42 research outputs found
Actuality and the a priori
We consider a natural-language sentence that cannot be formally represented in a first-order language for epistemic two-dimensional semantics. We also prove this claim in the âAppendixâ section. It turns out, however, that the most natural ways to repair the expressive inadequacy of the first-order language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal
Wierenga on theism and counterpossibles
Several theists, including Linda Zagzebski, have claimed that theism is somehow committed to nonvacuism about counterpossibles. Even though Zagzebski herself has rejected vacuism, she has offered an argument in favour of it, which Edward Wierenga has defended as providing strong support for vacuism that is independent of the orthodox semantics for counterfactuals, mainly developed by David Lewis and Robert Stalnaker. In this paper I show that argument to be sound only relative to the orthodox semantics, which entails vacuism, and give an example of a semantics for counterfactuals countenancing impossible worlds for which it fails
Counterfactuals, counteractuals, and free choice
In a recent paper, Pruss proves the validity of the rule beta-2 relative to Lewisâs semantics for counterfactuals, which is a significant step forward in the debate about the consequence argument. Yet, we believe there remain intuitive counter-examples to beta-2 formulated with the actuality operator and rigidified descriptions. We offer a novel and two-dimensional formulation of the Lewisian semantics for counterfactuals and prove the validity of a new transfer rule according to which a new version of the consequence argument can be formulated. This new transfer rule is immune to the counter-examples involving the actuality operator and rigidified descriptions. However, we show that counter-examples to this new rule can also be generated, demanding that the Lewisian semantics be generalized for higher dimensions where counter-examples can always be generated
âPeer Disagreementâ and Evidence of Evidence
What the rational thing to do in the face of disagreement by an epistemic peer is has been much discussed recently. Those who think that a peerâs disagreement is itself evidence against oneâs belief, as many do, are committed to a special form of epistemic dependence. If such disagreement is really evidence, it seems reasonable to take it into account and to adjust oneâs belief accordingly. But then it seems that the belief one ends up with depends, in part, on what someone else believes, even if one does not know why that someone believes what he does. While the practical impossibility of finding actual cases of peer disagreement has been often noted, its conceptual possibility has gone unquestioned. Here we challenge this consensus and argue, first, that, strictly speaking, peer disagreement is impossible and, second, that cases of â all-too-common â near-peer disagreement present no special puzzle and require nothing more than adhering to standard principles of sensible epistemic conduct. In particular, we argue that in such cases there is no good reason to adopt the widely accepted principle that evidence of evidence is evidence. If so, even if one takes a near-peerâs disagreement as a reason for reexamining oneâs belief, one is not epistemically dependent in the sense one would be if that disagreement were evidence concerning the matter in question
Can We Believe Without Sufficient Evidence? The James/Clifford Quarrel and the Response of Alvin Plantinga
This paper aims to be a brief discussion about the character of âevidentialismâ in the discussion between William Clifford and William James. Known under the topic âthe ethics of belief,â it discusses the problem of religious epistemology, specifically the status of the rationality of religious beliefs. After such discussion, we shall adduce in an introductory way Alvin Plantingaâs so-called âreformed epistemologyâ as a proper response to the problem of evidentialism
The Logic of Sequence Frames
This paper investigates and develops generalizations of two-dimensional modal logics to any finite dimension. These logics are natural extensions of multidimensional systems known from the literature on logics for a priori knowledge. We prove a completeness theorem for propositional n-dimensional modal logics and show them to be decidable by means of a systematic tableau construction
Freedom, Omniscience and the Contingent A Priori
One of the major challenges in the philosophy of religion is theological fatalismâroughly, the claim that divine omniscience is incompatible with free will. In this article, I present new reasons to be skeptical of what I consider to be the strongest argument for theological fatalism. First, I argue that divine foreknowledge is not necessary for an argument against free will if we take into account divine knowledge of contingent a priori truths. Second, I show that this argument can be generalized so that ordinary human knowledge of contingent a priori truths also leads to an argument against free will. This, I believe, results in an absurd conclusion that is unacceptable to both theists and non-theists. But if there is something wrong with this argument, there is something wrong, too, with the argument for theological fatalism. Although there is a range of possible responses, I suggest that the core issue in all cases is a closure principleâspecifically, the principle that âno choice aboutâ is closed under entailment (or strict implication)
A Puzzle About the Fixity of the Past
It is a widely held principle that no one is able to do something that would require the past to have been different from how it actually is. This principle of the fixity of the past has been presented in numerous ways, playing a crucial role in arguments for logical and theological fatalism, and for the incompatibility of causal determinism and the ability to do otherwise. I will argue that, assuming bivalence, this principle is in conflict with standard views about knowledge and the semantics for âactuallyâ. I also consider many possible responses to the argument
Rigidity and factivity
David Chalmers argued against the claim that for all p, or even for all entertainable p, it is knowable a priori that p iff actually p. Instead of criticizing Chalmersâs argument, I suggest that it can be generalized, in a sense, and in interesting ways, concerning other principles about contingent a priori truths. In particular, I will argue that the puzzle presented by Chalmers runs parallel to others that do not turn on âactuallyâ. Furthermore, stronger arguments can be presented that do not turn on apriority either, though they do entail the conclusion of Chalmersâs argument. All such puzzles involve interactions between rigidifying sentence-forming devices with factive operators
1-Lipschitz Layers Compared: Memory, Speed, and Certifiable Robustness
The robustness of neural networks against input perturbations with bounded
magnitude represents a serious concern in the deployment of deep learning
models in safety-critical systems. Recently, the scientific community has
focused on enhancing certifiable robustness guarantees by crafting 1-Lipschitz
neural networks that leverage Lipschitz bounded dense and convolutional layers.
Although different methods have been proposed in the literature to achieve this
goal, understanding the performance of such methods is not straightforward,
since different metrics can be relevant (e.g., training time, memory usage,
accuracy, certifiable robustness) for different applications. For this reason,
this work provides a thorough theoretical and empirical comparison between
methods by evaluating them in terms of memory usage, speed, and certifiable
robust accuracy. The paper also provides some guidelines and recommendations to
support the user in selecting the methods that work best depending on the
available resources. We provide code at
https://github.com/berndprach/1LipschitzLayersCompared