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)

Augustine’s discussion of our memoria of the liberal arts in Confessions X poses a series of challenging questions which are best tackled in the broader context of his ideas on teaching, learning, understanding and the acquisition of knowledge. The contents of the liberal arts are stored in our memory (a non-physical and non-spatial receptacle often meta­phorically depicted through spatial imagery) by themselves, and not through images (like the objects of sense-perception) or ‘notions’ (like the affections of the soul). When we (...) learn the disciplinae liberales, actually we do not absorb new information from our teachers, but we are triggered by their words to retrieve from the most remote ‘caves’ of our memory contents already present in a latent form since birth (I address the question of what exactly these con­tents might be). In the Confessions, unlike in earlier writings, Augustine cautiously eschews expressions which might suggest full-blown Platonic recollection of things known in previous lives and subsequently forgotten, and thus presuppose the pre-existence and reincarnation of the soul (not even the claim that cogitare is, literally, ‘re-collecting’ involves recalling forgotten knowledge). I argue that for Augustine divine illumination (as presented, e.g., in the De magistro and the De Trinitate) and recollection are not two rival and incompatible theo­ries, but two different and yet consistent sets of metaphors meant to illustrate the same family of ideas and intuitions (sometimes underdetermined in their details); I also explain why the illumination metaphor ultimately appears more appropriate. (shrink)

Most authors who work with moral status automatically dismiss the possibility that plants are the kinds of entities that have moral status. This dismissal coheres with our intuitions about common-sense morality: if plants do not have moral status then we do not have any direct moral obligations to plant life. An implication of such a view is that any suggestion otherwise commits one to be in favour of an absurd conclusion. However, given the recent literature and empirical evidence on plant (...) minds, there are reasons to accept a different perspective that finds the absurd conclusion plausible. (shrink)

Translation of: Introduction áa la philosophie chrâetienne.

Rescher has presented a proof that a completed science is logically impossible; not every truth can be known. I show that the proof is valid only if it is read de re. One of its premises, however, is an obvious truth only on a de dicto reading; read de re it is false. What the proof shows, therefore, is that science has no limits and any true proposition can be known. We can, however, know it only in the meagre de (...) re, and not in the informationally rich de dicto, sense of 'know'. (shrink)

In the traditional frame of classical electrodynamics, a hydrogen atom would emit electromagnetic waves and thus constantly lose energy, resulting in the fall of the electron on the proton over a finite period of time. The corresponding results were derived under the assumption of the instantaneous interaction between the proton and the electron. In 2004, Raju published a paper where he removed the assumption of the instantaneous interaction and studied the role of a time delay in the classical hydrogen atom. (...) He introduced a model of this effect that can be solved analytically. He calculated the radius rsel of a selected orbit, for which this effect and the radiation reaction force would cancel each other with respect to the tangential acceleration. It turned out that rsel is by an order of magnitude smaller than the Bohr radius. In the present paper we use Raju’s model for the corresponding gravitational situation. In frames of Newton’s gravity, we calculate analytically the radius and the energy Esel of a selected orbit, for which the retardation effect and the radiation reaction force would cancel each other out with respect to the tangential acceleration. Then we compare our outcome with some results of Kaplan’s solution for the two-body gravitational problem based on the Schwarzschild’s field. We show that Esel is very close to the minimum energy of bound states obtained by Kaplan in Einstein’s gravity. We emphasize that the selected orbit from the present paper represents the second only physical situation where the radiation reaction force is zero, but the radiation-caused energy loss is not zero. (shrink)

Epistemological issues associated with Cantorian set theory were at the center of the foundational debates from 1900 onward. Hermann Weyl, as a central actor, saw this as a smoldering crisis that burst into flames after World War I. The historian Herbert Mehrtens argued that this “foundations crisis” was part of a larger conflict that pitted moderns, led by David Hilbert, against various counter-moderns, who opposed the promotion of set theory and trends toward abstract theories. Among counter-moderns, L.E.J. Brouwer went a (...) step further by proposing new foundational principles based on his philosophy of intuitionism. Meanwhile, Felix Hausdorff emerged as a leading proponent of the new modern style. In this essay, I offer a reassessment of the foundations crisis that stresses the marginal importance of the various intellectual issues involved. Instead, I offer an interpretation that focuses on tensions within the German mathematical community that led to a dramatic power struggle for control of the journal Mathematische Annalen. (shrink)

This article focuses on what bodies know yet which cannot be expressed verbally. We started with a problem encountered during conventional interviewing in an ex-mining community in south Wales when some teen girls struggled to speak. This led us to focus on the body, corporeality and movement in improvisational dance workshops. By slowing down and speeding up video footage from the workshops, we notice movement patterns and speculate about how traces of gender body-movement practices developed within mining communities over time (...) become actualised in girls’ habitual movement repertoires. Inspired by the works of Gilles Deleuze, Felix Guattari and Erin Manning, a series of cameos are presented: room dancing; the hold; the wiggle; the leap and the dance of the not-yet. We speculate about relations between the actual movements we could see, the in-act infused with the history of place, and the virtual potential of movement. (shrink)

The article argues that civil disobedience must be perceived as an action with progressive and political significance, thus reflecting, from a Kantian perspective, the recognizable paradox between morality and law, as expressed in Kant’s moral and political writings. Hence, this article firstly analyzes on which grounds Kant claims rebellion to be unjust. Secondly, it examines how and if people, from a Kantian point of view, can defend themselves against an unjust sovereignty. On this basis, it argues that ‘civil disobedience’ can (...) be juxtaposed with the Kantian idea of ‘freedom of the pen,’ thus having the same function as a political corrective. However, two questions are still to be answered, namely if civil disobedience must be punished, and if civil disobedience as a political corrective can be justified? By considering civil disobedience primarily as political agency, both questions are answered in the affirmative. (shrink)

Across a wide range of legal contexts, E. Thomas Sullivan and Richard S. Frase identify three basic ways that government measures and private remedies have been ...

‘Quid vero fit, quod poeta hanc plantam, tanquam munus locustae inprimis gratum, commemoret, nemo dixit; nee ego dicere possum’—so Jacobs in his note on the seventh line of this epigram. Among later commentators, Mackail thinks ‘can hardly mean “leek” here’ and he assumes it to be ‘groundsel’; Dain in the Budé edition is satisfied with the rather prosaic explanation that it is an ‘observation très juste … la cigale ne se nourrit que des sues des plantes’. I hope to show (...) that the diet of leeks and dewdrops from the mouth is promised by the love-sick swain of Meleager's poem for the same specific reason—to refresh the grasshopper's ‘voice’ for a new day's beguilement by song and persuasion to the sleep which will again free him from the cares of love. Although the ancients were aware of the means by which such insects produced their incessant sound, they remained faithful to the poetic tradition, which made them drink dew as a prelude to their singing, first found in Hesiod, Scut. 395, and clearly expressed in a couplet of Antipater of Thessalonica. (shrink)