4,249 research outputs found
What do philosophers do? A few reflections on Timothy Williamson's "The Philosophy of Philosophy"
Con una risposta di Timothy Williamson (pp. 135-37)
The language of thought as a logically perfect language
Between the end of the nineteenth century and the first twenty years of the twentieth century, stimulated by the impetuous development of logical studies and taking inspiration from Leibniz's idea of a characteristica universalis, the three founding fathers of the analytic tradition in philosophy, i.e., Frege, Russell, and Wittgenstein, started to talk of a logically perfect language, as opposed to natural languages, all feeling that the latter were inadequate to their (different) philosophical purposes. In the second half of the twentieth century, however, the very idea of a logically perfect language ceased for various reasons to seem attractive to analytic philosophers. Thus, it might appear that this idea could be classified together with the many other bizarre ideas that from time to time surface in the history of philosophy-an idea that perhaps had a beneficial impact on the development of twentieth century logic, but which can now be put to rest. In this brief note, I contend that this conclusion may be too hasty. Indeed, if a well-known empirical hypothesis advanced in 1975 by Jerry Fodor turns out to be true, then there is a logically perfect language, after all. More precisely, I argue that, if it exists, Fodor's language of thought possesses the main characteristics a logically perfect language is required to have
ABJM -Bremsstrahlung at four loops and beyond
In ABJ(M) theory a generalized cusp can be constructed out of the 1/6 BPS
Wilson line by introducing an angle in the spacial contour and/or an
angle in the internal R-symmetry space. The small angles limits of its
anomalous dimension are controlled by corresponding Bremsstrahlung functions.
In this note we compute the internal space -Bremsstrahlung function to
four loops at weak coupling in the planar limit. Based on this result, we
propose an all order conjecture for the -Bremsstrahlung function.Comment: 40 pages; v2: references added, JHEP published extended versio
ABJM -Bremsstrahlung at four loops and beyond: non-planar corrections
We consider the Bremsstrahlung function associated to a 1/6-BPS Wilson loop
in ABJM theory, with a cusp in the couplings to scalar fields. We non-trivially
extend its recent four-loop computation at weak coupling to include non-planar
corrections. We have recently proposed a conjecture relating this object to
supersymmetric circular Wilson loops with multiple windings, which can be
computed via localization. We find agreement between this proposal and the
perturbative computation of the Bremsstrahlung function, including color
sub-leading corrections. This supports the conjecture and hints at its validity
beyond the planar approximation.Comment: 22 page
On the soft limit of closed string amplitudes with massive states
We extend our analysis of the soft behaviour of string amplitudes with
massive insertions to closed strings at tree level (sphere). Relying on our
previous results for open strings on the disk and on KLT formulae we check
universality of the soft behaviour for gravitons to sub-leading order for
superstring amplitudes and show how this gets modified for bosonic strings. At
sub-sub-leading order we argue in favour of universality for superstrings on
the basis of OPE of the vertex operators and gauge invariance for the soft
graviton. The results are illustrated by explicit examples of 4-point
amplitudes with one massive insertion in any dimension, including D=4, where
use of the helicity spinor formalism drastically simplifies the expressions. As
a by-product of our analysis we confirm that the `single valued projection'
holds for massive amplitudes, too. We briefly comment on the soft behaviour of
the anti-symmetric tensor and on loop corrections.Comment: 18+7 pages; added some important references and corrected some typo
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