Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such asreductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the 17th (...) century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titledSpecimina calculi rationalis, Leibniz develops a theory of propositional terms that allows him to derive the rule ofreductio ad absurdumin a purely categorical calculus in which every proposition is of the formA is B. We reconstruct Leibniz’s categorical calculus and show that it is strong enough to establish not only the rule ofreductio ad absurdum, but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz’s categorical calculus is a natural system of relevance logic known as RMI$_{{}_ \to ^\neg }$. (shrink)

This paper aims to outline an analysis and interpretation of the process that led to First-Order Logic and its consolidation as a core system of modern logic. We begin with an historical overview of landmarks along the road to modern logic, and proceed to a philosophical discussion casting doubt on the possibility of a purely rational justification of the actual delimitation of First-Order Logic. On this basis, we advance the thesis that a certain historical tradition was essential to the emergence (...) of modern logic; this traditional context is analyzed as consisting in some guiding principles and, particularly, a set of exemplars (i.e., paradigmatic instances). Then, we proceed to interpret the historical course of development reviewed in section 1, which can broadly be described as a two-phased movement of expansion and then restriction of the scope of logical theory. We shall try to pinpoint ambivalencies in the process, and the main motives for subsequent changes. Among the latter, one may emphasize the spirit of modern axiomatics, the situation of foundational insecurity in the 1920s, the resulting desire to find systems well-behaved from a proof-theoretical point of view, and the metatheoretical results of the 1930s. Not surprisingly, the mathematical and, more specifically, the foundational context in which First-Order Logic matured will be seen to have played a primary role in its shaping.Mathematical logic is what logic, through twenty-five centuries and a few transformations, has become today. (Jean van Heijenoort). (shrink)

How do Dutch people let each other know that they disagree? What do they say when they want to resolve their difference of opinion by way of an argumentative discussion? In what way do they convey that they are convinced by each other’s argumentation? How do they criticize each other’s argumentative moves? Which words and expressions do they use in these endeavors? By answering these questions this short essay provides a brief inventory of the language of argumentation in Dutch.

This paper examines the views of Fogelin, Woods, Johnstone, etc., concerning deep disa-greements, force-five standoffs, philosophical controversies, etc. My approach is to reconstruct their views and critiques of them as meta-arguments, and to elaborate the meta-argumentative aspects of radical disa-greements. It turns out that deep disagreements are resolvable to a greater degree than usually thought, but only by using special principles and practices, such as meta-argumentation, ad hominem argumentation, Ramsey’s principle, etc.

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)

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)

Jarmo Pulkkinen, The threat of logical mathematism. A study on the critique of mathematical logic in Germany at the turn of the 20th century. Frankfurt a.M:Peter Lang, 1994. Scandinavian University Studies in the Humanities and Social Sciences; 7). 186 pp. 24 DM. ISBN 3-631-47409-1.

This paper is concerned with De Morgan’s explanation of the validity of arguments that involve relational notions. It discusses De Morgan’s expansion of traditional logic aimed at accommodating those inferences, and makes the point that his endeavour is not successful in that the rules that made up his new logic are not sound. Nevertheless, the most important scholarly work on De Morgan’s logic, and contrary to that De Morgan’s mistake is not beyond repair. The rules that determine his new logic (...) are in fact monotonie replacement rules. And provided they are restricted in the correct way, these rules are demonstrably sound. (shrink)

Peter Geach describes the 'doctrine of distribution' as the view that a term is distributed if it refers to everything that it denotes, and undistributed if it refers to only some of the things that it denotes. He argues that the notion, so explained, is incoherent. He claims that the doctrine of distribution originates from a degenerate use of the notion of ?distributive supposition? in medieval supposition theory sometime in the 16th century. This paper proposes instead that the doctrine of (...) distribution occurs at least as early as the 12th century, and that it originates from a study of Aristotle's notion of a term's being ?taken universally?, and not from the much later theory of distributive supposition. A detailed version of the doctrine found in the Port Royal Logic is articulated, and compared with a slightly different modern version. Finally, Geach's arguments for the incoherence of the doctrine are discussed and rejected. (shrink)

Slippery slope arguments (SSAs) have often been viewed as inherently weak arguments, to be classified together with traditional fallacies of reasoning and argumentation such as circular arguments and arguments from ignorance. Over the last two decades several philosophers have taken a kinder view, often providing historical examples of the kind of gradual change on which slippery slope arguments rely. Against this background, Enoch (2001, Oxford Journal of Legal Studies 21(4), 629–647) presented a novel argument against SSA use that itself invokes (...) a slippery slope. Specifically, he argued that the very reasons that can make SSAs strong arguments mean that we should be poor at abiding by the distinction between good and bad SSAs, making SSAs inherently undesirable. We argue that Enoch’s meta-level SSA fails on both conceptual and empirical grounds. (shrink)

A number of areas of biology raise questions about what is of value in the natural environment and how we ought to behave towards it: conservation biology, environmental science, and ecology, to name a few. Based on my experience teaching students from these and similar majors, I argue that the field of environmental ethics has much to teach these students. They come to me with pent-up questions and a feeling that more is needed to fully engage in their subjects, and (...) I believe some exposure to environmental ethics can help focus their interests and goals. I identify three primary areas in which environmental ethics can con- tribute to their education. The first is an examination of who (or what) should be considered to be part of our moral community (i.e., the community to whom we owe direct duties). Is it humans only? Or does it include all sentient life? Or all life? Or ecosystems considered holistically? Often, readings implicitly assume one or more of these answers; the goal is to make the student more sensitive to these implicit claims and to get them to think about the different reasons that support them. The second area, related to the first, is the application of the different answers concerning the extent of the ethical community to real environmental issues and problems. Students need to be aware of how the different answers concerning the moral community can imply conflicting answers for how we should act in certain cases and to think about ways to move toward conflict resolution. The third area in which environmental ethics can contribute is a more conceptual one, focusing on central concepts such as biodiversity, sustainability, species, and ecosystems. Exploring and evaluating various meanings of these terms will make students more reflective and thoughtful citizens and biologists, sensitive to the implications that different conceptual choices make. (shrink)

This paper deals with the treatment of figures of speech in Perelman’s and Olbrechts-Tyteca’s Treatise on Argumentation (TA), and, more broadly, with the place of figures in argumentation theory. The contrast between two conceptions (or two domains)\n of rhetoric, “a rhetoric of figures” and “a rhetoric of argument” can be traced back to Ramus, and it has been revived in\n the seventies through the perception of an incommensurability between Perelman’s “New Rhetoric” and the École de Liège’s “General\n Rhetoric”. Modern theories (...) of argumentation, oriented towards the characterization and denunciation of fallacious discourse,\n emphasize the gap between sound argumentative discourse and rhetorical discourse seen as a “powerful instrument of error and\n deceit” (Locke). This concept of argument presupposes a vision of language as ideal/transparent—a revised language that is\n not the language of ordinary argumentation. Figures are not basically “decorative”; they are manifestations of the complex\n process of language structuring in speech. Thus rejecting figures amounts to a negation of discourse as such. The second section\n turns to a somewhat neglected aspect of the TA, its both decisive and somewhat cavalier theory of figures of speech, and its extended use and re-definition of a complex set of figures. We argue that the TA, in its quest for descriptive adequacy, breaks with the traditional and comfortable concept of figures as useless fallacious\n “ornaments” and provides us with the first description of what could be characterized as the semantic level of ordinary argumentative\n discourse. This will be shown on the case of “figures of choice, presence and communion”, and could be extended to the discursive\n construction of objects and participants, including the speaker and her emotions. (shrink)

Abstract Few theoretical insights have emerged from the extensive literature discussions of petitio principii argument. In particular, the pattern of petitio analysis has largely been one of movement between the two sides of a dichotomy, that of form and content. In this paper, I trace the basis of this dichotomy to a dualist conception of mind and world. I argue for the rejection of the form/content dichotomy on the ground that its dualist presuppositions generate a reductionist analysis of certain concepts (...) which are central to the analysis of petitio argument. I contend, for example, that no syntactic relation can assimilate within its analysis the essentially holistic nature of a notion like justification. In this regard, I expound a form of dialectical criticism which has been frequently employed in the philosophical arguments of Hilary Putnam. Here the focus of analysis is upon the way in which the proponent of a position proceeds to explain or argue for his/her own particular theses. My conclusion points to the use of such dialectic within future analyses of petitio principii. (shrink)

Charles Peirce is often credited for being among the first, perhaps even the first, to develop a scientific metaphysics of indeterminism. After rejecting the received view that Peirce developed his views from Darwin and Maxwell, I argue that Peirce's view results from his synthesis of Immanuel Kant's critical philosophy and George Boole's contributions to formal logic. Specifically, I claim that Kant's conception of the laws of logic as the basis for his architectonic, when combined with Boole's view of probability, yields (...) Peirce's metaphysics of probabilistic laws. Indeterminism provides, therefore, an excellent illustration of how Peirce attempted to use logic to clarify metaphysical problems.Since everyone must have conceptions of things in general, it is most important that they should be carefully constructed. I shall enter into no criticism of the different methods of metaphysical research, but shall merely say that in the opinions of several great thinkers, the only successful mode yet lighted upon is that of adopting our logic as our metaphysics. (W1: 490, 1866)2. (shrink)

This is a critical examination of Johnstone's thesis that all valid philosophical arguments are ad hominem. I clarify his notions of valid, philosophical, and ad hominem. I illustrate the thesis with his refutation ofthe claim that only ordinary language is correct. r discuss his three supporting arguments (historical, theoretical, and intermediate). And r criticize the thesis with the objections that if an ad hominem argument is valid, it is really ad rem; that it's unclear how his own theoretical argument can (...) be ad hominem; that if an ad hominem argument is really valid, it would have to be based on the proponent's own assumptions; and that the thesis is not true of philosophical arguments that are constructive rather than critical. (shrink)

This is a critical appreciation of Govier’s 2006 ISSA keynote address on the fallacy of composition, and of economists’ writings on this fallacy in economics. I argue that the “fallacy of composition” is a problematical concept, because it does not denote a distinctive kind of argument but rather a plurality, and does not constitute a distinctive kind of error, but rather reduces to oversimplification in arguing from micro to macro. Finally, I propose further testing of this claim based on examples (...) involving public vs. private debt in economics; oligarchic tendencies in politics, and the emergence of societal wholes in sociology. (shrink)

In this paper we study the inferential analysis of the use of fallacies as a source of absurd communication. Starting from a diachronic review of perpectives, criteria and classification of fallacies, we analyze the fallacious arguments used in absurd discourses which are meant to trigger humor as well as the dislocation of the communicative sense.

In IV, xvii, 19–22 of his Essay, Locke employs Latin labels for four kinds of argument, of which one (ad hominem) was already in circulation and one (ad judicium) has never had much currency. The present proposal seeks to locate and clarify what Locke was aiming to describe, and to contrast what he says with some subsequent uses that have been made of these labels as if they named fallacies. Though three of the four kinds of argument that Locke picks (...) out are often less than decisive, he casts no aspersion on the legitimacy of their use in debate. (shrink)

The world’s scientific community must be in a state of constant readiness to address the threat posed by newly emerging infectious diseases. Whether the disease in question is SARS in humans or BSE in animals, scientists must be able to put into action various disease containment measures when everything from the causative pathogen to route(s) of transmission is essentially uncertain. A robust epistemic framework, which will inform decision-making, is required under such conditions of uncertainty. I will argue that this framework (...) should have reasoning at its center and, specifically, that forms of reasoning beyond deduction and induction should be countenanced by scientists who are confronted with emerging infectious diseases. In previous articles, I have presented a case for treating certain so-called traditional informal fallacies as rationally acceptable forms of argument that can facilitate scientific inquiry when little is known about an emerging disease. In this article, I want to extend that analysis by highlighting the unique features of these arguments that makes them specially adapted to cope with conditions of uncertainty. Of course, such a view of the informal fallacies must at least be consistent with the reasoning practices of scientists, and particularly those scientists (viz. epidemiologists) whose task it is to track and respond to newly emerging infectious diseases. To this end, I draw upon examples of scientific reasoning from the UK’s BSE crisis, a crisis that posed a significant threat to both human and animal health. (shrink)

This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes non-specialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s two-volume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, (...) and a deductive logic by which the steps of the deduction proceed. Every demonstration produces knowledge of its conclusion for every person who comprehends the demonstration. Aristotle presented a general truth-and-consequence theory of demonstration meant to apply to all demonstrations: a demonstration is an extended argumentation that begins with premises known to be truths and that involves a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In short, a demonstration is a deduction whose premises are known to be true. Aristotle’s general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining theory of deduction was meant to apply to all deductions: any deduction that is not immediately evident is an extended argumentation that involves a chaining of immediately evident steps that shows its final conclusion to follow logically from its premises. His deductions, both direct and indirect, were rule-based and not tautology-based. The idea of tautology-based deduction, which dominated modern logic in the early years of the 1900s, is nowhere to be found in Analytics. Rule-based deduction was rediscovered by modern logicians. To illustrate his general theory of deduction, Aristotle presented a prototype: an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. With reference only to propositions of the four so-called categorical forms, he painstakingly worked out exactly what those immediately evident deductive steps are and how they are chained to complete deductions. In his specialized prototype theory, Aristotle explained how to deduce from a given categorical premise set, no matter how large, any categorical conclusion implied by the given set. He did not extend this treatment to non-categorical deductions, thus setting a program for future logicians. The prototype, categorical syllogistic, was seen by Boole as a “first approximation” to a comprehensive logic. Today, however it appears more as the first of the dozens of logics already created and as the first exemplification of a family that continues to expand. (shrink)

In Fallacies and Judgments of Reasonableness, Frans H. van Eemeren, Bart Garssen and Bert Meuffels report on their systematic empirical research of the conventional validity of the pragma-dialectical discussion rules. The experimental studies they carried out during more than ten years start from the pragma-dialectical theory of argumentation developed at the University of Amsterdam, their home university. In these studies they test methodically the intersubjective acceptability of the rules for critical discussion proposed in this theory by confronting ordinary arguers who (...) have not received any special education in argumentation and fallacies with discussion fragments containing both fallacious and non-fallacious argumentative moves. The research covers a wide range of informal fallacies. In this way, the authors create a basis for comparing the theoretical reasonableness conception of pragma-dialectics with the norms for judging argumentative moves prevailing in argumentative practice. Fallacies and Judgments of Reasonableness provides a unique insight into the relationship between theoretical and practical conceptions of reasonableness, supported by extensive empirical material gained by means of sophisticated experimental research. (shrink)