Relating Semantics for Epistemic Logic

The aim of this paper is to explore the advantages deriving from the application of relating semantics in epistemic logic. As a first step, I will discuss two versions of relating semantics and how they can be differently exploited for studying modal and epistemic operators. Next, I consider several standard frameworks which are suitable for modelling knowledge and related notions, in both their implicit and their explicit form and present a simple strategy by virtue of which they can be associated with intuitive systems of relating logic. As a final step, I will focus on the logic of knowledge based on justification logic and show how relating semantics helps us to provide an elegant solution to some problems related to the standard interpretation of the explicit epistemic operators.

The Practical Significance of Kant’s Categorical Imperative

On a standard interpretation, the aim of the formula of universal law is to provide a decision procedure for determining the deontic status of actions. By contrast, this chapter argues for the practical significance of the Categorical Imperative (CI) centering on Kant’s account of the dynamics of incentives. This approach avoids some widespread misconceptions about how the CI operates and false expectations about what it promises and delivers. In particular, it explains how it differs from deductive practical inferences. The CI is the supreme form of morality, and yet not in the sense that particular categorical principles can be derived deductively from it, once the relevant details are supplied. The efficacy of practical reasoning primarily concerns agents and consists in their reorientation toward the right end. Moral knowledge is knowledge about what we ought to do, but it is also a distinctive variety of self-knowledge, that is, knowledge of ourselves as rationally efficacious agents.

The general-relativistic case for super-substantivalism

Super-substantivalism (of the type we’ll consider) roughly comprises two core tenets: (1) the physical properties which we attribute to matter (e.g. charge or mass) can be attributed to spacetime directly, with no need for matter as an extraneous carrier “on top of” spacetime; (2) spacetime is more fundamental than (ontologically prior to) matter. In the present paper, we revisit a recent argument in favour of super-substantivalism, based on General Relativity. A critique is offered that highlights the difference between (various accounts of) fundamentality and (various forms of) ontological dependence. This affords a metaphysically more perspicuous view of what super-substantivalism’s tenets actually assert, and how it may be defended. We tentatively propose a re-formulation of the original argument that not only seems to apply to all classical physics, but also chimes with a standard interpretation of spacetime theories in the philosophy of physics.

The Spiritual Exercises of John Rawls

In this article I interpret John Rawls’s concept of the original position as a spiritual exercise. In addition to the standard interpretation of the original position as an expository device to select principles of justice for the fundamental institutions of society, I argue that Rawls also envisages it as a “spiritual exercise”: a voluntary personal practice intended to bring about a transformation of the self. To make this argument, I draw on the work of Pierre Hadot, a philosopher and classicist, who introduced the idea of spiritual exercises as central to ancient and modern conceptions of philosophy. By reading Rawls alongside Hadot, this article portrays Rawls as a thinker deeply concerned with the question of how subjects can lead more just and fulfilling lives. It also proposes that the original position as a spiritual exercise can help defend liberalism as a social and political doctrine.

The Laws of Nature Are the Laws of God in Leviathan

The standard interpretation that the laws of nature in Leviathan are not laws because he calls them theorems is mistaken. The theorems, or “dictates of reason,” are the propositions that Hobbes proves. But they need the force of a command to be, as he says “properly called Lawes.” Hobbes uses reason to prove them, and reason is the “undoubted word of God.” The author argues against John Deigh’s ingenious defense of the standard view. Deigh maintains that words in phrases that are technical terms do not retain their meaning outside of the phrase. But if that were true, then “civil laws” and “natural liberty” would not be laws or liberty respectively. Also, if they were not laws, Hobbes’s division of two kinds of law, civil and natural, would be absurd.

Out-of-sequence skeletal growth causing oscillatory zoning in arc olivines

Primitive olivines from the monogenetic cones Los Hornitos, Central-South Andes, preserve dendritic, skeletal, and polyhedral growth textures. Consecutive stages of textural maturation occur along compositional gradients where high Fo–Ni cores of polyhedral olivines (Fo92.5, Ni ~3500 ppm) contrast with the composition of dendritic olivines (Fo < 91.5, Ni < 3000 ppm), indicating sequential nucleation. Here we present a new growth model for oscillatory Fo–Ni olivine zoning that contrasts with the standard interpretation of continuous, sequential core-to-rim growth. Olivine grows rapidly via concentric addition of open-structured crystal frames, leaving behind compositional boundary layers that subsequently fill-in with Fo–Ni-depleted olivine, causing reversals. Elemental diffusion modeling reveals growth of individual crystal frames and eruption at the surface occurred over 3.5–40 days. Those timescales constrain magma ascent rates of 40–500 m/h (0.011 to 0.14 m/s) from the deep crust. Compared to ocean island basalts, where dendritic and skeletal olivines have been often described, magmas erupted at arc settings, experiencing storage and degassing, may lack such textures due to fundamentally different ascent histories.

Calculation of proton charges from the electric charges of the fermions of the quantum vacuum

The electric charge of the fermions of the quantum vacuum is calculated in this paper. The value of e 0 is 5.06532 × 10−45 C. From this value of e 0, together with the fundamental constants KO , c, <mml:math display="inline"> <mml:mi mathvariant="italic"> ħ </mml:mi> </mml:math> , and α = 1/137, the electric charge of the proton is calculated, achieving the value e = 1.6026 × 10−19 C, which is very close to the experimental e = 1.60218 × 10−19 C. This successful calculation represents the first objective evidence that something very fundamental is missing in the standard interpretation of quantum electrodynamics.

Categoricity by convention

On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results—for instance, Dedekind’s categoricity theorem for second-order and Zermelo’s quasi-categoricity theorem for second-order —these results require full second-order logic. So appealing to these results seems only to push the problem back, since the principles of second-order logic are themselves non-categorical: those principles are compatible with restricted interpretations of the second-order quantifiers on which Dedekind’s and Zermelo’s results are no longer available. In this paper, we provide a naturalist-friendly, non-revisionary solution to an analogous but seemingly more basic problem—Carnap’s Categoricity Problem for propositional and first-order logic—and show that our solution generalizes, giving us full second-order logic and thereby securing the categoricity or quasi-categoricity of second-order mathematical theories. Briefly, the first-order quantifiers have their intended interpretation, we claim, because we’re disposed to follow the quantifier rules in an open-ended way. As we show, given this open-endedness, the interpretation of the quantifiers must be permutation-invariant and so, by a theorem recently proved by Bonnay and Westerståhl, must be the standard interpretation. Analogously for the second-order case: we prove, by generalizing Bonnay and Westerståhl’s theorem, that the permutation invariance of the interpretation of the second-order quantifiers, guaranteed once again by the open-endedness of our inferential dispositions, suffices to yield full second-order logic.

Why Strict Compliance?

John Rawls defines ideal theory in terms of a strict compliance assumption. The standard interpretation of ideal theory is telic: the function of the strict compliance assumption is to help specify a realistic utopia as a telos for political decision making. The chapter defends an alternative, deontic interpretation of ideal theory, one based on the fundamental Rawlsian idea of society as a fair scheme of cooperation. It claims that the participants of a genuinely cooperative scheme are mutually accountable in that they have the standing to make demands of one another. It argues that the logic of these moral demands implies that the rules of any cooperative scheme must be justified on the basis of a strict compliance assumption. Since society as a whole constitutes a cooperative scheme in justice as fairness, the same conclusion holds of its principles of justice. The chapter also defends the possibility of a non-utopian ideal theory.