This book is a clear, concise, and conceptually unified treatment of various problems, both formal and philosophical, of inductive logic and probability. Ackermann's main concern throughout the book is the problem of adducing inductive support for various hypotheses, and of deciding between two competing hypotheses which is more reasonable given the available evidence. The author begins with a general consideration of the criteria to be met by satisfactory rules of inductive inference: accordance with intuitive notions of reasonableness in simple (...) cases, sensitivity to the given evidence, capacity for unambiguous intersubjective application. Ackermann quickly disposes of the argument that valid inductive rules must be made to rest upon a "postulate of the uniformity of nature": "If past projections of regularities suddenly begin to go wrong, nondeductive rules satisfying the criteria suggested above will begin to select regularities other than the ones which have failed." This clears the way for a consideration of the general problem of evidential support or confirmation, with its well-known paradoxes and difficulties. Ackermann, like Goodman, locates the source of these in problems bearing on the semantics of scientific language, and cautiously points to Goodman's theory of projection and entrenchment as the way out of most of the muddle. Succeeding chapters deal with the notion of probability of hypotheses, statistical inference, and the application of Bayesian techniques and decision theory to science. A well-chosen bibliography completes this modest but rewarding little book.—H. P. K. (shrink)

This is the most recent volume in that fine series, Rare Masterpieces of Science and Philosophy As in other volumes the reader will be much indebted to the editor and publisher for bringing out material which heretofore has been relatively inaccessible. In the present instance this material consists of the more important essays by De Morgan on the syllogism—essays which offer a valuable supplement to his well known Formal Logic and enable us to perceive more clearly why De Morgan (...) is justly recognized as one of the great logicians in history. With the publication of this volume there remain only a few unpublished essays of De Morgan, but these are of a minor and inconsequential nature. The present volume consists of five papers on the syllogism, an article on ‘Logic’ from the English Cyclopaedia, a ‘Syllabus of a Proposed System of Logic’, which supplements in certain particulars the Formal Logic of 1847, and a very brief article ‘Some Suggestions in Logical Phraseology’ from the Proceedings of the Philological Society. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

Descartes' conception of facultive inference is of a simple, primitive, unanalyzable, unmediated, unjustifiable "mental operation by which one grasps connections between one's ideas," in contrast to Aristotle's discursive inference consisting in "spelling out and analyzing its steps". Gaukroger shows why Descartes takes Aristotelian syllogistic to be merely presentative of material already known, and thus takes deduction to be only a way of ordering and displaying this knowledge. For Descartes, only synthesis leads to new knowledge. Thus it is a mistake to (...) give an "apriorist and deductivist interpretation of Descartes's method... whereby all scientific knowledge is... deduced from the cogito". One "problem with a purely deductive approach... is... that... first principles take us to every possible world". To settle which account is of the actual world, we must resort to experiment. Also leading to a nondeductive method in science is Descartes' doctrine of God's creation of truths which means that "human knowledge can no longer be modeled in any way on divine knowledge". Descartes' three-part problem-solving method, then, is to pose the problem in quantitative terms, test the solutions experimentally, and incorporate the solution into his system of natural philosophy. (shrink)

As Friedman has argued, Kant's argument for the ideality of space turns on the nondeductive character of geometrical reasoning in Euclid's system. Since geometry can be axiomatized, this argument fails. But ("pace" Russell) Leibniz's argument based on the unreality of constitutive relations is not thereby answered as well. I argue that what is needed in response to Leibniz is a properly post-Kantian conception of concepts as inferentially articulated. This conception, I suggest, is based on the same fundamental insight that (...) underlies the axiomatization of geometry. (shrink)

Human reasoning often involves explanation. In everyday affairs, people reason to hypotheses based on the explanatory power these hypotheses afford; I might, for example, surmise that my toddler has been playing in my office because I judge that this hypothesis delivers a good explanation of the disarranged state of the books on my shelves. But such explanatory reasoning also has relevance far beyond the commonplace. Indeed, explanatory reasoning plays an important role in such varied fields as the sciences, philosophy, theology, (...) medicine, forensics, and law. -/- This dissertation provides an extended study into the logic of explanatory reasoning via two general questions. First, I approach the question of what exactly we have in mind when we make judgments pertaining to the explanatory power that a hypothesis has over some evidence. This question is important to this study because these are the sorts of judgments that we constantly rely on when we use explanations to reason about the world. Ultimately, I introduce and defend an explication of the concept of explanatory power in the form of a probabilistic measure. This formal explication allows us to articulate precisely some of the various ways in which we might reason explanatorily. -/- The second question this dissertation examines is whether explanatory reasoning constitutes an epistemically respectable means of gaining knowledge. I defend the following ideas: The probability theory can be used to describe the logic of explanatory reasoning, the normative standard to which such reasoning attains. Explanatory judgments, on the other hand, constitute heuristics that allow us to approximate reasoning in accordance with this logical standard while staying within our human bounds. The most well known model of explanatory reasoning, Inference to the Best Explanation, describes a cogent, nondeductive inference form. And reasoning by Inference to the Best Explanation approximates reasoning directly via the probability theory in the real world. Finally, I respond to some possible objections to my work, and then to some more general, classic criticisms of Inference to the Best Explanation. In the end, this dissertation puts forward a clearer articulation and novel defense of explanatory reasoning. (shrink)

In 1910, only four years before his death, Peirce began an adumbration of a life's worth of major results concerning nondeductive logic—results that he had reached after more than forty-five years of extremely careful and detailed investigations2—as follows: "I must premiss that we, all of us, use this word ["probability"] with a degree of laxity which corrupts and rots our reasoning to a degree that very few of us are at all awake to."3 Peirce continued the adumbration by (...) outlining his mature theory, according to which, contrary to what is generally supposed, there is not just one measure of "falling short of certainty,"4 viz. probability. Rather, there are three utterly distinct and mutually incommensurable .. (shrink)

Many recent developments in artificial intelligence research are relevant for traditional issues in the philosophy of science. One of the developments in AI research we want to focus on in this article is diagnostic reasoning, which we consider to be of interest for the theory of explanation in general and for an understanding of explanatory arguments in economic science in particular. Usually, explanation is primarily discussed in terms of deductive inferences in classical logic. However, in recent AI research it (...) is observed that a diagnostic explanation is actually quite different from deductive reasoning. In diagnostic reasoning the emphasis is on restoring consistency rather than on deduction. Intuitively speaking, the problem diagnostic reasoning is concerned with is the following. Consider a description of a system in which the normal behavior of the system is characterized and an observation that conflicts with this normal behavior. The diagnostic problem is to determine which of the components of the system can, when assumed to be functioning abnormally, account for the conflicting observation. A diagnosis is a set of allegedly malfunctioning components that can be used to restore the consistency of the system description and the observation. In this article, this kind of reasoning is formalized and we show its importance for the theory of explanation. We will show how the diagnosis nondeductively explains the discrepancy between the observed and the correct system behavior. The article also shows the relevance of the subject for real scientific arguments by showing that examples of diagnostic reasoning can be found in Friedman's Theory of the Consumption Function. Moreover, it places the philosophical implications of diagnostic reasoning in the context of Mill's aprioristic methodology. (shrink)

This book is a version of a D.Phil. thesis done at Oxford under the direction of Richard Swinburne and Basil Mitchell. Its basic premise is one shared by both these philosophers, namely, the putative inadequacy of traditional deductive and inductive arguments in philosophical theology. The central argument of the book is that the alternative proposed by Mitchell is superior to the one proposed by Swinburne. Roughly half the book is devoted to supporting this claim. Particular attention is given to showing (...) that Bayes' theorem as used by Swinburne is inadequate for assessing the probability of a theistic hypothesis. Other chapters are devoted to informal reasoning in philosophical theology, criteria of explanatory adequacy within a nondeductive framework, causality, and God as a logically necessary being. In these chapters the author attempts to develop further Mitchell's work. A final chapter undertakes to defend the book's basic thesis against some positions that in various ways contradict the author's approach. It includes replies to two attacks on the very idea of philosophical theology by J. L. Mackie and Stewart Sutherland, a response to John Hick's most recent attack on the personhood of God, and a criticism of the version of Thomistic philosophical theology held by E. L. Mascall. (shrink)

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense (...) reasoning, expert systems implementation, deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its applications and thus presents (...) the state of the art in the area. (shrink)

The Editors express their gratitude and appreciation to the indi-viduals listed below who served as referees for Informal Logic for Volumes 31 (2011) and 32 (2012).

Martin Heidegger's 1925–26 lectures on truth and time provided much of the basis for his momentous work, Being and Time. Not published until 1976 as volume 21 of the Complete Works, three months before Heidegger's death, this work is central to Heidegger's overall project of reinterpreting Western thought in terms of time and truth. The text shows the degree to which Aristotle underlies Heidegger's hermeneutical theory of meaning. It also contains Heidegger’s first published critique of Husserl and takes major steps (...) toward establishing the temporal bases of logic and truth. Thomas Sheehan's elegant and insightful translation offers English-speaking readers access to this fundamental text for the first time. (shrink)

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found (...) in human reasoning. Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)