Language as a Geometry in Wittgenstein"s Tractatus

In TLP 4.011, while admitting that propositions expressed by the phonetic notation, or the alphabet, just like the written notes of a piece of music, do not seem at first sight to be pictures of what they represent, the Tractatus insists that those "sign-languages" (that is, the phonetic notation and the written musical notes) prove to be pictures of what they represent (that is, our speech and the piece of music, respectively) "even in the ordinary sense". (TLP 4.016 also says that "alphabetic script developed out of [hieroglyphic script] without losing what was essential to depiction".) So, contrary to the view of some commentators (e.g. Pears 1987, 115-121), instead of making an analogy here, the Tractatus holds that a proposition is a picture literally. How can a proposition be a picture literally

DISCUSSION: AGRICULTURAL TRANSITION AND IMPLICATIONS FOR AGRICULTURAL ECONOMICS EXTENSION PROGRAMS

Teaching/Communication/Extension/Profession,

Measuring stochastic gravitational-wave energy beyond general relativity

Gravity theories beyond general relativity (GR) can change the properties of gravitational waves: their polarizations, dispersion, speed, and, importantly, energy content are all heavily theory- dependent. All these corrections can potentially be probed by measuring the stochastic gravitational- wave background. However, most existing treatments of this background beyond GR overlook modifications to the energy carried by gravitational waves, or rely on GR assumptions that are invalid in other theories. This may lead to mistranslation between the observable cross-correlation of detector outputs and gravitational-wave energy density, and thus to errors when deriving observational constraints on theories. In this article, we lay out a generic formalism for stochastic gravitational- wave searches, applicable to a large family of theories beyond GR. We explicitly state the (often tacit) assumptions that go into these searches, evaluating their generic applicability, or lack thereof. Examples of problematic assumptions are: statistical independence of linear polarization amplitudes; which polarizations satisfy equipartition; and which polarizations have well-defined phase velocities. We also show how to correctly infer the value of the stochastic energy density in the context of any given theory. We demonstrate with specific theories in which some of the traditional assumptions break down: Chern-Simons gravity, scalar-tensor theory, and Fierz-Pauli massive gravity. In each theory, we show how to properly include the beyond-GR corrections, and how to interpret observational results.Comment: 18 pages (plus appendices), 1 figur

REPLY TO HEP-PH/0211241 "On the extra factor of two in the phase of neutrino oscillations"

Arguments continue to appear in the literature concerning the validity of the standard oscillation formula. We point out some misunderstandings and try to explain in simple terms our viewpoint.Comment: 4 pages [1 colored LaTex-fig], AMS-Te