We characterise explicitly the decidable predicates on integers of Infinite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down ζ, the least ordinal not the length of any eventual output of an Infinite Time Turing machine (halting or otherwise); using this the Infinite Time Turing Degrees are considered, and it is shown how the jump operator coincides with the production of mastercodes for the constructible hierarchy; further that the natural ordinals associated (...) with the jump operator satisfy a Spector criterion, and correspond to the L ζ -stables. It also implies that the machines devised are "Σ 2 Complete" amongst all such other possible machines. It is shown that least upper bounds of an "eventual jump" hierarchy exist on an initial segment. (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)

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)

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 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.

In the axiomatic development of the logic of nonrelativistic quantum mechanics it is not difficult to set down certain plausible axioms which ensure that the quantum logic of propositions has the structure of an orthomodular poset. This can be done in a number of ways, for example, as in Gunson [2], Mackey [4], Piron [5], Varadarajan [7] and Zierler [8], and we summarise one of these ways in §2 below.

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)

Introduction 1 P. D. Magnus and Jacob Busch 1. Form-driven vs. Content-driven Arguments for Realism 8 Juha Saatsi 2. Optimism about the Pessimistic Induction 29 Sherrilyn Roush 3. Metaphysics between the Sciences and Philosophies of Science 59 Anjan Chakravartty 4. Nominalism and Inductive Generalizations 78 Jessica Pfeifer 5. Models and Scientific Representations 94 Otávio Bueno 6. The Identical Rivals Response to Underdetermination 112 Gregory Frost-Arnold and P. D. Magnus 7. Scientific Representation and the Semiotics of Pictures 131 Laura Perini 8. (...) Philosophy of the Environmental Sciences 155 Jay Odenbaugh 9. Value Judgements and the Estimation of Uncertainty in Climate Modeling 172 Justin Biddle and Eric Winsberg 10. Feminist Standpoint Empiricism: Rethinking the Terrain in Feminist Philosophy of Science 198 Kristen Intemann 11. Naturalism and the Enlightenment Ideal: Rethinking a Central Debate in the Philosophy of Social Science 226 Daniel Steel 12. New Approaches to the Division of Cognitive Labor 250 Michael Weisberg. (shrink)

The titles of these lectures were "In Search of the Miraculous" and "The Problems of Death." In these lectures, which were to serve as an introduction to a book on my travels it was my intention to write, I said that in India the "miraculous" was ...

Many enhancement technologies are distributed by healthcare professionals—by physicians—who are held to the Hippocratic Oath and the goals of medicine. While the ethics of enhancement has been widely discussed with regard to the social justice, humanism, morals and normative values of these interventions, their place in medicine has not attracted a great deal of attention. This paper investigates the potential for enhancement technologies to fulfil the goals of medicine, arguing that they play a role in promoting the health of individuals, (...) and thus, an unavoidable place in medicine. It also warns of potential dangers, suggesting a set of guidelines to initiate conversations regarding the role and responsibilities of physicians practising in an era of enhancement. (shrink)

Consider the concept combination ‘pet human’. In word association experiments, human subjects produce the associate ‘slave’ in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of ‘pet’, or ‘human’ in isolation. In other words, the associate ‘slave’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this (...) article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified. (shrink)

The accepted narrative treats John Stuart Mill's Kinds as the historical prototype for our natural kinds, but Mill actually employs two separate notions: Kinds and natural groups. Considering these, along with the accounts of Mill's 19th-century interlocutors, forces us to recognize two distinct questions. First, what marks a natural kind as worthy of inclusion in taxonomy? Second, what exists in the world that makes a category meet that criterion? Mill's two notions offer separate answers to the two questions: natural groups (...) for taxonomy, and Kinds for ontology. This distinction is ignored in many contemporary debates about natural kinds and is obscured by the standard narrative which treats our natural kinds just as a development of Mill's Kinds. (shrink)

Wikipedia is a free encyclopedia that is written and edited entirely by visitors to its website. I argue that we are misled when we think of it in the same epistemic category with traditional general encyclopedias. An empirical assessment of its reliability reveals that it varies widely from topic to topic. So any particular claim found in it cannot be relied on based on its source. I survey some methods that we use in assessing specific claims and argue that the (...) structure of the Wikipedia frustrates them. (shrink)

There is a history of thinking that photographs provide a special kind of access to the objects depicted in them, beyond the access that would be provided by a painting or drawing. What is included in the photograph does not depend on the photographer’s beliefs about what is in front of the camera. This feature leads Kendall Walton to argue that photographs literally allow us to see the objects which appear in them. Current generative algorithms produce images in response to (...) users’ text prompts. Depending on the parameters, the output can resemble specific people or things which are named in the prompt. This resemblance does not depend on the user’s beliefs, so generated images are in this sense like photographs. Given this parallel, how should we think about AI-generated images? (shrink)

Experimental evidence strongly supports the view that the subdivision of organ anlagen into smaller structural units is an autonomous process. Dalcq &Pasteels' hypothesis which says that the boundaries between the different areas into which a morphogenetic field differentiates are determined by “Threshold values” in the “potential” of the field in question, is inconsistent with our present knowledge of biochemical reaction systems. Threshold values may only be used indescribing the spatial differentiation of a morphogenetic field. It is suggested that the latter (...) concept be replaced by the concept of “optimal values” in the intensity of a morphogenetic field-specific for the various chemo-differentiations characterizing the different regions into which a morphogenetic field will split up-and that each optimal value isdeterminative for the appearance of one particular differentiation within the morphogenetic field, each differentiation being formed within a certain range of intensity of the field. On the basis of the hypothesis formulated above a “virginal” morphogenetic field will necessarily differentiate into a number of smaller fields of second order, which in their turn will split up into fields of third order, etc. ” Pattern formation” may be defined as the differentiation of a morphogenetic field into an increasing number of smaller fields of higher order of qualitative different chemical and structural composition. Since differentiation of a morphogenetic field proceeds autonomously, the capacity for pattern formation is an intrinsic property of a morphogenetic field. In the light of these considerations it is suggested that a morphogenetic field action is responsible for the first differentiation of the developing embryo into regions with predominantly ectodermal, mesodermal or endodermal differentiation tendencies. The present knowledge about the characteristic pattern formation taking place in the axial mesoderm as well as in the overlying neural plate seems to be in good agreement with the implications of the present morphogenetic field concept. It is emphasized, however, that if the present morphogenetic field concept cannot be characterized further biochemically and biophysically, it will have to be replaced by another concept which can be defined more sharply and is more easily accessible to experimental analysis. Les preuves expérimentales confirment que la subdivision des ébauches des organes en unités structurelles plus petites est un processus autonome. L'hypothèse deDalcq &Pasteels disant que les bornes entre les différents domaines formées par la différenciation d'un champ morphogénétique sont déterminées par des „valeurs seuil” dans le „potentiel” du champ en question, n'est pas en harmonie avec notre connaissance actuelle des systèmes biochimiques. Des “valeurs seuil” ne peuvent être employés qu'en décrivant la différenciation spatiale d'un champ morphogénétique. On prend en considération de remplacer le concept des “valeurs seuil” par le concept des “valeurs optimales” dans l'intensité d'un champ morphogénétique. Ce seraient les valeurs spécifiques aux différenciations chimiques diverses qui caractérisent les différents domaines dans lesquels un champ morphogénétique se différencie. En outre, chaque valeur optimale serait déterminative à la formation d'une différenciation spéciale dans le champ morphogénétique, chaque différentiation se formant dans un certain trajet de l'intensité du champ. Par suite de l'hypothèse formulée ci-dessus un champ morphogénétique “virginal” va nécessairement se différencier en un nombre de champs plus petits de deuxième ordre, qui à leur tour se divisent en champs d'ordre troisième, etc. ... La régionalisation peut être définie comme la différenciation d'un champ morphogénétique dans un nombre de plus en plus élevé de champs plus petits d'ordre supérieur de composition chimique et structurelle qualitativement différente. Parce que la différenciation d'un champ morphogénétique se produit de façon autonome, le pouvoir de régionalisation est une propriété intrinsique d'un champ morphogénétique. Ces considérations nous mènent à proposer que l'action d'un champ morphogénétique est responsable de la première différenciation de l'embryon en régions qui possèdent des tendences de différenciation principalement ectodermiques, mésodermiques, ou bien endodermiques. La connaissance actuelle concernant la régionalisation caractéristique qui se produit dans le mésoderme axial ainsi que dans la plaque neurale superposée paraît se conformer aux conséquences du concept de champ morphogénétique. Cependant on souligne le fait que dans le cas òu le concept actuel du champ morphogénétique ne pourra pas être plus amplement caractérisé de façon biochimique et biophysique, il faudra le remplacer par un autre concept qui puit être défini plus nettement et qui est mieux accessible à l'analyse expérimentale. Die Auffassung, dass die Aufteilung von Organanlagen in kleineren Struktureinheiten ein selbständiger Prozess ist, findet Bestätigung in den experimentellen Ergebnissen. Die Hypothese vonDalcq &Pasteels , dass die Grenzen zwischen den unterschiedenen Gebieten, in denen ein morphogenetisches Feld sich differenziert, durch “Schwellenwerte” im “Potential” des genannten Feldes bestimmt werden, ist unvereinbar mit unserem heutigen Wissen über biochemischen Reaktionssystemen. Der Gebrauch des Begriffs “Schwellenwert” ist nur gestattet bei der Beschreibung der räumlichen Differenzierung eines morphogenetischen Feldes. Statt dieses Begriffs wird der Begriff “Optimaler Wert” vorgeschlagen; Werte also in der Intensität eines morphogenetischen Feldes, optimal und spezifisch für die verschiedene Chemodifferenzierungen, welche die Gebiete kennzeichnen, in denen ein morphogenetisches Feld sich differenzieren wird. Jeder optimaler Wert soll dann das Erscheinen einer bestimmten Differenzierung innerhalb des morphogenetischen Feldes veranlassen, welche Differenzierung sich bildet innerhalb eines bestimmten Bereichs der Feldintensität. Auf Grund der obigen Hypothese wird ein “virginelles” morphogenetisches Feld zwangsläufig sich differenzieren in eine Anzahl kleinerer Feldern zweiten Grades; diese in Felder dritten Grades, usw. Musterbildung könnte definiert werden als die Differenzierung eines morphogenetischen Feldes in eine zunehmende Anzahl kleinerer Felder höheren Grades von qualitativ verschiedener chemischen und strukturellen Zusammensetzung, Weil diese Differenzierung autonom vor sich geht, ist das Vermögen zur Musterbildung eine innewohnende Eigenschaft eines morphogenetischen Feldes. Im Lichte dieser Betrachtungen ist es naheliegend anzunehmen dass eine morphogenetische Feldwirkung verantwortlich ist für die erste Differenzierung des sich entwickelnden Embryos in Gebiete überwiegend ektodermalen, mesodermalen oder entodermalen Differenzierungstendenzen. Die heutigen Kenntnisse über die charakteristische Musterbildung im axialen Teil des Mesoderms und in der überliegenden Neuralplatte scheinen in guter Übereinstimmung zu sein mit den des morphogenetischen Feldbegriffs. Dennoch wird benachdruckt, dass, falls das gegenwärtige morphogenetische Feldbegriff nicht weiter biochemisch und biophysisch gekennzeichnet werden kann, anstatt dessen ein anderer Begriff entwickelt werden muß, der schärfer definiert werden kann und besser zugänglich ist für experimentelle Analyse. (shrink)

The fact that psychic life is not merely given externally and as mutual externality, but is given in its nexus, given by self-knowledge, by internal experience, constitutes the basic difference between psychological knowledge and knowledge of nature.

Medical ethics is that branch of applied philosophy which considers issues of values raised by medical practice, and should not be equated with 'principlism'. Clarification of facts/values distinctions is an important part of this work. The notion that medical philosophy can flourish in the hands of medical 'generalists' without specialist philosophers, is misguided. Both must work together to promote right reason and right action in medical education and practice.

We follow [8] in asking when a set of ordinals $X \subseteq \alpha$ is a countable union of sets in K, the core model. We show that, analogously to L, and X closed under the canonical Σ 1 Skolem function for K α can be so decomposed provided K is such that no ω-closed filters are put on its measure sequence, but not otherwise. This proviso holds if there is no inner model of a weak Erdős-type property.

A small large cardinal upper bound in V for proving when certain subsets of ω 1 (including the universally Baire subsets) are precisely those constructible from a real is given. In the core model we find an exact equivalence in terms of the length of the mouse order; we show that $\forall B \subseteq \omega_1 \lbrack B$ is universally Baire $\Leftrightarrow B \in L\lbrack r \rbrack$ for some real r] is preserved under set-sized forcing extensions if and only if there (...) are arbitrarily large "admissibly measurable" cardinals. (shrink)

P D Walsh; Value Education in a Pluralist Society, Journal of Philosophy of Education, Volume 10, Issue 1, 30 May 2006, Pages 24–33, https://doi.org/10.1111/j.1.

These are details of research conducted in November and December 2007. The file is meant as a supplement to publication, and I have not attempted here to provide any analysis of the results.