Edouard Machery (2017) argues that many traditional philosophical questions are beyond our capacity to answer. Answering them seems to require using the method of cases, a method that involves testing answers to philosophical questions against what we think about real or imagined cases. The problem, according to Machery, is that this method has proved unreliable; what we think about these kinds of

Edouard Machery (2017) argues that many traditional philosophical questions are beyond our capacity to answer. Answering them seems to require using the method of cases, a method that involves testing answers to philosophical questions against what we think about real or imagined cases. The problem, according to Machery, is that this method has proved unreliable; what we think about these kinds of

Many philosophers argue that the error theory should be rejected because it is incompatible with standard deontic logic and semantics. We argue that such formal objections to the theory fail. Our discussion has two upshots. First, it increases the dialectical weight that must be borne by objections to the error theory that target its content rather than its form. Second, it shows that standard deontic

I am grateful for Joshua Alexander and Jonathan Weinberg’s, Avner Baz’s and Max Deutsch’s insightful comments on Philosophy Within Its Proper Bounds. I have learned a lot thinking about them, identifying points of convergence and places where differences remain unbridgeable and trying to address the most pressing criticisms. In what follows, I will engage their commentaries in turn.

There is, in my view, a striking combination in Édouard Machery’s Philosophy Within Its Proper Bounds of philosophical modesty and philosophical presumptiveness. Its call upon philosophers to give up their ambitious pursuits of metaphysical necessities, or essences, and to content themselves instead with the elucidation or analysis of our concepts, is made from within a pre-Kantian framework that takes

The Analysis Trust is sad to announce the death of Prof. Hugh Mellor, our friend, former colleague and former chair. Mellor was a distinguished philosopher who made important contributions in metaphysics and the philosophy of science, well-known especially for work on time, causation and probability.

Epistemic norm correspondence and the belief–assertion parallel

AbstractA critical survey of recent work in epistemology on higher-order evidence. It discusses the nature of higher-order evidence, some puzzles it raises, responses to those puzzles, and problems facing them. It concludes by indicating connections between debates concerning higher-order evidence in epistemology and parallel debates in ethics and aesthetics.

Fictional Discourse: A Radical Fictionalist Semantics By PredelliStefanoOxford University Press, 2020. viii + 184 pp.

Julia Maskivker’s The Duty to Vote is a very welcome contribution to the discussion of the theory of citizen participation in politics.11 This is an area that has received far too little attention from philosophers and political theorists. It is receiving more attention recently due to the spate of books by mostly libertarian writers, which argue that citizens in a democracy tend to be poorly informed

Time Travel: Probability and Impossibility By EffinghamNikkOxford University Press, 2020. 256 pp.

AbstractThe modal argument against materialism, in its most standard form, relies on a compatibility thesis to the effect that the physical truths are compatible with the absence of consciousness. I propose an alternative modal argument that relies on an incompatibility thesis: The existence of consciousness is incompatible with the proposition that the physical truths provide (in a sense to be clarified)

AbstractWe examine an objection to analysing the epistemic ‘might’ and ‘may’ as existential quantifiers over possibilities. Some claims that a proposition “might” be the case appear felicitous although, according to the quantifier analysis, they are necessarily false, since there are no possibilities in which the proposition is true. We explain such cases pragmatically, relying on the fact that ‘might’-sentences

AbstractWe argue that permissibility-based solutions to the paradox of supererogation encounter a nested dilemma. Such approaches solve the paradox by distinguishing moral and rational permissions. If they do not also include a bridge condition that relates these two permissions, then they violate a very plausible monotonicity condition. If they do include a bridge condition, then permissibility-based

AbstractThe ‘Big Three’ theories of well-being – hedonism, desire-satisfactionism and objective list theory – attempt to explain why certain things are good for people by appealing to prudentially good-making properties. But they do not attempt to explain why the properties they advert to make something good for a person. Perfectionism, the view that well-being consists in nature-fulfilment, is often

AbstractA considerable literature has grown up around the claim of Uniqueness, according to which evidence rationally determines belief. It is opposed to Permissivism, according to which evidence underdetermines belief. This paper highlights an overlooked third possibility, according to which there is no rational doxastic attitude. I call this 'Nihilism'. I argue that adherents of the other two positions

AbstractLike other epistemic activities, inquiry seems to be governed by norms. Some have argued that one such norm forbids us from believing the answer to a question and inquiring into it at the same time. But another, hither-to neglected norm seems to permit just this sort of cognitive arrangement when we seek to confirm what we currently believe. In this paper, I suggest that both norms are plausible

AbstractI provide a novel argument in favour of majority rule. In particular, I consider the distribution of voter satisfaction in response to the outcome of a vote and prove that under certain conditions majority rule minimizes the level of inequality present in the distribution of voter satisfaction. This finding is reinforced by a computer simulation as well as an analysis of over four decades of

AbstractRecently there has been much philosophical interest in the analysis of concepts to determine whether they should be removed, revised, or replaced. Enquiry of this kind is referred to as conceptual engineering or conceptual ethics. We will call it revisionary conceptual analysis (RCA). It standardly involves describing the meaning of a concept, evaluating whether it serves its purposes, and

AbstractIt is commonly believed that blamees can dismiss hypocritical blame on the ground that the hypocrite has no standing to blame their target. Many believe that the feature of hypocritical blame that undermines standing to blame is that it involves an implicit denial of the moral equality of persons. After all, the hypocrite treats herself better than her blamee for no good reason. In the light

AbstractExistential claims are widely held to be grounded in their true instances. However, this principle is shown to be problematic by arguments due to Kit Fine. Stephan Krämer has given an especially simple form of such an argument using propositional quantifiers. This note shows that even if a schematic principle of existential grounds for propositional quantifiers has to be restricted, this does

AbstractMonism about being says that there is one way to be. Pluralism about being says that there are many ways to be. Recently, Trenton Merricks and David Builes have offered arguments against Pluralism. In this paper, I show how Pluralists who appeal to the relative naturalness of quantifiers can respond to these arguments.

AbstractDrawing from extensions of existing ideas in the logic of ground, a novel account of the grounds of necessity is presented, the core of which states that necessary truths are necessary because they stand in specific grounding connections.

Markosian (2020) presents an argument against certain theories of time based on the aesthetic value of music. He argues that turning a piece of music sideways in time destroys its intrinsic value, which would not be possible if the Spacetime Thesis were true. In this paper I show that sideways music poses no problems for any theory of time by demonstrating that turning a piece of music sideways does

Abstract It is a well-known fact – which can be shown by elementary calculus – that the volume of the unit ball in ℝn{\mathbb{R}^{n}} decays to zero and simultaneously gets concentrated on the thin shell near the boundary sphere as n↗∞{n\nearrow\infty}. Many rigorous proofs and heuristic arguments are provided for this fact from different viewpoints, including Euclidean geometry, convex geometry, Banach

Abstract In this paper, we investigate some growth properties of meromorphic solutions of higher-order linear difference equation A n ⁢ ( z ) ⁢ f ⁢ ( z + n ) + … + A 1 ⁢ ( z ) ⁢ f ⁢ ( z + 1 ) + A 0 ⁢ ( z ) ⁢ f ⁢ ( z ) = 0 , A_{n}(z)f(z+n)+\dots+A_{1}(z)f(z+1)+A_{0}(z)f(z)=0, where A n ⁢ ( z ) , … , A 0 ⁢ ( z ) {A_{n}(z),\dots,A_{0}(z)} are meromorphic coefficients of finite φ-order in the complex plane

Abstract A problem with parameter for an integro-differential equation is approximated by a problem with parameter for a loaded differential equation. The well-posedness of a problem with parameter for the integro-differential equation is established in the terms of the well-posedness of a problem with parameter for the loaded differential equation. A mutual relationship between the qualitative properties

Abstract We prove the existence of global analytic solutions to the nonlinear Schrödinger equation in one dimension for a certain type of analytic initial data in L 2 {L^{2}} .

Abstract Approximation using linear positive operators is a well-studied research area. Many operators and their generalizations are investigated for their better approximation properties. In the present paper, we construct and investigate a variant of modified (p,q)(p,q)-Baskakov operators, which reproduce the test function x2x^{2}. We have determined the order of approximation of the operators via

Abstract In this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two-dimensional bounded domain. The distributed optimal control problem is framed as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn–Hilliard–Navier–Stokes equations. We describe the first order necessary

Abstract As an extension of Lagrange interpolation, we introduce a class of interpolation formulas and study their existence and uniqueness. In the sequel, we consider some particular cases and construct the corresponding weighted quadrature rules. Numerical examples are finally given and compared.

Abstract Given a self-adjoint operator and a relatively trace class perturbation, one can associate the singular spectral shift function – an integer-valued function on the real line which measures the flow of singular spectrum, not only at points outside of the essential spectrum, where it coincides with the classical notion of spectral flow, but at points within the essential spectrum too. The singular

© 2020 Oxford University Press. This is a pre-copyedited, author-produced PDF of an article accepted for publication in Analysis following peer review. The version of record [Michelle Liu, The intuitive invalidity of the pain-in-mouth argument, Analysis, , anaa002, https://doi.org/10.1093/analys/anaa002] is available online at: https://doi.org/10.1093/analys/anaa002.

Abstract In this paper we will give q-analogues for the Pythagorean trigonometric identity sin 2 ⁡ z + cos 2 ⁡ z = 1 {\sin^{2}z+\cos^{2}z=1} in terms of Gosper’s q-trigonometry. We shall also give new q-analogues for the duplicate trigonometric identity sin ⁡ ( x - y ) ⁢ sin ⁡ ( x + y ) = sin 2 ⁡ x - sin 2 ⁡ y {\sin(x-y)\sin(x+y)=\sin^{2}x-\sin^{2}y} . Moreover, we shall give a short proof for an identity

Abstract We investigate the relationship between the discrete fractional difference ( Δ γ ∘ Δ β ∘ Δ α ⁢ f ) ⁢ ( t ) (\Delta^{\gamma}\circ\Delta^{\beta}\circ\Delta^{\alpha}f)(t) and the positivity or monotonicity of the function f. Our approach relies on interpreting the fractional difference as an appropriate convolution operator. The results we provide demonstrate that when compared to the double

How can you steal something that doesn’t exist? This question confronts those of us who (i) take an irrealist view of virtual objects and (ii) agree with the Supreme Court of the Netherlands that robbery took place when two boys used non-virtual violence to coerce a third boy into relinquishing his virtual amulet and mask. Here we outline this Puzzle of Virtual Theft, along with the closely related

Abstract We consider the three-dimensional Navier–Stokes equations whose initial data may have infinite kinetic energy. We establish unique existence of the mild solution to the Navier–Stokes equations for small initial data in the whole space ℝ 3 {\mathbb{R}^{3}} and a vertically periodic product space ℝ 2 × 𝕋 1 {\mathbb{R}^{2}\times\mathbb{T}^{1}} which may be constant in vertical direction so that

In a recent article, Ned Markosian gives an argument against four-dimensionalism understood as the view that time is one of four identical dimensions that constitute a single four-dimensional manifold. In this paper, I show that Markosian attacks a straw man as his argument targets a theory known to be false on empirical grounds. Four-dimensionalism rightly conceived in no way entails that time is

Abstract Triple sequence convergence plays an extremely important role in the fundamental theory of mathematics. This paper contains four types of convergence concepts, namely, convergence almost surely, convergence incredibility, trust convergence in mean, and convergence in distribution, and discuss the relationship among them and some mathematical properties of those new convergence.

Even dogs have probabilistic beliefs. At dinnertime, Fido sits near the children, not the adults, because he believes that the children are more likely to drop food onto the floor. Edgington worries that this fact makes trouble for my complex content account of probabilistic belief. As she puts it, believing a probabilistic content appears to require more “self-consciousness and conceptual apparatus”

Abstract In the present work, the interior spectral data is used to investigate the inverse problem for a diffusion operator with an impulse on the half line. We show that the potential functions q 0 ⁢ ( x ) {q_{0}(x)} and q 1 ⁢ ( x ) {q_{1}(x)} can be uniquely established by taking a set of values of the eigenfunctions at some internal point and one spectrum.

Abstract In this paper, we propose a viscosity-type algorithm to approximate a common solution of a monotone inclusion problem, a minimization problem and a fixed point problem for an infinitely countable family of ( f , g ) {(f,g)} -generalized k-strictly pseudononspreading mappings in a CAT ⁢ ( 0 ) {\mathrm{CAT}(0)} space. We obtain a strong convergence of the proposed algorithm to the aforementioned

Abstract This paper studies the Stokes system - Δ ⁢ 𝐮 + ∇ ⁡ ρ = 𝐟 {-\Delta{\mathbf{u}}+\nabla\rho={\mathbf{f}}} , ∇ ⋅ 𝐮 = χ {\nabla\cdot{\mathbf{u}}=\chi} in Ω with three boundary conditions: 𝐧 ⋅ 𝐮 = 𝐧 ⋅ 𝐠 , \displaystyle{\mathbf{n}}\cdot{\mathbf{u}}={{\mathbf{n}}\cdot\mathbf{g}}, 𝐧 × ( ∇ × 𝐮 ) = 𝐧 × 𝐡 \displaystyle{\mathbf{n}}\times(\nabla\times{\mathbf{u}})={\mathbf{n}}\times{% \mathbf{h}}

Abstract In this paper, we study the stability of k-Hessian overdetermined problems under small perturbations in R 2 {R^{2}} . Additionally, we give a proof for k-Hessian partially overdetermined problems and the related stability problems in R 2 {R^{2}} . The proof mainly replies to choosing a suitable auxiliary f.

Daniel C. Dennett has long maintained that the Consequence Argument for incompatibilism is confused. In a joint work with Christopher Taylor, he claims to have shown that the argument is based on a failure to understand Logic 101. Given a fairly plausible account of having the power to cause something, they claim that an inference rule that the argument relies on is invalid. In this paper, I show that

Professor Causey (in full tweed) and Ms. Neutra (a potential donor) walk down the hall of a gleaming research building. CAUSEY: . . . and so you see that our experimental causal decision-making lab has state-of-the-art facilities which – pardon me for a moment. Causey reaches down to what looks like an electrical outlet along the wall and sticks his finger in the socket. A buzzing sound is heard. CAUSEY:

Abstract The aim of this article is to form new existence theory for global solutions to nonlinear fractional differential equations. Traditional approaches to existence, uniqueness and approximation of global solutions for initial value problems involving fractional differential equations have been unwieldy or intractable due to the limitations of previously used methods. This includes, for example

Abstract In this paper we define and study rough convergence of triple sequences and the set of rough limit points of a triple sequence. We also investigate the relations between the set of cluster points and the set of rough limit points of Cauchy sequences of triple sequence spaces.

Abstract The Salem problem to verify whether Fourier–Stieltjes coefficients of the Minkowski question mark function vanish at infinity is solved recently affirmatively. In this paper by using methods of classical analysis and special functions we solve a Salem-type problem about the behavior at infinity of a linear combination of the Fourier–Stieltjes transforms. Moreover, as a consequence of the Salem

Abstract We give a proof of the Euler’s infinite product for the sine using elementary trigonometric identities, and Tannery’s theorem for infinite products.

We show that in infinite worlds, the following three conditions are incompatible: 1) The spatiotemporal ordering of individuals is morally irrelevant. 2) All else being equal, the act of bringing a ...

This paper presents a new cosmological argument based on considerations about grounding. I argue that, by assuming three plausible principles about grounding, we can construct a cosmological argument for the existence of a unique ungrounded being that ultimately grounds everything else. At the end of the paper I consider two possible objections, and offer my replies to them.

A wealth of cases—most notably blindsight and priming under inattention or suppression—have convinced philosophers and scientists alike that perception occurs outside awareness. In recent work (Phillips 2016a, 2018, Block and Phillips 2016, and Peters et al. 2017), I dispute this consensus, arguing that any putative case of unconscious perception faces a dilemma. The dilemma divides over how absence

In The Unity of Perception, Susanna Schellenberg proposes to reorient philosophical discussion of perception around the notion of “perceptual capacities” — personal-level capacities to single out distal, mind-independent particulars (including objects, property instance types, or event types), such as the capacity to discriminate and single out instances of red from instances of blue. She argues that

Abstract In this study, we present the basic concepts of statistical convergence for double sequences on an arbitrary product time scale. Moreover, we investigate the connection between statistical convergence for double sequences and double Cesàro summability on a product time scale.

Abstract In this paper, we prove the general solution and generalized Hyers–Ulam stability of n-dimensional functional equations of the form ∑ i = 1 i ≠ j ≠ k n f ⁢ ( - x i - x j - x k + ∑ l = 1 l ≠ i ≠ j ≠ k n x l ) = ( n 3 - 9 ⁢ n 2 + 20 ⁢ n - 12 6 ) ⁢ ∑ i = 1 n f ⁢ ( x i ) , \sum_{\begin{subarray}{c}i=1\\ i\neq j\neq k\end{subarray}}^{n}f\biggl{(}-x_{i}-x_{j}-x_{k}+\sum_{% \begin{subarray}{c}l=1\\

Abstract In this work, necessary and sufficient conditions are obtained such that every solution of nonlinear neutral first-order differential equations with several delays of the form ( x ⁢ ( t ) + r ⁢ ( t ) ⁢ x ⁢ ( t - τ ) ) ′ + ∑ i = 1 m ϕ i ⁢ ( t ) ⁢ H ⁢ ( x ⁢ ( t - σ i ) ) = f ⁢ ( t ) \bigl{(}x(t)+r(t)x(t-\tau)\bigr{)}^{\prime}+\sum_{i=1}^{m}\phi_{i}(t)H\bigl{(}% x(t-\sigma_{i})\bigr{)}=f(t) is

Abstract For N ≥ 4 {N\geq 4} , we let Ω be a smooth bounded domain of ℝ N {\mathbb{R}^{N}} , Γ a smooth closed submanifold of Ω of dimension k, with 1 ≤ k ≤ N - 2 {1\leq k\leq N-2} , and h a continuous function defined on Ω. We denote by ρ Γ ⁢ ( ⋅ ) := dist ⁡ ( ⋅ , Γ ) {\rho_{\Gamma}(\,\cdot\,):=\operatorname{dist}(\,\cdot\,,\Gamma)} the distance function to Γ. For σ ∈ ( 0 , 2 ) {\sigma\in(0,2)} ,

Some people claim that some instances of suffering are intrinsically bad in an impersonal way. If it were true, that claim might seem to count against virtue ethics and for consequentialism. Drawing on the works of Jason Kawall, Christine Swanton and Nietzsche, I consider some reasons for thinking that it is, however, false. I argue, moreover, that even if it were true, a virtue ethicist could consistently

Kurt Gödel’s version of the Ontological Proof derives rather than assumes the crucial (yet controversial) Possibility Claim, that is, the claim that it is possible that somethingGod-like exists. Gödel’s derivation starts oš with a proof of the Possible Instantiation of the Positive, that is, the principle that, if a property is positive, it is possible that there exists something that has that property