Section 1 recalls a point noted by A. N. Prior forty years ago: that a certain formula in the language of a purely implicational intermediate logic investigated by R. A. Bull is unprovable in that logic but provable in the extension of the logic by the usual axioms for conjunction, once this connective is added to the language. Section 2 reminds us that every formula is interdeducible with (i.e. added to intuitionistic logic, yields the same intermediate logic as) some (...) conjunction-free formula. Thus it would seem that any detour going via formulas with conjunction can be avoided, which raises a puzzle: how is this consistent with the point from Section 1? Sections 3 and 4 raise and discuss this puzzle. In fact, the puzzle turns out on closer inspection not to be so puzzling after all, but it does serve as a convenient centrepiece around which to organize a discussion of the phenomenon illustrated by the Bull–Prior example. Section 5 notes that Prior's observation can be extended to the case of the result of adding disjunction to Bull's logic, while Section 6 includes some further remarks aimed at diagnosing one source of possible residual puzzlement. A subtext of our discussion—spanning several of the notes—is that this work by Bull and Prior has been overlooked, their results having to be rediscovered, by many algebraists and logicians in more recent years. (shrink)

Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper shows an acute form of non-conservativeness, namely that the Boolean-free fragment of the Boolean extension of a relevant logic need not always satisfy the variable-sharing property. In fact, it is shown that such an extension can in fact yield classical logic. For a vast range of relevant logic, however, it is shown that the variable-sharing property, restricted to the Boolean-free fragment, still holds for the (...) Boolean extended logic. (shrink)

What philosophers have in mind when they think about vagueness are sorites cases. Unlike vague scientific or artificial expressions, however, vague natural language expressions do not display the kind of vagueness that we associate with the sorites; they rather display what I call cluster vagueness. A non-trivial consequence of this is that those legal definitions that state precisifications of natural language concepts not only add aspects of meaning to existing expressions but also effectively change the meanings of these expressions. From (...) this, in turn, it follows that we should avoid precisifying ordinary expressions with the help of legal definitions to the extent that we wish legal language to be in line with natural language. And being in line with natural language may help us to deal with gaps in our laws at the very moment we become aware of them, and not just afterwards. (shrink)

Many relevant logics can be conservatively extended by Boolean negation. Mares showed, however, that E is a notable exception. Mares’ proof is by and large a rather involved model-theoretic one. This paper presents a much easier proof-theoretic proof which not only covers E but also generalizes so as to also cover relevant logics with a primitive modal operator added. It is shown that from even very weak relevant logics augmented by a weak K-ish modal operator, and up to the strong (...) relevant logic R with a S5 modal operator, all fail to be conservatively extended by Boolean negation. The proof, therefore, also covers Meyer and Mares’ proof that NR—R with a primitive S4-modality added—also fails to be conservatively extended by Boolean negation. (shrink)

Exegesis, analysis and discussion of an argument deployed by Dana Scott in his 1973 paper ‘Background to Formalization’, rovide an ideal setting for getting clear about some subtleties in the apparently simple idea of conservative extension. There, Scott claimed in respect of two fundamental principles concerning implication that any generalized consequence relation respecting these principles is always extended conservatively by some similarly fundamental principles concerning conjunction and disjunction. This claim appears on the face of it to conflict with (...) cases in the literature in which adding principles governing conjunction or disjunction or both provides a non-conservative extension of the logic to which they are added, even if that logic does satisfy the intuitionistic conditions on implication. We explore the extent to which such cases can be transformed into counterexamples to Scott’s claim. Once one part of this claim is suitably disambiguated, we find no conflict after all, though we also find that Scott occasionally understates what the argument he provides in support of this claim actually establishes. The main goal, apart from getting straight about Scott’s argument, is to give an airing to various issues and distinctions in the general area of conservativity of extensions; as a side benefit, some semantic light will be thrown on a fragmentary intermediate logic of R. A. Bull, which A. N. Prior showed to be extended non-conservatively by the addition of conjunction, governed by the usual axioms. We will see exactly why, despite appearances, this is not a counterexample to Scott’s claim. (shrink)

It is known that many relevant logics can be conservatively extended by the truth constant known as the Ackermann constant. It is also known that many relevant logics can be conservatively extended by Boolean negation. This essay, however, shows that a range of relevant logics with the Ackermann constant cannot be conservatively extended by a Boolean negation.

Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe, then another perspective emerges: the theses of relevance logic, specifically the system R, may also be seen as the output of a conservative extension of the relation of classical consequence. We describe two ways in which this may be done. One is by defining a suitable closure (...) relation out of the set of theses of relevance logic; the other is by adding to the usual natural deduction system for it further rules with ‘projective constraints’, whose application restricts the subsequent application of other rules. The significance of the two constructions is also discussed. (shrink)

In this paper we define an augmentation mHC of the Heyting propositional calculus HC by a modal operator ?. This modalized Heyting calculus mHC is a weakening of the Proof-Intuitionistic Logic KM of Kuznetsov and Muravitsky. In Section 2 we present a short selection of attractive (algebraic, relational, topological and categorical) features of mHC. In Section 3 we establish some close connections between mHC and certain normal extension K4.Grz of the modal system K4. We define a translation of mHC (...) into K4.Grz and prove that this translation is exact, i. e. theorem-preserving and deducibility-invariant. We have established (however, in this note we do not present a proof of this) that the lattice of all extensions of mHC is isomorphic to the lattice of normal extensions of K4.Grz (a generalization of the Kuznetsov and Muravitsky theorem). (shrink)

This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A determines the extension of a function and f is a Skolem function for A.

This paper examines the conservative point of view about distributive justice. The first section explains the methodology used to develop this point of view. The second section describes one conservative point of view and briefly provides empirical evidence that it reflects the viewpoint of many ordinary conservatives. The third section explains how this conservative view can ground objections to social safety net programs, using as examples the recent health reform legislation and more extensive proposals for a true (...) national health system. The fourth section sketches ways that non-conservative philosophers might try to refute those objections. Examining a conservative point of view leads to several important conclusions. One is that the conservative point of view is not properly represented in contemporary philosophical discussions. Another is that the conservative point of view cannot be refuted by appealing to existing egalitarian writings. A third is that if progressive philosophers such as myself want to address the conservative point of view, we must expand the range of issues that we discuss in contemporary political philosophy. Doing so is a vital task, because otherwise we ignore the political views held by as much as half the American population. (shrink)

This paper deals with Peirce’s understanding of perceptual judgment, relating it to the conditions for the use of language defined by Michael Dummett. Namely, drawing on Dummett’s requirement for harmony between descriptive and evaluative aspects of our linguistic practice, we will try to give an interpretation of Peirce’s view of perception that implies rejecting the idea that the formation of a perceptual judgment has an inferential structure. On the other hand, since it is, in Peirce’s opinion, the structure of abductive (...) inference, this approach should enable us to draw some conclusions related to abduction in general. (shrink)

A conservative extension of general relativity is proposed by alleviating the differentiability of the metric and allowing for non-smooth solutions. We show that these metrics break some symmetries of the Riemann tensor, yielding a new scalar curvature invariant besides the usual Ricci scalar. To first order in the curvature, this adds a new piece of information to the action, containing interesting and unexplored physics. The spectrum of the theory reveals the presence of an additional massless spin-1 field apart (...) from the massless spin-2 graviton. We argue that this new contribution violates P and CP symmetries at leading order in the curvature and we discuss the possibility of observing these effects in existing experiments. (shrink)

Over the last few decades Michael Dummett developed a rich program for assessing logic and the meaning of the terms of a language. He is also a major exponent of Frege's version of logicism in the philosophy of mathematics. Over the last decade, Neil Tennant developed an extensive version of logicism in Dummettian terms, and Dummett influenced other contemporary logicists such as Crispin Wright and Bob Hale. The purpose of this paper is to explore the prospects for Fregean logicism within (...) a broadly Dummettian framework. The conclusions are mostly negative: Dummett's views on analyticity and the logical/non-logical boundary leave little room for logicism. Dummett's considerations concerning manifestation and separability lead to a conservative extension requirement: if a sentence S is logically true, then there is a proof of S which uses only the introduction and elimination rules of the logical terms that occur in S. If basic arithmetic propositions are logically true-as the logicist contends-then there is tension between this conservation requirement and the ontological commitments of arithmetic. It follows from Dummett's manifestation requirements that if a sentence S is composed entirely of logical terminology, then there is a formal deductive system D such that S is analytic, or logically true, if and only if S is a theorem of D. There is a deep conflict between this result and the essential incompleteness, or as Dummett puts it, the indefinite extensibility, of arithmetic truth. (shrink)

Constructive set theory a' la Myhill-Aczel has been extended in (Cantini and Crosilla 2008, Cantini and Crosilla 2010) to incorporate a notion of (partial, non--extensional) operation. Constructive operational set theory is a constructive and predicative analogue of Beeson's Inuitionistic set theory with rules and of Feferman's Operational set theory (Beeson 1988, Feferman 2006, Jaeger 2007, Jaeger 2009, Jaeger 1009b). This paper is concerned with an extension of constructive operational set theory (Cantini and Crosilla 2010) by a uniform operation of (...) Transitive Closure, \tau. Given a set a, \tau produces its transitive closure \tau a. We show that the theory ESTE of (Cantini and Crosilla 2010) augmented by \tau is still conservative over Peano Arithmetic. (shrink)

The technical contribution of this paper is threefold.First we show how to encode functionals in a ‘flat’ applicative structure by adding oracles to untyped λ-calculus and mimicking the applicative behaviour of the functionals with an impredicatively defined reduction relation. The main achievement here is a Church-Rosser result for the extended reduction relation.Second, by combining the previous result with the model construction based on partial equivalence relations, we show how to extend a λ-closed simple type structure to a model of the (...) polymorphic λ-calculus.Third, we specialize the previous result to a counter model against a simple minimization. This minimization is realized by a bar recursive functional, which contrasts the results of Spector and Girard which imply that the bar recursive functions are exactly those that are definable in the polymorphic λ-calculus. As a spin-off, we obtain directly the non-conservativity of the extensions of Gödel's T with bar recursion, fan functional, and Luckhardt's minimization functional, respectively. For the latter two extensions these results are new. (shrink)

Da Costa's paraconsistent systems of the series Cm (for finite m) (see [C1], [C2], and esp. [C3], pp. 237ff.) share important features with transitive logic, TL (which has been gone into in [P1] and [P2]), namely, they all coincide in that: (c1) they possess a strong negation, `¬', a conditional, `⊃', a conjunction, `∧', and a disjunction, `∨', with respect to which they are conservative extensions of CL or Classical Logic; (c2) they possess a non strong negation, `N' (notations (...) are different for systems C) which does not possess all properties of classical negation, but for which the following schemata are theorematic (I use the letters `p', `q', etc as schematic letters; my notational conventions are basically Church's: associativity leftwards; a dot stands for.. (shrink)

We investigate two large families of logics, differing from each other by the treatment of negation. The logics in one of them are obtained from the positive fragment of classical logic (with or without a propositional constant ff for “the false”) by adding various standard Gentzen-type rules for negation. The logics in the other family are similarly obtained from LJ+, the positive fragment of intuitionistic logic (again, with or without ff). For all the systems, we provide simple semantics which is (...) based on non-deterministic four-valued or three-valued structures, and prove soundness and completeness for all of them. We show that the role of each rule is to reduce the degree of non-determinism in the corresponding systems. We also show that all the systems considered are decidable, and our semantics can be used for the corresponding decision procedures. Most of the extensions of LJ+ (with or without ff) are shown to be conservative over the underlying logic, and it is determined which of them are not. (shrink)

We describe a prey–predator system incorporating constant prey refuge through provision of alternative food to predators. The proposed model deals with a problem of non-selective harvesting of a prey–predator system in which both the prey and the predator species obey logistic law of growth. The long-run sustainability of an exploited system is discussed through provision of alternative food to predators. We have analyzed the variability of the system in presence of constant prey refuge and examined the stabilizing effect on predator–prey (...) system. The steady states of the system are derived and dynamical behavior of the system is extensively analyzed around steady states. The optimal harvesting policy is formulated and solved with the help of Pontryagin’s maximal principle. Our objective is to maximize the monetary social benefit through protecting the predator species from extinction, keeping the ecological balance. Results finally illustrated with the help of numerical examples. (shrink)

How can an enterprise, such as Sloterdijk defines in his You Must Change Your Life and its satellite The Art of Philosophy, be “Enlightenment-conservative”? That is the question leading these reflections on the key terms that contain both works in nuce – practice of course, but also perspective and retrospective, transition, extension, explicitation, turn, return, and quarter turn –, reflections that shed light on Sloterdijk’s non-revolutionary conception of Enlightenment as a continuing modernity, without postmodernity, but in need of (...) a curator, a conservateur, and that expose the ontologico-ethical question of the authoritative or sublime imperative (you must) in its Heideggerian, Nietzschean, and finally pseudo-Kantian, even apocalyptic tones, and in its attempt to preserve not only the Enlightenment, but the Renaissance and Antiquity at the same time. (shrink)

We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher-order arithmetic. Let [Formula: see text] be the statement that a non-principal ultrafilter on ℕ exists and let [Formula: see text] be the higher-order extension of ACA0. We show that [Formula: see text] is [Formula: see text]-conservative over [Formula: see text] and thus that [Formula: see text] is conservative over PA. Moreover, we provide a program extraction method and show that from a proof (...) of a strictly [Formula: see text] statement ∀ f ∃ g A qf in [Formula: see text] a realizing term in Gödel's system T can be extracted. This means that one can extract a term t ∈ T, such that ∀ f A qf). (shrink)

The extension of quantum mechanics to a general functional space (“rigged Hilbert space”), which incorporates time-symmetry breaking, is applied to construct extract dynamical models of entropy production and entropy flow. They are illustrated by using a simple conservative Hamiltonian system for multilevel atoms coupled to a time-dependent external force. The external force destroys the monotonicity of the ℋ-function evolution. This leads to a model of the entropy flow that allows a steady nonequilibrium structure of the emitted field around (...) the unstable particles. (shrink)

Natura 2000 is a network of natural sites whose aim is to preserve species and habitats of relevance in the European Union. The policy underlying Natura 2000 has faced widespread opposition from land users and received extensive support from environmentalists. This paper addresses the ethical framework for Natura 2000 and the probable moral assumptions of its main stakeholders. Arguments for and against Natura 2000 were analyzed and classified according to “strong” or “weak” versions of the three main theories of environmental (...) ethics – anthropocentrism, biocentrism, and ecocentrism. Weak (intergenerational) anthropocentrism was found to underlie the Natura 2000 network itself and the positions of environmentalists, while strong (traditional) anthropocentrism pervaded the positions of economic developers. Land users seemed to fall somewhere between weak and strong anthropocentrism. The paper discusses the relation between ethics and different attitudes towards Natura 2000, highlighting some of the implications for the network’s ongoing implementation. It is shown that Natura 2000 achieves a strong reversal of the burden of proof from conservation to economic development and land use change under anthropocentrism. It is argued that the alleged theoretical divide between anthropocentrism and non-anthropocentrism in relation to the burden of proof does not seem to hold in practice. Finally, it is predicted that the weak versions of anthropocentrism, biocentrism, and ecocentrism, are likely to converge extensively in respect to nature conservation policy measures. (shrink)

Natura 2000 is a network of natural sites whose aim is to preserve species and habitats of relevance in the European Union. The policy underlying Natura 2000 has faced widespread opposition from land users and received extensive support from environmentalists. This paper addresses the ethical framework for Natura 2000 and the probable moral assumptions of its main stakeholders. Arguments for and against Natura 2000 were analyzed and classified according to “strong” or “weak” versions of the three main theories of environmental (...) ethics – anthropocentrism, biocentrism, and ecocentrism. Weak (intergenerational) anthropocentrism was found to underlie the Natura 2000 network itself and the positions of environmentalists, while strong (traditional) anthropocentrism pervaded the positions of economic developers. Land users seemed to fall somewhere between weak and strong anthropocentrism. The paper discusses the relation between ethics and different attitudes towards Natura 2000, highlighting some of the implications for the network’s ongoing implementation. It is shown that Natura 2000 achieves a strong reversal of the burden of proof from conservation to economic development and land use change under anthropocentrism. It is argued that the alleged theoretical divide between anthropocentrism and non-anthropocentrism in relation to the burden of proof does not seem to hold in practice. Finally, it is predicted that the weak versions of anthropocentrism, biocentrism, and ecocentrism, are likely to converge extensively in respect to nature conservation policy measures. (shrink)

This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation.

Natura 2000 is a network of natural sites whose aim is to preserve species and habitats of relevance in the European Union. The policy underlying Natura 2000 has faced widespread opposition from land users and received extensive support from environmentalists. This paper addresses the ethical framework for Natura 2000 and the probable moral assumptions of its main stakeholders. Arguments for and against Natura 2000 were analyzed and classified according to “strong” or “weak” versions of the three main theories of environmental (...) ethics – anthropocentrism, biocentrism, and ecocentrism. Weak (intergenerational) anthropocentrism was found to underlie the Natura 2000 network itself and the positions of environmentalists, while strong (traditional) anthropocentrism pervaded the positions of economic developers. Land users seemed to fall somewhere between weak and strong anthropocentrism. The paper discusses the relation between ethics and different attitudes towards Natura 2000, highlighting some of the implications for the network’s ongoing implementation. It is shown that Natura 2000 achieves a strong reversal of the burden of proof from conservation to economic development and land use change under anthropocentrism. It is argued that the alleged theoretical divide between anthropocentrism and non-anthropocentrism in relation to the burden of proof does not seem to hold in practice. Finally, it is predicted that the weak versions of anthropocentrism, biocentrism, and ecocentrism, are likely to converge extensively in respect to nature conservation policy measures. (shrink)

Sodium monofluoroacetate (1080) is a mammalian pesticide used in different parts of the world for the control of mammalian pest species. In New Zealand it is used extensively and very successfully as a conservation management tool for the control of brushtail possums (Trichosurus vulpecula) – an introduced marsupial that has become a substantial agricultural and conservation management pest. Possums pose a threat to cattle farming in New Zealand as they are a vector for bovine tuberculosis. In protected natural areas, possum (...) browsing is responsible for large scale defoliation of native vegetation. As with many other pesticides, there has been some degree of popular concern about the use of this toxin and its safety, with particular reference to non-target effects. These concerns have been associated with potential non-target effects on human health, and the health of animals of recreational value (e.g., hunting dogs and game animals). This has led to the development of a strong “anti-1080” lobby in New Zealand. In contrast, this study encompasses a science-based risk analysis focusing on the potential risks to non-target native wildlife with a particular focus on chronic toxicity. It finds that there is evidence that 1080 may have endocrine disrupting capabilities (with potential relevance for non-target wildlife) but that this still needs more detailed investigation. This can be clarified by further targeted research. Further research is also needed to test the degradation rates of 1080 and its breakdown products at ecologically-relevant temperatures (i.e., winter stream temperatures – below 11 °C). Such research may demonstrate that some adjustment to 1080 risk management is warranted in New Zealand, or it may help to put to rest the current controversy over the use of this cost effective conservation management tool. (shrink)

We study the conservation of energy, or lack thereof, when measurements are performed in quantum mechanics. The expectation value of the Hamiltonian of a system changes when wave functions collapse in accordance with the standard textbook treatment of quantum measurement, but one might imagine that the change in energy is compensated by the measuring apparatus or environment. We show that this is not true; the change in the energy of a state after measurement can be arbitrarily large, independent of the (...) physical measurement process. In Everettian quantum theory, while the expectation value of the Hamiltonian is conserved for the wave function of the universe, it is not constant within individual worlds. It should therefore be possible to experimentally measure violations of conservation of energy, and we suggest an experimental protocol for doing so. (shrink)

We study the representation of sets of desirable gambles by sets of probability mass functions. Sets of desirable gambles are a very general uncertainty model, that may be non-Archimedean, and therefore not representable by a set of probability mass functions. Recently, Cozman (2018) has shown that imposing the additional requirement of even convexity on sets of desirable gambles guarantees that they are representable by a set of probability mass functions. Already more that 20 years earlier, Seidenfeld et al. (1995) gave (...) an axiomatisation of binary preferences—on horse lotteries, rather than on gambles—that also leads to a unique representation in terms of sets of probability mass functions. To reach this goal, they use two devices, which we will call ‘SSK–Archimedeanity’ and ‘SSK–extension’. In this paper, we will make the arguments of Seidenfeld et al. (1995) explicit in the language of gambles, and show how their ideas imply even convexity and allow for conservative reasoning with evenly convex sets of desirable gambles, by deriving an equivalence between the SSK–Archimedean natural extension, the SSK–extension, and the evenly convex natural extension. (shrink)

A generic non-conservative force, applied to an interferometer particle for a period in the past and then turned off, leaves stationary phase and fringe shifts in the now force-free interferometer. Both Aharonov-Bohm and Aharonov-Casher topological phase and fringe shifts can be created in this way. The specific sources of the non-conservative forces behind Aharonov-Bohm and Aharonov-Casher stationary fringe shifts are, respectively, Faraday induction fields and Maxwell displacement currents, now off.

In this paper we prove polyadic counterparts of the Hájek, Paris and Shepherdson's conservative extension theorems of Łukasiewicz predicate logic to rational Pavelka predicate logic. We also discuss the algebraic correspondents of the provability and truth degree for polyadic MV-algebras and prove a representation theorem similar to the one for polyadic Pavelka algebras.

If the language is extended by new individual variables, in classical first order logic, then the deduction system obtained is a conservative extension of the original one. This fails to be true for the logics with infinitary predicates. But it is shown that restricting the commutativity of quantifiers and the equality axioms in the extended system and supposing the merry-go-round property in the original system, the foregoing extension is already conservative. It is shown that these restrictions (...) are crucial for an extension to be conservative. The origin of the results is algebraic logic. (shrink)

Rho GTPases are critically important and are centrally positioned regulators of the actomyosin cytoskeleton. By influencing the organization and architecture of the cytoskeleton, Rho proteins play prominent roles in many cellular processes including adhesion, migration, intra‐cellular transportation, and proliferation. The most important method of Rho GTPase regulation is via the GTPase cycle; however, post‐translational modifications (PTMs) also play critical roles in Rho protein regulation. Relative to other PTMs such as lipidation or phosphorylation that have been extensively characterized, protein oxidation is (...) a regulatory PTM that has been poorly studied. Protein oxidation primarily occurs from the reaction of reactive oxygen species (ROS), such as hydrogen peroxide (H2O2), with amino acid side chain thiols on cysteine (Cys) and methionine (Met) residues. The versatile redox modifications of cysteine residues exemplify their integral role in cell signalling processes. Here we review prominent members of the Rho GTPase family and discuss how lipidation, phosphorylation, and oxidation on conserved cysteine residues affects their regulation and function. (shrink)

In this paper, we develop the system LZF of set theory with the unrestricted comprehension in full linear logic and show that LZF is a conservative extension of ZF– i.e., the Zermelo-Fraenkel set theory without the axiom of regularity. We formulate LZF as a sequent calculus with abstraction terms and prove the partial cut-elimination theorem for it. The cut-elimination result ensures the subterm property for those formulas which contain only terms corresponding to sets in ZF–. This implies that (...) LZF is a conservative extension of ZF– and therefore the former is consistent relative to the latter. (shrink)

This paper presents completeness and conservative extension results for the boolean extensions of the relevant logic T of Ticket Entailment, and for the contractionless relevant logics TW and RW. Some surprising results are shown for adding the sentential constant t to these boolean relevant logics; specifically, the boolean extensions with t are conservative of the boolean extensions without t, but not of the original logics with t. The special treatment required for the semantic normality of T is (...) also shown along the way. (shrink)

In this paper, the endeavour to understand how to think of education ‘after progress’, viz. in an age in which progress has become problematic, is undertaken by focusing on the theme of time. Dovetailing Klaus Mollenhauer’s reflections on the rise of the Bildungszeit at the dawn of modernity with Thomas Popkewitz’s analyses of ‘cosmopolitan time’ presiding over pedagogical reform from the 19th century to the present, I shall, first, explore this temporal configuration of modern schooling (which goes hand in hand (...) with a specific understanding of the child). Against this backdrop, I shall, second, advance an interpretive hypothesis, that of substituting what will be called the ‘child-as-migrant’ for the ‘cosmopolitan child’, by appropriating, in an educational key, some insights of Thomas Nail’s ‘migrant cosmopolitanism’. I shall thereby suggest an alternative view of ‘progressivity’, construed not along modern-developmentalist lines but as a form of non-conservativeness, linked with a recognition of the ekstatikon (that is, destabilizing) character of time. This will require a revisiting of some Aristotelian intuitions about time as the rhythm of movement, reinterpreted as the affective experience of that ek-statikon without which there is no potential for the new. Accordingly, ‘progressive’ education (in the different interpretation investigated here) is the concern to allow all of us as ‘migrants’ to live actively in the abode of our ek-static and unpredictable condition and, therefore, to be vulnerable to the new, without merely remaining in a taken-for-granted ethos, cosmopolitan, inclusive, and progress-oriented though it may be. (Editor's note: This paper forms part of the suite entitled ‘Education After Progress’.). (shrink)

In [1], D. W. Hart and C. Mcginn considered two logics Al and A2. These logics embody part of a tradition about a priori knowledge and necessity. They proved that A2 is a conservative extension of a well-known modal logic S5 but left the problem whether Al is a conservative extension of S4 open. In this note, we shall show that Al is not a conservative extension of S4 but of S5, and also correct (...) an inadequate proof. (shrink)

This paper aims to give a correct proof of Tait's conservative extension theorem. Tait's own proof is flawed in the sense that there are some invalid steps in his argument, and there is a counterexample to the main theorem from which the conservative extension theorem is supposed to follow. However, an analysis of Tait's basic idea suggests a correct proof of the conservative extension theorem and a corrected version of the main theorem.