Wittgenstein gives voice to an aspiration that is central to his later philosophy, well before he becomes later Wittgenstein, when he writes in §4.112 of the Tractatus that philosophy is not a matter of putting forward a doctrine or a theory, but consists rather in the practice of an activity – an activity he goes on to characterize as one of elucidation or clarification – an activity which he says does not result in philosophische Sätze, in propositions of philosophy, but (...) rather in das Klarwerden von Sätzen, in our attaining clarity in our relation to the sentences of our language that we call upon to express our thoughts.1 To say that early Wittgenstein already aspired to such a conception of philosophy is not to gainsay that to aspire to practice philosophy in such a manner and to succeed in doing so are not the same thing. It is therefore not to deny that, by Wittgenstein’s later lights, the Tractatus is to be judged a work that is marked by forms of failure tied to its having failed fully to live up to such an aspiration. But if it is thus to be judged, then it is to some degree a failure even by Wittgenstein’s own earlier lights. This means that if one wants to understand the fundamental turn in Wittgenstein’s thinking as he moves from his earlier to his later philosophy, and why it is that he wanted the Tractatus to be published and read together with Philosophical Investigations, one needs to understand what sort of failure this is – and that requires coming to terms with the Tractatus’s own understanding of what sort of work it was trying to be. We think that readers of the Tractatus – be they admirers or detractors of Wittgenstein – have, on the whole, failed to do this. (shrink)

Logicism is, roughly speaking, the doctrine that mathematics is fancy logic. So getting clear about the nature of logic is a necessary step in an assessment of logicism. Logic is the study of logical concepts, how they are expressed in languages, their semantic values, and the relationships between these things and the rest of our concepts, linguistic expressions, and their semantic values. A logical concept is what can be expressed by a logical constant in a language. So the question “What (...) is logic?” drives us to the question “What is a logical constant?” Though what follows contains some argument, limitations of space constrain me in large part to express my Credo on this topic with the broad brush of bold assertion and some promissory gestures. (shrink)

This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. -/- The chapters of which this book is composed discuss the (...) subject from a rich variety of angles, including the history of logic, the proper interpretation of logical validity, natural deduction rules, the notions of harmony and of synonymy, the structure of proofs, the logical status of equality, intentional phenomena, and the proof theory of second-order arithmetic. All chapters relate directly to questions that have driven Schroeder-Heister's own research agenda and to which he has made seminal contributions. The extensive autobiographical chapter not only provides a fascinating overview of Schroeder-Heister's career and the evolution of his academic interests but also constitutes a contribution to the recent history of logic in its own right, painting an intriguing picture of the philosophical, logical, and mathematical institutional landscape in Germany and elsewhere since the early 1970s. The papers collected in this book are illuminatingly put into a unified perspective by Schroeder-Heister's comments at the end of the book. Both graduate students and established researchers in the field will find this book an excellent resource for future work in proof-theoretic semantics and related areas. (shrink)

In Tractatus 5.132 Wittgenstein argues that inferential justification depends solely on the understanding of the premises and conclusion, and is not mediated by any further act. On this basis he argues that Frege’s and Russell’s rules of inference are “senseless” and “superfluous”. This line of argument is puzzling, since it is unclear that there could be any viable account of inference according to which no such mediation takes place. I show that Wittgenstein’s rejection of rules of inference can be motivated (...) by taking account of his holistic construal of the relation between inference and understanding. (shrink)

This short book comprises “four largely self-contained studies … unified by a common interpretive approach”, the “investigation of the historical development of … Wittgenstein’s early philosophy”. Proops applies this historical approach to Wittgenstein’s conception of logic, his critique of “logical assertion,” his “picture theory” of language, and his discussion of the justification of deduction. He endeavors to “bring out how Wittgenstein develops his views … as foils to the positions developed by Frege and Russell”, arguing that “it is not Frege (...) but Russell whose work provides the most important background for … the Tractatus”. (shrink)

This thesis develops an account of ethics called the Linguistic Perspective, which is realist in a practical, non-theoretical sense, and is rooted Wittgenstein’s 'On Certainty'. On this account, normativity is intrinsic to human action and language; the norms of ethics are the logical limits of the most basic, unassailable concepts that practical reasoning requires for intelligibility. Part I lays the groundwork for this account by developing a Tractarian Reading of 'On Certainty'. Here, I contend that 'On Certainty' is primarily concerned (...) with the logical requirements and limits of language, and like the 'Tractatus' it develops these concerns in a realist direction. 'On Certainty', I argue, does so by advancing three key claims about logic: Everything descriptive of a language-game is part of logic; the boundary between logical and empirical propositions is not sharp; logic is founded on action. I investigate these claims, with particular emphasis on how natural human reactions provide logical conditions for the possibility of language. Hinge propositions, I argue, are rooted in these reactions; they point us to the limits of intelligibility of our concepts, though these limits are vague and inarticulable. In Part II, I discuss the practical syllogism and its validity. I argue that practical reasoning is distinct from theoretical reasoning and embodies a different standard of logical validity for inference. This standard is not strict and narrow, but creative and wide open; furthermore, it is an intrinsically ethical standard. Then, I advance my Linguistic Perspective on ethics, according to which human reactions provide the conditions for ethical normativity, just as they do for language. I argue that we can access ethical norms by reflecting on those linguistic concepts that are rooted in the most basic patterns of action, and by identifying the norms of behaviour that ensure the development of those concepts without contradiction. (shrink)

A running commentary is offered on the first half of Frege’s Grundlagen der Arithmetik, §17, and suggests that Frege anticipated the method of demonstration used by Paul Bernays for the Deduction Theorem.

We here propose a solution to the problem we have raised. Basically, the mathematical notion of entailment seems to be connected to the inferential rules from Classical Logic, so that if we have P: x belongs to the reals, and Q: x+2=5 => x=3, P |= Q. Notwithstanding, we would also have that if P: x belongs to the interval (7,10), and Q: x+2=5 => x=3, P |= Q. The second instance of entailment does not seem to be justifiable if (...) our intuition is consulted: Even though we could say that absurdity implies anything in Classical Logic, entailment should be a concept that belongs to the metalogic, not to the logic of the system, so that we should not be inside of the Classical Logic World by the time we assess things in what regards entailment. As another point, our discussions in Entailment led us to choose the sense has as a consequence for entailment, so that it is not really acceptable that we have, as a consequence, using normal language, of x being inside of the real interval (7,10) that if x+2=5, then x=3. If x is in that interval, x+2 should not be 5, unless we are talking about moduli of vectors. However, when we transfer to Classical Logic, in having the antecedent false, and the consequent false as well, we have that the implication, which some call material, is true. We here discuss this sort of matter in detail, and hope to get to the bottom of the issue, and perhaps to a universal solution. (shrink)