This is a review of Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena, written by Jon Barwise and Lawrence Moss and published by CSLI Publications in 1996.

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

This paper presents an axiomatic formalization of a theory of top-level relations between three categories of entities: individuals, universals, and collections. We deal with a variety of relations between entities in these categories, including the sub-universal relation among universals and the parthood relation among individuals, as well as cross-categorial relations such as instantiation and membership. We show that an adequate understanding of the formal properties of such relations – in particular their behavior with respect to time – is critical for (...) geographic information processing. The axiomatic theory is developed using Isabelle, a computational system for implementing logical formalisms. All proofs are computer verified and the computational representation of the theory is available online. (shrink)

This paper presents a unified, more-or-less complete, and largely pragmatic theory of indicative conditionals as they occur in natural language, which is entirely truth-functional and does not involve probability. It includes material implication as a special—and the most important—case, but not as the only case. The theory of conditional elements, as we term it, treats if-statements analogously to the more familiar and less controversial other truth-functional compounds, such as conjunction and disjunction.

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that (...) are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents. (shrink)

Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Jaśkowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks—the standard conduits of (...) the method to a generation of philosophers—with an eye to determining what the ‘essential characteristics’ of natural deduction are. (shrink)

Routley?s Formula says, for instance, that if it is believed there is a man then there is something which is believed to be a man. In this paper I defend the formula; first directly, but then by looking at work by Gensler and Hintikka against it, and at the original work of Routley, Meyer and Goddard for it. The argument ultimately reduces to a central point about the extensionality of objects in Routley, Meyer and Goddard?s intensional system, i.e. in its (...) formulation of transparency. (shrink)

The paper aims to provide an analysis and critique of Carl Wellman’s account of conduction presented in Challenge and Response and Morals and Ethics. It considers several issues, including: reason-ing vs. argument, the definition vs. the three patterns of conduction, pro and con arguments as dialogues, their assessment, the concept of validity, applications beyond moral arguments, argument type vs. as crite-rion of evaluation.

This essay attempts to give definitions and identity conditions for the two predominant senses of ‘Argument’ currently in use, the one involving reasons for a conclusion and the other denoting an expressed disagreement with ensuing verbal behaviour by two parties. I see Johnson's new concept of ‘Argument’, as developed in his book Manifest Rationality, as a hybrid of the two common senses of ‘Argument’, and, accordingly, I try to define and give the identity conditions of Johnson-arguments. Finally, I disagree with (...) Johnson on the nature of the definition he thinks he has proposed, and I conclude with observations suggesting that his logical perspective has dialectical and rhetorical components. (shrink)

The object of this paper is to show why recent research in the psychology of deductive and probabilistic reasoning does not have.

In this paper, we will explore two initiatives that focus on the importance of employing logical theories in educating people how to think and reason properly, one in Poland: The Lvov-Warsaw School; the other in North America: The Informal Logic Initiative. These two movements differ in the logical means and skills that they focus on. However, we believe that they share a common purpose: to educate students in logic and reasoning (logical education conceived as a process) so that they may (...) be able to apply their skills to analyze the issues in their society (logical culture as a result of logical education). The aim of the paper is to justify this claim by exploring research objectives and products that are common to both movements. (shrink)

This paper illustrates the difficulties that context-dependence poses for defining the so-called logical fallacies of affirming the consequent and denying the antecedent. In particular, I question whether these fallacies can be identified with specific argument patterns. I argue that judging such patterns as fallacious is relative to a) the type of underlying reasoning, and b) the world-knowledge deemed relevant to the argumentation at hand. It is concluded that a more context-sensitive definition should be pursued.

I will suggest, in this article, a possible explanation of the fact that legal language appears incoherent to the general public. I will present one legal text (an indictment), explaining why it appears incoherent to legal laypersons. I will argue that the traits making this particular text appear incoherent are, first, that a specialized legal meaning is conveyed implicitly and, second, that there are no key-words that could direct laypersons to the knowledge making this meaning obvious to legalists. I will (...) conclude that any legal text having these traits is likely to appear incoherent to the general public and suggest that the traits making my example appear incoherent might be rather common among the various texts of the various legal systems. On this suggestion there is no need to assume any causal relation between lawyers’ social interests and the apparent incoherence of legal language as it entails that this incoherence is inevitable. (I will argue that it is a result of the facts that legal language is ordinary language used, in the ordinary way, in the special context of the legal discourse.). (shrink)

To prove the equivalence one must start with one side, and the earlier-later side seems, for starting with, logically the clearer. The equivalence is provable on reasonable definitions of ‘past’, ‘present’ and ‘future’ in terms of the earlier-later structure of time. McTaggart's attempted distinction between the past-present-future A series and the earlier-later B series, as though they were rivals for the structure of time, is based on an unexamined, and false, assumption. The equivalence shows they are not rivals; they are (...) quite consistent with each other. A very serious consequence is that all subsequent argument, from the A side or the B, however sophisticated, is flawed to the extent that it accepts McTaggart's false distinction. (shrink)

This work studies manipulative use of language that can be called “deliberate failure of communication”; I characterize this kind of manipulation and show that it can be found in the discourse of marketing experts and legal professionals. Relying on relevance theory, I show that manipulation of this kind takes advantage of what van Dijk calls the “context model” of the addressees. I exemplify two ways in which the context models of some of the discourse’s participants might be misused in order (...) to manipulate them. One way is exemplified by a text from an advertisement, the other by a text from a criminal court file. I propose, finally, that the analysis supports van Dijk’s view that social, discursive, and epistemic inequalities reproduce one another in a kind of vicious circle. It suggests, in van Dijk’s terms, that manipulation by deliberate failure of communication is a discriminatory use of language employed by elite groups in order to reproduce their social power. (shrink)

The rhetoric-analytic critique of experimental psychology owes its apparent attractiveness to (a) some erroneous ideas about cognitive psychology and the rationale of experimentation, (b) the failure to distinguish between prior data and evidential data vis-à-vis the to-be-corroborated explanatory theory, and (c) evidential data owes their identity to a theory that is independent of the theory being tested. Theories in cognitive psychology are accepted because they can withstand concerted efforts to falsify them.

This essay on the social history of logic instruction considers the programmatic writings of Carnap/Neurath, but especially in the widely read book by Lillian Lieber, Mits, Wits and Logic, where Mits is the man in the street and Wits the woman in the street. In the ‘pre-Toulmin’ days it was seriously argued that the intense study of formal logic would create a more rational frame of mind and have many beneficial effects upon the social and political life. It arose from (...) the conviction that most metaphysical conundrums, religious and political problems and even fanaticism had their root in the irrationality of ordinary discourse, which had to be replaced by the more logical ‘ideal language’ of Principia Mathematica. The enthusiastic promotion of formal logic occurred at a time when it was widely thought that minds could be ‘made over’, ‘reprogrammed’ by proper intervention. This stands in stark contrast to the motivation for teaching informal logic and critical thinking, as it becomes apparent in a 1981 exchange between Ralph Johnson and Gerald Massey in Teaching Philosophy. Most of this essay focuses on Lillian Lieber, an earnest and enthusiastic advocate of the cause of formal logic, and on the reasons for the widespread conviction that, for the sake of peace and social harmony, formal logic should, if possible, be taught to every man, woman and child. (shrink)