Online research in philosophy

The most enlightening examination to date of the developments of Frege's thinking about his logic, this book introduces a new kind of logical language, one that ...

Our aim is to express in exact terms the old idea of solving problems by pure questioning. We consider the problem of derivability: Is A derivable from by classical propositional logic?. We develop a calculus of questions E *; a proof (called a Socratic proof) is a sequence of questions ending with a question whose affirmative answer is, in a sense, evident. The calculus is sound and complete with respect to classical propositional logic. A Socratic proof in E * can be transformed into a Gentzen-style proof in some sequent calculi. Next we develop a calculus of questions E **; Socratic proofs in E ** can be transformed into analytic tableaux. We show that Socratic proofs can be grounded in Inferential Erotetic Logic. After a slight modification, the analyzed systems can also be viewed as hypersequent calculi.

The concept of search scenario is explicated in terms of erotetic logic, i.e., the logic of questions. Different kinds of erotetic search scenarios are characterized. The basic logical properties of erotetic search scenarios are analyzed.

The main goal of this paper is to present and compare two approaches to formalizing cross-world comparisons like John might have been taller than he is in quantified modal logics. One is the standard method employing degrees and graded positives, according to which the example just given is to be paraphrased as something like The height that John has is such that he might have had a height greater than it, which is amenable to familiar formalization strategies with respect to quantified modal logic. The other approach, based on subjunctive modal logic, mimics the mixed indicative-subjunctive patterns typical of cross-world comparisons in many natural languages by means of explicit mood markers. This latter approach is new and should, for various reasons, appeal to linguists and philosophers. Along the way, I argue that attempts to capture cross-world comparison by means of sentential operators are either inadequate or subject to substantive logical and philosophical objections.

Putnam and others have argued that an examination of structures arising in quantum mechanics can lead to a non-classical propositional logic, quantum logic. In this paper it is argued that the procedure by which quantum logic is said to be discovered, a process called reading off, is fundamentally flawed. A parody fable shows that reading off leads to absurd consequences. The fable also leads one to cast doubt on the following claims central to the quantum logic program: (i) logic can be reformed locally; (ii) classical logic is read off classical physics; and (iii) reading off is a justifiable process because quantum logic resolves quantum paradoxes.

Whether mathematical truths are syntactical (as Rudolf Carnap claimed) or empirical (as Mill actually never claimed, though Carnap claimed that he did) might seem merely an academic topic. However, it becomes a practical concern as soon as we consider the role of questions. For if we inquire as to the truth of a mathematical statement, this question must be (in a certain respect) meaningless for Carnap, as its truth or falsity is certain in advance due to its purely syntactical (or formal-semantical) nature. In contrast, for Mill such a question is as valid as any other. These differing views have their consequences for contemporary erotetic logic.

particular alternative logic could be relevant to another one? The most important part of a response to this question is to remind the reader of the fact that independence friendly (IF) logic is not an alternative or “nonclassical” logic. (See here especially Hintikka, “There is only one logic”, forthcoming.) It is not calculated to capture some particular kind of reasoning that cannot be handled in the “classical” logic that should rather be called the received or conventional logic. No particular epithet should be applied to it. IF logic is not an alternative to our generally used basic logic, the received first-order logic, aka quantification theory or predicate calculus. It replaces this basic logic in that it is identical with this “classical” first-order logic except that certain important flaws of the received first-order logic have been corrected. But what are those flaws and how can they be corrected? To answer these questions is to explain the basic ideas of IF logic. Since this logic is not as well known as it should be, such explanation is needed in any case. I will provide three different but not unrelated motivations for IF logic.

This article discusses what is sometimes called the third paradox of material implication. Readers choosing to download this piece should please be so kind as to respect the author's wishes and download the published corrigendum as well, which is available via the "other links" tab.

A relativized concept of a possiblecorrect answer to a why-question is introduced. Acertain procedure of looking for acceptable answers towhy-questions is analyzed in terms of erotetic logic,i.e., the logic of questions.

Exactly what is meant by the requirement that witnesses swear in a court of law to tell "the whole truth"? It cannot mean simply the "truth," because that's a separate and prior requirement. It cannot mean "nothing but the truth," because that's also a separate requirement. It cannot mean "the whole story," because the adversary system not only does not require that, it does not even permit that. All it permits the witness to do is answer the questions put to him. Using erotetic logic, the author suggests an answer to what is meant by the requirement.