It is shown that the feasibly constructive arithmetic theory IPV does not prove LMIN, unless the polynomial hierarchy CPV-provably collapses. It is proved that PV plus LMIN intuitionistically proves PIND. It is observed that PV + PIND does not intuitionistically prove NPB, a scheme which states that the extended Frege systems are not polynomially bounded.

Loop quantum gravity predicts that spatial geometry is fundamentally discrete. Whether this discreteness entails a departure from exact Lorentz symmetry is a matter of dispute that has generated an interesting methodological dilemma. On one hand one would like the theory to agree with current experiments, but, so far, tests in the highest energies we can manage show no such sign of departure. On the other hand one would like the theory to yield testable predictions, and deformations of exact Lorentz symmetry (...) in certain yet– to–be–tested regimes may have phenomenological consequences. Exposing their shortcomings, here I discuss two arguments that exemplify this dilemma, and compare them to other cases from the history of physics that share their symptoms. (shrink)

We present an exact solution of the one-dimensional modified Klein Gordon and Duffin Kemmer Petiau equations with a step potential in the presence of minimal length in the uncertainty relation, where the expressions of the new transmission and reflection coefficients are determined for all cases. As an application, the Klein paradox in the presence of minimal length is discussed for all equations.

A well‐established principle of language is that there is a preference for closely related words to be close together in the sentence. This can be expressed as a preference for dependency length minimization (DLM). In this study, we explore quantitatively the degree to which natural languages reflect DLM. We extract the dependencies from natural language text and reorder the words in such a way as to minimize dependency length. Comparing the original text with these optimal linearizations (and (...) also with random linearizations) reveals the degree to which natural language minimizes dependency length. Tests on English data show that English shows a strong effect of DLM, with dependency length much closer to optimal than to random; the optimal English grammar also has many specific features in common with English. In German, too, dependency length is significantly less than random, but the effect is much weaker than in English. We conclude by speculating about some possible reasons for this difference between English and German. (shrink)

For X a separable metric space and $\alpha$ an infinite ordinal, consider the following three games of length $\alpha$ : In $G^{\alpha}_1$ ONE chooses in inning $\gamma$ an $\omega$ –cover $O_{\gamma}$ of X; TWO responds with a $T_{\gamma}\in O_{\gamma}$ . TWO wins if $\{T_{\gamma}:\gamma<\alpha\}$ is an $\omega$ –cover of X; ONE wins otherwise. In $G^{\alpha}_2$ ONE chooses in inning $\gamma$ a subset $O_{\gamma}$ of ${\sf C}_p(X)$ which has the zero function $\underline{0}$ in its closure, and TWO responds with a (...) function $T_{\gamma}\in O_{\gamma}$ . TWO wins if $\underline{0}$ is in the closure of $\{T_{\gamma}:\gamma<\alpha\}$ ; otherwise, ONE wins. In $G^{\alpha}_3$ ONE chooses in inning $\gamma$ a dense subset $O_{\gamma}$ of ${\sf C}_p(X)$ , and TWO responds with a $T_{\gamma}\in O_{\gamma}$ . TWO wins if $\{T_{\gamma}:\gamma<\alpha\}$ is dense in ${\sf C}_p(X)$ ; otherwise, ONE wins. After a brief survey we prove: 1. If $\alpha$ is minimal such that TWO has a winning strategy in $G^{\alpha}_1$ , then $\alpha$ is additively indecomposable (Theorem 4) 2. For $\alpha$ countable and minimal such that TWO has a winning strategy in $G^{\alpha}_1$ on X, the following statements are equivalent (Theorem 9): a) TWO has a winning strategy in $G^{\alpha}_2$ on ${\sf C}_p(X)$ . b) TWO has a winning strategy in $G^{\alpha}_3$ on ${\sf C}_p(X)$ . 3. The Continuum Hypothesis implies that there is an uncountable set X of real numbers such that TWO has a winning strategy in $G^{\omega^2}_1$ on X (Theorem 10). (shrink)

We prove determinacy for open length ω1 games. Going further we introduce, and prove determinacy for, a stronger class of games of length ω1, with payoff conditions involving the entire run, the club filter on ω1, and a sequence of ω1 disjoint stationary subsets of ω1. The determinacy proofs use an iterable model with a class of indiscernible Woodin cardinals, and we show that the games precisely capture the theory of the minimal model for this assumption.

We study normal ideals on Pκ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P_{\kappa} }$$\end{document} that are defined in terms of games of uncountable length.

Let μ,κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu, \kappa}$$\end{document} and λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\lambda}$$\end{document} be three uncountable cardinals such that μ=cf<κ=cf<λ.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu = {\rm cf} < \kappa = {\rm cf} < \lambda.}$$\end{document} The game ideal NGκ,λμ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${NG_{\kappa,\lambda}^\mu}$$\end{document} is a normal ideal on Pκ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P_\kappa }$$\end{document} defined using games (...) of length μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu}$$\end{document}. We show that if 2≤λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${2^{} \leq \lambda}$$\end{document} and there are no large cardinals in an inner model, then the diamond principle ♢κ,λ[NGκ,λμ]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamondsuit_{\kappa,\lambda} [{NG}_{\kappa,\lambda}^\mu]}$$\end{document} holds. We also show that if ♢κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamondsuit_\kappa }$$\end{document} holds, where S is a stationary subset of κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa}$$\end{document}, then ♢κ,λ:a∩κ∈S})\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamondsuit_{\kappa,\lambda} : a \cap \kappa \in S\})}$$\end{document} holds. (shrink)

This research was partially supported by Grant-in-Aid for Scientific Research (No. 06640178 and No. 06640336), Ministry of Education, Science and Culture of Japan Mathematics Subject Classification: 03E05 --> Abstract. Following Carr's study on diagonal operations and normal filters on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\cal P}_{\kappa}\lambda$\end{document} in [2], several weakenings of normality have been investigated. One of them is to consider normal filters without \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\kappa$\end{document}-completeness, for (...) example, see DiPrisco-Uzcategui [3]. The other is weakening normality itself while keeping \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\kappa$\end{document}-completeness such as in Mignone [10] and Shioya [11]. We take the second one so that all filters are assumed to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\kappa$\end{document}-complete. In Sect. 1 a hierarchy of filters on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\cal P}_{\kappa}\lambda$\end{document} is presented which corresponds to the length of diagonal intersections under which the filters are closed. It turns out that many ranks exist between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $FSF_{\kappa\lambda}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $CF_{\kappa\lambda}$\end{document}. We consider seminormal ideals in Sect. 2 and determine the minimal seminormal ideal extending Johnson's result in [6]. Its precise descripti on changes according to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $cf(\lambda )$\end{document} although we can write it in a single form as well. We also prove that a nonnormal seminormal ideal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $I\supset NS_{\kappa\lambda}$\end{document} exists if and only if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\lambda$\end{document} is regular. (shrink)

Most interpreting theories claim that different interpreting types should involve varied processing mechanisms and procedures. However, few studies have examined their underlying differences. Even though some previous results based on quantitative approaches show that different interpreting types yield outputs of varying lexical and syntactic features, the grammatical parsing approach is limited. Language sequences that form without relying on parsing or processing with a specific linguistic approach or grammar excel other quantitative approaches at revealing the sequential behavior of language production. As (...) a non-grammatically-bound unit of language sequences, frequency motif can visualize the local distribution of content and function words, and can also statistically classify languages and identify text types. Thus, the current research investigates the distribution, length and position-dependent properties of frequency motifs across different interpreting outputs in pursuit of the sequential generation behaviors. It is found that the distribution, the length and certain position-dependent properties of the specific language sequences differ significantly across simultaneous interpreting and consecutive interpreting output. The features of frequency motifs manifest that both interpreting output is produced in the manner that abides by the least effort principle. The current research suggests that interpreting types can be differentiated through this type of language sequential unit and offers evidence for how the different task features mediate the sequential organization of interpreting output under different demand to achieve cognitive load minimization. (shrink)

We prove that if an ultrafilter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}}$$\end{document} is not coherent to a Q-point, then each analytic non-σ-bounded topological group G admits an increasing chain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle G_\alpha:\alpha < \mathfrak b(\mathcal L)\rangle}$$\end{document} of its proper subgroups such that: (i) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bigcup_{\alpha}G_\alpha=G}$$\end{document}; and (ii) For every σ-bounded subgroup H of G there exists α such that \documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H\subset G_\alpha}$$\end{document}. In case of the group Sym(ω) of all permutations of ω with the topology inherited from ωω this improves upon earlier results of S. Thomas. (shrink)

Theoretical minimal RNA rings are candidate primordial genes evolved for non‐redundant coding of the genetic code's 22 coding signals (one codon per biogenic amino acid, a start and a stop codon) over the shortest possible length: 29520 22‐nucleotide‐long RNA rings solve this min‐max constraint. Numerous RNA ring properties are reminiscent of natural genes. Here we present analyses showing that all RNA rings lack dinucleotide CG (a mutable, chemically instable dinucleotide coding for Arginine), bearing a resemblance to known CG‐depleted genomes. (...) CG in “incomplete” RNA rings (not coding for all coding signals, with only 3–12 nucleotides) gradually decreases towards CG absence in complete, 22‐nucleotide‐long RNA rings. Presumably, feedback loops during RNA ring growth during evolution (when amino acid assignment fixed the genetic code) assigned Arg to codons lacking CG (AGR) to avoid CG. Hence, as a chemical property of base pairs, CG mutability restructured the genetic code, thereby establishing itself as genetically encoded biological information. (shrink)

We show that the length of a hierarchy of domains with totality, based on the standard domain for the natural numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\Bbb N}$\end{document} and closed under dependent products of continuously parameterised families of domains will be the first ordinal not recursive in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $^3E$\end{document} and any real. As a part of the proof we show that the domains of the hierarchy (...) share important properties with the types of continuous functionals. The main result can also be viewed as a representation theorem for recursion in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $^3E$\end{document}. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Consenting for Novel and Dangerous Surgical Procedures with Minimal Supporting EvidenceMichelle J. ClarkeFrank1 was a 19–year–old man referred to me after a workup for back pain led to the discovery of a large, aggressive tumor in his sacrum. The tumor wrapped around the nerves controlling bowel, bladder, and leg function. We performed a needle biopsy and learned that the tumor was an angiosarcoma, an extremely aggressive and usually deadly (...) form of cancer. However, the tumor was unique in that it theoretically could be cured if removed in one piece. But, to do so would necessitate sacrificing the nerves, leaving the patient irreversibly incontinent, lacking sexual function, and confined to a wheelchair.Once we knew the diagnosis, Frank came to the office with his family to discuss treatment options. He appeared terrified and was almost silent through the appointment, deferring most questions to his parents. Due to the speed of tumor growth, we discussed palliative therapy, conventional treatment, and the one–piece or “en bloc” surgery, which was new and unproven for his disease. Based on the remarkable tumor growth we noted during the work–up, with palliative treatment the patient would likely survive for less than six months. Conventional treatment, in which surgery is done to remove part of the tumor while sparing the nerves to bowel and bladder function, was known to have a high rate of recurrence and death. Further, this tumor didn’t respond well to radiation and chemotherapy, so chance of survival was limited, although his life might have been extended for a short period. Thus our conversation turned to the novel “en bloc” procedure.The en bloc procedure offered a hope of long–term survival unlike the other options. However, this came with an enormous cost. The surgery itself would be planned to occur over three days with five separate surgical teams and a very real chance of major complications or death. Nerves to bowel and bladder would be cut, irreversibly leaving the patient without sexual function, and completely incontinent with a urinary catheter and colostomy. Walking was expected to be disrupted or potentially impossible due to the nerve resection. We went to great lengths over the course of many visits to describe the impact of the surgery on the patient’s function, and the impact on his quality of life. To make matters more challenging, as this procedure was so new and the tumor so rare, research did not yet exist to quantify his likelihood of long–term survival.Personally I was very uncomfortable with the situation. From a medical standpoint, the surgery offered was the best distillation of research and professional experience. En bloc surgery offered the best—if not the only—chance for survival in [End Page 5] this young man. Additionally, having treated many spine–injured patients I was aware that many patients with similar deficits led happy and productive lives following an emotional and physical adjustment period. However the surgery was also extreme. I worried that we would not be able to accomplish the goal of a one–piece resection and would accidentally spill some of the tumor, creating all of the deficits but no survival benefit. Frankly, I thought there was a 25% chance that would happen, which was explained to the family preoperatively. Were we overreaching our abilities and making a dying patient’s life worse by proceeding?Second, I was uneasy about the social situation. The patient’s family was very supportive, traveling with him to all appointments and assisting with his care. The patient himself usually deferred all scheduling to his mother, which wasn’t entirely unusual for such a young man. However it was difficult to grasp how much the patient understood of his disease or supported the plan. We attempted to delve more deeply into his thoughts, including without his parents present, but got only short answers, which revealed little. While the family appeared to have accepted the diagnosis and wanted to get to the business of treatment, the patient seemed to me to still carry the shock of his recent cancer diagnosis. Pushed by the rapid tumor growth, we were limited in how long we could wait for... (shrink)

Ormerod and Chronicle reported that optimal solutions to traveling salesperson problems were judged to be aesthetically more pleasing than poorer solutions and that solutions with more convex hull nodes were rated as better figures. To test these conclusions, solution regularity and the number of potential intersections were held constant, whereas solution optimality, the number of internal nodes, and the number of nearest neighbors in each solution were varied factorially. The results did not support the view that the convex hull is (...) an important determinant of figural attractiveness. Also, in contrast to the findings of Ormerod and Chronicle, there were consistent individual differences. Participants appeared to be divided as to whether the most attractive figure enclosed a given area within a perimeter of minimum or maximum length. It is concluded that future research in this area cannot afford to focus exclusively on group performance measures. (shrink)

We estimate the derivation lengths of functionals in Gödel's system \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $T$\end{document} of primitive recursive functionals of finite type by a purely recursion-theoretic analysis of Schütte's 1977 exposition of Howard's weak normalization proof for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $T$\end{document}. By using collapsing techniques from Pohlers' local predicativity approach to proof theory and based on the Buchholz-Cichon and Weiermann 1994 approach to subrecursive hierarchies we define a (...) collapsing f unction\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\cal D}:T\to \omega$\end{document} so that for (closed) terms \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $a,b$\end{document} of Gödel's \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $T$\end{document} we have: If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $a$\end{document} reduces to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $b$\end{document} then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\omega>{\cal D}(a)>{\cal D}(b).$\end{document} By one uniform proof we obtain as corollaries: A derivation lengths classification for functionals in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $T$\end{document}, hence new proof of strongly uniform termination of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $T$\end{document}. A new proof of the Kreisel's classific ation of the number-theoretic functions which can be defined in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $T$\end{document}, hence a classification of the provably total functions of Peano Arithmetic. A new proof of Tait's results on weak normalization for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $T$\end{document}. A new proof of Troelstra's result on strong normalization for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $T$\end{document}. Additionally, a slow growing analysis of Gödel's \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $T$\end{document} is obtained via Girard's hierarchy comparison theorem. This analyis yields a contribution to two open pro blems posed by Girard in part two of his book on proof theory. For the sake of completeness we also mention the Howard Schütte bound on derivation lengths for the simple typed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\lambda$\end{document}-calculus. (shrink)

We show that arbitrary tautologies of Johansson’s minimal propositional logic are provable by “small” polynomial-size dag-like natural deductions in Prawitz’s system for minimal propositional logic. These “small” deductions arise from standard “large” tree-like inputs by horizontal dag-like compression that is obtained by merging distinct nodes labeled with identical formulas occurring in horizontal sections of deductions involved. The underlying geometric idea: if the height, h(∂), and the total number of distinct formulas, ϕ(∂), of a given tree-like deduction ∂ of a minimal (...) tautology ρ are both polynomial in the length of ρ, |ρ|, then the size of the horizontal dag-like compression ∂ᶜ is at most h(∂)×ϕ(∂), and hence polynomial in |ρ|. That minimal tautologies ρ are provable by tree-like natural deductions ∂ with |ρ|-polynomial h(∂) and ϕ(∂) follows via embedding from Hudelmaier’s result that there are analogous sequent calculus deductions of sequent ⇒ρ. The notion of dag-like provability involved is more sophisticated than Prawitz’s tree-like one and its complexity is not clear yet. Our approach nevertheless provides a convergent sequence of NP lower approximations of PSPACE-complete validity of minimal logic. (shrink)

Sequential decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameter-free theory of universal Artificial Intelligence. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline how the AIXI model can formally solve a number of problem classes, (...) including sequence prediction, strategic games, function minimization, reinforcement and supervised learning. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXItl that is still effectively more intelligent than any other time t and length l bounded agent. The computation time of AIXItl is of the order t x 2^l. The discussion includes formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other AI approaches. (shrink)

What if someone asked you to keep a four-kilometer-long ruler absolutely still so that you could measure deformations of length of ~1x10^-18m using light? On September 14, 2015, physicists and engineers at the Laser Interferometer Gravitational-Wave Observatory (LIGO) accomplished this absurd feat when they first detected gravitational wave signals—the result of the most violent events in our universe, such as the collision of two black holes—using two immense L-shaped instruments with arms four-kilometers in length and placed in what (...) seemed to be the middle of nowhere. -/- The focus of this dissertation centers on how scientists must have an intricate understanding of the environment surrounding LIGO’s instruments to understand the vast and active universe through the detection of gravitational waves. I explore how LIGO physicists and engineers constructed stillness to distinguish the surrounding natural and built environment from gravitational wave signals. I explore how the pre-LIGO and LIGO laboratory spaces became an expanded laboratory extending as an overlay into the surrounding environment and beyond. I show that the metes and bounds of the expanded laboratory are defined by what the interferometers are sensitive to. I further explore how physicists, engineers, and data scientists theorized an experiment that required such an extreme sensitivity (i.e., imagining stillness), developed methods to investigate, understand, and abate noise, disturbances, and aberrations (i.e., engineering stillness), found sites with minimal noise profiles, both physical and social, that would accommodate the size and function of the instruments despite land uses in conflict with the experiment (i.e., finding stillness), and understood the overlapping human and non-human uses of the land that jeopardized the ability to make these highly precise detections and mediate solutions that would allow for concurrent use of the land (i.e., negotiating stillness). -/- Through this history, I conclude that the level of sensitivity the physicists and engineers can attain in the LIGO interferometers is predicated on constructed stillness. This determines the instruments’ ability to measure the minute deformations in length caused by gravitational waves such that the physicists, engineers, and data scientists can rule out the geography of noise and make the claim that the heterogeneity of their locations at Hanford and Livingston does not negate their assertion of twin detections of gravitational wave signals across their two sites. (shrink)

Let Mn♯ denote the minimal active iterable extender model which has n Woodin cardinals and contains all reals, if it exists, in which case we denote by Mn the class-sized model obtained by iterating the topmost measure of Mn class-many times. We characterize the sets of reals which are Σ1-definable from R over Mn, under the assumption that projective games on reals are determined:1. for even n, Σ1Mn=⅁RΠn+11;2. for odd n, Σ1Mn=⅁RΣn+11.This generalizes a theorem of Martin and Steel for L, (...) that is, the case n=0. As consequences of the proof, we see that determinacy of all projective games with moves in R is equivalent to the statement that Mn♯ exists for all n∈N, and that determinacy of all projective games of length ω2 with moves in N is equivalent to the statement that Mn♯ exists and satisfies AD for all n∈N. (shrink)

There are various ways of attempting to defend an extreme liberal view on abortion, according to which a woman always has the right to control what happens inside her own body. First of all, there is the popular view that appeals to the idea that there is a fundamental, underived right that women have to control what occurs within their own bodies. Secondly, there is a related type of philosophical argument advanced by Judith Jarvis Thomson in her famous and oft-reprinted (...) article “A Defense of Abortion” for the slightly weaker claim that while abortion is not always permissible, since, as she says near the end of her essay, it is impermissible in, and only in, the following circumstances: “There may well be cases where carrying the child to term requires only Minimally Decent Samaritanism of the mother, and this is a standard w must not fall below.” Subsequently, Thomson’s type of argument was then developed and defended at much greater length by David Boonin in his very carefully argued book A Defense of Abortion, though Boonin does not discuss the case of the Minimally Decent Samaritan. I believe that there is a strong objection to the Thomson/Boonin approach to justifying abortion. It was set out in an article by Richard Langer, namely, in ‘Silverstein and the “Responsibility Objection”’, Social Theory and Practice 19/3. 345-58. Langer’s discussion is not, in general, very strong, but in a very important paragraph, on pages 351-2, Langer argues that if the responsibility objection to Thomson is unsound, then it follows that there will also be circumstances in which allowing one’s children to die, simply because one no longer wishes to care for them, will also be morally permissible. David Boonin replies to Langer’s objection in his A Defense of Abortion, but in discussing, on pages 182-3, Langer’s point about a parent’s responsibility to his or her children, Boonin relies upon a tacit consent argument that appears open to decisive objections. It seems to me, then, that the only possibility for a successful defense of an extreme liberal view concerning the justification of abortion will have to involve setting out a plausible account of what it is that gives something a right to life, and I think that the right answer is that neo-Lockean persons, and only neo-Lockean persons, have a right to continued existence. This leaves one with the scientific question of when developing humans become neo-Lockean persons. The answer to that question is perhaps still not firmly settled, although the extensive research that I carried out back in the 1970s seemed to me to support the conclusion that it is not until sometime that humans acquire the capacity for thought, a capacity that is necessary if a developing human is to be a neo-Lockean person. The upshot is that if one defends an extreme liberal view on abortion in the only way that seems to be satisfactory – that is, by setting out an account of what it is that gives something a right to life, and arguing that humans before birth do not have the relevant property, one must also address the question of infanticide, and that to fail to do so is intellectually unacceptable. (shrink)

There is a relatively recent trend in treating negation as a modal operator. One such reason is that doing so provides a uniform semantics for the negations of a wide variety of logics and arguably speaks to a longstanding challenge of Quine put to non-classical logics. One might be tempted to draw the conclusion that negation is a modal operator, a claim Francesco Berto, 761–793, 2015) defends at length in a recent paper. According to one such modal account, the (...) negation of a sentence is true at a world x just in case all the worlds at which the sentence is true are incompatible with x. Incompatibility is taken to be the key notion in the account, and what minimal properties a negation has comes down to which minimal conditions incompatibility satisfies. Our aims in this paper are twofold. First, we wish to point out problems for the modal account that make us question its tenability on a fundamental level. Second, in its place we propose an alternative, non-modal, account of negation as a contradictory-forming operator that we argue is superior to, and more natural than, the modal account. (shrink)

In this article we present a new experimental paradigm: comparative visual search. Each half of a display contains simple geometrical objects of three different colors and forms. The two display halves are identical except for one object mismatched in either color or form. The subject's task is to find this mismatch. We illustrate the potential of this paradigm for investigating the underlying complex processes of perception and cognition by means of an eye‐tracking study. Three possible search strategies are outlined, discussed, (...) and reexamined on the basis of experimental results. Each strategy is characterized by the way it partitions the field of objects into “chunks.” These strategies are: (i) Stimulus‐wise scanning with minimization of total scan path length (a “traveling salesman” strategy), (ii) scanning of the objects in fixed‐size areas (a “searchlight” strategy), and (iii) scanning of object sets based on variably sized clusters defined by object density and heterogeneity (a “clustering” strategy). To elucidate the processes underlying comparative visual search, we introduce besides object density a new entropy‐based measure for object heterogeneity. The effects of local density and entropy on several basic and derived eye‐movement variables clearly rule out the traveling salesman strategy, but are most compatible with the clustering strategy. (shrink)

I analyze the hierarchy of large cardinals between a supercompact cardinal and an almost-huge cardinal. Many of these cardinals are defined by modifying the definition of a high-jump cardinal. A high-jump cardinal is defined as the critical point of an elementary embedding j:V→M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${j: V \to M}$$\end{document} such that M is closed under sequences of length sup{j|f:κ→κ}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sup\{{j\,|\,f: \kappa \to \kappa}\}}$$\end{document}. Some of the (...) other cardinals analyzed include the super-high-jump cardinals, almost-high-jump cardinals, Shelah-for-supercompactness cardinals, Woodin-for-supercompactness cardinals, Vopěnka cardinals, hypercompact cardinals, and enhanced supercompact cardinals. I organize these cardinals in terms of consistency strength and implicational strength. I also analyze the superstrong cardinals, which are weaker than supercompact cardinals but are related to high-jump cardinals. Among the results, I highlight the following. Vopěnka cardinals are the same as Woodin-for-supercompactness cardinals.There are no excessively hypercompact cardinals.Furthermore, I prove some results relating high-jump cardinals to forcing, as well as analyzing Laver functions for super-high-jump cardinals. (shrink)

We investigate the timing of pre-answer inbreaths in order to shed light on the time course of response planning and execution in conversational turn-taking. Using acoustic and inductive plethysmography recordings of seven dyadic conversations in Dutch, we show that pre-answer inbreaths in conversation typically begin briefly after the end of questions. We also show that the presence of a pre-answer inbreath usually co-occurs with substantially delayed answers, with a modal latency of 576 vs. 100 ms for answers not preceded by (...) an inbreath. Based on previously reported minimal latencies for internal intercostal activation and the production of speech sounds, we propose that vocal responses, either in the form of a pre-utterance inbreath or of speech proper when an inbreath is not produced, are typically launched in reaction to information present in the last portion of the interlocutor's turn. We also show that short responses are usually made on residual breath, while longer responses are more often preceded by an inbreath. This relation of inbreaths to answer length suggests that by the time an inbreath is launched, typically during the last few hundred milliseconds of the question, the length of the answer is often prepared to some extent. Together, our findings are consistent with a two-stage model of response planning in conversational turn-taking: early planning of content often carried out in overlap with the incoming turn, and late launching of articulation based on the identification of turn-final cues. (shrink)

The capacity to self-generate mental content that is unrelated to the current environment is a fundamental characteristic of the mind, and the current experiment explored how this experience is related to the decisions that people make in daily life. We examined how task-unrelated thought varies with the length of time participants are willing to wait for an economic reward, as measured using an inter-temporal discounting task. When participants performed a task requiring minimal attention, the greater the amount of time (...) spent engaged in TUT the longer the individual was prepared to wait for an economic reward. These data indicate that self-generated thought engages processes associated with the successful management of long-term goals. Although immersion in the here and now is undeniably advantageous, under appropriate conditions the capacity to let go of the present and consider more pertinent personal goals may have its own rewards. (shrink)

Principles are central to physical reasoning, particularly in the search for a theory of quantum gravity, where novel empirical data are lacking. One principle widely adopted in the search for QG is ultraviolet completion: the idea that a theory should hold up to all possible high energies. We argue— contra standard scientific practice—that UV-completion is poorly motivated as a guiding principle in theory-construction, and cannot be used as a criterion of theory-justification in the search for QG. For this, we explore (...) the reasons for expecting, or desiring, a UV-complete theory, as well as analyse how UV-completion is used, and how it should be used, in various specific approaches to QG. 1Introduction 1.1Principles in theory development and evaluation 2Primer on UV-Completion, Renormalizability, and All That 2.1Renormalizability and UV-completion 2.2Other forms of UV-completion 3Why Should QG Be UV-Complete? 3.1UV-completion and fundamentality 3.2UV-completion and minimal length 4UV-Completion in Different Approaches to QG 4.1String theory 4.2Asymptotic safety 4.3Causal dynamical triangulation 4.4Higher derivative approaches 4.5Supergravity 4.6Causal set theory 4.7Canonical QG 4.8Loop quantum gravity 4.9Approaches based on alternative gravitational theories 4.10Emergent gravity approaches 5UV-Completion as a Guiding Principle in QG 6Conclusion. (shrink)

In a recent article Allan Buchanan and Robert Keohane defend the view that one of the necessary conditions for the legitimacy of global governance institutions such as the WTO and the IMF is that they respect basic human rights. I certainly agree that setting the minimal threshold of moral acceptability any lower would be entirely unreasonable. But, unfortunately, the view that global governance institutions have human rights obligations is far from uncontroversial. These institutions themselves go to great lengths to deny (...) such a claim. Their official stance finds strong normative support in the state-centric conception of human rights that dominates both normative debates about human rights and current human rights practice. In this article I challenge some of the normative assumptions behind the state-centric conception in order to defend a pluralist conception that ascribes human rights obligations not only to states but also to non-state actors such as global governance institutions. After briefly analyzing some of the proposals currently under discussion about how to legally entrench the obligation to respect human rights in those institutions, I will defend the feasibility of those proposals against the objection that their implementation is incompatible with the current state-system and thus it would require the creation of a world state. (shrink)

In this paper we prove some results about the complexity of proofs. We consider proofs in Hilbert-style formal systems such as in [17]. Thus a proof is a sequence offormulas satisfying certain conditions. We can view the formulas as being strings of symbols; hence the whole proof is a string too. We consider the following measures of complexity of proofs: length , depth and number of steps For a particular formal system and a given formula A we consider the (...) shortest length of a proof of A , the minimal depth of a proof of A and the minimal number of steps in a proof of A . The main results are the following: a bound on the depth in terms of the number of steps: Theorem 2.2, a bound on the depth in terms of the length: Theorem 2.3, a bound on the length in terms of the number of steps for restricted systems: Theorem 3.1. These results are applied to obtain several corollaries. In particular we show: a bound on the number of steps in a cut-free proof, some speed-up results, bounds on the number of steps in proofs of Paris-Harrington sentences. Some papers related to our research are listed in the references. We were especially influenced by Parikh's paper [17] on the famous conjecture of Kreisel . Many important problems in this field remain open. We hope that our paper will contribute to progress in this area. It should be noted that some results of this paper can be equally well obtained using unification theory , by translating a complexity-of-proof problem into a unification problem. A unification algorithm solving the unification problem can then be constructed and the complexity of the unification algorithm analyzed. As pointed out by the referee this method can be used to solve the problem stated in Section 3 for some non-simple schematic systems. (shrink)

The current contents of visual working memory can be disrupted by previously formed memories. This phenomenon is known as proactive interference, and it can be used to index the availability of old memories. However, there is uncertainty about the robustness and lifetime of proactive interference, which raises important questions about the role of temporal factors in forgetting. The present study assessed different factors that were expected to influence the persistence of proactive interference over an inter-trial interval in the visual recent (...) probes task. In three experiments, participants encoded arrays of targets and then determined whether a single probe matched one of those targets. On some trials, the probe matched an item from the previous trial, whereas on other trials the probe matched a more distant item. Prior studies have found that recent negative probes can increase errors and slow response times in comparison to non-recent negative probes, and this offered a behavioral measure of proactive interference. In Experiment 1, factors of array size and inter-trial interval were manipulated in the recent probes task. There was a reduction in proactive interference when a longer delay separated trials on one measure, but only when participants encoded two targets. When working memory capacity was strained by increasing the array size to four targets, proactive interference became stronger after the long delay. In Experiment 2, the inter-trial interval length was again manipulated, along with stimulus novelty. Proactive interference was modestly stronger when a smaller number of stimuli were used throughout the experiment, but proactive interference was minimally affected by the inter-trial interval. These findings are problematic for temporal models of forgetting, but Experiment 3 showed that proactive interference also resisted disruption produced by a secondary task presented within the inter-trial interval. Proactive interference was constantly present and generally resilient to the different manipulations. The combined data suggest a relatively durable, passive representation that can disrupt current working memory under a variety of different circumstances. (shrink)

The (Feynman) propagator G(x2,x1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G(x_2,x_1)$$\end{document} encodes the entire dynamics of a massive, free scalar field propagating in an arbitrary curved spacetime. The usual procedures for computing the propagator—either as a time ordered correlator or from a partition function defined through a path integral—requires introduction of a field ϕ(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi (x)$$\end{document} and its action functional A[ϕ(x)]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A[\phi (x)]$$\end{document}. (...) An alternative, more geometrical, procedure is to define a propagator in terms of the world-line path integral which only uses curves, xi(s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^i(s)$$\end{document}, defined on the manifold. I show how the world-line path integral can be reinterpreted as an ordinary integral by introducing the concept of effective number of quantum paths of a given length. Several manipulations of the world-line path integral becomes algebraically tractable in this approach. In particular I derive an explicit expression for the propagator GQG(x2,x1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_\mathrm{QG}(x_2,x_1)$$\end{document}, which incorporates the quantum structure of spacetime through a zero-point-length, in terms of the standard propagator Gstd(x2,x1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_\mathrm{std}(x_2,x_1)$$\end{document}, in an arbitrary curved spacetime. This approach also helps to clarify the interplay between the path integral amplitude and the path integral measure in determining the form of the propagator. This is illustrated with several explicit examples. (shrink)

This paper introduce a new variant of the Genetic Algorithm whichis developed to handle multivariable, multi-objective and very high search space optimization problems like the solving system of non-linear equations. It is an integer coded Genetic Algorithm with conventional cross over and mutation but with Inverse algorithm is varying its search space by varying its digit length on every cycle and it does a fine search followed by a coarse search. And its solution to the optimization problem will converge (...) to precise value over the cycles. Every equation of the system is considered as a single minimization objective function. Multiple objectives are converted to a single fitness function by summing their absolute values. Some difficult test functions for optimization and applications are used to evaluate this algorithm. The results prove that this algorithm is capable to produce promising and precise results. (shrink)

In Book 8 of his Geographike Hyphegesis Ptolemy gives coordinates for ca. 360 so-called noteworthy cities. These coordinates are the time difference to Alexandria, the length of the longest day, and partly the ecliptic distance from the summer solstice. The supposable original conversions between the coordinates in Book 8 and the geographical coordinates in the location catalogue of Books 2–7 including the underlying parameters and tabulations are here reconstructed. The results document the differences between the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Omega}$$\end{document} - and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Xi}$$\end{document} -recension. The known difference in the longitude of Alexandria underlying the conversion of the longitudes is examined more closely. For the ecliptic distances from the summer solstice of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Omega}$$\end{document} -recension, it is revealed that they were originally computed by means of a so far undiscovered approximate, linear conversion. Further it is shown that the lengths of the longest day could be based on a linear interpolation of the data in the Mathematike Syntaxis 2.6. (shrink)

This study investigates simple games. A fundamental research question in this field is to determine necessary and sufficient conditions for a simple game to be a weighted majority game. Taylor and Zwicker showed that a simple game is non-weighted if and only if there exists a trading transform of finite size. They also provided an upper bound on the size of such a trading transform, if it exists. Gvozdeva and Slinko improved that upper bound; their proof employed a property of (...) linear inequalities demonstrated by Muroga. In this study, we provide a new proof of the existence of a trading transform when a given simple game is non-weighted. Our proof employs Farkas’ lemma, and yields an improved upper bound on the size of a trading transform. We also discuss an integer-weight representation of a weighted simple game, improving the bounds obtained by Muroga. We show that our bound on the quota is tight when the number of players is less than or equal to five, based on the computational results obtained by Kurz. Furthermore, we discuss the problem of finding an integer-weight representation under the assumption that we have minimal winning coalitions and maximal losing coalitions. In particular, we show a performance of a rounding method. Finally, we address roughly weighted simple games. Gvozdeva and Slinko showed that a given simple game is not roughly weighted if and only if there exists a potent certificate of non-weightedness. We give an upper bound on the length of a potent certificate of non-weightedness. We also discuss an integer-weight representation of a roughly weighted simple game. (shrink)

The central thesis of this paper is that Epicurus held that swerves of the constituent atoms of agents' minds cause the agents' volitions from the bottom up. "De Rerum Natura" 2.216-93 is examined at length, and Lucretius is found to be making the following claims: both atoms and macroscopic bodies sometimes swerve as they fall, but so minimally that they are undetectable. Swerves are oblique deviations, not right-angled turns. Swerves must be posited to account both for cosmogonic collisions quite (...) generally and for every "free volition," including those of animals. All volitions are fresh starts of macroscopic motion, caused by that "something in our chests" which later philosophers would call 'the faculty of will.' Since nothing can come to be from nothing, volitions must be caused from the bottom up by swerves, fresh starts in the mind's atoms motions caused by the atoms' inherent swerviness. This is what Lucretius is saying, and what Epicurus had to say in order to defend both libertarianism and atomism. Modern scholars are wrong, then, in rejecting the interpretation of Guissani and Bailey, which was crudely stated, but substantively correct. The rival interpretations of Furley, Fowler, and Englert do not do justice to Epicurus' libertarianism, and that of Sedley does not do justice to his atomism, which entails universal bottom-up causation. Epicurus did not himself draw much attention to his positive doctrine of the swerve, preferring to emphasize the untenability of the deterministic alternative. The notoriety of the doctrine in Cicero's day is due primarily to Chrysippus, who insisted that swerves cannot occur, since they would be 'uncaused' motions, and secondarily to Carneades and Zeno of Sidon. (shrink)

In this paper, a novel approach for word extraction and character segmentation from the handwritten Bangla document images is reported. At first, a modified Run Length Smoothing Algorithm, called Spiral Run Length Smearing Algorithm, is applied for the extraction of words from the text lines of unconstrained handwritten Bangla document images. This technique has helped to overcome some of the drawbacks of standard horizontal and vertical RLSA techniques. SRLSA technique has been applied on the Bangla handwritten document image (...) database CMATERdb1.1.1 and the success rate of the word extraction is found to be 86.01%. In the second part of the work, we have presented a useful solution to the problem on how best word images of handwritten Bangla script can be segmented into constituent characters. Moreover, the technique can segment the words having discontinuity in Matra, a prominent feature of Bangla script. It also optimizes the trade-off between under/over segmentation as Matra region and segmentation points are estimated more precisely. As a result, better word segmentation accuracy is achieved with minimal data loss. Here, a success rate of 92.48% is observed on a dataset of 750 handwritten Bangla words which is 3.35% higher than that of our earlier techniques. (shrink)

The variance effective population size (NeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{eV}$$\end{document}) is frequently used to quantify the expected rate at which a population’s allele frequencies change over time. The purpose of this paper is to find expressions for the global NeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{eV}$$\end{document} of a spatially structured population that are of interest for conservation of species. Since NeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{eV}$$\end{document} depends on allele (...) frequency change, we start by dividing the cause of allele frequency change into genetic drift within subpopulations (I) and a second component mainly due to migration between subpopulations (II). We investigate in detail how these two components depend on the way in which subpopulations are weighted as well as their dependence on parameters of the model such a migration rates, and local effective and census sizes. It is shown that under certain conditions the impact of II is eliminated, and NeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{eV}$$\end{document} of the metapopulation is maximized, when subpopulations are weighted proportionally to their long term reproductive contributions. This maximal NeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{eV}$$\end{document} is the sought for global effective size, since it approximates the gene diversity effective size NeGD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{eGD}$$\end{document}, a quantifier of the rate of loss of genetic diversity that is relevant for conservation of species and populations. We also propose two novel versions of NeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{eV}$$\end{document}, one of which (the backward version of NeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{eV}$$\end{document}) is most stable, exists for most populations, and is closer to NeGD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{eGD}$$\end{document} than the classical notion of NeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{eV}$$\end{document}. Expressions for the optimal length of the time interval for measuring genetic change are developed, that make it possible to estimate any version of NeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{eV}$$\end{document} with maximal accuracy. (shrink)

This is a Swedish translation of the complete text of "In Defense of Abortion and Infanticide" from Moral Issues, edited by Jan Narveson, Oxford University Press, Toronto and New York, 1983, 215-233. -/- There are various ways of attempting to defend an extreme liberal view on abortion, according to which a woman always has the right to control what happens inside her own body. First of all, there is the popular view that appeals to the idea that there is a (...) fundamental, underived right that women have to control what occurs within their own bodies. Secondly, there is a related type of philosophical argument advanced by Judith Jarvis Thomson in her famous and oft-reprinted article “A Defense of Abortion” for the slightly weaker claim that while abortion is not always permissible, since, as she says near the end of her essay, it is impermissible in, and only in, the following circumstances: “There may well be cases where carrying the child to term requires only Minimally Decent Samaritanism of the mother, and this is a standard w must not fall below.” Subsequently, Thomson’s type of argument was then developed and defended at much greater length by David Boonin in his very carefully argued book A Defense of Abortion, though Boonin does not discuss the case of the Minimally Decent Samaritan. I believe that there is a strong objection to the Thomson/Boonin approach to justifying abortion. It was set out in an article by Richard Langer, namely, in ‘Silverstein and the “Responsibility Objection”’, Social Theory and Practice 19/3. 345-58. Langer’s discussion is not, in general, very strong, but in a very important paragraph, on pages 351-2, Langer argues that if the responsibility objection to Thomson is unsound, then it follows that there will also be circumstances in which allowing one’s children to die, simply because one no longer wishes to care for them, will also be morally permissible. David Boonin replies to Langer’s objection in his A Defense of Abortion, but in discussing, on pages 182-3, Langer’s point about a parent’s responsibility to his or her children, Boonin relies upon a tacit consent argument that appears open to decisive objections. It seems to me, then, that the only possibility for a successful defense of an extreme liberal view concerning the justification of abortion will have to involve setting out a plausible account of what it is that gives something a right to life, and I think that the right answer is that neo-Lockean persons, and only neo-Lockean persons, have a right to continued existence. This leaves one with the scientific question of when developing humans become neo-Lockean persons. The answer to that question is perhaps still not firmly settled, although the extensive research that I carried out back in the 1970s seemed to me to support the conclusion that it is not until sometime that humans acquire the capacity for thought, a capacity that is necessary if a developing human is to be a neo-Lockean person. The upshot is that if one defends an extreme liberal view on abortion in the only way that seems to be satisfactory – that is, by setting out an account of what it is that gives something a right to life, and arguing that humans before birth do not have the relevant property, one must also address the question of infanticide, and that to fail to do so is intellectually unacceptable. (shrink)

In this paper we prove some results about the complexity of proofs. We consider proofs in Hilbert-style formal systems such as in [17]. Thus a proof is a sequence offormulas satisfying certain conditions. We can view the formulas as being strings of symbols; hence the whole proof is a string too. We consider the following measures of complexity of proofs: length , depth and number of steps For a particular formal system and a given formula A we consider the (...) shortest length of a proof of A , the minimal depth of a proof of A and the minimal number of steps in a proof of A . The main results are the following: a bound on the depth in terms of the number of steps: Theorem 2.2, a bound on the depth in terms of the length: Theorem 2.3, a bound on the length in terms of the number of steps for restricted systems: Theorem 3.1. These results are applied to obtain several corollaries. In particular we show: a bound on the number of steps in a cut-free proof, some speed-up results, bounds on the number of steps in proofs of Paris-Harrington sentences. Some papers related to our research are listed in the references. We were especially influenced by Parikh's paper [17] on the famous conjecture of Kreisel . Many important problems in this field remain open. We hope that our paper will contribute to progress in this area. It should be noted that some results of this paper can be equally well obtained using unification theory , by translating a complexity-of-proof problem into a unification problem. A unification algorithm solving the unification problem can then be constructed and the complexity of the unification algorithm analyzed. As pointed out by the referee this method can be used to solve the problem stated in Section 3 for some non-simple schematic systems. (shrink)

For an observation time equal to the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at mH=1.35×10-69\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\mathrm{H}=1.35 \times 10^{-69}$$\end{document} kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to mH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\mathrm{H}$$\end{document} is, and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In (...) turns, is equated to the luminosity distance dH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H}$$\end{document} which corresponds to a red shift zH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}$$\end{document}. When using the Concordance-Model parameters, we get dH=8.4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H} = 8.4$$\end{document} Gpc and zH=1.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}=1.3$$\end{document}. Remarkably, dH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H}$$\end{document} falls quite short to the radius of the observable universe. According to this result, tensions in cosmological parameters could be nothing else but due to comparing data inside and beyond zH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}$$\end{document}. Finally, in terms of quantum quantities, the expansion constant H0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_0$$\end{document} reveals to be one order of magnitude above the smallest measurable energy, divided by the Planck constant. (shrink)

Notice that this paper has not claimed that all natural languages are CFL's. What it has shown is that every published argument purporting to demonstrate the non-context-freeness of some natural language is invalid, either formally or empirically or both.18 Whether non-context-free characteristics can be found in the stringset of some natural language remains an open question, just as it was a quarter century ago.Whether the question is ultimately answered in the negative or the affirmative, there will be interesting further questions (...) to ask. If it turns out that natural languages are indeed always CFL's, it will be reasonable to ask whether this helps to explain why speakers apparently recognize so quickly whether a presented utterance corresponds to a grammatical sentence or not, and to associate structural and semantic details with it. It might also be reasonable to speculate about the explanation for the universally context-free character of the languages used by humans, and to wonder whether evolutionary biological factors are implicated in some way (Sampson (1979) could be read in this light). And naturally, it will be reasonable to pursue the program put forward by Gazdar (1981, in press) to see to what extent CFL-inducing grammatical devices can be exploited to yield insightful descriptions of natural languages that capture generalizations in revealing ways.If a human language that is not a CFL is proved to exist, on the other hand, a different question will be raised: give the non-context-free character of human languages in general, why has this property been so hard to demonstrate that it has taken over twenty-five years to bring it to light since the issue was first explicitly posed? If human languages do not have to be CFL's, why do so many (most?) of them come so close to having the property of context-freeness? And, since the CFL's certainly constitute a very broad class of mathematically natural and computationally tractable languages, what property of human beings or their communicative or cognitive needs is it that has caused some linguistic communities to reach beyond the boundaries of this class in the course of evolving a linguistic system?Either way, we shall be interested to see our initial question resolved, and further questions raised. One cautionary word should be said, however, about the implications (or lack of them) that the answer will have for grammatical studies. Chomsky has repeatedly stated that he does not see weak generative capacity as a theme of central importance in the theory of grammar, and we agree. It is very far from being the case that the recent resurgence of interest in exploring the potential of CF-PSG or equivalent systems will, or should, be halted dead in its tracks by the discovery (if it is ever forthcoming) that some natural language is not a CFL. In the area of parsing, for instance, it seems possible that natural languages are not only parsed on the basis of constituent structure such as a CF-PSG would assign, but are parsed as if they were finite state languages (see Langendoen (1975) and Church (1980) for discussion along these lines). That is, precisely those construction-types that figure in the various proofs that English is not an FSL appear to cause massive difficulty in the human processing system; the sentences crucial to the proofs are for the most part unprocessable unless they are extremely short (yet the arguments for English not being and FSL only go through if length is not an issue). This means that in practice properties of finite state grammars are still of great potential importance to linguistic theory despite the fact that they do not provide the framework for defining the total class of grammatical sentences. The same would almost certannly be true of CF-PSG's if they were shown to be inadequate in a similar sense. It is highly unlikely that the advances made so far in far in phrase structure description could be nullified by a discovery about weak generative capacity. Moreover, there are known to be numerous ways in which the power of CF-PSG's can be marginally enhanced to permit, for example, xx languages to be generated without allowing anything like the full class of recursively enumerable or even context-sensitive languages (see Hopcroft and Ullmann (1979), Chapter 14) for an introduction to this topic, noting especially Figure 14.7 on p. 393. The obvious thing to do if natural languages were ever shown not to be CFL's in the general case would be to start exploring such minimal enhancements of expressive power to determine exactly what natural languages call for in this regard and how it could be effectively but parsimoniously provided in a way that closely modelled human linguistic capacities.In the meantime, it seems reasonable to assume that the natural languages are a proper subset of the infinite-cardinality CFL's until such time as they are validly shown not to be. (shrink)

There is a long history, dating back to the 50s, which examines the manner in which team roles contribute to effective team performance. However, much of this work has been built on ad-hoc teams working together for short periods of time under conditions of minimal stress. Additionally, research has been conducted with little attention paid to the importance of temporal factors, despite repeated calls for the importance of considering time in team research (e.g., Mohammed, Hamilton, & Lim, 2009). To begin (...) to understand team roles and how temporal aspects may impact the types of team roles employed when teams are working in extreme mission critical environments, the current manuscript uses a data-driven, bottom-up approach. Specifically, we employ the use of retrospective historical data as our input and a historiometric approach (Simonton, 2003). Source documents consist primarily of autobiographies, memoires, biographies, and first-hand accounts of crew interaction during spaceflight. Critical incidents regarding team interaction were extracted from these source documents and independently coded for team roles by two trained raters. Results of the study speak to the importance of task and social roles within teams that are predominantly intact and operating in extreme environments where mistakes can be life threatening. Evidence for the following task (i.e., coordinator, boundary spanner, team leader, evaluator, critic, information provider, team player, and innovator) and social roles (i.e., team builder, nurturer, harmonizer, entertainer, jokester, and the negative roles of attention seeker and negativist) were found. While it is often task roles that receive the greatest attention, results point to the importance of not neglecting the socioemotional health of the team (and the corresponding roles). Results also indicated that while some roles were consistently enacted independent of temporal considerations (e.g., mission length), the degree to which others were enacted varied across missions of differing lengths. Additionally, based on the current sample we see the following trends: (1) increased enactment of the team builder role as mission duration increases, (2) prominence of the entertainer role, and (3) increased emphasis on the visionary/problem solver role on missions over two years. (shrink)

We propose a Lorentz-covariant deformed algebra describing a -dimensional quantized spacetime, which in the nonrelativistic limit leads to undeformed one. The deformed Poincaré transformations leaving the algebra invariant are identified. In the classical limit the Lorentz-covariant deformed algebra yields the deformed Lorentz-covariant Poisson brackets. Kepler problem with the deformed Lorentz-covariant Poisson brackets is studied. We obtain that the precession angle of an orbit of the relativistic particle in the gravitational field depends on the mass of the particle, i.e. equivalence principle (...) is violated. We propose a condition for the recovery of the equivalence principle in the space with the deformed Poisson brackets. Comparing our analytical result with the experimental data for the precession angle of Mercury’s orbit we provide an estimation of minimal length. (shrink)

Among the quantificational notions neglected by classical logic are "many," "few," and "nearly all." Despite the apparent vagueness associated with these terms in ordinary discourse, in specific contexts we can and do draw strict inferences from statements in which they occur. In this pioneering work, Altham has attempted to uncover something of the formal logic that justifies such inferences. He begins by showing the mutual interdefinability of the three terms. If negation and any one of them are taken as primitive, (...) the other two are definable in terms of these. Selecting as his basic semantic notion the idea of a manifold or many-membered-set, he shows it is only necessary to fix upon a number n, greater than one, to represent the least number of elements to constitute a specific manifold and then one can construct a natural deductive system which uses the standard predicate logic. He develops at great length a weak system that yields principles of inference which are valid in every non-empty domain and in which the classical predicate logic appears as a limiting case. One point that emerges is that the three plurality operators may all be exhibited as involving a double quantification not characteristic of "some," "none," or "all." Next, two stronger systems are developed more briefly which are valid only in many-membered domains. The strongest can represent the largest set of informal arguments and seems to be the most natural of the three. Nevertheless, since these three systems admittedly do not give an exhaustive account of the use of these quantifiers in informal discourse, Altham explains three further systems which correspond more closely to the natural language use of these terms. Finally an appendix indicates what modifications would be required for an intuitionistic logic like Heyting's or the minimal logic of Kolmogorov-Johansson. The text is clearly written and requires no greater logical sophistication to understand than would be needed to follow Lemmon's Beginning Logic or Mates' Elementary Logic.--A. B. W. (shrink)

In the West, it is widely believed that, since Africans lack an emotional experience with romanticism and transcendentalism, they do not possess the philosophical prerequisites necessary to protect wilderness. However, the West’s disdain for African systems of thought has precluded examination of customary African views of wilderness. Examination of ethnographic reports on Kenya’s Highland Bantu reveals a complex view of phenomena that the West generally associates with wilderness. For the Bantu, wilderness is an extension of human living space, and through (...) concerted social action rather than individual initiative, it is, or at least can be, dominated by society. Wildlife is unnatural and alienated from human society, which is natural. Because wilderness is, consequently, understood to be fearsome and hostile, it is not a place that can provide inspiration or self-actualization. Almost all forests have a special spiritual relationship with humankind, and some trees have a special relationship with God. Althoughtraditional Bantu thought is contrary to a concept of wilderness as conserved, managed space filled with tourists and recreators, it does embrace a concept of wilderness as wildlands. The Bantu have gone to considerable length to develop an approach to wilderness that minimizes individual contact while requiring association with wilderness as a social activity. Population growth and want of vocational opportunities continue to thrust Highland Bantu into wilderness as a fundamental and traditional survival technique. (shrink)

In an issue of Common Knowledge given over to experiments in scholarly form and to the discussion of them, this piece is one of three on the genre of microhistory. The other two argue the merits and demerits of the genre, while this piece seeks to exemplify both its virtues and its risks. To show how microhistory offers intense deliberation on a narrowly defined topic, yet also a kind of hastiness — an impatience with demands for broader scope — Colin (...) Richmond examines one limited facet of the relationship between two Americans resident in England at the turn of the last century: the novelist Henry James and the painter Edwin Austin Abbey. Detailed evidence is mustered to document James's love of fresh hens' eggs and of the undignified lengths he would go to obtain them through the agency of Abbey and his wife. This short piece is written as if a parable, and while its moral goes unstated, the reader's attention is drawn to the unsettled question of whether James exerted maximal effort for minimal results, or whether he knew something about the value of freshness undreamed of by those more patient and dignified in pursuing their desires. (shrink)

Kanger [4] gives a set of twelve axioms for the classical propositional Calculus which, together with modus ponens and substitution, have the following nice properties: (0.1) Each axiom contains $\supset$ , and no axiom contains more than two different connectives. (0.2) Deletions of certain of the axioms yield the intuitionistic, minimal, and classical refutability1 subsystems of propositional calculus. (0.3) Each of these four systems of axioms has the separation property: that if a theorem is provable in such a system, then (...) it is provable using only the axioms of that system for $\supset$ , and for the other connectives, if any, actually occurring in that theorem. (0.4) All twelve axioms are independent. It is easily seen that two of Kanger's axioms can be shortened, and that two others can be replaced by a single axiom which is the same length as one of the two which it replaces, without disturbing properties (0.1)-(0.3). These alterations have advantages of simplicity and elegance, but bring property (0.4) into question, in that similarities among some of the axioms in the altered system make demonstrations of independence considerably more difficult. It is the purpose of this paper to show that independence is nonetheless provable for the simplified system, and in another system which also satisfies (0.1)-(0.3), in which f (falsehood) is taken to be primitive instead of ∼ (negation). Nonnormal truth-tables2 are used to obtain the independence of one of the axioms. (shrink)