The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan monoids may (...) be mapped by noninjective homomorphisms. The homomorphic preimages of C4 within DMM constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety within U are revealed here. There are just ten of them. In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety—in fact, every finite subdirectly irreducible algebra is projective. Beyond U, all covers of [or of ] within DMM are discriminator varieties. Of these, we identify infinitely many that are finitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids. (shrink)

We characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures. This allows us to strengthen a result of Bacsich, as follows: in any prevariety having at most \ non-logical symbols and an axiomatization requiring at most \ variables, if the epimorphisms into structures with at most \ elements are surjective, then so are all of the epimorphisms. Using these facts, we formulate and prove manageable ‘bridge theorems’, matching the surjectivity of all epimorphisms in (...) the algebraic counterpart of a logic \ with suitable infinitary definability properties of \, while not making the standard but awkward assumption that \ comes furnished with a proper class of variables. (shrink)

It was shown recently that epimorphisms need not be surjective in a variety K of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by the Rieger-Nishimura lattice, and all of its (locally finite) subvarieties that contain the original counter-example K . It is known that, whenever a variety of Heyting algebras has finite depth, then it has surjective epimorphisms. In contrast, we show that (...) for every integer $n \geq 2$ , the variety of all Heyting algebras of width at most n has a non-surjective epimorphism. Within the so-called Kuznetsov-Gerčiu variety (i.e., the variety generated by finite linear sums of one-generated Heyting algebras), we describe exactly the subvarieties that have surjective epimorphisms. This yields new positive examples, and an alternative proof of epimorphism surjectivity for all varieties of Gödel algebras. The results settle natural questions about Beth-style definability for a range of intermediate logics. (shrink)

We introduce prime products as a generalization of ultraproducts for positive logic. Prime products are shown to satisfy a version of Łoś’s Theorem restricted to positive formulas, as well as the following variant of the Keisler Isomorphism Theorem: under the generalized continuum hypothesis, two models have the same positive theory if and only if they have isomorphic prime powers of ultrapowers.

A quasivariety of algebras has the joint embedding property (JEP) if and only if it is generated by a single algebra A. It is structurally complete if and only if the free ℵ0‐generated algebra in can serve as A. A consequence of this demand, called ‘passive structural completeness’ (PSC), is that the nontrivial members of all satisfy the same existential positive sentences. We prove that if is PSC then it still has the JEP, and if it has the JEP and (...) its nontrivial members lack trivial subalgebras, then its relatively simple members all belong to the universal class generated by one of them. Under these conditions, if is relatively semisimple then it is generated by one ‐simple algebra. We also prove that a quasivariety of finite type, with a finite nontrivial member, is PSC if and only if its nontrivial members have a common retract. The theory is then applied to the variety of De Morgan monoids, where we isolate the sub(quasi)varieties that are PSC and those that have the JEP, while throwing fresh light on those that are structurally complete. The results illuminate the extension lattices of intuitionistic and relevance logics. (shrink)

The main purpose of this paper is to seek a reconciliation between two apparently conflicting views of mine. I have argued (for example, Smart, 1963) for realism about theoretical entities, for example electrons, protons, photons, possibly space-time points, perhaps the ‘Y’-wave of Schrödinger’s equation and so on. Quine has also plausibly argued that we should believe in mathematical entities, since in physics we quantify over them no less than over electrons and protons. I except cases in which in physics the (...) existential quantifications are part of merely pretence discourse. Perhaps in spherical astronomy talk of the celestial sphere should be treated in this way. Alternatively the celestial sphere could be thought of realistically as a sphere whose centre is that of the earth while the stars and planets are thought of (or correlated with) points or small areas on the sphere’s surface in their lines of sight. I am not concerned in this paper to delimit fact from fiction in scientific discourse. The settlement of borderline disputes can wait for another occasion. My main argument for scientific realism is the cosmic coincidence argument. Would it not be a cosmic coincidence if the world were merely as if there were electrons, protons, etc?1. (shrink)

Robert Boyle, one of the most important intellectuals of the seventeenth century, was a gifted experimenter, an exceptionally able philosopher, and a dedicated Christian. In Boyle’s two _Excellencies_, _The Excellency of Theology Compared with Natural Philosophy_ and _About The Excellency and Grounds of the Mechanical Hypothesis_, he explains and justifies his new philosophy of science while reconciling it with Christian theology. These pioneering works of early science and theology are now available in a modernized and accessible new edition. This Broadview (...) edition brings spelling and punctuation into line with current conventions and includes notes and references to set the works in their historical and philosophical context. The appendices include works by Boyle’s predecessors in the philosophy of science, other philosophical writings by Boyle, and an appendix of the other figures mentioned in the texts. (shrink)

We can contrast rationalising explanations of the form S φs because p with those of the form S φs because S believes that p. According the Common Kind View, the two sorts of explanation are the same. The Disjunctive View denies this. This paper sets out to elucidate the sense in which the Common Kind Theorist asserts, but the Disjunctivist denies, that the two explanations are the same. I suggest that, in the light of the distinction between kinds of explanation (...) and particular explanations, the relevant sameness thesis is ambiguous, thus giving us two distinct versions of the Common Kind View. I then argue that the only direct arguments for Disjunctivism available in the literature fail because they only succeed in undermining one version of the Common Kind View. I finish, however, by providing a fresh argument for the Disjunctive View which aims to undermine both versions of its competitor. (shrink)

It is now common to distinguish Metaphysical from Epistemological Disjunctivism. It is equally common to suggest that it is at least not obvious that the latter requires a commitment to the former: at the very least, a suitable bridge principle will need to be identified which takes one from the latter to the former. This paper identifies a plausible-looking bridge principle that takes one from the version of Epistemological Disjunctivism defended by John McDowell and Duncan Pritchard, which I label Reflective (...) Epistemological Disjunctivism, or (RED), to Metaphysical Disjunctivism. Moreover, it identifies a modification the proponent of (RED) could, and should, make to the Internalist component of their theory, and argues that the commitment to Metaphysical Disjunctivism remains, even if such a modification is made. The upshot is that the commitment to Metaphysical Disjunctivism on the part of (RED) is shown to be particularly robust. (shrink)

Here is a surprisingly neglected question in contemporary epistemology: what is it for an agent to believe that p in response to a normative reason for them to believe that p? On one style of answer, believing for the normative reason that q factors into believing that p in the light of the apparent reason that q, where one can be in that kind of state even if q is false, in conjunction with further independent conditions such as q’s being (...) a normative reason to believe that p. The primary objective of this paper is to demonstrate that that style of answer cannot be right, because we must conceive of believing for a normative reason as constitutively involving a kind of rationality-involving relation that can be instantiated at all only if there is a known fact on the scene, which the agent treats as a normative reason. A secondary objective, achieved along the way, is to demonstrate that in their Prime Time Errol Lord and Kurt Sylvan do not succeed in undermining the factoring picture in general, only a simple-minded version of it. (shrink)

Two essays on utilitarianism, written from opposite points of view, by J. J. C. Smart and Bernard Williams. In the first part of the book Professor Smart advocates a modern and sophisticated version of classical utilitarianism; he tries to formulate a consistent and persuasive elaboration of the doctrine that the rightness and wrongness of actions is determined solely by their consequences, and in particular their consequences for the sum total of human happiness. In Part II Bernard Williams offers a sustained (...) and vigorous critique of utilitarian assumptions, arguments and ideals. He finds inadequate the theory of action implied by utilitarianism, and he argues that utilitarianism fails to engage at a serious level with the real problems of moral and political philosophy, and fails to make sense of notions such as integrity, or even human happiness itself. This book should be of interest to welfare economists, political scientists and decision-theorists. (shrink)

Advances in the understanding of genetics have led to the belief that it may become possible to use genetic engineering to manipulate the DNA of humans at the embryonic stage to produce certain desirable traits. Although this currently cannot be done on a large scale, many people nevertheless object in principle to such practices. Most often, they argue that genetic enhancements would harm the children who were engineered, cause societal harms, or that the risks of perfecting the procedures are too (...) high to proceed. However, many of these same people do not have serious objections to what is called ‘genetic planning’ procedures (such as the selection of sperm donors with desirable traits) that essentially have the same ends. The author calls the view that genetic engineering enhancements are impermissible while genetic planning enhancements are permissible the ‘popular view’, and argues that the typical reasons people give for the popular view fail to distinguish the two practices. This paper provides a principle that can salvage the popular view, which stresses that offspring from genetic engineering practices have grounds for complaint because they are identical to the pre-enhanced embryo, whereas offspring who are the result of genetic planning have no such grounds. (shrink)

It’s one thing to do the right thing. It’s another to be creditable for doing the right thing. Being creditable for doing the right thing requires that one does the right thing out of a morally laudable motive and that there is a non-accidental fit between those two elements. This paper argues that the two main views of morally creditable action – the Right Making Features View and the Rightness Itself View – fail to capture that non-accidentality constraint: the first (...) because it morally credits agents who make heavy-duty moral mistakes; the second because it fails to generalise and is too conservative – a point which this paper gives renewed defence. The paper then goes on to defend and develop an alternative according to which moral worth is mediated by the agent’s knowing how to respond to the reasons of the type which make acting in that way right. It’s argued that this view avoids the problems for the alternatives, and it’s shown that in order for the view to avoid collapsing into a problematic form of Reliabilism we’ll have to think of states of knowing how as essentially successful in character. (shrink)

This paper begins with a Davidsonian puzzle in the epistemology of perception and introduces two solutions to that puzzle: the Truth-Maker View (TMV) and the Content Model. The paper goes on to elaborate (TMV), elements of which can be found in the work of Kalderon (2011) and Brewer (2011). The central tenant of (TMV) is the claim that one's reason for one's perceptual belief should, in all cases, be identified with some item one perceives which makes the proposition believed true. (...) I defend an argument against (TMV) which appeals to (a) the claim that the reason for which one believes should always to be identified with the explanans of the rationalising explanation to which one's belief is subject and (b) the claim that the explanantia of rationalising explanations must be identified with truths. I finish by replying to two objections to the argument. (shrink)

In this article I try to refute the so-called "libertarian" theory of free will, and to examine how our conclusion ought to modify our common attitudes of praise and blame. In attacking the libertarian view, I shall try to show that it cannot be consistently stated. That is, my dscussion will be an "analytic-philosophic" one. I shall neglect what I think is in practice an equally powerful method of attack on the libertarian: a challenge to state his theory in such (...) a way that it will fit in the modern biology and psychology, which are becoming increasingly physicalistic. (shrink)

Book reviewed in this article:F.H. Bradley, Collected Works Volumes 1–5.