Online research in philosophy

In December’s Quadrant James Franklin asked “Is Jensenism compatible with Christianity?” and claimed of Sydney Anglicans that they “fear the gospels, for the gospel message is inconvenient”. This brand of “narrow” “Bible-based” Christianity pits Paul against Jesus, he says; engages in selective reading of the Bible; and creates “an inwardlooking and recent sect.”.

Our main results are: Theorem 1. Con(ZFC + "every function $f : \omega_{1} \rightarrow \omega_1$ is dominated by a canonical function") implies Con(ZFC + "there exists an inaccessible limit of measurable cardinals"). [In fact equiconsistency holds.] Theorem 3. Con(ZFC + "there exists a non-regular uniform ultrafilter on ω1") implies Con(ZFC + "there exists an inaccessible stationary limit of measurable cardinals"). Theorem 5. Con (ZFC + "there exists an $\omega_{1}-sequence$ T of $\omega_{1}-complete$ uniform filters on ω1 s.t. every $A \subseteq \omega_1$ (...) is measurable w.r.t. a filter in T (Ulam property)") implies Con(ZFC + "there exists an inaccessible stationary limit of measurable cardinals"). We start with a discussion of the canonical functions and look at some combinatorial principles. Assuming the domination property of Theorem 1, we use the Ketonen diagram to show that $\omega_{2}^V$ is a limit of measurable cardinals in Jensen's core model $K_{MO}$ for measures of order zero. Using related arguments we show that $\omega_{2}^V$ is a stationary limit of measurable cardinals in $K_{MO}$ , if there exists a weakly normal ultrafilter on ω1. The proof yields some other results, e.g., on the consistency strength of weak*-saturated fiters on ω1, which are of interest in view of the classical Ulam problem. (shrink)

Nietzsche's Critique of Staticism Manuel Dries Part 1: Time, History, Method Nietzsche's Cultural Criticism and his Historical Methodology 23 Andrea Orsucci Thucydides, Nietzsche, and Williams 35 Raymond Geuss The Late Nietzsche's Fundamental Critique of Historical Scholarship 51 Thomas H. Brobjer Part II: Genealogy, Time, Becoming Nietzsche's Timely Genealogy: An Exercise in Anti-Reductionist Naturalism 63 Tinneke Beeckman From Kantian Temporality to Nietzschean Naturalism 75 R. Kevin Hill Nietzsche's Problem of the Past 87 John Richardson Towards Adualism: Becoming and Nihilism in Nietzsche's (...) Philosophy 113 Mamuel Dries Part III: Eternal Recurrence, Meaning, Agency Shocking Time: Reading Eternal Recurrence Literally 149 Lawrence J. Hatab Suicide, Meaning, and Redemption 163 Paul S. Loeb Nietzsche and the Temporality of (Self-)Legislation I91 Herman W. Siemens Part IV: Nietzsche's Contemporaries Geschichte or Historie? Nietzsche's Second Untimely Meditation in the Context of Nineteenth-Century Philological Studies 213 Anthonyl K. Jensen 'An Uncanny Re-Awakening': Nietzsche's Renascence of the Renaissance out of the Spirit of Jacob Burckhardt 231 Martin A. Ruehl Part V: Tragic and Musical Time Metaphysical and Historical Claims in The Birth of Tragedy 275 Katherine Harloe Nietzsche's Musical Conception of Time 291 Jonathan R. Cohen. (shrink)

Where $\underline{a}$ is a Turing degree and ξ is an ordinal $ , the result of performing ξ jumps on $\underline{a},\underline{a}^{(\xi)}$ , is defined set-theoretically, using Jensen's fine-structure results. This operation appears to be the natural extension through $(\aleph_1)^{L^\underline{a}}$ of the ordinary jump operations. We describe this operation in more degree-theoretic terms, examine how much of it could be defined in degree-theoretic terms and compare it to the single jump operation.

Where AR is the set of arithmetic Turing degrees, 0 (ω ) is the least member of { $\mathbf{\alpha}^{(2)}|\mathbf{a}$ is an upper bound on AR}. This situation is quite different if we examine HYP, the set of hyperarithmetic degrees. We shall prove (Corollary 1) that there is an a, an upper bound on HYP, whose hyperjump is the degree of Kleene's O. This paper generalizes this example, using an iteration of the jump operation into the transfinite which is based on (...) results of Jensen and is detailed in [3] and [4]. In $\S1$ we review the basic definitions from [3] which are needed to state the general results. (shrink)