This paper offers an interpretation of multiple-conclusion sequents as a kind of meta-inference rule: just as single-conclusion sequents represent inferences from sentences to sentences, so multiple-conclusion sequents represent a certain kind of inference from single-conclusion sequents to single-conclusion sequents. The semantics renders sound and complete the standard structural rules of reflexivity, monotonicity (or thinning), and transitivity (or cut). The paper is not the first one to attempt to account for multiple-conclusion sequents without invoking notions of truth or falsity—but unlike earlier (...) such efforts, which have typically helped themselves to primitive notions of both acceptance and rejection, the present one makes do with the former alone. For technical reasons, the treatment is limited to sequents with non-empty succedents. (shrink)

In a series of publications beginning in the 1980s, John Etchemendy has argued that the standard semantical account of logical consequence, due in its essentials to Alfred Tarski, is fundamentally mistaken. He argues that, while Tarski's definition requires us to classify the terms of a language as logical or non-logical, no such division is guaranteed to deliver the correct extension of our pre-theoretical or intuitive consequence relation. In addition, and perhaps more importantly, Tarski's account is claimed to be incapable of (...) explaining an essential modal/epistemological feature of consequence, namely, its necessity and apriority. Bernard Bolzano (1781-1848) is widely recognized as having anticipated Tarski's definition in his Wissenschaftslehre (or Theory of Science ) of 1837. Because of the similarities between his account and Tarski's, Etchemendy's arguments have also been extended to cover Bolzano. The purpose of this article is to consider Bolzano's theory in the light of these criticisms. We argue that, due to important differences between Bolzano's and Tarski's theories, Etchemendy's objections do not apply immediately to Bolzano's account of consequence. Moreover, Bolzano's writings contain the elements of a detailed philosophical response to Etchemendy. (shrink)

Should we explicate truth in terms of meaning, or meaning in terms of truth? Ramsey, Prior and Strawson all favoured the former approach: a statement is true if and only if things are as the speaker, in making the statement, states them to be; similarly, a belief is true if and only if things are as a thinker with that belief thereby believes them to be. I defend this explication of truth against a range of objections.Ramsey formalized this account of (...) truth as follows: B is true =df ∃P; in §i, I defend this formula against the late Peter Geach's objection that its right‐hand side is ill‐formed. Davidson held that Ramsey and co. had the whole matter back to front: on his view, we should explicate meaning in terms of truth, not vice versa. In §ii, I argue that Ramsey's approach opens the way to a more promising approach to semantic theorizing than Davidson's. Ramsey presents his formula as a definition of truth, apparently contradicting Tarski's theorem that truth is indefinable. In §iii, I show that the contradiction is only apparent: Tarski assumes that the Liar‐like inscription he uses to prove his theorem has a content, but Ramsey can and should reject that assumption. As I explain in §iv, versions of the Liar Paradox may be generated without making any assumptions about truth: paradox arises when the impredicativity that is found when a statement's content depends on the contents of a collection of statements to which it belongs turns pathological. Since they do not succeed in saying anything, such pathological utterances or inscriptions pose no threat to the laws of logic, when these are understood as universal principles about the ways things may be said or thought to be. There is, though, a call for rules by following which we can be sure that any conclusion deduced from true premisses is true, and hence says something. Such rules cannot be purely formal, but in §v I propose a system of them: this opens the way to the construction of deductive theories even in circumstances where producing a well‐formed formula is no guarantee of saying anything. (shrink)

The phenomenon of quantification into attitude ascriptions has haunted broadly Fregean views, according to which co-referential proper names are not always substitutable salva veritate in attitude ascriptions. Opponents of Fregeanism argue that a belief ascription containing a proper name such as ‘Michael believes that Lindsay is charitable’ is equivalent to a quantified sentence such as ‘there is someone such that Michael believes that she is charitable, and that person is Lindsay’. They conclude that the semantic contribution of a name such (...) as ‘Lindsay’ is the same as the semantic contribution of a variable under an assignment, which these opponents suggest is merely the object assigned to that variable. However, renewed interest in variables suggests that they make a more complicated contribution to the semantic processing of sentences that contain them. In particular, a variable contributes both an assignment-unsaturated and an assignment-saturated semantic value. I use this dual role of the semantics of variables to develop a response to the argument from quantifying in. I take as my point of departure Cumming's () view that an attitude ascription relates the subject of an attitude to the assignment-unsaturated semantic value of an open sentence. I argue that this approach fails. I propose an alternative, according to which the truth of a belief ascription depends on both the assignment-saturated and the assignment-unsaturated semantic value of the open sentence in its that-clause. This approach reverses standard assumptions concerning the relation between quantification and substitution. (shrink)

. “The Notebook Corner,” edited by Enrico Pattaro, makes its first appearance here as a new section of Ratio Juris. This new section can be described in a sense as an offshoot of the project for A Treatise of Legal Philosophy and General Jurisprudence, a work still in progress composed of five theoretical volumes and six historical ones. The theoretical volumes receive a brief presentation in the paper immediately below, with a specific focus on Volume 1, entitled The Law and (...) the Right: A Reappraisal of the Reality That Ought to Be. This volume is then discussed as well by Rosaria Conte and Cristiano Castelfronchi in the second paper of this “Notebook Corner”. (shrink)

Truth and realism have effectively disappeared as critical standards in American television criticism. McConnell researched writings in this area to find what little has been said about truth and realism since 1983. He theorizes that a closed ideological hegemony that is American television makes objective truth uncomfortable, leading to disappearance of truth and realism as a critical standard.

The concept of information has well-known difficulties. Among the many issues that have been discussed is the alethic nature of a semantic conception of information. Floridi :197–222, 2004; Philos Phenomenol Res 70:351–370, 2005; EUJAP 3:31–41, 2007; The philosophy of information, Oxford University Press, Oxford, 2011) argued that semantic information must be truthful. In this article, arguments will be presented in favor of an alethically neutral conception of semantic information and it will be shown that such a conception can withstand Floridi’s (...) criticism. In particular, it is argued that an alethically neutral conception of semantic information can manage the so-called Bar-Hillel Carnap paradox, according to which contradictions have maximum informational content. This issue, as well as some of Floridi’s other arguments, is resolved by disentangling the property of being information from the property of being informative. The essay’s final conclusion is that although semantic information is alethically neutral, a veridical conception of semantic information can, and should, be retained as a subconcept of semantic information, as it is essential for the analysis of informativity, which, unlike the property of being information, depends on truth. (shrink)

A response to critics, Douglas Patterson and Mark Textor, on Künne's modest theory of truth in *Conceptions of Truth*.

A response to certain parts of Rumfitt : I defend Davidson's project in semantics, suggest that Rumfitt's use of sentential quantification renders his definition of truth needlessly elaborate, and pose a question for Rumfitt's handling of the strengthened Liar.

Carnap's philosophy is examined from new viewpoints, including three important distinctions: (i) language as calculus vs language as universal medium; (ii) different senses of completeness: (iii) standard vs nonstandard interpretations of (higher-order) logic. (i) Carnap favored in 1930-34 the "formal mode of speech," a corollary to the universality assumption. He later gave it up partially but retained some of its ingredients, e.g., the one-domain assumption. (ii) Carnap's project of creating a universal self-referential language is encouraged by (ii) and by the (...) author's recent work. (iii) Carnap was aware of (iii) and occasionally used the standard interpretation, but was not entirely clear of the nature of the contrast. (shrink)

Friedrich Nietzsche and Luitzen Egbertus Jan Brouwer had strong personalities and freely expressed unconventional opinions. In particular, they dared to challenge the traditional view that considered Aristotelian logic as being absolute and intrinsic to man. Although they formed this opinion in different ways and in different contexts, they both based it on a view of life that considered it as a struggle for power in which logic was a weapon. Therefore, it is interesting to carry out an in-depth analysis on (...) the origins, the core of their opinions concerning logic and the consequences. As a matter of fact, a detailed analysis and a comparison of their contributions to the philosophy of logic have not yet been carried out. In this paper, I intend to present the results of my research.. (shrink)

Though deceptively simple and plausible on the face of it, Craig's interpolation theorem (published 50 years ago) has proved to be a central logical property that has been used to reveal a deep harmony between the syntax and semantics of first order logic. Craig's theorem was generalized soon after by Lyndon, with application to the characterization of first order properties preserved under homomorphism. After retracing the early history, this article is mainly devoted to a survey of subsequent generalizations and applications, (...) especially of many-sorted interpolation theorems. Attention is also paid to methodological considerations, since the Craig theorem and its generalizations were initially obtained by proof-theoretic arguments while most of the applications are model-theoretic in nature. The article concludes with the role of the interpolation property in the quest for "reasonable" logics extending first-order logic within the framework of abstract model theory. (shrink)

Though deceptively simple and plausible on the face of it, Craig's interpolation theorem has proved to be a central logical property that has been used to reveal a deep harmony between the syntax and semantics of first order logic. Craig's theorem was generalized soon after by Lyndon, with application to the characterization of first order properties preserved under homomorphism. After retracing the early history, this article is mainly devoted to a survey of subsequent generalizations and applications, especially of many-sorted interpolation (...) theorems. Attention is also paid to methodological considerations, since the Craig theorem and its generalizations were initially obtained by proof-theoretic arguments while most of the applications are model-theoretic in nature. The article concludes with the role of the interpolation property in the quest for "reasonable" logics extending first-order logic within the framework of abstract model theory. (shrink)

The main thesis of this paper is that we sometimes are disposed to accept false and even jointly inconsistent claims by virtue of our semantic competence, and that this comes to light in the sorites and liar paradoxes. Among the subsidiary theses are that this is an important source of indeterminacy in truth conditions, that we must revise basic assumptions about semantic competence, and that classical logic and bivalence can be upheld in the face of the sorites paradox.

W. V. Quine thinks logical truth can be defined in purely extensional terms, as follows: a logical truth is a true sentence that exemplifies a logical form all of whose instances are true. P. F. Strawson objects that one cannot say what it is for a particular use of a sentence to exemplify a logical form without appealing to intensional notions, and hence that Quine's efforts to define logical truth in purely extensional terms cannot succeed. Quine's reply to this criticism (...) is confused in ways that have not yet been noticed in the literature. This may seem to favour Strawson's side of the debate. In fact, however, a proper analysis of the difficulties that Quine's reply faces suggests a new way to clarify and defend the view that logical truth can be defined in purely extensional terms. (shrink)

In section 1, I develop epistemic communism, my view of the function of epistemically evaluative terms such as ‘rational’. The function is to support the coordination of our belief-forming rules, which in turn supports the reliable acquisition of beliefs through testimony. This view is motivated by the existence of valid inferences that we hesitate to call rational. I defend the view against the worry that it fails to account for a function of evaluations within first-personal deliberation. In the rest of (...) the paper, I then argue, on the basis of epistemic communism, for a view about rationality itself. I set up the argument in section 2 by saying what a theory of rational deduction is supposed to do. I claim that such a theory would provide a necessary, sufficient, and explanatorily unifying condition for being a rational rule for inferring deductive consequences. I argue in section 3 that, given epistemic communism and the conventionality that it entails, there is no such theory. Nothing explains why certain rules for deductive reasoning are rational. (shrink)

Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate (...) Q is one whose existentialization, ∃ x Q, is logically true; otherwise, Q is existential-import-free or simply import-free.How abundant or widespread is existential import? How abundant or widespread are existential-import predicates in themselves or in comparison to import-free predicates? We show that existential-import predicates are quite abundant, and no less so than import-free predicates. Existential.. (shrink)

I present a notion of invariance under arbitrary surjective mappings for operators on a relational finite type hierarchy generalizing the so-called Tarski-Sher criterion for logicality and I characterize the invariant operators as definable in a fragment of the first-order language. These results are compared with those obtained by Feferman and it is argued that further clarification of the notion of invariance is needed if one wants to use it to characterize logicality.

I present a notion of invariance under arbitrary surjective mappings for operators on a relational finite type hierarchy generalizing the so-called Tarski-Sher criterion for logicality and I characterize the invariant operators as definable in a fragment of the first-order language. These results are compared with those obtained by Feferman and it is argued that further clarification of the notion of invariance is needed if one wants to use it to characterize logicality.

This article, after briefly discussing Alfred Tarski's influential theory of truth, turns to a more recent theory of truth, a deflationary, or minimalist, theory. One of the chief elements of a deflationary, or minimalist, theory of truth is that it replaces the question of what truth is with the question of what “true” does. After setting out the central features of the minimalist theory of truth, the article explains the motivation for opting for such a position. In addition, it provides (...) some reasons for thinking that such a theory of truth is “minimal” or “deflationary” in the way that contemporary truth theorists have claimed it to be. (shrink)

We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ?On the Concept of Following Logically?. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, we note (...) more than 400 differences. Several dozen of these are substantive differences due to revisions by Tarski to the Polish version which he did not incorporate in the German version. With respect to these revisions the Polish version should be regarded as more authoritative than the German. Hence scholars limited to an English translation should use ours. (shrink)