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 develop and apply a multi-dimensional conception of explanatory depth towards a comparative analysis of inflationary and bouncing paradigms in primordial cosmology. Our analysis builds on earlier work due to Azhar and Loeb (2021) that establishes initial condition fine-tuning as a dimension of explanatory depth relevant to debates in contemporary cosmology. We propose dynamical fine-tuning and autonomy as two further dimensions of depth in the context of problems with instability and trans-Planckian modes that afflict bouncing and inflationary approaches respectively. In (...) the context of the latter issue, we argue that the recently formulated trans-Planckian censorship conjecture leads to a trade-off for inflationary models between dynamical fine-tuning and autonomy. We conclude with the suggestion that explanatory preference with regard to the different dimensions of depth is best understood in terms of differing attitudes towards heuristics for future model building. (shrink)

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.

When I offered this title, I was engaging myself to investigate an apparent difference between two kinds of intentionality, in the hope that I should be able to find some firm logical criterion to distinguish them. I was less successful in this than I had hoped. I think I have gained a certain amount of insight into the logic and semantics of one kind of intentional context, largely due to the work I was doing while visiting the University of Pennsylvania (...) on Frege and on Michael Dummett’s monumental commentary on Frege. But as regards the other variety of intentionality I am still very much in the dark; so I am giving you thus far merely a progress report on that. (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 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 that Leitgeb’s dependence operator of Leitgeb is a \-operator and that this is best possible.

P S Wilson; Child-Centred Education, Journal of Philosophy of Education, Volume 3, Issue 1, 30 May 2006, Pages 105–126, https://doi.org/10.1111/j.1467-9752.1969.

In this essay, P. Taylor Webb and Kalervo N. Gulson argue that educational policy is a spatial process and that implementation processes in particular produce crucial emergent geographies for policy research. Webb and Gulson describe how emergent geographies are produced when policy folds actors through senses and enactments of policy. The idea that policy is sensed and enacted is developed into the concept of a policy intension that extends approaches to spatial and, in particular, micropolitical analyses in policy research. Webb (...) and Gulson conclude by discussing cartographical methods that better map the geographies of subjectivity produced through policy intensions. (shrink)

We consider notions of truth and logical validity defined in various recent constructions of Hartry Field. We try to explicate his notion of determinate truth by clarifying the path-dependent hierarchies of his determinateness operator.

In this desolate ancient country, which is a semicolony, all activities [seemed to have] stopped. People's lives have also become meaningless. The warm breeze blown from other countries stirred the curiosity of youth. Go! Let us go to the free world. And so, many people left the motherland for France in Europe, as if even workers there were happier than gentlemen here. But what was the reality? They were unable to do very hard work like the average workers. So their (...) idealized country became the target of their curses. (shrink)

The conception of “prospective potency” was defined by its author H.Driesch as “the sum of the possible modes of development of a given part of the embryo”. However, in the language of science the word “potency” usually means “power”, not “possibility”. Therefore this conception from the beginning possessed a certain ambiguity, that it retained up to the present. The distinction of “active” and “passive” potency, introduced by Roux, has found no general acceptance. It appeared necessary to submit the conception of (...) “potency” to a profound analysis. In the first place it is shown, that the ambiguity of this conception vanishes, if we understand by the word “potency” those fundamental properties of the embryonic material, that are responsible for its various developmental possibilities. We can distinguish among these properties the “reactive powers”, by which the embryonic material reacts to inductive stimulations, and its own “developmental tendencies”. These faculties only differ by their strength; a “reactive power” may change into a “tendency”, when its intensity increases during development; conversely, a “tendency” may change into a mere “reactive power” by a decrease of its strength. The determination of the material results from the conflict of its tendencies. The inductive actions interfere by strengthening or weakening different tendencies, and by activating new tendencies by reinforcement of the “reactive powers” of the embryonic material.La conception de „prospektive Potenz” fut définie par son auteur H.Driesch comme „l'ensemble des modes de développement possibles d'une certaine partie de l'embryon”. Cependant, le, mot „Potenz” dans le langage de la science répond plutôt à la „puissance” qu'à la „possibilité”. De là résulte, que cette conception dès son origine avait une certaine ambiguïté, qui se fait sentir jusqu'à présent. La distinction entre „potentialité active” et „potentialité passive”, proposée par Roux, n'est pas acceptée généralement. Il se trouvait nécessaire, que la conception de „Potenz” fût soumise à une. analyse profonde. D'abord il est démontré, que l'ambiguïté de cette conception disparaît, si on entend par le mot „Potenz” les propriétés fondamentales du matériel embryonnaire, qui sont à la base de ses diverses possibilités de développement. On peut distinguer parmi ces propriétés les „pouvoirs réactifs”, en vertu desquels le matériel embryonnaire répond à des inductions morphogénétiques, et les „tendances propres” du matériel. Ils ne diffèrent que par leur intensité; un „pouvoir réactif” peut se changer en „tendance” par suite d'un renforcement au cours du développement, une „tendance” peut se changer en „pouvoir réactif” par une diminution d'intensité. La détermination du matériel se réalise par une „lutte” entre les tendances. Les actions inductives influent sur cette lutte en renforçant ou en diminuant l'intensité des diverses tendances, et en activant de nouvelles tendances par le renforcement de „pouvoirs réactifs”. (shrink)