We study and compare two combinatorial lowness notions: strong jump-traceability and well-approximability of the jump, by strengthening the notion of jump-traceability and super-lowness for sets of natural numbers. A computable non-decreasing unbounded function h is called an order function. Informally, a set A is strongly jump-traceable if for each order function h, for each input e one may effectively enumerate a set Te of possible values for the jump JA, and the number of values enumerated is at most h. A′ (...) is well-approximable if can be effectively approximated with less than h changes at input x, for each order function h. We prove that there is a strongly jump-traceable set which is not computable, and that if A′ is well-approximable then A is strongly jump-traceable. For r.e. sets, the converse holds as well. We characterize jump-traceability and strong jump-traceability in terms of Kolmogorov complexity. We also investigate other properties of these lowness properties. (shrink)
We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic (↓), for example, can be thought of as a particular case of a memory logic where the memory is an indexed list of elements of the domain.
We define a program size complexity function $H^\infty$ as a variant of the prefix-free Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in ${\{0,1\}}^\omega$ relative to the $H^\infty$ complexity. We prove that the classes of Martin-Löf random sequences and $H^\infty$-random sequences coincide and that the $H^\infty$-trivial sequences are exactly the recursive ones. We also study some properties of $H^\infty$ and compare it with other complexity functions. In particular, $H^\infty$ (...) is different from $H^A$, the prefix-free complexity of monotone machines with oracle A. (shrink)
In this paper we study the Kolmogorov complexity for non-effective computations, that is, either halting or non-halting computations on Turing machines. This complexity function is defined as the length of the shortest input that produce a desired output via a possibly non-halting computation. Clearly this function gives a lower bound of the classical Kolmogorov complexity. In particular, if the machine is allowed to overwrite its output, this complexity coincides with the classical Kolmogorov complexity for halting computations relative to the first (...) jump of the halting problem. However, on machines that cannot erase their output –called monotone machines–, we prove that our complexity for non effective computations and the classical Kolmogorov complexity separate as much as we want. We also consider the prefix-free complexity for possibly infinite computations. We study several properties of the graph of these complexity functions and specially their oscillations with respect to the complexities for effective computations. (shrink)
We consider the question of randomness of the probability ΩU[X] that an optimal Turing machine U halts and outputs a string in a fixed set X. The main results are as follows: ΩU[X] is random whenever X is $\Sigma _{n}^{0}$-complete or $\Pi _{n}^{0}$-complete for some n ≥ 2. However, for n ≥ 2, ΩU[X] is not n-random when X is $\Sigma _{n}^{0}$ or $\Pi _{n}^{0}$ Nevertheless, there exists $\Delta _{n+1}^{0}$ sets such that ΩU[X] is n-random. There are $\Delta _{2}^{0}$ sets (...) X such that ΩU[X] is rational. Also, for every n ≥ 1, there exists a set X which is $\Delta _{n+1}^{0}$ and $\Sigma _{n}^{0}$-hard such that ΩU[X] is not random. We also look at the range of ΩU as an operator. We prove that the set {ΩU[X]: X ⊆ 2<ω} is a finite union of closed intervals. It follows that for any optimal machine U and any sufficiently small real r, there is a set X ⊆ 2<ω recursive in ∅′ ⊕ r, such that ΩU[X] = r. The same questions are also considered in the context of infinite computations, and lead to similar results. (shrink)
We do not dispute the findings of Ceci et al.'s study, though they are based on survey research which does not always reflect real-life experiences. We report on cases we have defended on the basis of the tenure system, few of which mirror the situations reported in the target article. We end with a strong defense of the tenure system in the modern university. (Published Online February 8 2007).
Dorothy Sayers' Gaudy Night, published in 1936, explores still-topical questions about the relation of epistemological and ethical values, and about the place of women in the life of the mind. In her wry reflections on the radical differences between today's feminist philosophy and Sayers' no-nonsense observation that “women are more like men than anything else on earth,” Susan Haack draws both on this detective story and on Sayers' wonderfully brisk essay, ‘Are Women Human?’.
Dorothy Emmet, in two books, one of which was based on extensive personal contact with Robert Merton and Columbia sociology, provides the closest thing we have to an authorized philosophical defense of Merton. It features a deflationary account of functionalism which dispenses with the idea of general teleological ends. What it replaces it with is an account of “structures” that have various consequences and that are maintained because, on Emmet’s account, of the mutual reinforcement of motives produced by the (...) structure. (shrink)
This paper provides a methodological schema for interpreting Hume's Dialogues concerning Natural Religion that supports the traditional thesis that Philo represents Hume's views on religious belief. To understand the complexity of Hume's ‘naturalism’ and his assessment of religious belief, it is essential to grasp the manner in which Philo articulates a consistently Humean position in the Dialogues.
Cooper, Austin The Oxford or Tractarian Movement and later Ritualists and Anglo-Catholics schooled numerous converts in elements of the Catholic faith. Foremost among them was John Henry Cardinal Newman, one of the original founders of the Oxford Movement. Converts numbered in the hundreds and included another cardinal, Henry Edward Manning, the second Archbishop of Westminster, the religious foundress Cornelia Connelly, the priest novelist Robert Hugh Benson and later literary figures such as G.K. Chesterton, Evelyn Waugh and Mgr Ronald Knox. American (...) historian, Patrick Allitt, has argued that on both sides of the Atlantic converts dominated Catholic intellectual life between 1840 and 1960. While such 'Tractarian' converts have indeed greatly influenced Catholic life, many 'Tractarians' who never converted have also had a considerable impact on English-speaking Catholicism. C.S. Lewis is an obvious example. But there have been others, including author Charles Williams, poet T.S. Eliot and theologians John Macquarrie and Michael Ramsey. The author Dorothy L. Sayers also deserves to be counted among their number. (shrink)
Alfred North Whitehead is rightly considered a Cambridge philosopher. His intellectual life falls into three periods, of which the first was in Cambridge, the second in London, and the third in Cambridge, Mass. But he always saw himself as a Cambridge person, and was a Life Fellow of Trinity College. Moreover, though each of these periods is associated with a different kind of philosophy, some ideas and concerns from the Cambridge period carry right through.
he Kansas Board of Education voted 6 to 4 to remove evolution, and the Big Bang theory as well, from the state's science curriculum. In so doing, the board transported its jurisdiction to a never-never land where a Dorothy of the new millennium might exclaim, "They still call it Kansas, but I don't think we're in the real world anymore." The new standards do not forbid the teaching of evolution, but the subject will no longer be included in statewide (...) tests for evaluating students—a virtual guarantee, given the realities of education, that this central concept of biology will be diluted or eliminated, thus reducing courses to something like chemistry without the periodic table, or American history without Lincoln. (shrink)
The article reflects on the therapeutic and ethical potential of literature, the theme which is often marginalized and overlooked by literary critics, in the novel Mister Pip by Lloyd Jones. Matilda, the main character of the analyzed novel, finds salvation in the times of war and oppression thanks to Charles Dickens’s masterpiece, Great Expectations, and the only white man on the island−her teacher, Mr. Watts. Matilda’s strong identification with Dickensian Pip and imagination make her escape to another world, (...) become a self-conscious person and reunite with her father. The paper also discusses relationships between Matilda, Mr. Watts and her mother, Dolores. I attempt to show the emotional development of the characters, their interactions, changes, sense of identity, and, having analyzed their actions, I compare them to protagonists created by Charles Dickens. Needless to say, drawing the reader’s attention to British culture and traditions, Lloyd Jones avoids focusing on the negative aspects of the postcolonial views, pointing out that “the white man” can be an example of a Dickensian gentleman. (shrink)
This article looks at the feminist activism of particular women in the ancestry of the eminent Canadian sociologist, Dorothy E. Smith, and at the archival data that confirm the traces of their influence found in her theory-building. Using the method of interpretative historical sociology and a conceptual framework drawn from Marx called the `productive forces', the article examines the feminist theology of her Quaker ancestor, Margaret Fell, and the militant suffrage activism of her mother and her grandmother, Dorothy (...) Foster Place and Lucy Ellison Abraham, respectively. The article argues that the household labour of the remarkable women in her family line became a `productive force' that facilitated her imagining of the feminist theory, `the standpoint of women'. (shrink)
Walter Conn's theory of Christian Conversion (1986) provides an illuminating lens for understanding Dorothy Day's conversion experience. Day's story, conversely, offers an opportunity to test selected features of Conn's theory, specifically the affective, cognitive, moral, and religious categories of analysis. The dialectic is a fruitful one, yielding insight into both Day's story and Conn's theory, while at the same time raising provocative questions about and contributing to the current debate regarding an "ethic of care" as distinct from an "ethic (...) of justice.". (shrink)
