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)

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.

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)

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)

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)

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)

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...

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.

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)

'Chains of Being' argues that there can be infinite chains of dependence or grounding. Cameron also defends the view that there can be circular relations of ontological dependence or grounding, and uses these claims to explore issues in logic and ontology.

Ross P. Cameron argues that the flow of time is a genuine feature of reality. He suggests that the best version of the A-Theory is a version of the Moving Spotlight view, according to which past and future beings are real, but there is nonetheless an objectively privileged present. Cameron argues that the Moving Spotlight theory should be viewed as having more in common with Presentism than with the B-Theory. Furthermore, it provides the best account of truthmakers for claims (...) about what was or will be the case. Cameron goes on to defend an account of the open future, and argues that this is a better account than that available to the Growing Block theory. (shrink)

Paul Sheehy has argued that the modal realist cannot satisfactorily allow for the necessity of God's existence. In this short paper I show that she can, and that Sheehy only sees a problem because he has failed to appreciate all the resources available to the modal realist. God may be an abstract existent outside spacetime or He may not be: but either way, there is no problem for the modal realist to admit that He exists at every concrete possible world.

Reply in Book Symposium on James Ladyman, Don Ross: 'Everything must go: metaphysics naturalized', Oxford: Oxford University Press, 2007.

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)

I address an intuition commonly endorsed by metaphysicians, that there must be a fundamental layer of reality, i.e., that chains of ontological dependence must terminate: there cannot be turtles all the way down. I discuss applications of this intuition with reference to Bradley’s regress, composition, realism about the mental and the cosmological argument. I discuss some arguments for the intui- tion, but argue that they are unconvincing. I conclude by making some suggestions for how the intuition should be argued for, (...) and discussing the ramifications of giving the justification I think best. (shrink)

Many have been tempted to invoke a primitive notion of grounding to describe the way in which some features of reality give rise to others. Jessica Wilson argues that such a notion is unnecessary to describe the structure of the world: that we can make do with specific dependence relations such as the part–whole relation or the determinate–determinable relation, together with a notion of absolute fundamentality. In this paper I argue that such resources are inadequate to describe the particular ways (...) in which some parts of reality give rise to others, and thus that we do in fact need grounding. (shrink)

What are the ontological commitments of a sentence? In this paper I offer an answer from the perspective of the truthmaker theorist that contrasts with the familiar Quinean criterion. I detail some of the benefits of thinking of things this way: they include making the composition debate tractable without appealing to a neo-Carnapian metaontology, making sense of neo-Fregeanism, and dispensing with some otherwise recalcitrant necessary connections.

In this paper I further elucidate and defend a metaontological position that allows you to have a minimal ontology without embracing an error-theory of ordinary talk. On this view 'there are Fs' can be strictly and literally true without bringing an ontological commitment to Fs. Instead of a sentence S committing you to the things that must be amongst the values of the variables if it is true, I argue that S commits you to the things that must exist as (...) truthmakers for S if it is true. I rebut some recent objections that have been levelled against this metaontological view. (shrink)