We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological fields, which encompasses ordered or p‐valued differential fields, we find a partial Galois correspondence and we show one cannot expect more in general. In the class of ordered differential fields, using elimination of imaginaries in, we establish a relative Galois correspondence for relatively definable subgroups (...) of the group of differential order automorphisms. (shrink)

The basic bimodal systemK/K can be interpreted as an analysis of the logic of ability developed in [1]. Where in [1] we would express the claimI can bring it about that P using the formula, with its non-normal operator, we will now use the formula. Here is a normal alethic possibilitation operator.is a normal necessitation operator, but it is independent of, and not subject to an alethic interpretation. Rather, is interpreted to meanI bring it about that P. (...) The result is a simplification and clarification of a combined logic of ability and action like that in [2], but employing only normal operators.A number of extensions of the basic systemK/K are constructed, first by strengthening the two normal sublogics independently and then by linking the two sublogics via axiom schemata involving both operators. The result is a series of increasingly strong systems which more and more adequately fulfill our expectations for a satisfactory logic of action and ability. (shrink)

We offer a new outlook on the vexed question of the reference of natural-kind terms. Since Kripke and Putnam, there is a widespread assumption that natural-kind terms function just like proper names: they designate their referents directly and they are rigid designators: their reference is unchanged even in worlds in which the referent lacks some or all the properties associated with it in the actual world, and which are useful to us in identifying that referent. There have, however, been heated (...) debates about what should be taken as a natural-kind term. Some challenge the very existence of a separate category of natural-kind terms ; some their being directly referential ; some raise the possibility that direct reference extends to terms beyond those usually assumed to fall under the category, e.g. to ‘polemical’ terms. When these debates turn on the question of what natural kinds are, they take on a strong epistemological or metaphysical dimension. We think the issues can be clarified within the limits of the philosophy of language: by looking into what ranges of general terms are perceived by speakers as rigid designators of natural kinds. The first step to take is to ground the various kinds of semantic externalism in distinct brands of semantic deference. This we define as speakers’ being disposed to use words in line with the norms of their linguistic community and as consenting to being corrected when it is manifest that their use and understanding of a word does not match common practice. When those dispositions are present, speakers defer semantically to something beyond themselves. Here, our focus is on spotting the words for which speakers would defer not to the current usage of the word in the linguistic community, nor to the current experts of the field to which the word pertains, but ultimately to the very nature of the referent of the term. When speakers’ deference conforms to that pattern, we argue, that is evidence that indexical externalism provides the right metasemantic account of how the meaning of the word is determined. In other words, one can say that the word is treated like a natural-kind term. But how can patterns of deference be measured? In an ongoing survey, participants are confronted with conditions that may prompt them to revise certain classificatory statements, e.g. An emu is a bird. Each condition makes salient one of the targets we have identified for deference: the community usage, the experts, the ‘world as it is’. In the condition that seeks to tap into the latter kind of deference, participants are presented with a scenario in which future scientific discoveries result in excluding from the extension of a term certain members currently thought to fall under that extension, e.g. discoveries that require excluding certain species now thought to be birds from the Aves class. The scenario is such that it is clear that the ‘discoveries’ bring us closer to the actual essence, if there is one, of birds. Our reasoning is that, if participants significantly modify their statements in the light of that scenario, they can be taken to ‘defer’ to the nature of the referent, thus vindicating indexical externalism. We test if words not normally assumed to be natural-kind terms – for instance summer, contract or rape – exhibit patterns of deference similar to those for bird. If so, then there’s a case for an extension of indexical externalism beyond the usual set of terms. What would be shown in this way is that speakers have something like realist intuitions with respect to words whose meaning is usually taken to be purely conventional or polemical. We are at the pre-test stage for the survey. We cannot yet report on our results. We should, however, have initial results by March, which, we believe, will enrich the observations made by previous empirical studies. References: Braisby, N., Franks, B. & Hampton, J. 1996. Essentialism, word use, and concepts. Cognition 59, 247-74./Genone, J. & Lombrozo, T. 2012. Concept possession, experimental semantics, and hybrid theories of reference. Philosophical Psychology 25, 717-742./Häggqvist, S. & Wikforss, Å. 2015. Experimental semantics: the case of natural kind terms, in J. Haukioja, Experimental Philosophy of Language, London, Bloomsbury./Jylkkä, J., Railo, H. & Haukioja, J. 2009. Psychological essentialism and semantic externalism: Evidence for externalism in lay speakers’ language use. Philosophical Psychology 22, 37-60./Mallon, R., Machery, E., Nichols, S. & Stich, S. 2009. Against arguments from reference, Philosophy and Phenomenological Research 79, 332-356./ Marconi, D. 1997. Language, Speech, and Communication. Lexical Competence. Cambridge : MIT Press./Moravcsik, J. 2016. Meaning, Creativity, and the Partial Inscrutability of the Human Mind, 2nd ed. Stanford: CSLI./Schroeter, L. & Schroeter, F. 2014. Normative concepts: a connectedness model, Philosophers’ Imprint 14, 1-26./ Wikforss, Å. 2010. Are natural kind terms special?, in H. Beebee and N. Sabbarton-Leary, The Semantics and Metaphysics of Natural Kinds, New York, Routledge, 64-83. (shrink)

Let K be the least normal modal logic and BK its Belnapian version, which enriches K with ‘strong negation’. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships (...) between special extensions and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK. (shrink)

This paper introduces a natural extension of Kolchin's differential Galois theory to positive characteristic iterative differential fields, generalizing to the non-linear case the iterative Picard—Vessiot theory recently developed by Matzat and van der Put. We use the methods and framework provided by the model theory of iterative differential fields. We offer a definition of strongly normal extension of iterative differential fields, and then prove that these extensions have good Galois theory and that a G-primitive element theorem holds. (...) In addition, making use of the basic theory of arc spaces of algebraic groups, we define iterative logarithmic equations, finally proving that our strongly normal extensions are Galois extensions for these equations. (shrink)

In this paper we use “generic submodels” to prove that each normal extension of G.3 (K4.3W) has the finite model property, by which we establish that each proper normal extension of G.3 is G.3Altn for some n≥0.

We prove that every normal extension of the bi-modal system S52 is finitely axiomatizable and that every proper normal extension has NP-complete satisfiability problem.

Building upon earlier work of Donna Carr, Don Pelletier, Chris Johnson, Shu-Guo Zhang and others, we show that a normal ideal J on Pκ is strongly normal if and only if J+→< 2 for every μ < κ, and we describe the least normal ideal J on Pκ such that J+ →< 2.

This paper proves the finite model property and the finite axiomatizability of a class of normal modal logics extending K4.3. The frames for these logics are those for K4.3, in each of which every point has a bounded number of irreflexive successors if it is after an infinite ascending chain of (not necessarily distinct) points.

In this paper, we present an extension of λμ-calculus called λμ++-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on data types. This calculus allows also to program the parallel-or.

We show that every proper normal extension of the bi-modal system S5 2 has the poly-size model property. In fact, to every proper normal extension L of S5 2 corresponds a natural number b(L) - the bound of L. For every L, there exists a polynomial P(·) of degree b(L) + 1 such that every L-consistent formula is satisfiable on an L-frame whose universe is bounded by P(||), where || denotes the number of subformulas of . It is (...) shown that this bound is optimal. (shrink)

The Craig interpolation property and interpolation property for deducibility are considered for special kind of normal extensions of the Brouwer logic.

We use the apparatus of the canonical formulas introduced by Zakharyaschev [10] to prove that all finitely axiomatizable normal modal logics containing K4.3 are decidable, though possibly not characterized by classes of finite frames. Our method is purely frame-theoretic. Roughly, given a normal logic L above K4.3, we enumerate effectively a class of frames with respect to which L is complete, show how to check effectively whether a frame in the class validates a given formula, and then apply (...) a Harropstyle argument to establish the decidability of L, provided of course that it has finitely many axioms. (shrink)

Three variants of Beth's definability theorem are considered. Let L be any normal extension of the provability logic G. It is proved that the first variant B1 holds in L iff L possesses Craig's interpolation property. If L is consistent, then the statement B2 holds in L iff L = G + {0}. Finally, the variant B3 holds in any normal extension of G.

We shall be concerned with the modal logic BK—which is based on the Belnap–Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding ‘strong negation’. Though all four values ‘truth’, ‘falsity’, ‘neither’ and ‘both’ are employed in its Kripke semantics, only the first two are expressible as terms. We show that expanding the original language of BK to include constants for ‘neither’ or/and ‘both’ leads to quite unexpected results. To be (...) more precise, adding one of these constants has the effect of eliminating the respective value at the level of BK-extensions. In particular, if one adds both of these, then the corresponding lattice of extensions turns out to be isomorphic to that of ordinary normal modal logics. (shrink)

Purely parallel neural networks can model object recognition in brief displays – the same conditions under which illusory conjunctions have been demonstrated empirically. Correcting errors of illusory conjunction is the “tag-assignment” problem for a purely parallel processor: the problem of assigning a spatial tag to nonspatial features, feature combinations, and objects. This problem must be solved to model human object recognition over a longer time scale. Our model simulates both the parallel processes that may underlie illusory conjunctions and the serial (...) processes that may solve the tag-assignment problem in normal perception. One component of the model extracts pooled features and another provides attentional tags that correct illusory conjunctions. Our approach addresses two questions: How can objects be identified from simultaneously attended features in a parallel, distributed representation? How can the spatial selectional requirements of such an attentional process be met by a separation of pathways for spatial and nonspatial processing? Our analysis of these questions yields a neurally plausible simulation of tag assignment based on synchronizing feature processing activity in a spatial focus of attention. (shrink)

Normal 0 21 false false false MicrosoftInternetExplorer4 This article will present an interpretation of Wittgenstein ’ s understanding of the relationship between ethics and aesthetics. In extension, it will inform recent discussions regarding a special kind of nonsensicality , which forms a central part of ethical and aesthetical expressions. Instead of identity between ethics and aesthetics, we should understand the relationship in terms of interdependence . Both attitudes provide a view sub specie aeternitatis and thus permit a view of (...) the world as a whole. Employing the vocabulary of Charles Taylor and Harry Frankfurt, it must be remembered that rather than a neutral view from nowhere, such wholeness arises out of strong evaluations that are made against the backdrop of a constitutive framework of intelligibility. At this point, the epistemic gain of actualizing Wittgenstein will reveal itself: it will put us in a position where it is possible to differentiate between ethical and aesthetical forms of identification that Taylor and Frankfurt neglect. However, in order to actualize Wittgenstein ’ s ideas, it is necessary to argue that Tractatus should not be understood in a Kantian fashion as suggested by Tilghman for instance. (shrink)

Philologus, founded in 1846, is one of the oldest and most respected periodicals in the field of Classics. It publishes articles on Greek and Latin literature, historiography, philosophy, history of religion, linguistics, reception, and the history of scholarship. The journal aims to contribute to our understanding of Greco-Roman culture and its lasting influence on European civilization. The journal Philologus, conceived as a forum for discussion among different methodological approaches to the study of ancient texts and their reception, publishes original scholarly (...) contributions with a strong international focus. Publications languages are: German, English, Italian, French. As of 2014 the publication of supplementary volumes will be resumed. The series Philologus. Supplemente / Philologus. Supplementary Volumes will publish monographs and edited volumes pertaining to all aspects of the study of ancient literature and its reception, with a special focus on topics concerning literary theory, philosophy and the history of scholarship from an interdisciplinary perspective. (shrink)

For every uncountable regular cardinalκ and any cardinalλ≧κ,P κ λ denotes the set $\left\{ {x \subseteqq \lambda :\left| x \right|< \kappa } \right\}$ . Furthermore, < denotes the binary operation defined inP κ λ byx (...) + denotes the setP κ λ−I, andI * the filter dual toI.An idealI overP κ λ is said to benormal iff every functionf:P κ λ→λ with the property that {x∈P κ λ:f(x)∈x}∈I + is constant on a set inI +.I is said to bestrongly normal iff every functionf:P κ λ→P κ λ with the property that {x∈P κ λ:x∩xκ≠Ø∧f(x)strongly normal ideal is normal. However, the converse of this is false.In this paper, we completely characterize those pairs (κ, λ) for whichP κ λ bears a strongly normal ideal, and describe the smallest such ideal for these pairs. As well, we show that for each of these pairs, the operator∇ < defined on the set of all ideals overP κ λ by where $$\nabla _< \left\{ {X_a :a \in P_\kappa \lambda } \right\} = \left\{ {x \in P_\kappa \lambda :x \cap \kappa = \phi \vee \left( {\exists a< x} \right)\left( {x \in X_a } \right)} \right\}$$ is idempotent. Our results include the following theorems. (shrink)

This collection examines the instrumental role of intersubjectivity in Husserl's philosophy and explores the potential for developing novel ways of addressing and resolving contemporary philosophical issues on that basis. This is the first time Iso Kern offers an extensive overview of this rich field of inquiry for an English-speaking audience. Guided by his overview, the remaining articles present new approaches to a range of topics and problems that go to the heart of its core theme of intersubjectivity and methodology. Specific (...) topics covered include intersubjectivity and empathy, intersubjectivity in meaning and communication, intersubjectivity pertaining to collective forms of intentionality and extended forms of embodiment, intersubjectivity as constitutive of normality, and, finally, the central role of intersubjectivity in the sciences. The authors' perspectives are strongly influenced by Husserl's own methodological concerns and problem awareness and are formed with a view to applicability in current debates - be it within general epistemology, analytic philosophy of language, philosophy of mind, meta-ethics or philosophy of science. With contributions written by leading Husserl scholars from across the Analytic and Continental traditions, Husserl's Phenomenology of Intersubjectivity is a clear and accessible resource for scholars and advanced students interested in Husserl's phenomenology and the relevance of intersubjectivity to philosophy, sociology, and psychology. (shrink)

The "traditional" view of normative decision theory, as reported (for example) in chapter 2 of Luce and RaiÃa's [1957] classic work, Games and Decisions, proposes a reduction of sequential decisions problems to non-sequential decisions: a reduction of extensive forms to normal forms. Nonetheless, this reduction is not without its critics, both from inside and outside expected utility theory, It islay purpose in this essay to join with those critics by advocating the following thesis.

In lieu of an abstract, here is a brief excerpt of the content:Barrow and Newton E. W. STRONG As E. A. Buxrr HAS ADDUCED,Isaac Barrow (1630-1677) in his philosophy of space, time, and mathematical method strongly influenced the thinking of Newton: The recent publication of an early paper written by Newton (his De gravitatione et aequipondio fluidorum)2 affords evidence not known to Burtt of Newton's indebtedness in philosophy to Barrow, his teacher. Prior to its publication in 1962, this paper (...) was utilized by Alexandre Koyrd in his essay, "Newton and Descartes," 3 a study based on the third Horblit Lecture in the History of Science which he gave at Harvard University, March 8, 1961. Koyr8 maintains that there is a radical opposition in Newton's Principia not only to Descartes' purely scientific theories but also to the Cartesian philosophy. Yet, as he remarks, "we do not find in the Principia an open criticism of the philosophy of Descartes.... " He attributes this fact principally "to the very structure of the Principia: it is essentially a book on rational mechanics, which provides principles for physics and astronomy. In such a book there is a normal place for the discussion of Cartesian optics, but not of the conception of the relations of mind and body, and other such things." Koyrd asserts, nonetheless, that the criticism is not absent. It lurks in Newton's carefully worded definitions of fundamental concepts--those of space, time, motion, and matter--and becomes more apparent in the Optice of 1706 and in the second odition of the Principia. In support of this argument, he makes much of young Newton's unfini.~hed paper. He holds that this essay is of exceptional value "as it enables us to get some insight into the formation of Newton's thought, and to recognize that preoccupation with philosophic problems was not an external additatmentum but an integral dement of his thinking." 4 As concerns "young Newton's conception of space in its being and in its relation to God and time," Koyrd remarks that we learn from this essay The Metaphysical Foundations of Modern Physical Science (New York, 1927), p. 144. A. Rupert Hall and Marie Boas Hall, Unpublished Scientific Papers of Isaac Newton (Cambridge, 1962), Introduction, pp. 75-88; Latin text, pp. 90-121; English translation, pp. 121156. " Newtonian Studies (Harvard University Press, 1965), pp. 53-114. " Newtonian Studies, pp. 82-83. In his De gravitatione et aequipondio fluidorum, Newton is indeed engrossed with philosophic problems. With regard, however, to the announced purpose of his paper, namely, "to treat of the science of gravity and solid bodies in fluids by two methods," does Newton represent kis metaphysical "explanation of the nature of body" as an element of his science essential to its completeness7 He does not do so. At the end of his explanation he remarks: "I have already digressed enough; let us return to the main theme." He proceeds to set forth fifteen more definitions and then turns to the demonstration of two "Propositions on Non-Elastic Fluids." [155] 156 HISTORY OF PHILOSOPHY "that space is necessary, eternal, immutz~ble, and unmovable, that though we can imagine that there is nothing in space we cannot think space is not.., and that if there is no space, God would be nowhere. We learn also that all points of space are simultaneous and that, therefore, the divine omnipresence does not introduce composition in God.... " What we here learn from Newton about space in confutation of Descartes is to be found in Barrow's tenth mathematical lecture, "'Of Space, and Impenetrability." 5 In this lecture, Barrow opposes both Descartes and Hobbes. He objects, as does Newton, to the position taken by Descartes in his Principia Philosophiae, namely, "it is necessary.forMatter to be infinitely extended." He proceeds, as does Newton, to show how "very much Cartesius's great Subtility has failed him in this Case" to conclude that there is space empty of matter and distinct from magnitude from which an infinity of matter cannot be deduced. The correspondence of arguments tendered by Barrow and Newton indicates that the tenth lecture constituted a source from which Newton gleaned principal objections to Descartes' Principia Philosophiae. Although Koyr~ makes reference to Burtt's... (shrink)

We show that for solvable games, the calculation of the strategies which survive iterative elimination of dominated strategies in normal games is equivalent to the calculation of the backward induction outcome of some extensive game. However, whereas the normal game form does not provide information on how to carry out the elimination, the corresponding extensive game does. As a by-product, we conclude that implementation using a subgame perfect equilibrium of an extensive game with perfect information is equivalent to (...) implementation through a solution concept which we call guided iteratively elimination of dominated strategies which requires a uniform order of elimination. Journal of Economic Literature Classification Number: C72. (shrink)

It has become quite common for people to develop `personal'' relationships nowadays, exclusively via extensive correspondence across the Net. Friendships, even romantic love relationships, are apparently, flourishing. But what kind of relations really are possible in this way? In this paper, we focus on the case of close friendship. There are various important markers that identify a relationship as one of close friendship. One will have, for instance, strong affection for the other, a disposition to act for their well-being and (...) a desire for shared experiences. Now obviously, while all these features of friendship can gain some expression through extensive correspondence on the Net, such expression is necessarily limited –you cannot, e.g., physically embrace the other, or go on a picnic together. The issue we want to address here however, is whether there might be distinctive and important influences on the structure of interaction undertaken on the Net, that affect the kind of identity ``Net-friends'''' can develop in relation to one another. In the normal case, one develops a close friendship, and in doing so, one''s identity, in part, is shaped by the friendship. To some extent, through extensive shared experience, one comes to see aspects of the world (and of oneself) through the eyes of one''s friend and so, in part, one''s identity develops in an importantly relational way, i.e., as the product of one''s relation with the close friend. In our view, however, on account of the limits of, and/or the kind of, shared contact and experience one can have with another via correspondence on the Net, there are significant structural barriers to developing the sort of relational identity that is a feature of close friendship. In arguing our case here, and by using the case of Net ``friendship'''' as our foil, we aim to shed light on the nature and importance of certain sorts of self-expression and relational interaction found in close friendship. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 10.2 (2003) 161-167 [Access article in PDF] Social, Cognitive, and Neural Constraints on Subjectivity and Agency:Implications for Dissociative Identity Disorder Peter Q. Deeley In this commentary, I consider Matthew's argument after making some general observations about dissociative identity disorder (DID). In contrast to Matthew's statement that "cases of DID, although not science fiction, are extraordinary" (p. 148), I believe that there are natural analogs of (...) the disorder that, when considered, make it seem less puzzling and exotic. After discussing these examples, I examine the relations between social, cognitive, and neural processes supporting subjectivity and agency, to identify sources of personal identity in cases of DID that can be used as a basis for assessing Matthew's points against Behnke and Sinnott-Armstrong. I am not proposing a comprehensive theory, but rather identifying what I believe are components of such a theory. I then outline an approach to determining criminal responsibility in DID, drawing on analogies with other psychiatric disorders. Dissociative Identity Disorder DID is a disorder described in DSM-IV, which "is characterised by the presence of two or more distinct identities or personality states that recurrently take control of the individual's behaviour accompanied by an inability to recall important personal information that is too extensive to be explained by ordinary forgetfulness" (American Psychiatric Association, p. 519). Recognizing Personal Identity How is personal identity recognized in normal cognition? If we take personhood to involve recognition of continuity of social, psychological, and physical identity for a given individual, then such judgments are routinely made rapidly and automatically as an aspect of what has come to be termed social cognition (Adolphs 2003). There is likely to be considerable redundancy in [End Page 161] the types of information used to make judgments about whether a person is the same as one who was previously encountered, or perhaps heard about—for example, facial features, movement patterns, speech prosody, dress, speech content, gender, ethnicity, social role, among other features, all provide information about individual identity, and hence personhood. When uncertainty exists, it is likely to reflect a loss or alteration of cues that would ordinarily be used in a rapid, automatic, unexamined way (Adolphs 2003). In such extreme cases (for example, severe mental illness or disfigurement), the problem of identification becomes the subject of explicit reasoning (and hence of potential disagreement, because we then engage in post hoc rationalizations to establish criteria for determining personhood, whereas normally we rely on essentially automatic, implicit abilities that work in most circumstances, some of which make little use of linguistic representations and formal reasoning—for example, individual facial identity recognition, which may occur as quickly as 170 ms after stimulus onset [Adolphs 2003]). Nevertheless, examining our judgments and intuitions in cases that force us to explicitly consider whether personal identity is preserved may provide analogies and clues for how we should proceed with DID. Let us consider, then, some natural analogs of DID. Natural Analogs of DID Method Acting I suggest that method acting is an analog of DID (Manderino 1985). Method acting refers to an approach to acting training and performance in which emphasis is placed on intensely imagining and identifying with the mental life of the character being portrayed. Training courses and manuals list many techniques and practices that can be used to facilitate absorption in a role, drawing on different kinds of memory—for example, experiential memories, memories of others, general knowledge (semantic memory), and memories of sensations and feelings, to creative a vivid sense of the subjective experience and actions of the character. Manderino, a method acting teacher, comments: "it is important to investigate the way in which your own mental makeup can improperly influence a character. Insecurities, self-consciousness, shyness or self-doubts can maintain a strong hold, and permitting any of these feelings to enter a performance is to remain the actor and not enter into the mental life of the character. For some, acting allows personal problems to be left behind, and they are thankful for the complete escape that... (shrink)

Philologus, founded in 1846, is one of the oldest and most respected periodicals in the field of Classics. It publishes articles on Greek and Latin literature, historiography, philosophy, history of religion, linguistics, reception, and the history of scholarship. The journal aims to contribute to our understanding of Greco-Roman culture and its lasting influence on European civilization. The journal Philologus, conceived as a forum for discussion among different methodological approaches to the study of ancient texts and their reception, publishes original scholarly (...) contributions with a strong international focus. Publications languages are: German, English, Italian, French. As of 2014 the publication of supplementary volumes will be resumed. The series Philologus. Supplemente / Philologus. Supplementary Volumes will publish monographs and edited volumes pertaining to all aspects of the study of ancient literature and its reception, with a special focus on topics concerning literary theory, philosophy and the history of scholarship from an interdisciplinary perspective. (shrink)

Inductive characterizations of the sets of terms, the subset of strongly normalizing terms and normal forms are studied in order to reprove weak and strong normalization for the simply-typed λ-calculus and for an extension by sum types with permutative conversions. The analogous treatment of a new system with generalized applications inspired by generalized elimination rules in natural deduction, advocated by von Plato, shows the flexibility of the approach which does not use the strong computability/candidate style à la Tait (...) and Girard. It is also shown that the extension of the system with permutative conversions by η-rules is still strongly normalizing, and likewise for an extension of the system of generalized applications by a rule of ``immediate simplification''. By introducing an infinitely branching inductive rule the method even extends to Gödel's T. (shrink)

This paper consists primarily of a survey of results of Harvey Friedman about some proof-theoretic aspects of various forms of Kruskal's tree theorem, and in particular the connection with the ordinal Γ0. We also include a fairly extensive treatment of normal functions on the countable ordinals, and we give a glimpse of Verlen hierarchies, some subsystems of second-order logic, slow-growing and fast-growing hierarchies including Girard's result, and Goodstein sequences. The central theme of this paper is a powerful theorem due (...) to Kruskal, the ‘tree theorem’, as well as a ‘finite miniaturization’ of Kruskal's theorem due to Harvey Friedman. These versions of Kruskal's theorem are remarkable from a proof-theoretic point of view because they are not provable in relatively strong logical systems. They are examples of so-called ‘natural independence phenomena’, which are considered by most logicians as more natural than the metamathematical incompleteness results first discovered by Gödel. Kruskal's tree theorem also plays a fundamental role in computer science, because it is one of the main tools for showing that certain orderings on trees are well founded. These orderings play a crucial role in proving the termination of systems of rewrite rules and the correctness of Knuth-Bendix completion procedures. There is also a close connection between a certain infinite countable ordinal called Γo and Kruskal's theorem. Previous definitions of the function involved in this connection are known to be incorrect, in that, the function is not monotonic. We offer a repaired definition of this function, and explore briefly the consequences of its existence. (shrink)

Modal logics have proven to be a very successful tool for reasoning about games. However, until now, although logics have been put forward for games in both normal form and games in extensive form, and for games with complete and incomplete information, the focus in the logic community has hitherto been on games with pure strategies. This paper is a first to widen the scope to logics for games that allow mixed strategies. We present a modal logic for games (...) in normal form with mixed strategies, and demonstrate its soundness and strong completeness. Characteristic for our logic is a number of infinite rules. (shrink)

With less than 0# two generic extensions ofL are identified: one in which ${\aleph_1}$ , and the other ${\aleph_2}$ , is almost precipitous. This improves the consistency strength upper bound of almost precipitousness obtained in Gitik M, Magidor M (On partialy wellfounded generic ultrapowers, in Pillars of Computer Science, 2010), and answers some questions raised there. Also, main results of Gitik (On normal precipitous ideals, 2010), are generalized—assumptions on precipitousness are replaced by those on ∞-semi precipitousness. As an (...) application it is shown that if δ is a Woodin cardinal and there is an ${f:\omega_1 \to \omega_1}$ with ${\|f\|=\omega_2}$ , then after ${Col(\aleph_2,\delta)}$ there is a normal precipitous ideal over ${\aleph_1}$ . The existence of a pseudo-precipitous ideal over a successor cardinal is shown to give an inner model with a strong cardinal. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:MONADOLOGY OF 7HE BROTHERS KARAMAZOV by Michael Wreen THE WORLD AND THOUGHT of Dostoyevsky's The Brothers Karamazov are not easily entered into. There is something, some barrier, which seems to hinder, if not prevent, a feeling of belonging, a feeling of ease, citizenship, and camaraderie. What is it diat holds die reader back, what makes him feel particularly Ul-at-ease in the world of The Brothers Karamazov, and especially in (...) die presence of the Karamazovs? The answer is that the world of the novel resembles the world of Leibniz's Monadology, a world so different from the world of our everyday conceptions, and so different from the world of most novels, that the reader is left "freefloating," so to speak, until he, as a spirit, has been accommodated and then assimilated by it. To begin with, there is the matter of setting. There are practically no landscapes in The Brothers Karamazov and no extended descriptions of nature. Secondly, buildings, both their interiors and exteriors, are barely sketched, and when described at all, it is usually the psychological state that the human design excites ("It was an odd arrangement ofrooms") that is important, and not the design or structure itself. Objects existing in their own right and "pure surfaces" are not to be found. The one building (with grounds) that is described at length is the monastery, but even here description is used symbolically, as a reflection ofthe spiritual states ofthe monks and The Elder. Similarly, clothing exists only as a clue to the psychological or spiritual state of its wearer. Dmitri's rag with the 1,500 roubles is the analogue of his condition, just as Smerdyakov's hoped-for foppish apparel is of his. 318 Michael Wreen319 Still more unusual is the infrequent mention of two of the biological necessities of life, food and sleep. Food seems to be something that the characters can take or leave, but more often than not, simply forget about; the stomach does not seem to exist for any except one of them. Once or twice the characters do eat, but eating seems to be an accidental side-effect of spending time with, a spiritual infection caught from, the thoroughly carnal Fyodor. The monks, it must be admitted, are concerned with food — though it would be more accurate to say diat they are concerned with die lack of it, or even more strongly, widi maintaining the lack of it. As for sleep, collapse from complete exhaustion (from sustained physical exertion and/or emotional excitement, or from orgiastic debauchery), sickness, and brain fever seem to be preferred to normal sleep. Days are long— so long, in fact, that night is more like an extension of day dian night. Another descriptive element which warrants notice is the physical appearances and personal histories of die dramatic personae. The truth, as far as physical appearances are concerned, is clear and simple: everyone, with the exception ofIvan, is described once and briefly. In the first thirtyfive pages or so, most of the major personages are introduced, "outfitted" with noses, eyes, ears, bearings, statures, mannerisms, traits, etc., and — here we come to the second aspect noted above — then given summary histories. After that, diey are set in dramatic motion. The opening chapters are descriptive and expository, a report of what was and is the case as far as mise en scene and physical equipage are concerned; and except for brief moments when the never-named narrator indulges in short "sermons" about man or God, the mode of narration never returns to descriptive exposition, but remains dramatic and focused on the interplay and clash of personality. Characters do act and think for themselves, and we see diem directly in the acting out of dieir lives. A bit of background information having been provided, we don't have to be told anydiing more; we can observe for ourselves, from the inside. The catalogue offacts is discarded, and in its place is put the experience of events and feelings. The objective, external perspective yields to the internal, subjective perspective, and the reader crosses over from the familiar and cozy world of Dickensian externality to the strange and disconcerting world ofDostoyevskian intemality... (shrink)

Graph normal form, introduced earlier for propositional logic, is shown to be a normal form also for first-order logic. It allows to view syntax of theories as digraphs, while their semantics as kernels of these digraphs. Graphs are particularly well suited for studying circularity, and we provide some general means for verifying that circular or apparently circular extensions are conservative. Traditional syntactic means of ensuring conservativity, like definitional extensions or positive occurrences guaranteeing exsitence of fixed points, (...) emerge as special cases. (shrink)

In this paper we will study the properties of the least extension n(Λ) of a given intermediate logic Λ by a strong negation. It is shown that the mapping from Λ to n(Λ) is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n(Λ). This summarizes results that can be found already in [13, 14] and [4]. Furthermore, we determine the (...) structure of the lattice of extensions of n(LC). (shrink)

In this paper, the following are proved:Theorem A. The quotient algebra ${\cal P} (\kappa )/I$ is complete if and only if the only non-trivial I -closed ideals extending I are of the form $I\lceil A$ for some $A\in I^+$ .Theorem B. If $\kappa$ is a stationary cardinal, then the quotient algebra ${\cal P} (\kappa )/ NS_\kappa$ is not complete.Corollary. (1) If $\kappa$ is a weak compact cardinal, then the quotient algebra ${\cal P} (\kappa )/NS_\kappa$ is not complete.(2) If $\kappa$ bears (...) $\kappa$ -saturated ideal, then the quotient algebra ${\cal P} (\kappa )/NS_\kappa$ is not complete.Theorem C. Assume that $\kappa$ is a strongly compact cardinal, I is a non-trivial normal $\kappa$ -complete ideal on $\kappa$ and B is an I -regular complete Boolean algebra. Then if ${\cal P} (\kappa )/I$ is complete, it is B -valid that for some $A\subseteq\check\kappa$ , ${\cal P} (\kappa )/({\bf J}\lceil A)$ is complete, where J is the ideal generated by $\check I$ in $V^B$ .Corollary. Let M be a transitive model of ZFC and in M , let $\kappa$ be a strongly compact cardinal and $\lambda$ a regular uncountable cardinal less than $\kappa$ . Then there exists a generic extension M [ G ] in which $\kappa =\lambda^+$ and $\kappa$ carries a non-trivial $\kappa$ -complete ideal I which is completive but not $\kappa^+$ -saturated. (shrink)

Reviews of the papers mentioned in the title.

We study axiomatic extensions of the propositional constructive logic with strong negation having the disjunction property in terms of corresponding to them varieties of Nelson algebras. Any such varietyV is characterized by the property: (PQWC) ifA,B V, thenA×B is a homomorphic image of some well-connected algebra ofV.We prove:• each varietyV of Nelson algebras with PQWC lies in the fibre –1(W) for some varietyW of Heyting algebras having PQWC, • for any varietyW of Heyting algebras with PQWC the least and (...) the greatest varieties in –1(W) have PQWC, • there exist varietiesW of Heyting algebras having PQWC such that –1(W) contains infinitely many varieties (of Nelson algebras) with PQWC. (shrink)

We give an extension of the Jónsson‐Tarski representation theorem for both normal and non‐normal modal algebras so that it preserves countably many infinite meets and joins. In order to extend the Jónsson‐Tarski representation to non‐normal modal algebras we consider neighborhood frames instead of Kripke frames just as Došen's duality theorem for modal algebras, and to deal with infinite meets and joins, we make use of Q‐filters, which were introduced by Rasiowa and Sikorski, instead of prime filters. By (...) means of the extended representation theorem, we show that every predicate modal logic, whether it is normal or non‐normal, has a model defined on a neighborhood frame with constant domains, and we give a completeness theorem for some predicate modal logics with respect to classes of neighborhood frames with constant domains. Similarly, we show a model existence theorem and a completeness theorem for infinitary modal logics which allow conjunctions of countably many formulas. (shrink)

We show that classical two-valued logic is included in weak extensions of normal three-valued logics and also that normal three-valued logics are best viewed not as deviant logics but instead as strong extensions of classical two-valued logic obtained by adding a modal operator and the right axioms. This article develops a general method for formulating the right axioms to construct a two-valued system with theorems that correspond to all of the logical truths of any normal (...) three-valued logic. The extended classical system can then express anything that can be expressed in the three-valued logic, so there can be no reason to abandon two-valued logic in favor of three-valued logic. Moreover, the two-valued modal system is preferable, because it enables us to study interactions of different operators with different rationales. It also makes it easier to introduce quantifiers and iteration. Nothing is lost and much is gained by choosing the extended two-valued approach over normal three-valued logics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Alzheimer's Disease, Mild Cognitive Impairment, and the Biology of Intrinsic AgingThomas B. L. Kirkwood (bio)Keywordsaging, Alzheimer’s disease, genetic mutation, mild cognitive impairment, telomereThe article by Gaines and Whitehouse (2006) raises key questions about the uncertain relationship between (i) the intrinsic, "normal" aging process, and (ii) the clinicopathologic states represented by the labels of Alzheimer's disease (AD) and mild cognitive impairment (MCI). This short commentary offers a perspective on (...) this debate that is drawn from a consideration of underlying biological mechanisms.Because age is unquestionably the greatest single risk factor associated with AD and MCI, I begin by asking what we know about the intrinsic processes of aging. The central feature of current understanding of intrinsic aging is that it consists of the gradual, lifelong accumulation of a wide variety of molecular and cellular faults that begins very early in life and eventually leads to overt functional impairments resulting in age-related frailty, disability, and disease (Kirkwood 2005). This is an essentially bottom-up process. A strong consensus has emerged in recent years that there is no active program for aging and that there are no genetic factors that have evolved specifically to cause aging or age-related diseases. Unquestionably, there are genes that influence susceptibility to disease and even length of life, but these genes are genes for maintenance and repair functions, not for aging. It is the limitation in the past evolutionary pressure to invest in greater longevity than was required, within an environment where life was usually truncated by hazards such as starvation, injury, or infection, that means that our maintenance systems—good as they are—are insufficient to keep us going indefinitely. Added to this is the idea that there are probably also genes that program processes that are good for the young organism, but which may in later life have harmful effects. Processes like inflammation and apoptosis, which are seen to occur extensively in aged tissues, including brain, surely evolved to help cope with infection and cellular damage arising earlier in life. That they are called into play in aged tissues is a direct, but secondary, consequence of accumulated damage.With this general framework to understand the intrinsic biology of aging, let us now ask what we might expect a priori for the aging of an organ such [End Page 79] as the brain. Although we cannot pretend complete ignorance of how the brain actually does age, our enquiry can be based entirely on data from other organ systems, so we can develop our predictions about brain aging without prejudice.Aging begins very early during human development, faults accumulating from the first stages of embryonic development. Each time a cell divides, each of the daughter cells is likely to acquire a few new mutations. We know this from the estimates for the error rate in DNA replication and the size of the human genome. It is confirmed by direct evidence that at individual gene loci where mutations have been measured, mutation frequency increases with age (Morley 1998; Vijg 2000). In addition to replication errors, DNA is damaged on a daily basis to a very considerable degree by agents such as reactive oxygen species (free radicals), which are formed as byproducts of normal cellular metabolism. Although most of this damage is corrected by repair, the repair mechanisms themselves are not error free and additional mutations accumulate through this route. If a mutation is lethal to the cell, the cell dies and thus the mutation is eliminated. However, the majority of mutations are nonlethal, either because the mutation is recessive and the cell carries an intact gene copy on the other chromosome, because the gene is not currently required, or because the mutation produces only a delayed deleterious effect. Examples of genes that produce delayed deleterious effects include the genes responsible for familial AD. It is interesting to reflect that on statistical grounds alone, it is almost certain that each of us carries a randomly determined fraction of cells in our brains that bear amyloid precursor protein or presenilin mutations associated with AD. We also carry a heterogeneous array of random mutations that compromise essential cell maintenance functions. How many such... (shrink)

We provide a Hilbert-style axiomatization of the logic of , as well as a two-dimensional semantics with respect to which our logics are sound and complete. Our completeness results are quite general, pertaining to all such actuality logics that extend a normal and canonical modal basis. We also show that our logics have the strong finite model property and permit straightforward first-order extensions.

(This version was submitted to Behavioral and Brain Science. A revised version was published by Biological Theory) Estimates of autism’s incidence increased 5-10 fold in ten years, an increase which cannot be genetic. Though many mutations are associated with autism, no mutation seems directly to cause autism. We need to find the direct cause. Complexity science provides a new paradigm - confirmed in biology by extensive hard data. Both the body and the personality are complex dynamic systems which spontaneously self-organize (...) from simple dynamic systems. Autism may therefore be caused by the failure of a simple dynamic system. We know that infants who cannot track their mother’s face often become autistic, that eye-contact initiates intersubjectivity which is blocked in autism, and that the infant-mother pair seems designed to promote eye-contact, as does the eye’s appearance. This author earlier proposed that failure of eye-contact might directly cause autism and that early non-maternal childcare, including television/video, would therefore be statistically linked to autism. Waldman et al. (2008; 2006) recently proved that autism is strongly linked to precipitation (indoor activity) and to the introduction of cable. The most plausible explanation? Early exposure to television/video is linked to autism. Furthermore a normal developmental cascade (blocked in autism) has been deciphered: (a) Infant-mother eye-contact triggers increased maternal attention. (b) Early maternal attention permanently increases not only baseline vasopressin but also that oxytocin release which is triggered by subsequent maternal attention. (c) Vasopressin and oxytocin promote face recognition, gazing-at-the-eyes, emotion recognition, and social bonding. The eye-contact hypothesis suggests a clinical study addressing prevention: recruit prospective parents who agree to curtail television/video/computer/wi-fi in their families; measure autism’s incidence in their children. (shrink)

This paper presents a systematic discussion, mainly for non-economists, on economic approaches to the concept of sustainable development. As a first step, the concept of sustainability is extensively discussed. As a second step, the argument that it is not possible to consider sustainability only from an economic or ecological point of view is defended; issues such as economic-ecological integration, inter-generational and intra-generational equity are considered of fundamental importance. Two different economic approaches to environmental issues, i.e. neo-classical environmental economics and ecological (...) economics, are compared. Some key differences such as weak versus strong sustainability, commensurability versus incommensurability and ethical neutrality versus different values acceptance are pointed out. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Commentary on “Minds, Memes, and Multiples”Michael Bavidge (bio)Multiple Personality Disorder challenges the idea we have of ourselves—selves whose essential characteristics are simplicity, identity, transparency. Stephen Clark argues that we should look behind the myth of a unitary self to an older tradition which represents personal integration not as a given but as something to be striven for, “a distant, luminous goal,” a “light” over the multiple parts of the (...) human personality, a therapeutic and personal ideal of ourselves as persons separate from the ideas that invade us and the experiences that flow through us.He argues that this notion has a number of advantages. It is compatible with the data of Multiple Personality Disorder. It avoids Cartesian myths while providing a self substantial enough to meet both philosophers’ demands for an explanation of the coherence of experience and clinicians’ requirements for a therapeutic objective.Clark sees Multiple Personality Disorder as an exotic manifestation of the unstable and fractured nature of familiar experience. He points up the complexities of our personalities and the passivity of our normal experience. So our everyday experience comes together with the psychiatric disorder to encourage a looser, more dispersed notion of the self than has been felt necessary since Descartes.The notion of self which we think of as Cartesian (though, Clark suggests, Descartes may never have accepted it), caught on as part of the settlement between the emerging sciences and older wisdom. The basis of the settlement was that the world was to be made amenable to scientific investigation and our innermost selves were to be protected from it. This requires that the self has to be all the things that the rest of the world is not—non-spatial, privately accessible, outside determinist, causal chains, simple and indivisible. The settlement was never stable, and, as contemporary arguments over the cognitive sciences demonstrate, it is as controversial today as ever. Multiple Personality Disorder adds psychiatric considerations to the evidence piling up against the Cartesian self.However, the diagnosis is extremely controversial. A highly critical editorial in the British Journal of Psychiatry in March 1995 suggests that the condition is largely generated within therapy. 1 The diagnosis, as the New Scientist (June 17, 1995) reported, seems excessively subject to trends and fashions. 2 Clark shares these reservations, but he concludes that there is now strong evidence of a “real condition.” Yet he does not discuss what he means by a “real condition.” Certainly he intends to exclude malingering or mere therapist suggestion. Nevertheless, he prefers to interpret the disorder as a matter of one [End Page 29] person having different strategies for dealing with a stressful world, rather than as the emergence of a plurality of persons. Some psychiatrists will think that his acceptance, however qualified, is too much of a concession, while others may feel that he is not allowing the alters, and therefore the condition itself, to be “real” enough.Clark’s philosophical remarks are also circumspect, but ambitious claims are there. He wants a re-appraised, strong theory of the self, though he doubts that the truth of such a theory could ever be established. Nevertheless, for Clark, we need a notion of self as “substance, a real being”; we discover and rediscover it; “it becomes aware of itself in me.”Apart from its philosophical advantages, the notion of self he wishes to revive has therapeutic value. Autonomy is the therapeutic target. Understood in Cartesian terms, Multiple Personality Disorder presents paradoxes of autonomy. Cognitive autonomy is the defining characteristic of the Cartesian self; when we have multiple persons, the question arises: autonomy for whom? The difficulties are softened if our idea of self allows for plurality, opacity and divergence within the one person, so the prospect held out to the patient is the possibility of repossessing the fragmented parts of his or her life.Clark engages in a two-fold maneuver for making sense of Multiple Personality Disorder. He revives a looser philosophical concept of self, and he interprets the disorder as an extension of ordinary experience in which there is a divergence of coping strategies rather than a plurality of egos. One could argue that Clark is too optimistic... (shrink)

A logic \ is called self-extensional if it allows to replace occurrences of a formula by occurrences of an \-equivalent one in the context of claims about logical consequence and logical validity. It is known that no three-valued paraconsistent logic which has an implication can be self-extensional. In this paper we show that in contrast, the famous Dunn–Belnap four-valued logic has exactly one self-extensional four-valued extension which has an implication. We also investigate the main properties of this logic, determine the (...) expressive power of its language, and provide a cut-free Gentzen-type proof system for it. (shrink)

That Kuhn is mistaken in drawing a sharp line between normal and revolutionary phases of science is shown by re-examining the role of models in extending theories to new phenomenal domains. In the light of this revision of the role of models, theory extension, which Kuhn includes in normal science, is shown to be continuous with theory replacement, which Kuhn includes in revolutionary science. Both involve language changes and the 'gestalt switches' associated with revolutionary science. These characteristics cannot (...) be used to demarcate the two phases as Kuhn seems to think. (shrink)

In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a classical recapture (...) result based on the two logics. In the second part of the paper, we compare the approach in terms of normality operators with an established approach to classical recapture, namely minimal inconsistency. Finally, we discuss technical issues connecting LPe and Ke3 to the tradition of Logics of Formal Inconsistency and Underterminedness. (shrink)

We introduce modal propositional substructural logics with strong negation, and prove the completeness theorems (with respect to Kripke models) for these logics.

We show that in the [Formula: see text] extension of a certain Chang-type model of determinacy, if [Formula: see text], then the restriction of the club filter on [Formula: see text] Cof[Formula: see text] to HOD is an ultrafilter in HOD. This answers Question 4.11 of [O. Ben-Neria and Y. Hayut, On [Formula: see text]-strongly measurable cardinals, Forum Math. Sigma 11 (2023) e19].