Tractatus Logico-Philosophicus by Ludwig Wittgenstein: three parallel tree-structured editions. (1) Tree-structured arrangement of the German text, edited by David G. Stern, Joachim Schulte and Katia Saporiti. (2) Tree-structured arrangement of the English translation by Ogden and Ramsey, edited by David G. Stern. (3) Tree-structured arrangement of the English translation by Pears and McGuinness, edited by David G. Stern.

What makes it true when we say that something is not the case? Truthmaker maximalists think that every truth has a truthmaker—some fact in the world—that makes it true. No such facts can be found for the socalled negative truths. If a proposition is true when it has a truthmaker, then it would be false when it has no truthmaker. I therefore argue that negative truths, such as t<p>, are best understood as falsehoods, f<p>.

According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of (...) this notion. Another main part of the paper is concerned with a modification of this notion as it occurs in Michael Dummett’s book The Logical Basis of Metaphysics. The two notions are compared and there is a discussion of how they fare as a foundation for a theory of meaning. It is noted that Dummett’s notion has a simpler structure, but it is argued that it is less appropriate for the foundation of a theory of meaning, because the possession of a valid argument for a sentence in Dummett’s sense is not enough to be warranted to assert the sentence. (shrink)

In this ambitious and highly original study, McCabe presents an intricately structured argument designed to demonstrate Plato’s concern with fundamental issues of rationality and personhood. In doing so, she pursues themes announced in her Plato’s Individuals and in Form and Argument in Late Plato, a collection she co-edited with Christopher Gill. The development of her position via consideration of the philosophical importance of characterization and the dialogue form in the Theaetetus, Sophist, Statesman, and Philebus leads her to focus in particular (...) on Plato’s depiction of his predecessors. These include, firstly, the Theaetetus’s Protagoras and Heraclitean flux theorists and the Sophist’s Parmenides and materialist giants, all “mean-minded opponents” whose views threaten the very possibility of rational inquiry. Refutation of them, accordingly, is Plato’s means of establishing certain basic principles of reason. (shrink)

The thesis that, in a system of natural deduction, the meaning of a logical constant is given by some or all of its introduction and elimination rules has been developed recently in the work of Dummett, Prawitz, Tennant, and others, by the addition of harmony constraints. Introduction and elimination rules for a logical constant must be in harmony. By deploying harmony constraints, these authors have arrived at logics no stronger than intuitionist propositional logic. Classical logic, they maintain, cannot be justified (...) from this proof-theoretic perspective. This paper argues that, while classical logic can be formulated so as to satisfy a number of harmony constraints, the meanings of the standard logical constants cannot all be given by their introduction and/or elimination rules; negation, in particular, comes under close scrutiny. (shrink)

Truthmaker maximalism is the claim that every truth has a truthmaker. The case of negative truths leads some philosophers to postulate negative states of affairs or to give up on truthmaker maximalism. This paper defends a version of the incompatibility view of negative truths. Negative truths can be made true by positive facts, and thus, truthmaker maximalism can be maintained without postulating negative states of affairs.

Volume 3, Issue 2, June 2019, Page 214-238.

ABSTRACT At the centre of Plato’s Euthydemus lie a series of arguments in which Socrates’ interlocutors, the sophists Euthydemus and Dionysodorus propose a radical account of truth (‘chopped logos’) according to which there is no such thing as falsehood, and no such thing as disagreement (here ‘counter-saying’). This account of truth is not directly refutable; but in response Socrates offers a revised account of ‘saying’ focussed on the different aspects of the verb (perfect and imperfect) to give a rich account (...) of saying, of truth and of knowledge. I argue that Socrates’ response has much to offer, notably in its amplification of the process of saying and cognition, and the development of virtue. (shrink)

The focus of this paper are Dummett's meaning-theoretical arguments against classical logic based on consideration about the meaning of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett's outlook on the theory of meaning. In particular, I (...) shall grant Dummett his general bias towards verificationism, encapsulated in the slogan 'meaning is use'. The second general assumption I see no need to question is Dummett's particular breed of molecularism. Some of Dummett's assumptions will have to be given up, if classical logic is to be vindicated in his meaning-theoretical framework. A major result of this paper will be that the meaning of negation cannot be defined by rules of inference in the Dummettian framework. (shrink)

This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the meanings of (...) modal operators in terms of rules of inference. (shrink)

This is a commentary on MM McCabe's "First Chop your logos... Socrates and the sophists on language, logic, and development". In her paper MM analyses Plato's Euthydemos, in which Plato tackles the problem of falsity in a way that takes into account the speaker and complements the Sophist's discussion of what is said. The dialogue looks as if it is merely a demonstration of the silly consequences of eristic combat. And so it is. But a main point of MM's paper (...) is that there is serious philosophy in the Euthydemos, too. MM argues that to counter the sophist brothers Euthydemos and Dionysodoros, Socrates points out that that there are different aspects to the verb 'to say' that run in parallel to the different aspects of the very 'to learn'. So just as there is continuity rather than ambiguity between 'to learn' and 'to understand', so there is continuity between the different aspects of saying. Thus Socrates puts forward a teleological account of both learning and meaning. Following up on some of MM's thoughts, I argue that the sophists subscribe, despite appearance, to a theory of meaning that respects serious and widely accepted philosophical theses on meaning. -/- Forthcoming in the Australasian Philosophical Review. The curator of the volume is Fiona Leigh, and the committee also has Hugh Benson and Tim Clarke. You can find MM's paper as well as the commentaries by Nicholas Denyer and Russell E. Jones and Ravi Sharma (and myself) by registering. (shrink)

Molnar argues that the problem of truthmakers for negative truths arises because we tend to accept four metaphysical principles that entail that all negative truths have positive truthmakers. This conclusion, however, already follows from only three of Molnar´s metaphysical principles. One purpose of this note is to set the record straight. I provide an alternative reading of two of Molnar´s principles on which they are all needed to derive the desired conclusion. Furthermore, according to Molnar, the four principles may be (...) inconsistent. By themselves, however, they are not. The other purpose of this note is to propose some plausible further principles that, when added to the four metaphysical theses, entail a contradiction. (shrink)

According to the truthmaker theory that we favour, all contingent truths are made true by existing facts or states of affairs. But if that is so, then it appears that we must accept the existence of the negative facts that are required to make negative truths (such as 'There is no hippopotamus in the room.') true. We deny the existence of negative facts, show how negative truths are made true by positive facts, point out where the (reluctant) advocates of negative (...) facts (Russell, Armstrong, et al.) went wrong, and demonstrate the superiority of our solution to the alternatives. (shrink)

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...) results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)