We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula ${\phi}$ in the propositional modal language with A, there is a formula ${\psi}$ not containing A such that ${\phi}$ and ${\psi}$ are materially equivalent at the actual world in every Kripke model (respectively, neighborhood model). Inspection of the proofs leads to corresponding proof-theoretic results concerning the eliminability of the actuality (...) operator in the actuality extension of any normal propositional modal logic and of any “classical” modal logic. As an application, we provide an alternative proof of a result of Williamson’s to the effect that the compound operator A□ behaves, in any normal logic between T and S5, like the simple necessity operator □ in S5. (shrink)

Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...) considering a Sheffer function for intuitionistic logic. (shrink)

The logic of paradox, LP, is a first-order, three-valued logic that has been advocated by Graham Priest as an appropriate way to represent the possibility of acceptable contradictory statements. Second-order LP is that logic augmented with quantification over predicates. As with classical second-order logic, there are different ways to give the semantic interpretation of sentences of the logic. The different ways give rise to different logical advantages and disadvantages, and we canvass several of these, concluding that it will be extremely (...) difficult to appeal to second-order LP for the purposes that its proponents advocate, until some deep, intricate, and hitherto unarticulated metaphysical advances are made. (shrink)

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

Logics that have many truth values—more than just True and False—have been argued to be useful in the analysis of very many philosophical and linguistic puzzles. In this paper, which is a followup to, we will start with a particularly well-motivated four-valued logic that has been studied mainly in its propositional and first-order versions. And we will then investigate its second-order version. This four-valued logic has two natural three-valued extensions: what is called a “gap logic”, and what is called a (...) “glut logic”. We mention various results about the second-order version of these logics as well. And we then follow our earlier papers, where we had added a specific conditional connective to the three valued logics, and now add that connective to the four-valued logic under consideration. We then show that, although this addition is “conservative” in the sense that no new theorems are generated in the four-valued logic unless they employ this new conditional in their statement, nevertheless the resulting second-order versions of these logics with and without the conditional are quite different in important ways. We close with a moral for logical investigations in this realm. (shrink)

Il platonista sostiene che le verità della matematica e della logica siano letteralmente vere, ossia che descrivano (in qualche modo: non voglio legare la definizione a una particolare teoria semantica) realtà che non sono create o decise da noi. Il convenzionalista sostiene invece che le proposizioni che chiamiamo verità della matematica siano in qualche misura convenzionali: esse esprimerebbero convenzioni che abbiamo adottato noi, o certe loro conseguenze. Le due posizioni sono apparenteme...

There are good reasons to want logics, including many-valued logics, to have usable conditionals, and we have explored this in certain logics. However, it turns out that we “accidentally” chose some favourable logics. In this paper, we look at some of the unfavourable logics and describe where usable conditionals can be added and where it is not possible.

A questionnaire on the attitudes towards the functions of research ethical committees was sent to members of selected research ethical committees in Wessex and some controls. Almost all respondents felt there was a need for ethical review of research projects; 42 per cent thought there was a need for some training before joining a committee; 67 per cent thought the system could be improved and 47 per cent thought that monitoring or follow-up procedures should be adopted. Ethical committees were thought (...) to be purely advisory, as opposed to mandatory, by 33 per cent, and 63 per cent thought they should restrict their review to ethical problems as opposed to scientific or design problems. Views about the function of non-medical members ranged from 'none at all' to 'very important'. Of the 10 controls who were asked whether they would become a member of an ethical committee if asked, seven said that on balance they would and the reasons stated varied from the view that it was a 'very important committee' to the feeling that it was 'a necessary but irksome job'. (shrink)

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

In order to model any macroscopic system, it is necessary to aggregate both spatially and taxonomically. If average processes are assumed, then kinetic equations of “population dynamics” can be derived. Much effort has gone into showing the important effects introduced by non-average effects (fluctuations) in generating symmetry-breaking transitions and creating structure and form. However, the effects of microscopic diversity have been largely neglected. We show that evolution will select for populations which retain “variability,” even though this is, at any given (...) time, loss-making, predicting that we shall not observe populations with “optimal behavior,” but populations which can “learn.” This lesser short-term efficiency may be why natural diversity is so great. Evolution is seen to be “driven” by the noise to which it leads. (shrink)

The manifest appearance of function and purpose in living systems is responsible for the prevalence of apparently teleological explanations of organismic structure and behavior in biology. Although the attribution of function and purpose to living systems is an ancient practice, teleological notions are largely considered ineliminable from modern biological sciences, such as evolutionary biology, genetics, medicine, ethology, and psychiatry, because they play an important explanatory role. Historical and recent examples of teleological claims include the following: The chief function of the (...) heart is the transmission and pumping of the blood through the arteries to the extremities of the body. (Harvey 1616 [1928: 49]) The Predator Detection hypothesis remains the strongest candidate for the function of stotting [by gazelles]. (Caro 1986: 663) The geographic range of human malaria is much wider than the range of the sickle-cell gene. As it happens, other antimalarial genes take over the protective function of the sickle-cell gene in … other warm parts. (Diamond 1994: 83) Despite the substantial amount of data we now have on theropod dinosaurs, more information is necessary in order to determine the likelihood that early feathers served an adaptive function in visual display as opposed to other proposed adaptive functions such as thermoregulation. (Dimond et al. 2011: 62) The ubiquity of claims such as these raises the question: how should apparently teleological notions in biology be understood? Most post-Darwinian approaches attempt to naturalize teleology in biology, in opposition to nineteenth-century viewpoints which grounded it theologically. Nevertheless, biologists and philosophers have continued to question the legitimacy of teleological notions in biology. For instance, Ernst Mayr (1988), identified four reasons why teleological notions remain controversial in biology, namely that they are: vitalistic (positing some special ‘life-force’); requiring backwards causation (because goal-directed explanations seem to use future outcomes to explain present traits); incompatible with mechanistic explanation (because of 1 and 2); mentalistic (attributing the action of mind where there is none). A fifth complaint is that they are not empirically testable (Allen & Bekoff 1995). The current philosophical literature offers both Darwinian and non-Darwinian accounts of teleology in biology that aim to avoid these concerns. In this article, we hope to bring some clarity to the contemporary debates over the role of teleological notions in biology by sketching a taxonomy of the various accounts of biological function on offer (see Allen & Bekoff 1995 for a more comprehensive taxonomy that forms the basis of this presentation). We primarily focus on naturalistic accounts of biological function, since this is where we see the most lively and productive current debates (see, e.g., Garson 2016 for an extended survey). We also briefly discuss the notion of goal-directedness in section 2. (shrink)

In this interview, C. P. Goodman invites British Polanyi scholar Richard T. Allen to reflect on his interest in Polanyi’s philosophical ideas and share what he believes is valuable in his thought.

As John Henry Newman reflected on 'The Idea of a University' more than a century and a half ago, Bradley C. S. Watson brings together some of the nation's most eminent thinkers on higher education to reflect on the nature and purposes of the American university today. Their mordant reflections paint a picture of the American university in crisis. This book is essential reading for thoughtful citizens, scholars, and educational policymakers.

Hegel may be read as endorsing a republican conception of freedom as non-domination. This may then be allied to an expressive conception of freedom not as communal integration and non-alienation, but rather as the development of new powers and capabilities. To this extent, he may be understood as occupying a position between nondomination and expressive freedom. This not only informs contemporary discussions of republicanism and democracy, but also suggests a ‘capabilities solution’ to the otherwise intractable problem of the rabble. Key (...) Words: creativity • democracy • domination • expression • freedom • G.W.F.Hegel • rabble • republicanism. (shrink)

There is a large body of empirical work that has investigated the relationship between parents’ child-directed speech and their children’s Theory of Mind development. That such a relationship should exist is well motivated from both Theory Theory and Socio-Cultural perspectives. Despite this general convergence, we argue that theoretical differences between the two perspectives suggests nuanced differences in the expected outcomes of the empirical work. Further, the different ontological commitments of the two approaches have guided the design, coding, and analysis of (...) existing research and imply different future directions. We discuss five areas of extant research that can be extended and diversified most coherently by adopting a SC framework. (shrink)

Thousands of texts discuss Egytpain cosmology and cosmogony. James Allen has selected sixteen to translate and discuss in order to shed light on one of the questions that clearly preoccupied ancient intellectuals; the origins of the world.