Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

Begging the question — roughly, positing in the premises what is to be proved in the conclusion — is a perplexing fallacy.1 Are not question-begging arguments valid? Yes, we may find ourselves saying, but they are fallacious despite their validity, owing to their inability to establish the truth of a conclusion which is not already known. But are not question-begging arguments sometimes effective in bringing an audience to an awareness of the truth of the conclusion? How can a dialectical maneuver (...) which is capable of effecting epistemic progress be a fallacy, an illegitimate maneuver? In such cases of success, we can reply, the audience was simply in need of some logical coaching — a question-begging argument is of its very nature ill-suited for producing new knowledge in someone who is being fully rational. But then are not all valid arguments question-begging, since the conclusions are at least implicitly contained in the premises in such a way that a fully rational individual can never augment his knowledge through such arguments? No, we may answer, only those valid arguments in which the proposition constituting the conclusion appears, whether distinguised or not, as a distinct premise are question-begging; if several premises go together to imply a conclusion, the argument does not beg the question, But why is it legitimate to posit premises which more-or-less implicitly contain the conclusion, while it is illegitimate to posit premises which more-or-less explicitly contain the conclusion? Because, we are tempted to say, a question-begging argument is one in which what is to be proved in the conclusion is posited in the premises, and this positing must be more-or-less explicit in order for a fallacy to be committed! (shrink)

In this important contribution to the revived interest in McTaggart's philosophy, Professor Geach clearly expounds the main lines of his metaphysical thought. McTaggart has produced some immensely interesting and significant arguments; in particular, his rigorous reasoning against the trustworthiness of sense perception and the reality of time deserves serious consideration. McTaggart presents his mystical vision of love--the element of our experience that brings us closest to absolute reality--with lucidity and deep conviction. This study will make stimulating reading for all students (...) of philosophy and religion. (shrink)

This is a new release of the original 1949 edition.

If one looks to the current textbook lore for reliable taxonomic and analytical information about the petitio principii, one is met with conceptual disarray and much too much nonsense. The present writers have recently attempted to furnish the beginnings of a theoretical reconstruction of this fallacy which is at once faithful to its formidable complexity yet useful as guide for its detection and avoidance. The fact is that the petitio has had a lengthy and interesting history, and in this paper (...) we shall want to explore certain features of its development, such as it may have been. The principal origins of the concept of circular argument are to be found in Aristotle. The Aristotelian doctrine recurs with variations in the sophismata literature of the middle ages and in logic texts and manuals right up to the present day. (shrink)

This book offers a new theory of begging the question as an informal fallacy, within a pragmatic framework of reasoned dialogue as a normative theory of critical argumentation. The fallacy of begging the question is analyzed as a systematic tactic to evade fulfillment of a legitimate burden of proof by the proponent of an argument. The technique uses a circular structure of argument to block the further progress of dialogue and, in particular, the capability of the respondent to ask legitimate (...) critical questions in reply to the argument. Walton analyzes the concept of burden of proof in argument, and provides chapters on the use of argument diagramming as a technique of argument reconstruction. This powerful method of argument analysis developed therein is then applied to more than 100 case studies of circular argumentation where the charge of begging the question is or has been thought to be an appropriate criticism. Throughout this work, Walton throws light on the relationship between the problem of circular reasoning and broader issues in the critical analysis of argumentation. Ground-breaking use is made of the pragmatic theory of argument as interactive dialogue. Rules for several kinds of dialogue framework provide standards of good reasoning to validate or to refute the criticism that a particular argument begs the question. This book is directed to students and professionals in the fields of speech communication, philosophy, linguistics, logic, dispute mediation, and education. (shrink)

Several of the so-called “fallacies” in Aristotle are not in fact mistaken inference-types, but mistakes or breaches of rules in the questioning games which were practiced in the Academy and in the Lyceum. Hence the entire Aristotelian theory of “fallacies” ought to be studied by reference to the author's interrogative model of inquiry, based on his theory of questions and answers, rather than as a part of the theory of inference. Most of the “fallacies” mentioned by Aristotle can in fact (...) be diagnosed by means of the interrogative model, including petitio principii, multiple questions, “babbling’, etc., and so can Aristotle's alleged anticipation of the fallacy of argumentum ad hominem. The entire Aristotelian conception of inquiry is an interrogative one. Deductive conclusions caught Aristotle's attention in the form of answers that every rational interlocutor must give, assuming only his own earlier answers. Several features of Aristotle's methodology can be understood by means of the interrogative model, including the role of endoxa in it. Theoretically, there is also considerable leeway as to whether “fallacies” are conceived of as mistakes in questioning or as breaches of the rules that govern questioning games. (shrink)

To be truly provocative and outrageous the superior philosophical sophistry will commonly possess four somewhat adventitious features. I shall rate it as classic if it has all four. First, and least adventitiously, the argument will be crisp and initially seductive. Second, by the standard the sophistry sets direct rebuttal will be laborious and diffuse. Third, the recipe for the latter will prescribe that we pick out some hitherto unarticulated logical principle such that if the principle be true then the sophistical (...) argument must be invalid, and then, on the strength of that consequence assume the principle to be true. Consequently and fourth, as an antidote parody is supreme. With a persuasive absence of fuss and bias we can turn the tables if we show that, if the sophistical argument were really valid, then some structurally similar argument would prove just as consummately far too much. In short, from the rhetorical point of view at least, Gaunilo is more lethal than Kant. Even if the similarity is defective, the sophist will lose some of his adventitious and insufferable poise, if he ventures to show why. (shrink)

Provides translations and interpretations of the texts of works by the great figures of early Greek philosophy.

From the Editor’s Introduction: -/- THE INTERNAL LIMITATIONS OF HUMAN UNDERSTANDING -/- We carry, unavoidably, the limits of our understanding with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and mist of speculation. -/- (...) The limitations in view here are not due to the mere finitude of our understanding of ourselves and of the world in which we live. They are limitations that come automatically and necessarily with any form of understanding. They are, as we shall see, part and parcel of any organization or ordering of data that we call information. -/- The consequences of these limitations are varied: As a result of them, hermeneutics cannot help but be hermetic; scientific theories of necessity are circumscribed by the boundaries of the ideas that define them; formal systems must choose between consistency and comprehensiveness; philosophical study, because it includes itself within its own proper subject matter, is forced to be reflexive in its self-enclosure. The fundamental dynamic shared by all forms of understanding testifies to an internal limitative keystone. (shrink)

A primary purpose of argument is to increase the degree of reasonable confidence that one has in the truth of the conclusion. A question begging argument fails this purpose because it violates what W. E. Johnson called an epistemic condition of inference. Although an argument of the sort characterized by Robert Hoffman in his response (Analysis 32.2, Dec 71) to Richard Robinson (Analysis 31.4, March 71) begs the question in all circumstances, we usually understand the charge that an argument is (...) question begging with reference to the beliefs of the person, or the sort of person, to whom the argument is directed. (shrink)

According to John A Barker, whether an argument begs the question is purely a matter of logical form. According to me, it is also a matter of epistemic conditions; some arguments which beg the question in some contexts need not beg the question in every context. I point out difficulties in Barker's treatment and defend my own views against some of his criticisms. In the concluding section, "Alleged difficulties with disjunctive syllogism," I defend the validity of disjunctive syllogism against the (...) views of Alan Ross Anderson and Nuel D Belnap, Jr., ask pointed questions about the notion of intensional disjunction, and suggest how my treatment of begging the question can be extended to deal with the so-called paradoxes of strict implication. (shrink)

In this dissertation we discuss infinite regress arguments from both a historical and a logical perspective. Throughout we deal with arguments drawn from various areas of philosophy. ;We first consider the regress generating portion of the argument. We find two main ways in which infinite regresses can be developed. The first generates a regress by defining a relation that holds between objects of some kind. An example of such a regress is the causal regress used in some versions of the (...) Cosmological Argument. The second sort of regress is generated by defining a certain procedure that can be repeated indefinitely many times. This will often be a procedure of analysis or of explanation. ;We then argue that for purposes of discussing regressive viciousness it is helpful to divide regresses into two main types. One type raises primarily epistemological issues. In this class we find the regress of justification often used in foundational arguments in epistemology. We also discuss certain arguments that treat theories of predication as attempts to explain predication. Our other class contains those regresses that raise primarily metaphysical problems. This class includes the causal regress as well as those arguments concerned with predication as an ontological problem. ;We agree with some philosophers that one problem that arises in the case of vicious regression is circularity. We show how this problem can be generalized to include other apparently non-circular regresses. The other main problem in epistemological regresses arises as a result of certain conditions that are placed on the relation involved. We look in detail at the epistemological justification regress to illustrate this last point. ;With respect to metaphysical regresses we again find several types of viciousness arguments. One problem is whether the infinite collection required for the regress is even possible. Another problem is whether an infinite number of events can occur in a finite time. These we deal with only briefly. The main difficulty with these regresses, considered as regresses and not just as infinite sets, again turns out to be certain conditions built into the relation involved. We focus on some arguments about causal regression to illustrate this point. ;Finally, we find no absolutely general conditions for regressive viciousness. There is, however, a certain limited range of ways in which a regress may be vicious. We make these ways explicit. (shrink)

We know from more than two millenia of experience that self-referential statements, such as the liar's ("This very statement is false"), can be debated by philosophers and logicians for millenia without producing consensus on their solutions. We should not be surprised, then, if self-referential laws produce paradoxes which puzzle lawyers. What is surprising, though, is that some of these paradoxes bother only the logicians and philosophers who study law from outside, and do not bother lawyers at all. This fact should (...) interest philosophers of law even more than the paradoxes themselves. (shrink)

If one looks to the current textbook lore for reliable taxonomic and analytical information about the petitio principii, one is met with conceptual disarray and much too much nonsense. The present writers have recently attempted to furnish the beginnings of a theoretical reconstruction of this fallacy which is at once faithful to its formidable complexity yet useful as guide for its detection and avoidance. The fact is that the petitio has had a lengthy and interesting history, and in this paper (...) we shall want to explore certain features of its development, such as it may have been. The principal origins of the concept of circular argument are to be found in Aristotle. The Aristotelian doctrine recurs with variations in the sophismata literature of the middle ages and in logic texts and manuals right up to the present day. (shrink)

Consider the following exchanges: 1. Gerda: So you believe that all belief is the product of custom and circumstance (or: childhood buffets, class struggle...). Isn't that position self-limiting? Mustn't you see yourself as reflecting only a single complex of circumstances? Grobian: Your objection is inapplicable, for it is merely the product of blind forces. Moreover, your childhood buffets were pernicious and regrettable, for they have set you against this truth.

One of the most effective ways of winning an argument is to show that your opponent has begged the question. If you are sufficiently skilful in asking him leading questions and have a good sense of timing you can usually succeed in stripping him to his bare principles, with no ascertainable means for their support. That such a tactic of debate should be so effective suggests that it is more than just a ploy. Indeed some philosophers would say that it (...) takes advantage of a characteristic which is inherent in the nature of argument itself, for all arguments must be question-begging. However, few would voice this conviction publicly—for fear of being accused of begging the question. (shrink)