This paper presents proof that Buss's S22 can prove the consistency of a fragment of Cook and Urquhart's PV from which induction has been removed but substitution has been retained. This result improves Beckmann's result, which proves the consistency of such a system without substitution in bounded arithmetic S12. Our proof relies on the notion of "computation" of the terms of PV. In our work, we first prove that, in the system under consideration, if an equation is proved and either (...) its left- or right-hand side is computed, then there is a corresponding computation for its right- or left-hand side, respectively. By carefully computing the bound of the size of the computation, the proof of this theorem inside a bounded arithmetic is obtained, from which the consistency of the system is readily proven. This result apparently implies the separation of bounded arithmetic because Buss and Ignjatović stated that it is not possible to prove the consistency of a fragment of PV without induction but with substitution in Buss's S12. However, their proof actually shows that it is not possible to prove the consistency of the system, which is obtained by the addition of propositional logic and other axioms to a system such as ours. On the other hand, the system that we have considered is strictly equational, which is a property on which our proof relies. (shrink)

We extend Barbanera and Berardi's symmetric lambda calculus [2] to second-order classical propositional logic and prove its strong normalization.

ναξ and βασιλες are the two most important titles applied to the top stratum of Homeric aristocracy., usually translated as ′lord′ or ′master′, and βασιλες, usually translated as ′king′, often apply to the same individuals, and can at times appear to be very close in meaning, allowing translators to render ναξ as ′king′ and βασιλες as ′lord′. There are, however, significant differences between the two. As Lexikon des friihgriechischen Epos now conveniently summarizes for us, avat; can be divine or human, (...) can be a master of a state, of gods, of men, of animals, or of his household, and can be used as an address in the vocative, whereas fiaoiXevs is only applied to humans in Homer, often in a political context, and is never used in the vocative. (shrink)

Phoenix's speech in Book 9 of the Iliad is generally considered prophetic of what happens to Achilles later in the story. Many scholars have argued that Achilles is punished by Zeus through τη which causes the death of Patroclus, just as anyone who spurns the Litai in the allegory of Phoenix will be punished by Ate sent by Zeus. The Meleager episode is also regarded as reflecting almost exactly what happens later: the Achaeans have difficulty in the battle due to (...) Achilles' withdrawal, just as the Aetolians have when Meleager refuses to fight. Achilles, like Meleager, receives a set of three supplications to go back to the battle, and, just as Meleager loses his prize because he rejects the supplications, Achilles loses Patroclus because he does not listen to the pleas of the Embassy. This seems to be, in outline, the present orthodoxy. (shrink)

The discipline of nursing has long maintained that is has a unique contribution to make within the health care arena. This assertion of uniqueness lies in great part in the discipline's claim to a distinct body of knowledge. Nursing knowledge is characterized by diverse and multiple forms of knowing and underpins the work of all nurses, regardless of field of practice. Unfortunately, it has been challenging for the discipline to take full ownership of its epistemological diversity, largely due to factors (...) such as competing worldviews, and ideological and binary positioning. A philosophical middle ground stance is proposed as a way for the discipline to contemplate, discuss and develop nursing knowledge; a middle space that provides the freedom to consider competing worldviews while still allowing for the discipline to fully express itself in all of its epistemological diversity. In being able to enact its multiple forms of knowledge in a creative and open space that is open to different ideas and worldviews, not only can nursing take full ownership of its practice and its unique knowledge, it can also demonstrate how best to navigate an increasingly polarized world. In a world that is increasingly fixated on binary solutions and dualistic points of view, it is time for nursing to celebrate its epistemological diversity. (shrink)

A multimodal person representation contains information about what a person looks like and what a person sounds like. However, little is known about how children form these face-voice mappings. Here, we explored the possibility that two cognitive tools that guide word learning, a one-to-one mapping bias and fast mapping, also guide children’s learning about faces and voices. We taught 4- and 5-year-olds mappings between three individual faces and voices, then presented them with new faces and voices. In Experiment 1, we (...) found that children rapidly learned face-voice mappings from just a few exposures, and furthermore spontaneously mapped novel faces to novel voices using a one-to-one mapping bias (that each face can produce only one voice). In Experiment 2, we found that children’s face-voice representations are abstract, generalizing to novel tokens of a person. In Experiment 3, we found that children retained in memory the face-voice mappings that they had generated via inference (i.e., they showed evidence of fast mapping), and used these newly formed representations to generate further mappings between new faces and voices. These findings suggest that preschoolers’ rapid learning about faces and voices may be aided by biases that are similar to those that support word learning. (shrink)

七代目子孫が初めて語る...江戸時代、600以上の荒廃した農村を復興させた金次郎のとっておきの教え。運命を高める55の金言。.

This paper discusses verse 1074 of the Suttanipāta’s Upasīvamāṇavapucchā. While various interpretations of the verse are possible due to a lack of textual sources to draw from for interpretation, I attempt to understand this verse—which describes the state of nibbāna using the metaphor of an extinguished fire—through a philological examination of the text itself and other contemporary ones. Specifically, I focus on whether the verse implies that nibbāna takes place in the present life or at and after the end of (...) life by examining the compound nāmakāya and the phrase atthaṃ paleti that appear in it. Arguing that the former term is a dvandva meaning “name-and-body” and that the latter means “goes down”, I conclude that in this verse the Buddha is discussing nibbāna at and after the end of life. However, I do not deny that different interpretations are possible. When dealing with an ancient verse, the interpretation of one word can affect one’s understanding of the verse itself or the sutta overall, possibly leading to perspectives on early Buddhist thought completely different from the original meaning or original intention of the author of the sutta. Taking this into consideration, this paper adopts a meticulous approach to philologically examining early Pāli texts. (shrink)

A rare academic study on what John Rawls, Peter Singer, and Derek Parfit acknowledge as the finest book in ethics -- The Methods of Ethics. With a rather shocking conclusion that "none of us can match Sidgwick," Mariko Nakano-Okuno lucidly analyzes Henry Sidgwick's impacts on contemporary ethics.

The Bulletin of Symbolic Logic, Volume 20, Issue 3, Page 411-416, SEPTEMBER 2014.