America’s unfinished revolution The_revolutionary spirit that runs through American history and whose_founding_father and greatest advocate was Thomas Paine is fiercely traced in Thomas Paine and the Promise of America ._Showing how Paine turned Americans into radicals—and how we have remained radicals at heart ever since—Harvey J. Kaye presents the nation’s democratic story with wit, subtlety, and, above all, passion. Paine was one of the most remarkable political writers of the modern world and the greatest radical of a radical age._Through (...) writings like Common Sense —and words such as “The sun never shined on a cause of greater worth,” “We have it in our power to begin the world over again,” and “These are the times that try men’s souls”—he not only turned America’s colonial rebellion into a revolutionary war but, as Kaye demonstrates, articulated an American identity charged with exceptional purpose and promise. Beginning with Paine’s life and ideas and following their vigorous influence through to our own day, Thomas Paine and the Promise of America reveals how, while the powers that be repeatedly sought to suppress, defame, and most recently co-opt Paine’s memory, generations of radical and liberal Americans turned to Paine for inspiration as they endeavored to expand American freedom, equality, and democracy. (shrink)

Two countable well orderings are weakly comparable if there is an order preserving injection of one into the other. We say the well orderings are strongly comparable if the injection is an isomorphism between one ordering and an initial segment of the other. In [5], Friedman announced that the statement “any two countable well orderings are strongly comparable” is equivalent to ATR 0 . Simpson provides a detailed proof of this result in Chapter 5 of [13]. More recently, Friedman has (...) proved that the statement “any two countable well orderings are weakly comparable” is equivalent to ATR 0 . The main goal of this paper is to give a detailed exposition of this result. (shrink)

Based on the relevant logic R, the system R# was proposed as a relevant Peano arithmetic. R# has many nice properties: the most conspicuous theorems of classical Peano arithmetic PA are readily provable therein; it is readily and effectively shown to be nontrivial; it incorporates both intuitionist and classical proof methods. But it is shown here that R# is properly weaker than PA, in the sense that there is a strictly positive theorem QRF of PA which is unprovable in R#. (...) The reason is interesting: if PA is slightly weakened to a subtheory P+, it admits the complex ring C as a model; thus QRF is chosen to be a theorem of PA but false in C. Inasmuch as all strictly positive theorems of R# are already theorems of P+, this nonconservativity result shows that QRF is also a nontheorem of R#. As a consequence, Ackermann's rule γ is inadmissible in R#. Accordingly, an extension of R# which retains its good features is desired. The system R##, got by adding an omega-rule, is such an extension. Central question: is there an effectively axiomatizable system intermediate between R# and R##, which does formalize arithmetic on relevant principles, but also admits γ in a natural way? (shrink)

Edmund D. Pellegrino, John Collins Harvey, Kevin T. Fitzgerald, SJ; Must the Church be Mute Lest Its Truths be Distorted? A Response to Engelhardt, Christian bi.

In the spring of 2013, project leaders who received funding from the John Templeton Foundation’s program “Can GM Crops Help to Feed the World?” met in England to discuss progress on funded projects and to identify common objectives and research interests. The collection of essays in this special symposium is one outcome of that meeting. This introduction provides background on the symposium’s theme of understanding the challenges to smallholder farmers having a voice. Farmer voice is important not only in debates (...) about genetically modified crops but also for policies, technologies and other efforts designed by interests seeking ostensibly to improve the livelihoods of smallholder farmers. (shrink)

We study the formalization within sybsystems of second-order arithmetic of theorems concerning periodic points in dynamical systems on the real line. We show that Sharkovsky's theorem is provable in WKL0. We show that, with an additional assumption, Sharkovsky's theorem is provable in RCA0. We show that the existence for all n of n-fold iterates of continuous mappings of the closed unit interval into itself is equivalent to the disjunction of Σ02 induction and weak König's lemma.

Contemplating the catastrophic course of the Nazi Revolution we may well find it all too easy to see nothing in the spectacle but the nether darkness made visible; and if we are advised that it is not merely permissible but highly advisable to learn from the enemy, we may be tempted to think that whatever the Nazi war-machine has to teach the strategist and the technician, the political history of Germany in the last decade, and in particular the political ideology (...) that has imposed itself upon the German mind with such apparent thoroughness, can yield only the negative lesson of a warning, by displaying upon the world-wide stage the doomful consequences of wrong principles ruthlessly pushed to their extreme. But it is certainly an error to deny that nothing of more positive value has emerged out of the revolutionary cauldron: and indeed it would be more than strange, where such whole-hearted energies of mind are being enlisted in the evil cause of Nazism, if none of its votaries had ever stumbled for a time into wisdom. (shrink)

The life, works, and philosophy of rabbi Hasdai Crescas.

El presente trabajo complemenJa las referencias a la lengua aut6ctona de los día­ guitas chilenos, en la encrucijada histórica de la conquista hispana en el siglo Xlll , cuya primera parte se publicó en WGOS N 2 l.En este número conJrastamos las hipó­ tesis de don Ricardo Latcham con la crftica de don Jorge /ribarren; se ofrece, aderruís, un suscinJo panorama de la situación lingüística en el noroeste argenJino, y las anota­ ciones espedficamenJe lingüísticas sobre el "cacán" de Antonio Tovar, (...) Cestmir Lou­ kotka y RodtJ/fo Schuller, y nuestras propias conclusiones. The following information about the chilean diaguitas'indigenous tongue for the historie period of the spanish conquest complemenJs the previous report published in thefirst issue of the magazine LOCOS. Ricardo Latcham's hypothesis and Jorge lribarren critica/ position are here confronJed in addition to a brief account of the linguistic situation in south-western ArgenJina. There is also a presenJation of sorne specif eally linguistic statemenJs about "cacán" by Antonio Tovar, Cestmir Loukotka and Rodolfo Schuller as well as our own conclusions. (shrink)

The subtle, almost ineffable, and ineffable cardinals were introduced in an unpublished 1971 manuscript of R. Jensen and K. Kunen. The concepts were extended to that of k-subtle, k-almost ineffable, and k-ineffable cardinals in 1975 by J. Baumgartner. In this paper we give a self contained treatment of the basic facts about this level of the large cardinal hierarchy, which were established by J. Baumgartner. In particular, we give a proof that the k-subtle, k-almost ineffable, and k-ineffable cardinals define three (...) properly intertwined hierarchies with the same limit, lying strictly above “total indescribability” and strictly below “arrowing ω”. The innovation here is presented in Section 2, where we take a distinctly minimalist approach. Here the subtle cardinal hierarchy is characterized by very elementary properties that do not mention closed unbounded or stationary sets. This development culminates in a characterization of the hierarchy by means of a striking universal second-order property of linear orderings. (shrink)

We now fix A ⊆ Q. We study a fundamental class of digraphs associated with A, which we call the A-digraphs. An A,kdigraph is a digraph (Ak,E), where E is an order invariant subset of A2k in the following sense. For all x,y ∈ A2k, if x,y have the same order type then x ∈ E ↔ y ∈ E.

MARX’s debt to Aristotle is acknowledged in part 1 of Capital, admittedly the most difficult and, as will be argued, the most fundamental part of his principal work. His principal work is the one which establishes that the labor theory of value holds not only in the state of nature, as for Locke, nor only in primitive society, as for Adam Smith, but also in the highest civilized society and, as against Ricardo, in such a way as to prove that (...) the proletariat is and must be exploited but will and can never exploit. With the analysis and reduction of capital into labor, the possibility of freedom in this new meaning, which is merely asserted in the "humanism" of his earlier writings, is proven and secured with the necessity of science. (shrink)

We consider properties of sets in an intuitionistic setting corresponding to large cardinals in classical set theory. Adding such ‘large set axioms’ to intuitionistic ZF set theory does not violate well-know metamathematical properties of intuitionistic systems. Moreover, we consider statements in constructive analysis equivalent to the consistency of such ‘large set axioms’.

In a modal system of arithmetic, a theory S has the modal disjunction property if whenever $S \vdash \square\varphi \vee \square\psi$ , either $S \vdash \square\varphi$ or $S \vdash \square\psi. S$ has the modal numerical existence property if whenever $S \vdash \exists x\square\varphi(x)$ , there is some natural number n such that $S \vdash \square\varphi(\mathbf{n})$ . Under certain broadly applicable assumptions, these two properties are equivalent.

Certainty (and the lack thereof) is a major issue in mathematics and computer science. Mathematicians strongly believe in a special kind of certainty for their theorems.

An unprovable theorem is a mathematical result that can-not be proved using the com-monly accepted axioms for mathematics (Zermelo-Frankel plus the axiom of choice), but can be proved by using the higher infinities known as large cardinals. Large car-dinal axioms have been the main proposal for new axioms originating with Gödel.

We have been recently engaged in this search, and have announced a long series of successively simpler and more convincing examples. See [Fr09-10].

We give a complete proof that all 3 quantifier sentences in the primitive notation of set theory (Œ,=), are decided in ZFC, and in fact in a weak fragment of ZF without the power set axiom. We obtain information concerning witnesses of 2 quantifier formulas with one free variable. There is a 5 quantifier sentence that is not decided in ZFC (see [Fr02]).

At least four different frameworks — psychiatric, cognitive, functional and decision-making — are used in the evaluation of competence, all of which remain more or less unrelated in the literature. In the first section of this paper we consider various meanings of competence, in order to arrive at a definition of the term relevant to the medical and legal setting. Patient or client competence, we conclude, refers to the practical abilities that individuals employ in pursuing their own autonomous goals in (...) life. We then show how a systematic categorization of these practical abilities — which we call a taxonomy of practical judgment — allows us to show when the traditional frameworks for the evaluation of competence may or may not be useful in the evaluation of a particular competence.In the final section we explore some of the normative considerations underlying the taxonomy. For instance, competence is not only related to intrinsic abilities but to resources available in the community. Here we touch on questions related to the fair distribution of community resources. (shrink)

This is widely accepted, inside and outside philosophy, but one can spend an entire career clarifying, justifying, and amplifying on this statement. Certainly a graduate student career.

S. Adams, W. Ambrose, A. Andretta, H. Becker, R. Camerlo, C. Champetier, J.P.R. Christensen, D.E. Cohen, A. Connes. C. Dellacherie, R. Dougherty, R.H. Farrell, F. Feldman, A. Furman, D. Gaboriau, S. Gao, V. Ya. Golodets, P. Hahn, P. de la Harpe, G. Hjorth, S. Jackson, S. Kahane, A.S. Kechris, A. Louveau,, R. Lyons, P.-A. Meyer, C.C. Moore, M.G. Nadkarni, C. Nebbia, A.L.T. Patterson, U. Krengel, A.J. Kuntz, J.-P. Serre, S.D. Sinel'shchikov, T. Slaman, Solecki, R. Spatzier, J. Steel, D. Sullivan, S. (...) Thomas, A. Valette, V.S. Varadarajan, B. Velickovic, B. Weiss, J.D.M. Wright, R.J. Zimmer. (shrink)

The classical Ulm theory provides a complete set of invariants for countable abelian p-groups, and hence also for countable torsion abelian groups. These invariants involve countable ordinals. One can read off many simple structural properties of such groups directly from the Ulm theory. We carry out a reverse mathematics analysis of several such properties. In many cases, we reverse to ATR0, thereby demonstrating a kind of necessary use of Ulm theory.

BRT is always based on a choice of BRT setting. A BRT setting is a pair (V,K), where V is an interesting family of multivariate functions. K is an interesting family of sets. In this talk, we will only consider V,K, where V is an interesting family of multivariate functions from N into N. K is an interesting family of subsets of N.