for various ${\mathrm{\Sigma }}_{3}^{0}$ -games in the L-hierarchy in order to prove the following: Theorem 1. KP+Σ₂-Comprehension $\vdash \exists \alpha L_{\alpha}\ models"\Sigma _{2}-{\bf KP}+\Sigma _{3}^{0}-\text{Determinacy}."$ Alternatively: ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ "there is a β-model of ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17 em}}{\mathrm{\Sigma }}_{3}^{0}$ -Determinacy." The implication is not reversible. (The antecedent here may be replaced with ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left({\mathrm{\Pi }}_{3}^{1}\right)-{\mathrm{C}\mathrm{A}}_{0}:\text{\hspace{0.17em}}{\mathrm{\Pi }}_{3}^{1}$ instances of Comprehension with only ${\mathrm{\Pi }}_{3}^{1}$ -lightface definable parameters—or even weaker theories.) Theorem 2. KP +Δ₂-Comprehension +Σ₂-Replacement + ${\mathrm{\Sigma }}_{3}^{0}\phantom{\rule{0ex}{0ex}}$ -Determinacy. (Here AQI (...) is the assertion that every arithmetical quasi-inductive definition converges.) Alternatively: $\Delta _{3}^{1}{\rm CA}_{0}+{\rm AQI}\nvdash \Sigma _{3}^{0}$ -Determinacy. Hence the theories: ${\mathrm{\Pi }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0},\text{\hspace{0.17em}}{\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}+\text{\hspace{0.17em}}{\mathrm{\Sigma }}_{3}^{0}-\mathrm{D}\mathrm{e}\mathrm{t}\phantom{\rule{0ex}{0ex}}$ -Det, ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}+\mathrm{A}\mathrm{Q}\mathrm{I}$ , and ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ are in strictly descending order of strength. (shrink)

We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta’s theory of truth over arithmetic using \emph{fully varied revision} sequences yields a complete \Pi13 set of integers; (iii) the set of \emph{stably categorical} sentences using their revision operator ψ is similarly \Pi13 and which (...) is complete in Gödel’s universe of constructible sets L; (iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points. (shrink)

The figure of Peter the Tomb, various aspects of his life and activity, as well as the era called by his name, have long been the subject of study by numerous scholars, comprehensive and meticulous research. It is enough to mention the works of M.Grushevsky, A.Zhukovsky, V.Klimov, A.Kolodny, V.Nichik, O.Sarapin, L.Filipovich and V.Shevchenko, in which the phenomenon of the metropolitan, his spiritual and religious dominant, is thoroughly and thoroughly explained, the influence of P. Mogila's heritage on the past and present. (...) And yet it is impossible to talk about the exhaustiveness of this topic, because such inexhaustibility is dictated by the very universe of its multidimensional activity. This is what determines the relevance of the proposed article. And this, in turn, gives rise to reflections on the need for scientific innovative understanding of religious philosophy as a constant basis of thinking of Petro Mohyla, which, in particular, was reflected in his "Notebook", which is still a little-studied phenomenon of Ukrainian spiritual culture, for the first time it saw the world only in 1995, more than 60 years after its invention by M. Grushevsky. This work, like all narratives on the spiritual and religious themes that make up it, is an integral part of the metropolitan's religious and philosophical heritage. (shrink)

Evolutionary fitness threats and rewards are associated with subjectively unpleasant and pleasant sensations, respectively. Initially, these correlations appear explainable via adaptation by natural selection. But here I analyse the major metaphysical perspectives on consciousness – physicalism, dualism, and panpsychism – and conclude that none help to understand the adaptive-seeming correlations via adaptation. I also argue that a recently proposed explanation, the phenomenal powers view, has major problems that mean it cannot explain the adaptive-seeming correlations via adaptation either. So the mystery (...) – call it the evolutionary paradox of consciousness – remains. Some have used this mystery to argue for non-naturalistic (e.g. theistic) explanations. But I propose a naturalistic, non-adaptive explanation of the adaptive-seeming correlations: namely, ‘sensational associative learning’ during development. In this perspective, pairing of particular sensations with unconditioned stimuli – fitness rewards or threats – cause the sensations themselves to come to be interpreted as good or bad, respectively. Sensations, like colours, that are not reliably paired with either fitness rewards or threats remain largely unvalenced. Sensational associative learning also provides explanations for adaptive-seeming structural aspects of sensations, such as the observation that sounds of different pitch are experienced as ordinal in correspondence to their wavelengths while the same is not true of colours of different hue. The sensational associative learning perspective appears compatible with physicalism, panpsychism, and dualism (though not epiphenomenalism). (shrink)

Do the ethical features of an artwork bear on its aesthetic value? This movie endorses misogyny, that song is a civil rights anthem, the clay constituting this statue was extracted with underpaid labor—are facts like these the proper bases for aesthetic evaluation? I argue that this debate has suffered from a false presupposition: that if the answer is “yes” (for at least some such ethical features), such considerations feature as pro tanto contributions to an artwork’s overall aesthetic value, i.e., as (...) merits or flaws which make something have more or less overall aesthetic value. As the case of ethically laden aesthetic evaluation makes clear, however, good aesthetic judgement is irreducibly multi-dimensional, e.g., “the movie has an engaging soundtrack, tasteful camera work, and takes a misogynistically purient perspective on its female lead.” Such a “non-summative” judgement refuses to reduce those various dimensions of aesthetic value to a single aggregate aesthetic evaluation, like “it’s a 6/10” or “it’s a pretty good movie!” I defend both the modest claim that such non-summative evaluations are not mistaken and the extremist claim that summative (i.e., unidimensional) aesthetic evaluation is defective by considering other domains of normative assessment in which summing seems inappropriate, notably including evaluations of people’s character. (shrink)

Open peer commentary on the article “Perception-Action Mutuality Obviates Mental Construction” by Martin Flament Fultot, Lin Nie & Claudia Carello. Upshot: In my view, the clash between ecological psychology, enactivism, and constructivism in general has more to do with irreconcilable metaphysical and theoretical incommensurabilities than disagreements about specific mechanisms or processes of perception. Even with mutual enabling of action and perception, some internal process of self-modification is still needed if novel behavior is to be adequately explained.

Problem: Ernst von Glasersfeld’s radical constructivism has been highly influential in the fields of mathematics and science education. However, its relevance is typically limited to analyses of classroom interactions and students’ reasoning. Methods: A project that aims to support improvements in the quality of mathematics instruction across four large urban districts is framed as a case with which to illustrate the far-reaching consequences of von Glasersfeld’s constructivism for mathematics and science educators. Results: Von Glasersfeld’s constructivism orients us to question the (...) standard view of policy implementation as a process of travel down through a system and to conceptualize it instead as the situated reorganization of practice at multiple levels of a system. In addition, von Glasersfeld’s constructivism orients us to understand rather than merely evaluate policies by viewing the actions of the targets of policies as reasonable from their point of view. Implications: The potential contributions of von Glasersfeld’s constructivism to mathematics and science education have been significantly underestimated by restricting the focus to classroom actions and interactions. The illustrative case of research on the application of these ideas also indicates the relevance of constructivism to researchers in educational policy and educational leadership. (shrink)