Search results for "a posteriori"

The Role of Synthetic A Priori Propositions in the Development of Kant’s Account of Practical Autonomy: A Critique of Watkins’ Reading of Kant’s Prol…

2021

AbstractI draw attention to a 12-page Vorarbeit to Kant’s Prolegomena from the so-called Scheffner-Nachlaß and argue that the parallel Kant draws there between the possibility of theoretical and practical synthetic a priori propositions provides important insight into the development of his account of practical autonomy in the Groundwork. Based on a brief sketch of the role synthetic a priori propositions play in the development of Kant’s critical philosophy, I conclude that for Kant the objective validity of any science depends on the objective validity of a number of synthetic a priori propositions.

Per una rilettura kantiana del principio di causalità

2018

There is no contradiction between Kant’s statement that the proposition, “every alteration has its cause,” is of no interest to the Critique of Pure Reason because of its dependence on empirical contents (KrV, B 3) and his use of the same proposition as an example of pure a priori knowledge (KrV, B 5). There is only the arduousness and sometimes also the ambiguity of a passage in which Kant attempts to establish a new basis for the validity of the principle of causality.

Technical support for a judge when assessing a priori odds

2015

A Challenge to Boghossian's Incompatibilist Argument

1998

The paradox arises as we realize that (3) is clearly not knowable a priori, but (1) and (2) are. (2) holds 'a priori' because, according to Boghossian, it "just is the view that I have called the doctrine of privileged self-knowledge" (p. 202). The core of the paper is devoted, though, to argue that an externalist (i.e., someone who holds the view that "... facts external to a thinker's skin are relevant to the individuation of (certain of) his mental contents" (p. 199). is bound to concede that (1) is knowable 'a priori'. It would follow that, contrary to intuition, (3) can be known a priori since is the conclusion of an inference that relies on two premises that are, in

Black holes in five-dimensional Palatinif(R)gravity and implications for the AdS/CFT correspondence

2014

We show that theories having second-order field equations in the context of higher-dimensional modified gravity are not restricted to the family of Lovelock Lagrangians, but can also be obtained if no a priori assumption on the relation between the metric and affine structures of space-time is made (the Palatini approach). We illustrate this fact by considering the case of Palatini $f(R)$ gravities in five dimensions. Our results provide an alternative avenue to explore new domains of the AdS/CFT correspondence without resorting to ad hoc quasitopological constructions.

Nonlocally-induced (fractional) bound states: Shape analysis in the infinite Cauchy well

2015

Fractional (L\'{e}vy-type) operators are known to be spatially nonlocal. This becomes an issue if confronted with a priori imposed exterior Dirichlet boundary data. We address spectral properties of the prototype example of the Cauchy operator $(-\Delta )^{1/2}$ in the interval $D=(-1,1) \subset R$, with a focus on functional shapes of lowest eigenfunctions and their fall-off at the boundaries of $D$. New high accuracy formulas are deduced for approximate eigenfunctions. We analyze how their shape reproduction fidelity is correlated with the evaluation finesse of the corresponding eigenvalues.

A posteriori estimates for a coupled piezoelectric model

2017

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)

Localized forms of the LBB condition and a posteriori estimates for incompressible media problems

2018

The inf–sup (or LBB) condition plays a crucial role in analysis of viscous flow problems and other problems related to incompressible media. In this paper, we deduce localized forms of this condition that contain a collection of local constants associated with subdomains instead of one global constant for the whole domain. Localized forms of the LBB inequality imply estimates of the distance to the set of divergence free fields. We use them and deduce fully computable bounds of the distance between approximate and exact solutions of boundary value problems arising in the theory of viscous incompressible fluids. The estimates are valid for approximations, which satisfy the incompressibility …

A priori bounds and multiplicity of solutions for an indefinite elliptic problem with critical growth in the gradient

2019

Let $\Omega \subset \mathbb R^N$, $N \geq 2$, be a smooth bounded domain. We consider a boundary value problem of the form $$-\Delta u = c_{\lambda}(x) u + \mu(x) |\nabla u|^2 + h(x), \quad u \in H^1_0(\Omega)\cap L^{\infty}(\Omega)$$ where $c_{\lambda}$ depends on a parameter $\lambda \in \mathbb R$, the coefficients $c_{\lambda}$ and $h$ belong to $L^q(\Omega)$ with $q>N/2$ and $\mu \in L^{\infty}(\Omega)$. Under suitable assumptions, but without imposing a sign condition on any of these coefficients, we obtain an a priori upper bound on the solutions. Our proof relies on a new boundary weak Harnack inequality. This inequality, which is of independent interest, is established in the gener…

Maximal regularity via reverse Hölder inequalities for elliptic systems of n-Laplace type involving measures

2008

In this note, we consider the regularity of solutions of the nonlinear elliptic systems of n-Laplacian type involving measures, and prove that the gradients of the solutions are in the weak Lebesgue space Ln,∞. We also obtain the a priori global and local estimates for the Ln,∞-norm of the gradients of the solutions without using BMO-estimates. The proofs are based on a new lemma on the higher integrability of functions.