The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the problem solver, unitarily computes the corresponding solution and reads it by the final measurement. This simple extension creates a new perspective from which to see the quantum algorithm. First, it highlights the relevance of time-symmetric quantum mechanics to quantum computation: the problem-setting and (...) problem solution, in their quantum version, constitute pre- and post-selection, hence the process as a whole is bound to be affected by both boundary conditions. Second, it forces us to enter into relational quantum mechanics. There must be a representation of the quantum algorithm with respect to Bob, and another one with respect to Alice, from whom the outcome of the initial measurement, specifying the setting and thus the solution of the problem, must be concealed. Time-symmetrizing the quantum algorithm to take into account both boundary conditions leaves the representation to Bob unaltered. It shows that the representation to Alice is a sum over histories in each of which she remains shielded from the information coming to her from the initial measurement, not from that coming to her backwards in time from the final measurement. In retrospect, all is as if she knew in advance, before performing her problem-solving action, half of the information that specifies the solution of the problem she will read in the future and could use this information to reach the solution with fewer computation steps. This elucidates the quantum computational speedup in all the quantum algorithms examined. (shrink)
This article aims at reconstructing the logic and assessing the force of Socrates' argument against Protagoras' 'Measure Doctrine' at Theaetetus 171a–c. I examine and criticise some influential interpretations of the passage, according to which, e.g., Socrates is guilty of ignoratio elenchi by dropping the essential Protagorean qualifiers or successfully proves that md is self-refuting provided the missing qualifiers are restored by the attentive reader. Having clarified the meaning of MD, I analyse in detail the broader section 170a–171d and argue, against (...) an extensive scholarly consensus, that it contains two slightly different formulations of the same argument, and not two distinct arguments, that Socrates does not highlight his own strategy at 171a–c as especially clever, and that his argument successfully shows that md turns out to be untenable for Protagoras himself when submitted to scrutiny in dialectical contexts, without aiming at proving its absolute falsehood. Finally, I clarify the philosophical import of the final image of Protagoras' momentary return from the underworld. (shrink)
René Girard, Theology, and Pop Culture provides a fresh and engaging introduction to and the application of René Girard's mimetic theory. From movies to social media, television to graphic novels, the contributors explore popular culture's theological depths and challenge readers to consider what culture reveals about them.
Editor James Fetzer presents an analytical and historical introduction and a comprehensive bibliography together with selections of many of Carl G. Hempel's most important studies to give students and scholars an ideal opportunity to appreciate the enduring contributions of one of the most influential philosophers of science of the 20th century.