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)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

This paper concerns the apparent fact — discussed by Sinan Dogramaci and Brian Weatherson — that inductive reasoning often interacts in disastrous ways with patterns of reasoning that seem perfectly fine in the deductive case. In contrast to Dogramaci's and Weatherson's own suggestions, I argue that these cases show that we cannot reason inductively about arbitrary objects. Moreover, as I argue, this prohibition is neatly explained by a certain hypothesis about the rational basis of inductive reasoning — namely, the hypothesis (...) that inductive reasoning is fundamentally reasoning about what normally happens. (shrink)

This paper concerns the apparent fact — discussed by Sinan Dogramaci and Brian Weatherson — that inductive reasoning often interacts in disastrous ways with patterns of reasoning that seem perfectly fine in the deductive case. In contrast to Dogramaci's and Weatherson's own suggestions, I argue that these cases show that we cannot reason inductively about arbitrary objects. Moreover, as I argue, this prohibition is neatly explained by a certain hypothesis about the rational basis of inductive reasoning — namely, the hypothesis (...) that inductive reasoning is fundamentally reasoning about what normally happens. (shrink)

Although there has been a recent swell of interest in theories of truth that attempt solutions to the liar paradox and the other paradoxes affecting our concept of truth, many of these theories have been criticized for generating new paradoxes, called revenge paradoxes. The criticism is that the theories of truth in question are inadequate because they only work for languages lacking in the resources to generate revenge paradoxes. Theorists facing these objections offer a range of replies, and the matter (...) seems now to be at a standoff. I aim, first, to bolster the revenge objections by considering a relation, internalizability, between languages and theories of truth. A theory of truth is internalizable for a language iff there is an extension of that language in which the theory is expressible and for which the theory provides an accurate and complete assignment of semantic values. There are good reasons to think that acceptable theories of truth are internalizable for any language. With this internalizability requirement in hand, I argue that properly formulated revenge objections are decisive and that the replies to them are inadequate. Second, I show that the internalizability requirement can be met by a certain theory of truth. The central claim of this theory is that truth is an inconsistent concept and should be replaced with a pair of consistent concepts that can then be used to provide a semantics for our truth predicates. This theory is compatible with classical logic, does not give rise to revenge paradoxes of any kind, and satisfies the internalizability requirement. (shrink)

It is a platitude that when we reason, we often take things for granted, sometimes even justifiably so. The chemist might reason from the fact that a substance turns litmus paper red to that substance being an acid. In so doing, they take for granted, reasonably enough, that this test for acidity is valid. We ordinarily reason from things looking a certain way to their being that way. We take for granted, reasonably enough, that things are as they look Although (...) it is a platitude that we often take things for granted when we reason—whether justifiably or not—one might think that we do not have to. In fact, it is a natural expectation that were we not pressed by time, lack of energy or focus, we could always in principle make explicit in the form of premises every single presupposition we make in the course of our reasoning. In other words, it is natural to expect it to be true that presuppositionless reasoning is possible. In this essay, I argue that it is false: presuppositionless reasoning is impossible. Indeed, I think this is one of the lessons of a long-standing paradox about inference and reasoning known as Lewis Carroll’s (1985) regress of the premises. Many philosophers agree that Carroll’s regress teaches us something foundational about reasoning. I part ways about what it is that it teaches us. What it teaches us is that the structure of reasoning is constitutively presuppositional. (shrink)

This essay argues that the main lesson of Lewis Carroll's Regress is that arguments are constitutively presuppositional.

Can it ever be rational to revise one's own logic by one's own lights? In this paper I argue that logic is never rationally revisable, even if one's own logic gives rise to paradoxes and allows one to derive any conclusion whatsoever. Instead of revising logic, we need to revise a certain widely held position in the philosophy of logic, one tied to the standard conception of validity and to the alleged monotonicity of deductive reasoning. I develop the alternative conception (...) of validity and of deductive reasoning, which explains why we are generally entitled to the conclusions of deductive reasoning, even though we rationally do not accept them in certain circumstances tied to paradoxes. (shrink)

True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: the orthodox definition given (...) in terms of interpretations or models, a metaphysical definition given in terms of possible worlds, and a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference. (shrink)

If the reliability of a source of testimony is open to question, it seems epistemically illegitimate to verify the source’s reliability by appealing to that source’s own testimony. Is this because it is illegitimate to trust a questionable source’s testimony on any matter whatsoever? Or is there a distinctive problem with appealing to the source’s testimony on the matter of that source’s own reliability? After distinguishing between two kinds of epistemically illegitimate circularity—bootstrapping and self-verification—I argue for a qualified version of (...) the claim that there is nothing especially illegitimate about using a questionable source to evaluate its own reliability. Instead, it is illegitimate to appeal to a questionable source’s testimony on any matter whatsoever, with the matter of the source’s own reliability serving only as a special case. (shrink)

This paper critically examines currently influential transparency accounts of our knowledge of our own beliefs that say that self-ascriptions of belief typically are arrived at by “looking outward” onto the world. For example, one version of the transparency account says that one self-ascribes beliefs via an inference from a premise to the conclusion that one believes that premise. This rule of inference reliably yields accurate self-ascriptions because you cannot infer a conclusion from a premise without believing the premise, and so (...) you cannot infer from a premise that you believe the premise unless you do believe it. I argue that this procedure cannot be a source of justification, however, because one can be justified in inferring from p that q only if p amounts to strong evidence that q is true. This is incompatible with the transparency account because p often is not very strong evidence that you believe that p. For example, unless you are a weather expert, the fact that it will rain is not very strong evidence that you believe it will rain. After showing how this intuitive problem can be made precise, I conclude with a broader lesson about the nature of inferential justification: that beliefs, when justified, must be underwritten by beliefs, when justified, must be underwritten by evidential relationships between the facts or propositions which those beliefs represent. (shrink)

Applying good inductive rules inside the scope of suppositions leads to implausible results. I argue it is a mistake to think that inductive rules of inference behave anything like 'inference rules' in natural deduction systems. And this implies that it isn't always true that good arguments can be run 'off-line' to gain a priori knowledge of conditional conclusions.