This book contains a selection of the papers presented at the Logic, Reasoning and Rationality 2010 conference in Ghent. The conference aimed at stimulating the use of formal frameworks to explicate concrete cases of human reasoning, and conversely, to challenge scholars in formal studies by presenting them with interesting new cases of actual reasoning. According to the members of the Wiener Kreis, there was a strong connection between logic, reasoning, and rationality and that human reasoning is rational in so far (...) as it is based on logic. Later, this belief came under attack and logic was deemed inadequate to explicate actual cases of human reasoning. Today, there is a growing interest in reconnecting logic, reasoning and rationality. A central motor for this change was the development of non-classical logics and non-classical formal frameworks. The book contains contributions in various non-classical formal frameworks, case studies that enhance our apprehension of concrete reasoning patterns, and studies of the philosophical implications for our understanding of the notions of rationality. (shrink)

Responding to the paradox of inference and the related problems in philosophy of logic, this paper argues for the necessity of distinguishing between two different objects of justification: logica utens and logica docens. Then, equipped with Peirce’s critical common-sensist conception of logica utens and his classification of sciences, I propose a diagnosis of and a solution to the problem of justification of logic. I argue that this alternative approach successfully avoids circularity in which most attempts in philosophy of logic have (...) been inescapably trapped. I also anticipate and respond to possible objections to taking a Peircean turn in justifying logic. (shrink)

In “Truth by Convention” W.V. Quine gave an influential argument against logical conventionalism. Even today his argument is often taken to decisively refute logical conventionalism. Here I break Quine’s arguments into two— the super-task argument and the regress argument—and argue that while these arguments together refute implausible explicit versions of conventionalism, they cannot be successfully mounted against a more plausible implicit version of conventionalism. Unlike some of his modern followers, Quine himself recognized this, but argued that implicit conventionalism was explanatorily (...) idle. Against this I show that pace Quine’s claim that implicit conventionalism has no content beyond the claim that logic is firmly accepted, implicit rules of inference can be used to distinguish the firmly accepted from the conventional. As part of my case, I argue that positing syntactic rules of inference as part of our linguistic competence follows from the same methodology that leads contemporary linguists and cognitive scientists to posit rules of phonology, morphology, and grammar. The upshot of my discussion is a diagnosis of the fallacy in Quine’s master critique of logical conventionalism and a re-opening of possibilities for an attractive conventionalist theory of logic. (shrink)

Many arguments that show p to be enthymematic (in an argument for q) rely on claims like “if one did not believe that p, one would not have a reason for believing that q.” Such arguments are susceptible to the neg-raising fallacy. We tend to interpret claims like “X does not believe that p” as statements of disbelief (X's belief that not-p) rather than as statements of withholding the belief that p. This article argues that there is a tendency to (...) equivocate in arguments for the enthymematicity of arguments (e.g., Lewis Carroll's paradox, Hume's problem) as well as in arguments for the enthymematicity of action explanations (e.g., arguments for psychologism and for explanatory individualism). The article concludes with a warning, because the equivocation is often helpful in teaching and because neg-raising verbs include philosophically vital verbs: desire, want, intend, think, suppose, imagine, expect, feel, seem, appear. (shrink)

Lewis Carroll's famous puzzle leads to an explanatory challenge: what must we know to grasp the logical necessity of deductive arguments? This paper argues that intellectualism lacks a philosophically satisfying explanation to that puzzle.

Infinite regress arguments are part of a philosopher's tool kit of argumentation. But how sharp or strong is this tool? How effectively is it used? The typical presentation of infinite regress arguments throughout history is so succinct and has so many gaps that it is often unclear how an infinite regress is derived, and why an infinite regress is logically problematic, and as a result, it is often difficult to evaluate infinite regress arguments. These consequences of our customary way of (...) using this tool indicate that there is a need for a theory to re-orient our practice. My general approach to contribute to such a theory, consists of collecting and evaluating as many infinite regress arguments as possible, comparing and contrasting many of the formal and non-formal properties, looking for recurring patterns, and identifying the properties that appeared essential to those patterns. Two very general questions guided this work: How are infinite regresses generated in infinite regress arguments? How do infinite regresses logically function as premises in an argument? In answering these questions I clarify the notion of an infinite regress; identify different logical forms of infinite regresses; describe different kinds of infinite regress arguments; distinguish the rhetoric from the logic in infinite regress arguments; and suggest ways of improving our discussion and our practice of constructing and evaluating these arguments. (shrink)

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with (...) other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems). (shrink)