We apply Mints’ technique for proving the termination of the epsilon substitution method via cut-elimination to the system of Peano Arithmetic with Transfinite Induction given by Arai.

We propose a new method for constructing Turing ideals satisfying principles of reverse mathematics below the Chain–Antichain (CAC) Principle. Using this method, we are able to prove several new separations in the presence of Weak König’s Lemma (WKL), including showing that CAC+WKL does not imply the thin set theorem for pairs, and that the principle “the product of well-quasi-orders is a well-quasi-order” is strictly between CAC and the Ascending/Descending Sequences principle, even in the presence of WKL.

Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic.

We extend theories of reverse mathematics by a non-principal ultrafilter, and show that these are conservative extensions of the usual theories ACA0, ATR0, and [Formula: see text].

In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from RT, Ramsey's Theorem for Pairs. These principles tend to fall outside of the "big five" systems of reverse mathematics and a complicated picture of subsystems below RT has emerged. In this paper, we answer two open questions concerning these subsystems, specifically that ADS is not equivalent to CAC and that EM is not equivalent to RT.

The technique of using infinitary rules in an ordinal analysis has been one of the most productive developments in ordinal analysis. Unfortunately, one of the most advanced variants, the Buchholz Ωμ rule, does not apply to systems much stronger than -comprehension. In this paper, we propose a new extension of the Ω rule using game-theoretic quantifiers. We apply this to a system of inductive definitions with at least the strength of a recursively inaccessible ordinal.

In reverse mathematics, it is possible to have a curious situation where we know that an implication does not reverse, but appear to have no information on how to weaken the assumption while preserving the conclusion (other than reducing all the way to the tautology of assuming the conclusion). A main cause of this phenomenon is the proof of a $\Pi^1_2$ sentence from the theory $\mathbf{\Pi^{\textbf{1}}_{\textbf{1}}-CA_{\textbf{0}}}$. Using methods based on the functional interpretation, we introduce a family of weakenings of $\mathbf{\Pi^{\textbf{1}}_{\textbf{1}}-CA_{\textbf{0}}}$ (...) and use them to give new upper bounds for the Nash-Williams Theorem of wqo theory and Menger's Theorem for countable graphs. (shrink)

We give a short, explicit proof of Hindman's Theorem that in every finite coloring of the integers, there is an infinite set all of whose finite sums have the same color. We give several examples of colorings of the integers which do not have computable witnesses to Hindman's Theorem.

We present a realizability interpretation for classical analysis–an association of a term to every proof so that the terms assigned to existential formulas represent witnesses to the truth of that formula. For classical proofs of Π2 sentences ∀x∃yA(x,y), this provides a recursive type 1 function which computes the function given by f(x)=y iff y is the least number such that A(x,y).

We characterize the completely determined Borel subsets of HYP as exactly the [Formula: see text] subsets of HYP. As a result, HYP believes there is a Borel well-ordering of the reals, that the Borel Dual Ramsey Theorem fails, and that every Borel d-regular bipartite graph has a Borel perfect matching, among other examples. Therefore, the Borel Dual Ramsey Theorem and several theorems of descriptive combinatorics are not theories of hyperarithmetic analysis. In the case of the Borel Dual Ramsey Theorem, this (...) answers a question of Astor, Dzhafarov, Montalbán, Solomon and the third author. (shrink)

The \-substitution method is a technique for giving consistency proofs for theories of arithmetic. We use this technique to give a proof of the consistency of the impredicative theory \ using a variant of the cut-elimination formalism introduced by Mints.

We show that any countable model of a model complete theory has an elementary extension with a “pseudofinite-like” quasi-dimension that detects dividing.

Extending Gödel's Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees.

According to the Furstenberg-Zimmer structure theorem, every measure-preserving system has a maximal distal factor, and is weak mixing relative to that factor. Furstenberg and Katznelson used this structural analysis of measure-preserving systems to provide a perspicuous proof of Szemer\'edi's theorem. Beleznay and Foreman showed that, in general, the transfinite construction of the maximal distal factor of a separable measure-preserving system can extend arbitrarily far into the countable ordinals. Here we show that the Furstenberg-Katznelson proof does not require the full strength (...) of the maximal distal factor, in the sense that the proof only depends on a combinatorial weakening of its properties. We show that this combinatorially weaker property obtains fairly low in the transfinite construction, namely, by the $\omega^{\omega^\omega}$th level. (shrink)

We describe an Aldous–Hoover-type characterization of random relational structures that are exchangeable relative to a fixed structure which may have various equivalence relations. Our main theorem gives the common generalization of the results on relative exchangeability due to Ackerman \)-invariant measures: part I, 2015. arXiv:1509.06170) and Crane and Towsner and hierarchical exchangeability results due to Austin and Panchenko :809–823, 2014).

So much for the Aesthetic. We can now proceed to the Analytic, the philosophical importance of which is much greater. Kant's main contentions in this part of his work can be summed up in; two propositions: human understanding contains certain a priori concepts, and on these are based certain non-empirical principles; these concepts are only general concepts of a phenomenal object, and therefore the principles in question are only prescriptive to sense-experience. As has already been said, interest in the first (...) proposition has distracted attention from the fact that the important thing Kant has to say is contained in the second. (shrink)

This book constitutes one of the most important contributions to recent Kant scholarship. In it, one of the pre-eminent interpreters of Kant, Henry Allison, offers a comprehensive, systematic, and philosophically astute account of all aspects of Kant's views on aesthetics. The first part of the book analyses Kant's conception of reflective judgment and its connections with both empirical knowledge and judgments of taste. The second and third parts treat two questions that Allison insists must be kept distinct: the normativity (...) of pure judgments of taste, and the moral and systematic significance of taste. The fourth part considers two important topics often neglected in the study of Kant's aesthetics: his conceptions of fine art, and the sublime. (shrink)

Few books have so firmly established their place in American literature as The Education of Henry Adams. When it was first published in 1918, it became an instant bestseller and went on to win the Pulitzer Prize. More than eighty years later, in an age of self-reflection and exhaustive memoirs, The Education still stands as perhaps the greatest American autobiography. The son of a diplomat, the grandson and great-grandson of two American presidents, a man of extraordinary gifts and learning (...) in his own right, Henry Adams recounts his life from his birth in 1838 and upbringing as a Boston Brahmin, through the Civil War, the nation's industrial expansion, and its emergence as a world power. In the process, he gives us a brilliant history of a changing country as well as a thoughtful, humane, often tender exploration of himself. From the original publisher, this edition of The Education of Henry Adams, newly introduced by Donald Hall, celebrates and honors this classic work on what it means to be an American. (shrink)

I introduce game-theoretic models for threats to the discussion of threats in speech act theory. I first distinguish three categories of verbal threats: conditional threats, categorical threats, and covert threats. I establish that all categories of threats can be characterized in terms of an underlying conditional structure. I argue that the aim—or illocutionary point—of a threat is to change the conditions under which an agent makes decisions in a game. Threats are moves in a game that instantiate a subgame in (...) which the addressee is ‘under threat’. (shrink)

The system presented by the author in The Logical Foundations of Statistical Inference suffered from certain technical difficulties, and from a major practical difficulty; it was hard to be sure, in discussing examples and applications, when you had got hold of the right reference class. The present paper, concerned mainly with the characterization of randomness, resolves the technical difficulties and provides a well structured framework for the choice of a reference class. The definition of randomness that leads to this framework (...) is simplified and clarified in a number of respects. It resolves certain puzzles raised by S. Spielman and W. Harper in their contributions to Profiles: Henry E. Kyburg, Jr. and Isaac Levi 1982). (shrink)

Organizations continue to show renewed focus on managing their ethics programs by developing organizational infrastructures to support their ethics implementation efforts. An important part of this process has been the creation of an ethics officer position. Whether individuals appointed to the position are successful in the role or not may depend on a number of factors. This study presents a suggested framework for their effectiveness. The framework includes a focus on personal, organizational and situational factors to predict performance in the (...) role. The study examines the complex nature of the role. These include task complexity, low task visibility, role conflict, and role ambiguity. Personal, organizational and situational factors that can serve as buffers against the complexities associated with the role are presented. The study suggests that individuals with certain competencies and orientations may be better suitable for the ethics position, and firms need to consider key organizational and situational issues critical to the performance of an ethics officer. The research and practice implications of the study are given. (shrink)

The original text, written in the language and style of 1909, is almost completely unreadable in 2011. I have taken the liberty of editing it and paraphrasing it for the sake of readability; I have made every effort to preserve the author’s original meaning. Section headings and tables have been added by Prof. Steinhart. Note that Figure 1 is by Adams.

We are often justified in acting on the basis of evidential confirmation. I argue that such evidence supports belief in non-quantificational generic generalizations, rather than universally quantified generalizations. I show how this account supports, rather than undermines, a Bayesian account of confirmation. Induction from confirming instances of a generalization to belief in the corresponding generic is part of a reasoning instinct that is typically (but not always) correct, and allows us to approximate the predictions that formal epistemology would make.

Henry Richardson argues that we can determine our ends rationally. He constructs a rich and original theory of how we can reason about our final goals. Richardson defuses the counter-arguments for the limits of rational deliberation, and develops interesting ideas about how his model might be extended to interpersonal deliberation of ends, taking him to the borders of political theory. Along the way Richardson offers illuminating discussions of, inter alia, Aristotle, Aquinas, Sidgwick, and Dewey, as well as the work (...) of several contemporary philosophers. (shrink)

I am going to be discussing a mode of moral responsibility that anglophone philosophers have largely neglected. It is a type of responsibility that looks to the future rather than the past. Because this forward-looking moral responsibility is relatively unfamiliar in the lexicon of analytic philosophy, many of my locutions will initially strike many readers as odd. As a matter of everyday speech, however, the notion of forward-looking moral responsibility is perfectly familiar. Today, for instance, I said I would be (...) responsible for watching my nieces while they swam. Neglecting this responsibility would have been a moral fault. When people marry, they undertake responsibilities, of moral import, of fidelity and mutual support. When people have children, they accrue moral responsibilities to feed, rear, and educate them. Not all forward-looking responsibilities are moral. While finishing this essay, I have had to keep an eye on a number of my administrative responsibilities, and, while reading it, you may well be occasionally distracted by some of your own. The notion of a responsibility that we accrue or take on, to look out for some range of concerns over some range of the future, is, then, perfectly familiar. Because this common notion of forward-looking responsibility has not been integrated into recent moral theory, however, my philosophical discussion of it will initially seem strange. (shrink)

Giroux argues that challenge gives new meaning to the importance of resistance, the relevance of pedagogy, and the significance of political agency.

First, a comment on a pessimistic note: Salmon says we can't be sure there is any such thing as inductive inference: in demanding that some explanations have the form of correct inductive inferences, “we may be laying down a requirement which cannot be fulfilled.” To doubt that we can fulfill that requirement is to doubt that we can formalize inductive logic. It may be true, but why begin the fight by throwing in the sponge? It is also true that there (...) are difficulties involved in formalizing acceptance rules for inductive conclusions, but these difficulties may be overcome. It is false to claim that we ‘cannot claim to know exactly’ what these acceptance rules are. Only two years ago I did just that. It was true that my claim was shown to be erroneous a year later, but that fate can befall almost any worthwhile claim. (shrink)

Henri Bergson (1859-1941) is one of the truly great philosophers of the Modernist period, and there is currently a major renaissance of interest in his unduly neglected texts and ideas amongst philosophers, literary theorists, and social theorists. Mind-Energy is a collection of essays and lectures from the period 1901-13 and has long been out of print. It features essays on life and consciousness, soul and body, mind and brain, and on dreams, memory and the phenomenon of false recognition; the insights (...) Bergson develops in them remain highly pertinent to contemporary work in the philosophy of mind. (shrink)

I wish to speak a word for Nature, for absolute freedom and wildness, as contrasted with a freedom and culture merely civil,—to regard man as an inhabitant, or a part and parcel of Nature, rather than a member of society. I wish to make an extreme statement, if so I may make an emphatic one, for there are enough champions of civilization: the minister and the school committee and every one of you will take care of that.