We study the fine structure of the core model for one Woodin cardinal, building of the work of Mitchell and Steel on inner models of the form . We generalize to some combinatorial principles that were shown by Jensen to hold in L. We show that satisfies the statement: “□κ holds whenever κ the least measurable cardinal λ of order λ++”. We introduce a hierarchy of combinatorial principles □κ, λ for 1 λ κ such that □κ□κ, 1 □κ, λ □κ, (...) κ□κ*. We prove that if holds in V. As an application, we show that ZFC + PFA Con. We also obtain one Woodin cardinal as a lower bound on the consistency strength of stationary reflection at κ+ for a singular, countably closed limit cardinal κ such that # exists; likewise for the failure of □κ* at such a κ. (shrink)

We present a general construction of a □κ-sequence in Jensen's fine structural extender models. This construction yields a local definition of a canonical □κ-sequence as well as a characterization of those cardinals κ, for which the principle □κ fails. Such cardinals are called subcompact and can be described in terms of elementary embeddings. Our construction is carried out abstractly, making use only of a few fine structural properties of levels of the model, such as solidity and condensation.

We define what it means for a function on ω1 to be a collapsing function for λ and show that if there exists a collapsing function for +, then there is no precipitous ideal on ω1. We show that a collapsing function for ω2 can be added by forcing. We define what it means to be a weakly ω1-Erdös cardinal and show that in L[E], there is a collapsing function for λ iff λ is less than the least weakly ω1-Erdös (...) cardinal. As a corollary to our results and a theorem of Neeman, the existence of a Woodin limit of Woodin cardinals does not imply the existence of precipitous ideals on ω1. We also show that the following statements hold in L[E]. The least cardinal λ with the Chang property ↠ is equal to the least ω1-Erdös cardinal. In particular, if j is a generic elementary embedding that arises from non-stationary tower forcing up to a Woodin cardinal, then the minimum possible value of j is the least ω1-Erdös cardinal. (shrink)

“Rational beings pursue and value truth. Intellectual conduct is to be judged, accordingly, by how well it aids our pursuit of that ideal.” What does this mean, and is it true? Even if intelligent life had never evolved or otherwise existed, Venus would still have orbited the Sun, so it would still have been true that Venus orbited the Sun. It is not the being thus true of what is true that we value indiscriminately. Some truths are good, but not (...) all, far from it. In loving the truth, then, what we value is not the being true of the truths. What we value in pursuing truth is rather our grasping it, our having it. What does this mean? Only through believing it does one relevantly have a truth : we have the truth that snow is white by believing that snow is white. In pursuing the truth what we want is true beliefs. Suppose you enter your dentist’s waiting room and find all the magazines taken. Deprived of reading matter, you’re sure to doze off, but you need no sleep. Are you then rationally bound to reach for the telephone book in pursuit of truth? Were you not to do so, you would forfeit a chance to pluck some desired goods within easy reach. If random telephone numbers do not elicit a wide enough yawn, consider a randomly selected cubic foot of the Sahara. Here is a trove of facts, of the form grain x is so many millimeters in direction D from grain y, than which few can be of less interest. Or take some bit of trivia known to me at the moment: say, that it was sunny in Rhode Island at noon on October 21, 1999. I confess that I will not rue my loss of this information, nor do I care either that or how early it will be gone. As interpreted so far, the view that we rationally want truth as such reduces to absurdity, or is at best problematic. What then is it we want in pursuing truth? If it is not after all true beliefs indiscriminately, what then is it? A manageable number of true beliefs? Obviously not; it is not just a matter of numbers. (shrink)

Much has been written about the interpretation of Plato in the last thirty years. Once interpreted as a revolutionary of the left, and a prophet of Socialism, he has lately been interpreted as a revolutionary of the Right and a forerunner of Fascism. In this book Plato appears as himself âe" a revolutionary indeed, and even an authoritarian, but a revolutionary of the pure idea of the Good, and an authoritarian of the pure reason, unattached either to the Right or (...) the Left. (shrink)

HUME’S PHILOSOPHICAL SUBVERSION OF RELIGION, NATURAL AND REVEALED, WAS LIFELONG: THE "RELIGIOUS HYPOTHESIS" IS EMPTY. SO I HAVE ARGUED IN A NEW READING OF THE "DIALOGUES". THE ONLY HOPE FOR HUMANITY LIES IN MAN HIMSELF. HUME DISTINGUISHES BETWEEN THE "VULGAR" AND THE "ENLIGHTENED." AT THE APEX OF THE "ENLIGHTENED" STAND THE "HEROES IN PHILOSOPHY," OF WHOM ONLY GALILEO AND NEWTON ARE SPECIFIED. THE "ENLIGHTENED" PROVIDE LEADERSHIP AND KNOWLEDGE, A DUTY WE MAY VIEW AS THE "RELIGION OF MAN." QUITE POSSIBLY HUME (...) CONSIDERED HIMSELF THE THIRD "HERO IN PHILOSOPHY." EVIDENCE IS PROVIDED BY HIS TRIUMPHAL RECEPTION IN PARIS, 1763-1765: "THEY CONSIDER ME AS ONE OF THE GREATEST GENIUSES IN THE WORLD." THUS THE "RELIGION OF MAN" IRONICALLY CONSTITUTES HUME’S PERSONAL RELIGION. (shrink)

This is a review of a volume including Locke's Second Treatise, Rousseau's Social Contract, and Hume's "Of the Original Contract." The Rousseau essay is translated by Gerard Hopkins, and Ernest Baker provides an introduction to the texts.

William of Auvergne and His Treatise De Anima I. Introduction William of Auvergne, Bishop of Paris from until his death in, is of interest to us chiefly ...

A. Knowledge and Justification: The nature of epistemic justification and its supervenience.B. Understanding and Validation: Two projects of epistemology, one to understand justification, the other to promote it.

True, the believing could not in those cir- cumstances be there the object of belief being there. accept a notion of correspondence or reference according to which a word or a brain state of ours can refer to some external or or independent (This no more forces.

Satire on politics, literature and art. James Joyce, Lenin, and Dadaist, Tristan Tzara come together in the memories of an obscure English diplomat (Henry Wilfred Carr) in Zurich.

The first paragraph of the article reads: "Classical analysis is concerned neither with cataloguing usage nor with intellectual therapy (except of course by aiming to satisfy curiosity and remove puzzlement). Of recent sorts of analysis, it's the attempt to find the "logical structure of the world" or the "logical form" of various facts that chiefly claims our attention. But philosophers in every period have been absorbed by such analysis. Think of the Greek search for real definitions. Or think of metaphysical (...) appearance/reality distinctions, and attempted reductions of appearance to reality: to monads, to spirits and ideas, or to atomic facts.". (shrink)

We prove that if image is a Jensen extender model, then image satisfies the Gap-1 morass principle. As a corollary to this and a theorem of Jensen, the model image satisfies the Gap-2 Cardinal Transfer Property → for all infinite cardinals κ and λ.

According to nomological accounts of causation causal connections among events or states must be mediated by contingent laws of nature. Three types of causal connection are cited and discussed in opposition to such nomological accounts: (a) material causation (as when a zygote is generated by the union of an ovum and a sperm); (b) consequentialist causation (as when an apple is chromatically colored as a result of being red); (c) inclusive causation (as when a board is on a stump in (...) consequence of its having been placed there by a carpenter). These are all source-consequence relations or result-yielding relations and they are all cases of necessitation, each with its own distinguishing features. (shrink)

Truth centered epistemology puts truth at the center in more ways than one. For one thing, it makes truth a main cognitive goal of inquiry. For another, it explains other main epistemic concepts in terms of truth. Knowledge itself, for example, is explained as belief that meets certain other conditions, among them being true. And a belief is said to be rationally or epistemically justified or apt, which it must be in order to be knowledge, only if it derives from (...) a truth-conducive faculty, an intellectual virtue. What defensible theories of truth are open to such truth-centered epistemology? That is our main question. (shrink)

Hume's Dialogues Concerning Natural Religion are still much with us. What appears to be the definitive edition was published by Professor Norman Kemp Smith in 1935 with a learned introduction which, among other things, assembled a mass of evidence pointing to the conclusion that Philo is to be identified with Hume himself, and that Hume in the Dialogues is deliberately trying to undermine the religious hypothesis. Though these conclusions have been widely accepted, Dr. B. M. Laing, in the April issue (...) of Philosophy , strenuously attacked them in an ingenious argument based in part on his already published thesis that Hume's fundamental philosophy is not really the scepticism so long assigned him. Dr. Laing takes the opportunity in passing to indicate his sympathy with the recent position of a distinguished British poet that Voltaire, also, has been traditionally abused in the assumption that on the question of religion he wrote with his tongue in his cheek. The present examination is not designed to inquire into this new mode of making the wicked pious; nor to push the question back from the Dialogues to Hume's basic philosophy; nor to press the writer's conviction [“The Enigma of Hume,” Mind , XLV pp. 334–349] that not only is Philo to be identified as Hume, but in addition, Cleanthes as Joseph Butler, and Demea as Samuel Clarke. The present purpose is solely to indicate certain unhistorical bases of Dr. Laing's attack on the more traditional view so ably championed by Professor Norman Kemp Smith. (shrink)