For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. It (...) is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories. (shrink)

Cosmic Justice Hypotheses. -/- This applied-logic lecture builds on [1] arguing that character traits fostered by logic serve clarity and understanding in ethics, confirming hopeful views of Alfred Tarski [2, Preface, and personal communication]. Hypotheses in one strict usage are propositions not known to be true and not known to be false or—more loosely—propositions so considered for discussion purposes [1, p. 38]. Logic studies hypotheses by determining their implications (propositions they imply) and their implicants (propositions that imply them). Logic also (...) studies hypotheses by seeing how variations affect implications and implicants. People versed in logical methods are more inclined to enjoy working with hypotheses and less inclined to dismiss them or to accept them without sufficient evidence. Cosmic Justice Hypotheses (CJHs), such as “in the fullness of time every act will be rewarded or punished in exact proportion to its goodness or badness”, have been entertained by intelligent thinkers. Absolute CJHs, ACHJs, imply that it is pointless to make sacrifices, make pilgrimages, or ask divine forgiveness: once acts are done, doers must ready themselves for the inevitable payback, since the cosmos works inexorably toward justice. Ceteris Paribus CJHs, CPCJHs, on the other hand, such as “in the fullness of time every act will be rewarded or punished in exact proportion to its goodness or badness—other things being equal”, leave room for exceptions. For example, some people subscribing to Ceteris Paribus CJHs think that certain bad acts can be performed with impunity as long as certain procedures are carried out previous to, or simultaneous with, or even after the acts. Belief Ceteris Paribus CJHs has been exploited by unscrupulous “spiritual leaders” who claim to have power to grant exceptions. In opposition to belief in CPCJHs are CJHs that hold belief in CPCJHs to be inherently wrong and subject to punishment. Other variants of CJHs are Cumulative Cosmic Justice Hypotheses, such as “in the fullness of time every person will be rewarded or punished in exact proportion to the net goodness or badness of their acts”. Still other variants include the Hereditary Cumulative Cosmic Justice Hypotheses, such as “in the fullness of time every person will be rewarded or punished in exact proportion to the net goodness or badness of their ancestors’ acts”. [1] JOHN CORCORAN, Inseparability of Logic and Ethics, Free Inquiry, S. 1989, pp. 37–40. [2] ALFRED TARSKI, Introduction to Logic, Dover, 1995. (shrink)

JOHN CORCORAN AND WILIAM FRANK. Surprises in logic. Bulletin of Symbolic Logic. 19 253. Some people, not just beginning students, are at first surprised to learn that the proposition “If zero is odd, then zero is not odd” is not self-contradictory. Some people are surprised to find out that there are logically equivalent false universal propositions that have no counterexamples in common, i. e., that no counterexample for one is a counterexample for the other. Some people would be surprised to (...) find out that in normal first-order logic existential import is quite common: some universals “Everything that is S is P” —actually quite a few—imply their corresponding existentials “Something that is S is P”. Anyway, perhaps contrary to its title, this paper is not a cataloging of surprises in logic but rather about the mistakes that did or might have or might still lead people to think that there are no surprises in logic. The paper cataloging of surprises in logic is on our “to-do” list. -/- ► JOHN CORCORAN AND WILIAM FRANK, Surprises in logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: [email protected] There are many surprises in logic. Peirce gave us a few. Russell gave Frege one. Löwenheim gave Zermelo one. Gödel gave some to Hilbert. Tarski gave us several. When we get a surprise, we are often delighted, puzzled, or skeptical. Sometimes we feel or say “Nice!”, “Wow, I didn’t know that!”, “Is that so?”, or the like. Every surprise belongs to someone. There are no disembodied surprises. Saying there are surprises in logic means that logicians experience surprises doing logic—not that among logical propositions some are intrinsically or objectively “surprising”. The expression “That isn’t surprising” often denigrates logical results. Logicians often aim for surprises. In fact, [1] argues that logic’s potential for surprises helps motivate its study and, indeed, helps justify logic’s existence as a discipline. Besides big surprises that change logicians’ perspectives, the logician’s daily life brings little surprises, e.g. that Gödel’s induction axiom alone implies Robinson’s axiom. Sometimes wild guesses succeed. Sometimes promising ideas fail. Perhaps one of the least surprising things about logic is that it is full of surprises. Against the above is Wittgenstein’s surprising conclusion : “Hence there can never be surprises in logic”. This paper unearths basic mistakes in [2] that might help to explain how Wittgenstein arrived at his false conclusion and why he never caught it. The mistakes include: unawareness that surprise is personal, confusing logicians having certainty with propositions having logical necessity, confusing definitions with criteria, and thinking that facts demonstrate truths. People demonstrate truths using their deductive know-how and their knowledge of facts: facts per se are epistemically inert. [1] JOHN CORCORAN, Hidden consequence and hidden independence. This Bulletin, vol.16, p. 443. [2] LUDWIG WITTGENSTEIN, Tractatus Logico-Philosophicus, Kegan Paul, London, 1921. -/-. (shrink)

Despite Newman’s negligible direct familiarity with the works and thought of John Duns Scotus, there has been recent discussion of affinities between the two along a range of philosophical approaches and sensibilities. These notes introduce the thesis that both Scotus and Newman share a disposition to appeal to aesthetic rationality when it comes to asserting certain basic truths critical to Christian understanding. Recent Scotus studies have demonstrated the deep and pervasive presence of the aesthetic dimension in Duns Scotus’s thought. In (...) the latter half of this paper I argue for the importance of aesthetic rationality in understanding Newman’s illative sense, which is perhaps his most important contribution to philosophical thought. (shrink)

From Marcus Tullius Cicero’s philosophical writings, the author first draws out a modest network of ideas that informs his understanding of what it means to be a good man (vir bonus). Then, he finds in Cicero the idea of a befitting mutuality among four distinctively human capacities: a faculty for inquiry into and love for truth manifest in words and actions (reason); a disposition for the recognition of and attraction to things of worth beyond self-interest (the honorable); an acute sense (...) of one own spheres of responsibility along with facility for speaking and acting appropriately within them (appropriate action), and fostering and extending the bonds of mutual personal relations grounded in justice and benevolence (society). Against the background of deep commitments in modernity to hedonism and autonomous individualism, the author proposes a retrieval of the virtue of the honorable as an attractive alternative. (shrink)

The idea of translating Gerdil into English is brilliant, the translation is very good and the introduction of William Frank precise and inspiring.... Rousseau proposes a complete break with tradition. A new man will arise who is severed from the whole heritage of the past. With him the history of mankind begins anew. In one sense we have here a transposition in the field of philosophy of education of the Cartesian cogito. The subject begins with himself. To this philosophical project (...) Gerdil opposes the idea of tradition. We have not made ourselves. Our parents have procreated us. The parents do not only procreate their offspring, they also introduce them into the natural and social reality, that is they educate. No education is possible without a lively dialogue with history and society. Since the beginning man stands in a close relationship to others, is made for the human society.... In these our times one form of modernity is collapsing and the mood of the day is an unclear postmodernity that in some of its versions could well be a return to barbarianism. All the more important is then that another form of modernity be rediscovered and brought to the attention of the American public. - Rocco Buttiglione, University of St. Pius V, Rome A timely translation of a compelling 18th century critique of Rousseau by the neglected Italian author, Hyacinth S. Gerdil. Gerdil's Anti-Emile may have been written as a critique of Rousseau's Emile, but it can equally be read as a critique of the philosophy embraced by the American educational establishment. Through the influence of John Dewey, Rousseau came to inform much of the educational theory regnant in the United States, with disastrous consequences, now acknowledge by nearly all. In a valuable preface to his translation, Professor Frank, drawing upon his experience both here and abroad, not only places Emile in context, but defends Gerdil's time-transcending, classical view of education against its modern detractors. "Gerdil," Frank tells us, "addressed his Anti-Emile to elders responsible for education, be they parents, teachers, or political authorities, who might find themselves swayed by the powerful rhetoric of Rousseau's Emile." The same may be said of this translation and its informative prefatory material, for it is clearly a study that will be valued by anyone interested in principled education. - Jude P. Dougherty, Catholic University of America Cover image: "Adam and Eve" by Tintoretto. St. Augustine's Press acknowledges the kind permission granted by la Scuola Grande di San Rocco, Venice, for the use of the image. All rights reserved by la Scuola Grande di San Rocco. (shrink)

With this book Allan Wolter makes available the essential writings of Duns Scotus on the will and morality. The book fills a major lacuna in medieval and Scotistic studies. In making the book Wolter tells us that his primary purpose was twofold. First of all, he wished to "correct common misconceptions that arose because of [Scotus's] voluntarist notion of God's relationship to creatures". The means he chose toward this therapeutic end in the history of philosophy is simply a matter of (...) putting forth an accurate and complete report of Scotus's teaching. The second purpose was "to show the unity of [Scotus's] ethical system based on right reason". Measured by these criteria, I would judge the book to be remarkably successful. Duns Scotus on Will and Morality gives a complete view of Scotus's ethical system. The selections are made carefully and generously so that the reader can appreciate the fullness of Scotistic moral teachings. (shrink)

In this book the foremost philosophical exegete of Scotus's thought presents an extensive commentary on a metaphysical masterpiece of the great Franciscan master. As many well know, A Treatise on God is one of the most sustained purely philosophical arguments for the existence and nature of God to come from the middle ages. But the original work makes hard reading. Informing Scotus's argumentation are a host of vital metaphysical doctrines that barely reach the surface of the written text. Without a (...) knowledge of these submerged positions Scotus's thought in the Treatise strikes one as a hardly penetrable code. Typical hurdles for the reader include severely foreshortened arguments, almost complete absence of examples, and obliquely relevant objections. In addition, Scotus seems to be working through an intellectual agenda that involves a sophisticated conversation with the great minds of the metaphysical tradition. The reader needs to be cognizant of the terms and principals of this dialogue. Wolter's commentary is a superb companion that clearly establishes the context and flow of argumentation in Scotus's treatise. (shrink)

With this book Allan Wolter makes available the essential writings of Duns Scotus on the will and morality. The book fills a major lacuna in medieval and Scotistic studies. In making the book Wolter tells us that his primary purpose was twofold. First of all, he wished to "correct common misconceptions that arose because of [Scotus's] voluntarist notion of God's relationship to creatures". The means he chose toward this therapeutic end in the history of philosophy is simply a matter of (...) putting forth an accurate and complete report of Scotus's teaching. The second purpose was "to show the unity of [Scotus's] ethical system based on right reason". Measured by these criteria, I would judge the book to be remarkably successful. Duns Scotus on Will and Morality gives a complete view of Scotus's ethical system. The selections are made carefully and generously so that the reader can appreciate the fullness of Scotistic moral teachings. (shrink)

James Ross tells us that his is the most sustained and systematic account of analogy in 500 years; he places his work beside the classical theories of Aristotle, Aquinas, and Cajetan. The boast may not be far off the mark, for this is a most significant treatise. What we have here is an explanation of a deeply pervasive feature of language. Its subject matter is the obvious occurrence in speech of the same word with different meanings. In its systematic explanation (...) the book classifies the variety of same word/different meaning relationships, identifies the basic principles and underlying structures of the phenomena, and shows the necessities at work in the generation of meaning through this analogy feature of language. The thesis boldly stated reads: "analogy of meaning... is the consequence of underlying synchronic structure composed of linguistic inertia... and linguistic force". Ross calls his work a portrayal rather than a science, and properly so, for the key predicates in his account are metaphorically extended from other realms of discourse. Words such as linguistic inertia, force, dominate, entrenchment, craftbound, and benchmark are given extended life in this special discourse on analogy. (shrink)

Aquinas on Human Action: A Theory of Practice by Ralph McInerny; The Question of Christian Ethics by Ralph McInerny.

This book collects Stephen Toulmin's thoughts about philosophical cosmology as it has developed over the past thirty years. The development shows three distinct phases. Representing the first phase is Part 1 of the book entitled "Scientific Mythology". Part 2 is entitled "A Consideration of Cosmologists". And his latest thinking is developed in Part 3, "The Future of Cosmology: Postmodern Science and Natural Religion." The last part is the most interesting, and is surely the reason for the book. Because of it, (...) the book's title is an honest one. (shrink)

This massive study makes an important contribution to the history of philosophy for two reasons. First of all, it stands as the most complete and careful philosophical analysis of Ockham's thought to date. Adams's expositions and analyses will become the gloss which generations of students will have to reckon with as they confront the text of Ockham. Secondly, this work represents an exemplary method of philosophical commentary, one that proves to be a remarkably illuminating way into the mind of a (...) medieval scholastic disputant. Because Ockham's thought is intensely dialectical and argumentative, Adams appropriately exposes his doctrines through an exacting recovery of his argument within its dialogical context. For example, in the crucial chapter 2, "Universals Are Not Things other than Names," we come to understand Ockham's nominalism as it emerges from his rejection of moderate realism; Adams presents this rejection through a reconstruction of Ockham's encounter with the living tradition of Aquinas, Scotus, Walter Burleigh, William of Alnwick, Nervaeus Natalis, and Henry of Harclay. As the dialectic proceeds from figure to figure, the issue of the universal reshapes itself with great sophistication. Adams's formidable analytic powers and her sharp focus on the key philosophical issue enable her to succeed in this method. The reader also gets the sense that Adams herself believes one can come to truth through philosophical argument, and not just the truth of what Ockham taught but the truth of what he sought. This earnestness enables her to keep a fix on the dialectic's "emerging rule" which becomes the source of unity in what could otherwise degenerate into a bewildering complexity of historical detail or the vanity of analytic logic-chopping. (shrink)