We introduce a class of forcing notions, called forcing notions of type S, which contains among other Sacks forcing, Prikry-Silver forcing and their iterations and products with countable supports. We construct and investigate some formalism suitable for this forcing notions, which allows all standard tricks for iterations or products with countable supports of Sacks forcing. On the other hand it does not involve internal combinatorial structure of conditions of iterations or products. We prove that the class of forcing (...) notions of type S is closed under products and certain iterations with countable supports. (shrink)

The main results of the present paper are the following theorems: 1. There is no e ∈ ω such that for any A, B ⊆ ω, SA = Wmath image is simple in A, and if A′ [TRIPLE BOND]TB′, then SA =* SB. 2 There is an e ∈ ω such that for any A, B ⊆ ω, MA = We is incomplete maximal in A, and if A =* B, then MA [TRIPLE BOND]TMB.

Dicotyledons are polarly organised in several ways. In plant morphology polarity, a principle allowing comparison of different plant structures has until yet not been studied. A division** of the vegetative plant in shoot and root as polar structures leads to the distinction of four instead of three basic organs: leaf, shoot axis, root axis and root cap together with the root hairs. The flower is also polarly organised, its poles are formed by the carpels and the stamens. The foliage leaves (...) are also polarly organised which is reflected by the morphological relationship of foliage leaf, stamen and carpel. The stamen uses the hypophyll*** as base of construction and the carpel uses the epiphyll**** as base of construction. Hypophyll and epiphyll are the two poles of the foliage leaf. Root and shoot, the polar entities of the vegetative plant and stamen and carpel, the polar entities of the generative plant, are morphologically correlated. Stamen and carpel can be understood as a combination of the basic organs of vegetative and generative parts of the plant. The basic organs of the generative plant are pollen grain and embryo sack with their gametophytes. The quantitative comparison of variable proportions is supplemented by a qualitative comparison of polarities. The result is, that the organisation type of the dicotyledons can yet be understood as constituted of morphological related parts.* in german Grundorgane. (shrink)

Name der Zeitschrift: Der Islam Jahrgang: 94 Heft: 2 Seiten: 606-609.

The Sacks Density Theorem [7] states that the Turing degrees of the recursively enumerable sets are dense. We show that the Density Theorem holds in every model of P - + BΣ 2 . The proof has two components: a lemma that in any model of P - + BΣ 2 , if B is recursively enumerable and incomplete then IΣ 1 holds relative to B and an adaptation of Shore's [9] blocking technique in α-recursion theory to models of (...) arithmetic. (shrink)

We study cardinal invariants of systems of meager hereditary families of subsets of ω connected with the collapse of the continuum by Sacks forcing S and we obtain a cardinal invariant yω such that S collapses the continuum to yω and y ≤ yω ≤ b. Applying the Baumgartner-Dordal theorem on preservation of eventually narrow sequences we obtain the consistency of y = yω < b. We define two relations $\leq _{0}^{\ast}$ and $\leq _{1}^{\ast}$ on the set $(^{\omega}\omega)_{{\rm Fin}}$ (...) of finite-to-one functions which are Tukey equivalent to the eventual dominance relation of functions such that if $\germ{F}\subseteq (^{\omega}\omega)_{Fin}$ is $\leq _{1}^{\ast}$ -unbounded, well-ordered by $\leq _{1}^{\ast}$ , and not $\leq _{0}^{\ast}$ -dominating, then there is a nonmeager p-ideal. The existence of such a system F follows from Martin's axiom. This is an analogue of the results of [3], [9, 10] for increasing functions. (shrink)

Let ${\mathcal{P}_s}$ be the lattice of degrees of non-empty ${\Pi_1^0}$ subsets of 2 ω under Medvedev reducibility. Binns and Simpson proved that FD(ω), the free distributive lattice on countably many generators, is lattice-embeddable below any non-zero element in ${\mathcal{P}_s}$ . Cenzer and Hinman proved that ${\mathcal{P}_s}$ is dense, by adapting the Sacks Preservation and Sacks Coding Strategies used in the proof of the density of the c.e. Turing degrees. With a construction that is a modification of the one (...) by Cenzer and Hinman, we improve on the result of Binns and Simpson by showing that for any ${\mathcal{U} < _s \mathcal{V}}$ , we can lattice embed FD(ω) into ${\mathcal{P}_s}$ strictly between ${deg_s(\mathcal{U})}$ and ${deg_s({\mathcal V})}$ . We also note that, in contrast to the infinite injury in the proof of the Sacks Density Theorem, in our proof all injury is finite, and that this is also true for the proof of Cenzer and Hinman, if a straightforward simplification is made. (shrink)

The purpose of this review is to bring to the attention to a wider, specialised audience a special issue of the UK journal, Ethnographic Studies. The special issue, compiled and edited by Andrew Carlin and Roger Slack, is a Festschrift in honour of Egon Bittner (1921–2011). The readership of Human Studies might be aware of Egon Bittner as one of the circle surrounding Harold Garfinkel and Harvey Sacks in the early and preparatory days of ethnomethodology between 1955 and 1965.This (...) collection of papers can be divided into three sets. The introduction, biographical, and “contribution pieces,” give an account of parts of Bittner’s life, his work with others and the contribution he made within the various collaborations and seminars which he attended and where his contributions were recorded. The second set, probably most valuable to the ethnomethodological reader, are the papers which could be described as Bittner’s contributions to sociological method and methodology. Contained within th .. (shrink)

This essay is my review of Philip Booth’s ...and the Pursuit of Happiness: Wellbeing and the Role of Government. The book is an anthology of original articles by eminent researchers in modern happiness economics, such as: Booth himself; Paul Omerod; David Sacks, Betsey Stephenson, and Justin Wolfers; Christopher Snowden; J. R. Shackleton; Christian Bjornskov; Peter Boettke and Christopher Coyne; and Pedro Schwartz. I conclude by offering several criticisms of the work.

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{P}_s}$$\end{document} be the lattice of degrees of non-empty \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^0}$$\end{document} subsets of 2ω under Medvedev reducibility. Binns and Simpson proved that FD(ω), the free distributive lattice on countably many generators, is lattice-embeddable below any non-zero element in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{P}_s}$$\end{document}. Cenzer and Hinman proved that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{P}_s}$$\end{document} is (...) dense, by adapting the Sacks Preservation and Sacks Coding Strategies used in the proof of the density of the c.e. Turing degrees. With a construction that is a modification of the one by Cenzer and Hinman, we improve on the result of Binns and Simpson by showing that for any \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{U} < _s \mathcal{V}}$$\end{document}, we can lattice embed FD(ω) into \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{P}_s}$$\end{document} strictly between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${deg_s(\mathcal{U})}$$\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}$${deg_s({\mathcal V})}$$\end{document}. We also note that, in contrast to the infinite injury in the proof of the Sacks Density Theorem, in our proof all injury is finite, and that this is also true for the proof of Cenzer and Hinman, if a straightforward simplification is made. (shrink)

One way in which the characteristic gestures of philosophy and criticism differ from each other lies in their involvements with disillusionment, with the undoing of our naivete, especially regarding what we take ourselves to know about the meaning of what we say. Philosophy will often find less than we thought was there, perhaps nothing at all, in what we say about the “external” world, or in our judgments of value, or in our ordinary psychological talk. The work of criticism, on (...) the other hand, frequently disillusions by finding disturbingly more in what is said than we precritically thought was there. In our relation to the meaningfulness of what we say, there is a disillusionment of plentitude as well as of emptiness. And no doubt what is “less” for one discipline may be “more” of what someone else is looking for.In recent years, metaphor has attracted more than its share of both philosophical and critical attention, including philosophical denials of the obvious, as well as critical challenges to the obviousness of the ways we talk about metaphor. In this paper I discuss a problem of each sort and suggest a complex of relations between them. The particular denial of the obvious that I’m interested in is the claim recently made by Donald Davidson that “a metaphor doesn’t say anything beyond its literal meaning ,” nor is it even correct to speak of metaphor as a form of communication.1 There’s disillusionment with a vengeance; and even if not strictly believable, it is still not without its therapeutic value, as we shall see. 1. Donald Davidson, “What Metaphors Mean,” in On Metaphor, ed. Sheldon Sacks , p. 30; hereafter abbreviated “WMM.” Davidson’s view has found supporters among both philosophers and literary theorists. It is, for example, important to the early argument of Richard Rorty’s recent book. See his Contingency, Irony, and Solidarity , p. 18. Richard Moran is an assistant professor of philosophy at Princeton University. He is currently working on a book on subjectivity and contemporary concepts of personhood. (shrink)

Let A[ω]ω be a maximal almost disjoint family and assume P is a forcing notion. Say A is P-indestructible if A is still maximal in any P-generic extension. We investigate P-indestructibility for several classical forcing notions P. In particular, we provide a combinatorial characterization of P-indestructibility and, assuming a fragment of MA, we construct maximal almost disjoint families which are P-indestructible yet Q-destructible for several pairs of forcing notions . We close with a detailed investigation of iterated Sacks indestructibility.

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 26.1 (2002) 207-215 [Access article in PDF] Notes and Fragments Poetics of Sentimentality Rick Anthony Furtak IN HIS MAJOR WORK, The Passions, Robert Solomon argues that emotions are judgments. 1 Through a series of persuasive examples, he shows that emotions are best understood as mental states which involve certain beliefs about the world. This means that every emotion has an object: if I am angry at (...) John for stealing my car, the object of my anger is the fact (or what I take to be a fact) that my car has been stolen by John. If I find out that this is not the case, that my car has not even left the garage, then my anger should vanish along with its justification. 2 The key point here is that anger, like any other emotion, may be reasonable or inappropriate depending on the situation. If there is nothing to be angry about, then it would be irrational for me to cultivate anger simply because I enjoy having this particular emotion. In general, emotional responses are cognitively flawed whenever they are at odds with the properties of their objects. If we want our judgments to be realistic and not delusional, then we must avoid this kind of error.It is curious, then, that Solomon has written an essay in which he categorically declares that "there is nothing wrong with sentimentality." 3 For it would appear that his theory of emotion provides precisely the terms needed in order to specify what is wrong with it. If emotions are judgments, then "sentimentality" ought to be an important critical term to designate the habit of having emotions that involve either impaired or mistaken judgment. Nevertheless, Solomon is willing to defend any and every episode of tender emotion, of the kind associated with the [End Page 207] death of Little Nell in The Old Curiosity Shop (S, p. 240). He suggests that the more we can muster up this sort of response to literature or life, the better. What he seeks to encourage, in other words, is what Hume would call "delicacy" of (aesthetic) taste and of (ethical) passion. 4 But while Hume acknowledges that sensitivity to beauty and to ugliness are two sides of the same coin, such that anyone who is susceptible to lively enjoyments is also liable to undergo pungent sorrows, Solomon wants to promote only the tender aspect of emotion.On the principle of passionate maximization, it is good if I can be tenderly affected by a poem—any poem! The problem with such crass emotion-stoking is that it precludes the possibility of distinguishing between, for instance, the two stanzas below. Both are by Wilfred Owen: the first was written in 1914 and the second in 1918. 5 I O meet it is and passing sweet To live in peace with others, But sweeter still and far more meet To die in war for brothers. II Bent double, like old beggars under sacks, Knock-kneed, coughing like hags, we cursed through sludge, Till on the haunting flares we turned our backs And towards our distant rest began to trudge. Men marched asleep. Many had lost their boots But limped on, blood-shod. All went lame; all blind; Drunk with fatigue; deaf even to the hoots Of tired, outstripped Five-Nines that dropped behind. Only if emotions did not involve rational judgment could a person's passionate response to these two stanzas be a matter of indifference. But it seems that, on the contrary, an essential component of understanding them is recognizing that they express irreconcilable cognitive attitudes. The tone of the 1918 stanza is strikingly different from that of the earlier one, even though they share roughly the same topic. The latter stanza is stark and ominous, and filled with vivid detail; the one from 1914 is sweet and vague. Clearly, we might describe the earlier of the two as "sentimental"—the question is, what kind of judgment does [End Page 208] it involve? I suggest that its insipid jingles endorse the view that war is a delightful opportunity to nurture brotherhood and gain... (shrink)

Working in the language of first-order arithmetic we consider models of the base theory P - . Suppose M is a model of P - and let M satisfy induction for σ 1 -formulas. First it is shown that the Friedberg-Muchnik finite injury argument can be performed inside M, and then, using a blocking method for the requirements, we prove that the Sacks splitting construction can be done in M. So, the "amount" of induction needed to perform the known (...) finite injury priority arguments is Σ 1 -induction. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:84 Reviews THE WAYS OF THE WITTGENSTEINS ACCORDING TO A WAUGH Richard Henry Schmitt U. of Chicago Chicago, il 60637, usa [email protected] AlexanderWaugh. TheHouseofWittgenstein:aFamilyatWar. London: Bloomsbury, 2008. Pp. 366. isbn: 0-7475-9185-7. £20.00 (hb). New York: Doubleday, 2009. Pp. 333. isbn: 0-385-52060-3. us$28.95 (hb). Ezach family is happy and unhappy in its own ways. This is hardly surprising zgiven that the family lies at the crossroad of so much human (...) experience. It is the scene for playing out genetics and for working through the rearing and civilizing of children, both nature and nurture. In economic life it constitutes the primary unit, the household. Despite Tolstoy’s ideal, none can ever be com­ pletely happy for every member all the time. And, there is no reason to think that basically happy families are any more the same than unhappy ones. But then none can ever be completely unhappy; or rather, when a family is com­ pletely unhappy it is unlikely that it will remain one. One other factor, however, intrudes on this picture: we tend to be more interested in bad or scandalous news than good. Vicarious experience brings catharsis, possibly helpful in a way. Yet, as the German language recognizes with the word “Schadenfreudez”, we can experience joy at someone else’s sorrow, despite the questions it raises about our empathy. Alexander Waugh is himself the member of a famous family. He has written December 2, 2009 (5:28 pm) E:\CPBR\RUSSJOUR\TYPE2901\russell 29,1 060 red.wpd E:\CPBR\RUSSJOUR\TYPE2901\russell 29,1 060 red.wpd Reviews 85 its “autobiography” in Fathers and Sons,1 where he is principally concerned with his father Auberon (“Bron”), his grandfather Evelyn, his great-uncle Alec, and his great-grandfather Arthur. Given the family documentation at his disposal and the span of generations, that book covers enough territory, in enough detail, to give us some sense of Waugh family character. You learn what it was like to grow up in the family, down to the odour of Uncle Auberon Herbert’s cologne, “smelling like Cleopatra in her barge on her way to meet Antony for the Wrst time” according to Bron (p. 370, paperback ed.), and the family suspicion that this uncle may have been the illegitimate son of Hilaire Belloc (p. 276). The fathers and sons, from Arthur down to Alexander, all wrote for a living, witty, stylish prose, and sometimes poetry. They especially liked writing about each other in letters, essays, and novels, often to each other in public letters and dedications; and as a consequence Alexander’s book is rich, amusing, intimate, and a bit indiscrete. Arthur’s turn-of-the-century avoidance of emotion in sentimentality grew outmoded, but it was replaced in the family business with newer models, with more Xash and cynicism. When it came to Alexander’s fa­ ther Bron, he was known for his talent at vituperation, and got into verbal and legal scrapes with C. P. Snow and Bertrand Russell among others (p. 407), which led to his getting sacked but only made his journalism more widely read and more valuable to publishers. In Alexander’s disclosure of his family history, there is a sureness of touch that comes from working within his ken. Waugh studied music, and worked as a music critic. In his easy, self-depreci­ ating way, he told an interviewer for The Wall Street Journalz that he got the idea to write this book because of “the most appalling boil on my right index Wnger”. This curtailed his routine enjoyment at the piano, “But then as I sat down and pressed a chord with my left hand I thought of Paul Wittgenstein. I knew about the concerto that Ravel composed for him and I knew that he was Ludwig’s brother. He was bound to have an interesting story.”2 With access to some Witt­ genstein family papers through one of Paul Wittgenstein’s daughters, he began. But a biography of the one-armed pianist soon turned into this “family history”, in part because of the author’s previous success with his own family, but also... (shrink)

A set S of degrees is said to be an initial segment if c ≤ d ∈ S→-c∈S. Shoenfield has shown that if P is the lattice of all subsets of a finite set then there is an initial segment of degrees isomorphic to P. Rosenstein [2] (independently) proved the same to hold of the lattice of all finite subsets of a countable set. We shall show that “countable set” may be replaced by “set of cardinality at most that of (...) the continuum.” This result is also an extension of [3, Corollary 2 to Theorem 15], which states that there is a sublattice of degrees isomorphic to the lattice of all finite subsets of 2N. (A sublattice of degrees is a subset closed under ∪ and ∩; an initial segment closed under ∪ is necessarily a sublattice, but not conversely.)It seems worth noting that the proof of the present result was preceded in time by our proof [4] of the analogous theorem for hyperdegrees, and is in fact an adaptation of that proof. Thus the present work has been influenced much more directly by the Gandy-Sacks forcing construction of a minimal hyperdegree [1] than by previous work on initial segments of degrees. (shrink)

We present an exposition of Section VI.1 and most of Section VI.2 from Shelah’s book Proper and Improper Forcing. These sections offer proofs of the preservation under countable support iteration of proper forcing of various properties, including proofs that ωω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega^\omega}$$\end{document} -bounding, the Sacks property, the Laver property, and the P-point property are preserved by countable support iteration of proper forcing.

The main purpose of this dissertation is to apply and develop new forcing techniques to obtain models where several cardinal characteristics are pairwise different as well as force many (even more, continuum many) different values of cardinal characteristics that are parametrized by reals. In particular, we look at cardinal characteristics associated with strong measure zero, Yorioka ideals, and localization and anti-localization cardinals.In this thesis we introduce the property “F-linked” of subsets of posets for a given free filter F on the (...) natural numbers, and define the properties “ $\mu $ -F-linked” and “ $\theta $ -F-Knaster” for posets in a natural way. We show that $\theta $ -F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. These kinds of posets led to the development of a general technique to construct $\theta $ - $\textrm {Fr}$ -Knaster posets (where $\textrm {Fr}$ is the Frechet ideal) via matrix iterations of ${<}\theta $ -ultrafilter-linked posets (restricted to some level of the matrix). The latter technique allows proving consistency results about Cichoń’s diagram (without using large cardinals) and to prove the consistency of the fact that, for each Yorioka ideal, the four cardinal characteristics associated with it are pairwise different. Another important application is to show that three strongly compact cardinals are enough to force that Cichoń’s diagram can be separated into 10 different values. Later on, it was shown by Goldstern, Kellner, Mejía, and Shelah that no large cardinals are needed for Cichoń’s maximum (J. Eur. Math. Soc. 24 (2022), no. 11, p. 3951–3967).On the other hand, we deal with certain types of tree forcings including Sacks forcing, and show that these increase the covering of the strong measure zero ideal $\mathcal {SN}$. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates that this covering number is consistently larger than any other classical cardinal characteristics of the continuum. Even more, Sacks forcing can be used to force that $\operatorname {\mathrm{non}}(\mathcal {SN})<\operatorname {\mathrm{cov}}(\mathcal {SN})<\operatorname {\mathrm{cof}}(\mathcal {SN})$, which is the first consistency result where more than two cardinal characteristics associated with $\mathcal {SN}$ are pairwise different. To obtain another result in this direction, we provide bounds for $\operatorname {\mathrm{cof}}(\mathcal {SN})$, which generalizes Yorioka’s characterization of $\mathcal {SN}$ (J. Symbolic Logic 67.4 (2002), p. 1373–1384). As a consequence, we get the consistency of $\operatorname {\mathrm{add}}(\mathcal {SN})=\operatorname {\mathrm{cov}}(\mathcal {SN})<\operatorname {\mathrm{non}}(\mathcal {SN})<\operatorname {\mathrm{cof}}(\mathcal {SN})$ with ZFC (via a matrix iteration forcing construction).We conclude this thesis by combining creature forcing approaches by Kellner and Shelah (Arch. Math. Logic 51.1–2 (2012), p. 49–70) and by Fischer, Goldstern, Kellner, and Shelah (Arch. Math. Logic 56.7–8 (2017), p. 1045–1103) to show that, under CH, there is a proper $\omega ^\omega $ -bounding poset with $\aleph _2$ -cc that forces continuum many pairwise different cardinal characteristics, parametrized by reals, for each one of the following six types: uniformity and covering numbers of Yorioka ideals as well as both kinds of localization and anti-localization cardinals, respectively. This answers several open questions from Klausner and Mejía (Arch. Math. Logic 61 (2022), pp. 653–683).Abstract prepared by Miguel Antonio Cardona-MontoyaE-mail: [email protected]: https://repositum.tuwien.at/handle/20.500.12708/19629. (shrink)

Understanding, for Kant, does not intuit, and intuition—which involves empirical information, i.e., sense-data—does not entail thinking. What is crucial to Kant’s famous claim that intuitions without concepts are blind and concepts without intuitions are empty is the idea that we have no knowledge unless we combine concepts with intuition. Although concepts and intuition are radically separated mental powers, without a way of bringing them together (i.e., synthesis) there is no knowledge for Kant. Thus Kant’s metaphysical-scientific dualism: (scientific) knowledge is limited (...) to the world of phenomena—the world of appearance—while the thing-in-itself is unknowable because there is no intuition that can correspond to the it. This paper sets to cull Béatrice Longuenesse’s recent work on the first-person ‘I’ and put forth a novel Kantian approach to the first-person reference of mental states, working in the tradition of P.F. Strawson, Rudolf Carnap, and Wilfrid Sellars, while offering an empirical study of deafferentation to ground the thesis that the binding of representations is separate from phenomenal consciousness. Accordingly, we stake a kind of self-consciousness vis-à-vis the Fundamental Reference-Rule qua apperception that, while intimately connected to consciousness of one’s own body, apperception is nevertheless distinct from it and is, moreover, the condition for any use of ‘I’. We compliment neuroscientist Oliver Sacks’ research with Ned Block’s recent work on “no-post‐perceptual cognition” and attentional variation to couch Kant’s schema in perceptual psychology. We navigate Kant’s work on intuitions (viz. sensation, perception, and the empirical side of the cognitive faculties) and indirect realism/weak representationism first via Sellars’ naturalization of Kant’s inaccessible thing-in-itself, before challenging Sellars’ functionalist and inferentialist conception of perception and discursive intentionality. We ultimately endeavor to conceptualize the limit-conditions regarding our having reportable knowledge about our access to percepts and concepts. (shrink)

Let $T$ be a theory in a countable fragment of $\mathcal{L}_{\omega_{1},\omega}$ whose extensions in countable fragments have only countably many types. Sacks proves a bounding theorem that generates models of high Scott rank. For this theorem, a tree hierarchy is developed for $T$ that enumerates these extensions. In this paper, we effectively construct a predecessor function for formulas defining types in this tree hierarchy as follows. Let $T_{\gamma}\subseteq T_{\delta}$ with $T_{\gamma}$- and $T_{\delta}$-theories on level $\gamma$ and $\delta$, respectively. Then (...) if $\ulcorner p\urcorner $ is a formula that defines a type for $T_{\delta}$, our predecessor function provides a formula for defining its subtype in $T_{\gamma}$. By constructing this predecessor function, we weaken an assumption for Sacks’s result. (shrink)

In this thesis, we study Turing degrees in the context of classical recursion theory. What we are interested in is the partially ordered structures $\mathcal {D}_{\alpha }$ for ordinals $\alpha <\omega ^2$ and $\mathcal {D}_{a}$ for notations $a\in \mathcal {O}$ with $|a|_{o}\geq \omega ^2$.The dissertation is motivated by the $\Sigma _{1}$ -elementary substructure problem: Can one structure in the following structures $\mathcal {R}\subsetneqq \mathcal {D}_{2}\subsetneqq \dots \subsetneqq \mathcal {D}_{\omega }\subsetneqq \mathcal {D}_{\omega +1}\subsetneqq \dots \subsetneqq \mathcal {D}$ be a $\Sigma _{1}$ (...) -elementary substructure of another? For finite levels of the Ershov hierarchy, Cai, Shore, and Slaman [Journal of Mathematical Logic, vol. 12, p. 1250005] showed that $\mathcal {D}_{n}\npreceq _{1}\mathcal {D}_{m}$ for any $n < m$. We consider the problem for transfinite levels of the Ershov hierarchy and show that $\mathcal {D}_{\omega }\npreceq _{1}\mathcal {D}_{\omega +1}$. The techniques in Chapters 2 and 3 are motivated by two remarkable theorems, Sacks Density Theorem and the d.r.e. Nondensity Theorem.In Chapter 1, we first briefly review the background of the research areas involved in this thesis, and then review some basic definitions and classical theorems. We also summarize our results in Chapter 2 to Chapter 4. In Chapter 2, we show that for any $\omega $ -r.e. set D and r.e. set B with $D<_{T}B$, there is an $\omega +1$ -r.e. set A such that $D<_{T}A<_{T}B$. In Chapter 3, we show that for some notation a with $|a|_{o}=\omega ^{2}$, there is an incomplete $\omega +1$ -r.e. set A such that there are no a-r.e. sets U with $A<_{T}U<_{T}K$. In Chapter 4, we generalize above results to higher levels. We investigate Lachlan sets and minimal degrees on transfinite levels and show that for any notation a, there exists a $\Delta ^{0}_{2}$ -set A such that A is of minimal degree and $A\not \equiv _T U$ for all a-r.e. sets U.prepared by Cheng Peng.E-mail: [email protected]. (shrink)

We are free to get our theories where we will. As Einstein said, the emergence of a theory is like an egg laid by a chicken, "auf einmal ist es da.1" In practice theories are usually derived as improvements on earlier theories, as better tools are refinements of earlier, cruder ones; and they are directed explanatorily not at the facts of their own construction but at independently specifiable facts which, left unexplained by earlier theories, have therefore refuted them. A new (...) theory should cogently and directly explain all that its predecessors explain and in addition those particular facts which they conspicuously do not explain. The ideal is to have the simplest possible premises explaining most precisely the widest possible range of problematical facts. · 1. Ronald W. Clark, Einstein: The Life and Times , p.173 n. Ralph W. Rader has written Tennyson's "Maud": The Biographical Genesis. Among his influential articles are "Literary Form in Factual Narrative: The Example of Boswell's Johnson" and "The Concept of Genre and Eighteenth-Century Studies." He is professor of English at the University of California at Berkeley. His contributions to Critical Inquiry are "Explaining Our Literary Understanding: A Response to Jay Schleusener and Stanley Fish" , "The Dramatic Monologue and Related Lyric Forms", and "The Literary Theoretical Contribution of Sheldon Sacks". (shrink)

“O, rocks!” Molly exclaims in impatience with Bloom’s first definition of metempsychosis, “tell us in plain words” . Looking forward, then, we remember that Bloom asks Murphy if he has seen the Rock of Gibraltar and asks further what year that would have been and if Murphy remembers the boats that plied the strait. “I’m tired of all them rocks in the sea,” replies Murphy . Bloom’s interest derives from Molly’s connection with Gibraltar, and Molly herself in her monologue remembers (...) the boats well and thinks of missing the boat at Algeciras , just before the book ends with her thoughts of the awful deepdown torrent,” the tide that moves like a river through the strait. Imaginatively she moves with that torrent, figuratively the torrent of time that plunges from the future to the past, which she accepts, with her yes, going deeply with the flow of life, and with her goes Murphy/Joyce, touching on Gibraltar at last. Molly remembers Ulysses S. Grant getting off a boat in Gibraltar, an occurrence that Adams sees as unduly stretching probability merely in order to bring Molly in incidental touch with a man named Ulysses.19 But remembering that Murphy is a “wily old customer,” we may remember also that the Ulysses of Joyce’s favorite Dante cannot rest with Penelope but, in search of knowledge and excellence, moves on through the two rocks of the straits of Gibraltar, the pillars of Hercules, to further adventure and also to destruction; and we may then think that with this reference, Joyce took pains to tell us that the Ulysses of this book here completes in hidden climax the design and purpose of his work, and sails on to oblivion, or rather to dispersion and reconstitution as everyone in the new adventure of Finnegans Wake. 19. See Adams, Surface and Symbol, p. 233. Ralph W. Rader, professor of English at the University of California, Berkeley, is the author of Tennyson’s “Maud”: The Biographical Genesis. He is currently working on a theoretical study of form in the novel and other genres. His previous contributions to Critical Inquiry include “The Literary Theoretical Contribution of Sheldon Sacks” and “The Dramatic Monologue and Related Lyric Forms”. (shrink)

We extend work of H. Friedman, L. Harrington and P. Welch to the third level of the projective hierarchy. Our main theorems say that (under appropriate background assumptions) the possibility to select definable elements of non-empty sets of reals at the third level of the projective hierarchy is equivalent to the disjunction of determinacy of games at the second level of the projective hierarchy and the existence of a core model (corresponding to this fragment of determinacy) which must then contain (...) all real numbers. The proofs use Sacks forcing with perfect trees and core model techniques. (shrink)

Originally published in 1936, this book presents the ancient Greek text of the paraphrases and quotations of Zeno's philosophical arguments, together with a facing-page English translation and editorial commentary. Detailed notes are incorporated throughout and a bibliography is also included. This book will be of value to anyone with an interest in Zeno and ancient philosophy.

Explores mind-body philosophy from an Asian perspective.

In lieu of an abstract, here is a brief excerpt of the content:The Adoro Te Devote of St. Thomas AquinasSr. Lucia Marie of the Visitation Langford O.P.The Adoro te devote is perhaps the most well-beloved Eucharistic hymn of our time, popularly attributed to St. Thomas Aquinas, the medieval Dominican friar known for his theological treatises as well as his Eucharistic hymnography. Unlike most of Aquinas's work, the poem reveals the intensely personal side of his faith. Rich in theological content and (...) inspiring deep Eucharistic devotion, this poem amply repays a closer investigation. We will look first at the questions of authorship, background, and structure before moving on to a discussion of the text itself.The "Disputed Question" of AuthorshipWhile the Adoro te has traditionally been attributed to St. Thomas Aquinas, the Thomistic authorship of the text was contested in the twentieth century, with two main objections being raised. The first claims that the content of the poem contradicts Thomas's own teachings and cannot have flowed from the same pen. The second objection is historical, claiming that a lack of evidence makes Thomistic authorship improbable.The first objection, claiming that the content of the poem is irreconcilable with Thomistic authorship, takes objection to a line in the poem which seems to claim that sense perception is unreliable and inaccurate, at least with regard to the Eucharist. The text of the Adoro te uses the word fallitur (deceived) with reference to the senses: "Visus, tactus, gustus in te fallitur"—"Sight, touch, taste in you are deceived." Some scholars have claimed that this line contradicts the teaching of Aquinas that the senses are [End Page 365] infallible in regard to their proper sensibles.1 Robert Wielockx addresses this charge in his study of the Adoro te, arguing that "the text does not contradict the continuous teaching of Thomas according to which the senses are not wrong when they judge their proper object, which as far as the Eucharist is concerned, is only the sacramental species."2 The substantial presence of Christ in the Eucharist is a mystery which is not knowable by the senses, and as Paul Murray, O.P., observes: "That's surely the point St. Thomas is making."3 However, the Thomistic insistence that all knowledge comes through our senses is not missing even here. While sight, touch, and taste fall short of comprehending the truth before them, the Adoro te itself proclaims that it is another sense—hearing—which reveals the mystery: "sed auditu solo tute creditur"—"but by hearing alone it is safely believed."4Thus there is no solid objection to Thomistic authorship based on the poem's content. But what about the historical evidence? Dom André Wilmart published a comprehensive study of the manuscript tradition in 1929. Noting that there were no extant copies of the text dating to Aquinas's lifetime and that the biography of Aquinas written by his own Dominican confrere and contemporary, William of Tocco, made no mention of the Adoro te, he considered it most probable that the poem was authored at a later date and ascribed to Aquinas.5However, Dom Wilmart did not know that he was not working with William of Tocco's final version of his work. The publication of a critical edition of William of Tocco's Ystoria Sancti Thome de Aquino in 1996 demonstrated that Tocco published his work in four successive redactions. The fourth and final version of his text (unknown to Dom Wilmart) was finished just before his death in 1323, and in this final version, Tocco includes the text of the Adoro te, attributing its authorship to St. Thomas.6 [End Page 366] Furthermore, Wielockx published a study of the Adoro te in 1998; his investigation of the manuscript tradition found that, of fifty-one sources, forty-four explicitly cite St. Thomas as their author. The remaining sources simply lacked any attribution. We may thus conclude with Wielockx: "External evidence, which must be given priority in sound criticism, wholly favors Thomas Aquinas's authorship of the poem."7BackgroundWith the attribution of the poem to St. Thomas Aquinas on secure footing, we now move to the background of the poem. Unlike Aquinas's Eucharistic hymns such as... (shrink)

Self-esteem can influence educational success, and educational success can also be influenced by self-esteem. Hence, high self-esteem has been recognized as a key predictor of academic success in students. Thus, this study investigates the relationship between self-esteem and anxiety of senior high school students. Employing descriptive-correlational design with 194 senior high school students enrolled in private schools during the school year 2021-2022. Based on the statistical analysis, there is a correlation between self-esteem and anxiety (r.=.125).

The ontic structural realist stance is motivated by a desire to do philosophical justice to the success of science, whilst withstanding the metaphysical undermining generated by the various species of ontological underdetermination. We are, however, as yet in want of general principles to provide a scaffold for the explicit construction of structural ontologies. Here we will attempt to bridge this gap by utilizing the formal procedure of quantization as a guide to ontic structure of modern physical theory. The example of (...) non-relativistic particle mechanics will be considered and, for that case, it will be shown that a viable candidate for an ontic structural realism framework can be constituted in terms of the combination of a state-space with Poisson bracket structure, and a set of observables, with Lie algebra structure. 1 Introduction2 Formulation Underdetermination and Structural Ontologies3 Quantization and Structural Ontologies4 The Case of Non-relativistic Particle Mechanics4.1 Formulation underdetermination4.2 The classical ontology4.3 Quantum theory and the generalized structural ontology4.4 Interpretation of results5 Conclusion and Prospects. (shrink)

Cheating is a serious issue among business students worldwide. However, research investigating the social factors that may help prevent cheating in Chinese higher education is rare. The present study examined two key social relationship factors of perceived teacher-student relationships and peer relationships by the students. It attempted to build a model which addressed the effects of two variables on Chinese business students’ cheating behaviour: the teacher’s approachability and the relationship goal of the students. Two important social influence factors were also (...) tested as mediators: neutralizing attitudes and perceived cheating norms of the students. A student survey was conducted with 1329 questionnaires collected. The results showed the negative effects of both social relationship variables on cheating, and that their effects were fully mediated by neutralizing attitudes. Moreover, perceived cheating norms fully mediated the effect of the teacher’s approachability, but not so for the relationship goal of the students. This study provided novel insights and recommendations for promoting academic integrity in Chinese business schools and universities. (shrink)

Beliefs are freely attributed to God nowadays in Anglo–American philosophical theology. This practice undoubtedly reflects the twentieth–century popularity of the view that knowledge consists of true justified belief . The connection is frequently made explicit. If knowledge is true justified belief then whatever God knows He believes. It would seem that much recent talk of divine beliefs stems from Nelson Pike's widely discussed article, ‘Divine Omniscience and Voluntary Action’. In this essay Pike develops a version of the classic argument for (...) the incompatibility of divine foreknowledge and free will in terms of divine forebelief. He introduces this shift by premising that ‘ A knows X ’ entails ‘A believes X ’. As a result of all this, philosophers have increasingly been using the concept of belief in defining ‘omniscience’. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Sacramental Wisdom:Humilitatio, Eruditio, Exercitatio in the Scholastics and TodaySr. Albert Marie Surmanski O.P.IntroductionThe relationship between human nature and the sacraments is often characterized in a way that takes away from the beauty and power of the sacraments. Sacraments are sometimes viewed today as something basically irrelevant to human life, an interesting spiritual "option" for those who find comfort in ritual. This view leads to a sacramental practice that is (...) occasional, irregular, or nonexistent. Many young people who fail to grasp religion as important to their reality implicitly embrace this perspective. The difficulty parishes have had in the past few years in convincing parishioners to return to liturgical prayer after each wave of the coronavirus pandemic demonstrates this viewpoint.In another perspective, the sacraments might be viewed precisely as expressions of what it means to be human, or one might say, to be human in a world in which God reveals himself at all times.1 In this view, the sacraments [End Page 1391] are our own graced self-expression as a community. They merely make thematic what already happens each moment. Alternatively, they celebrate who we are, and perhaps can be radically updated to reflect changing categories of social identity. 2Both of these viewpoints overlook the fallen state of human nature that cries out for healing from God. The first view does not preclude knowledge of human violence and fragility, but fails to recognize the sacraments as a medicine needed for the remedy of human ills. The second viewpoint, while professing a need for Christ, looks to the human person or community for healing rituals. This approach risks being enmeshed with human nature in a disordered state in such a way that it celebrates human disorder instead of healing it. Alternatively, the viewpoint may lead to the abandonment eschatological hope and wither into inanity.There are profound metaphysical and anthropological issues that play out in these two opposite but strangely united viewpoints. Rather than directly analyze these errors, this paper would like to propose the recovery of a medieval viewpoint that offers another perspective. This is Hugh of St. Victor's explanation that the sacraments fit and heal human nature through offering humanity humility, instruction, and exercise. 3 This paper will briefly survey Hugh's contribution, analyze its reception by several of the thirteenth-century Scholastics, shows its deep rootedness in biblical wisdom, and then show how it fruitfully opposes current-day challenges.Hugh of St. VictorHugh of St. Victor was a twelfth-century canon of the Parisian Abbey of St. Victor. The most influential writer of the Victorine school, his work is characterized by an Augustinian concern for the re-formation of the image of God in man, a sense of the wise ordering of salvation history, and an emphasis on both virtue and liturgical practice. In his masterwork, De Sacramentis Christianae Fidei, Hugh of St. Victor divides the works of God into two main periods: the work of creation and the work of restoration. Within the [End Page 1392] work of restoration, there are three periods: the period of the natural law, that of the Mosaic or written law, and that of grace, inaugurated by Christ.4 His book's division into two parts cuts across these distinctions: Part 1 of Hugh's text covers creation, the restoration in general, faith, sacraments in general, as well as particulars of the sacraments of the periods of the natural and written law. Part 2 includes the Incarnation, the Church, various Christian rituals, and the final restoration of Christ's return.Hugh is writing around the time when theologians began to list the number of the sacraments of the Church as seven. Emerging from the wider use of the term, Hugh uses the word "sacrament" in a wide sense, but distinguishes several categories of sacraments. Following Dominique Poirel, scholars recognize that Hugh uses the word sacramentum in five main ways.5 The first is a general definition: (1) any sign of anything sacred. The second through fourth are more specific usages, to which we do not commonly give the term "sacrament" today: (2) Scripture, which signifies sacred realities both through its text and the... (shrink)