1,016,508 research outputs found
Reflection, Intelligibility, and Leibniz’s Case Against Materialism
Leibniz’s claim that it is possible for us to gain metaphysical knowledge through reflection on the self has intrigued many commentators, but it has also often been criticized as flawed or unintelligible. A similar fate has beset Leibniz’s arguments against materialism. In this paper, I explore one of Leibniz’s lesser-known arguments against materialism from his reply to Bayle’s new note L (1702), and argue that it provides us with an instance of a Leibnizian “argument from reflection”. This argument, I further show, does not constitute a flawed appeal to mere introspection, but is in fact securely grounded in an important corollary of the Principle of Sufficient Reason: Leibniz’s Principle of Intelligibility
"Not only defended but also applied": The perceived absurdity of Bayesian inference
The missionary zeal of many Bayesians of old has been matched, in the other
direction, by a view among some theoreticians that Bayesian methods are
absurd-not merely misguided but obviously wrong in principle. We consider
several examples, beginning with Feller's classic text on probability theory
and continuing with more recent cases such as the perceived Bayesian nature of
the so-called doomsday argument. We analyze in this note the intellectual
background behind various misconceptions about Bayesian statistics, without
aiming at a complete historical coverage of the reasons for this dismissal.Comment: 10 pages, to appear in The American Statistician (with discussion
Renormalization of the asymptotically expanded Yang-Mills spectral action
We study renormalizability aspects of the spectral action for the Yang-Mills
system on a flat 4-dimensional background manifold, focusing on its asymptotic
expansion. Interpreting the latter as a higher-derivative gauge theory, a
power-counting argument shows that it is superrenormalizable. We determine the
counterterms at one-loop using zeta function regularization in a background
field gauge and establish their gauge invariance. Consequently, the
corresponding field theory can be renormalized by a simple shift of the
spectral function appearing in the spectral action.
This manuscript provides more details than the shorter companion paper, where
we have used a (formal) quantum action principle to arrive at gauge invariance
of the counterterms. Here, we give in addition an explicit expression for the
gauge propagator and compare to recent results in the literature.Comment: 28 pages; revised version. To appear in CMP. arXiv admin note:
substantial text overlap with arXiv:1101.480
On ‘a new cosmological argument’
Richard Gale and Alexander Pruss contend that their ‘new cosmological
argument’ is an improvement over familiar cosmological arguments because it
relies upon a weaker version of the Principle of Sufficient Reason than that used in
those more familiar arguments. However, I note that their ‘weaker’ version of the
Principle of Sufficient Reason entails the ‘stronger’ version of that principle which is
used in more familiar arguments, so that the alleged advantage of their proof turns
out to be illusory. Moreover, I contend that, even if their argument did rely on a
weaker version of the Principle of Sufficient reason, nontheists would still be
perfectly within their rights to refuse to accept the conclusion of the argument.</jats:p
Sagnac delay in the Kerr-dS space-time: Implications for Mach's principle
Relativistic twin paradox can have important implications for Mach's
principle. It has been recently argued that the behavior of the time asynchrony
(different aging of twins) between two flying clocks along closed loops can be
attributed to the existence of an absolute spacetime, which makes Mach's
principle unfeasible. In this paper, we shall revisit, and support, this
argument from a different viewpoint using the Sagnac delay. This is possible
since the above time asynchrony is known to be exactly the same as the Sagnac
delay between two circumnavigating light rays re-uniting at the orbiting
source/receiver. We shall calculate the effect of mass and cosmological
constant on the delay in the general case of Kerr-de Sitter
spacetime. It follows that, in the independent limits , spin
and , while the Kerr-dS metric reduces
to Minkowski metric, the clocks need not tick in consonance since there will
still appear a non-zero observable Sagnac delay. While we do not measure
spacetime itself, we do measure the Sagnac effect, which signifies an absolute
substantive Minkowski spacetime instead of a void. We shall demonstrate a
completely different limiting behavior of Sagnac delay, heretofore unknown,
between the case of non-geodesic and geodesic source/observer motion.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1709.0841
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