Bolzano's deducibility and tarski's logical consequence

In this paper I argue that Bolzano's concept of deducibility and Tarski's concept of logical consequence differ with respect to their philosophical intent. I distinguish between epistemic and ontic approaches to logic, and argue that Bolzano's deducibility presupposes an epistemic approach, while Tarski's logical consequence presupposes an ontic approach.     

On Bolzano's Concept of a Sum

Alongside his groundbreaking work in logic, Bernard Bolzano (1781–1848) made important contributions to ontology, notably with his theory of collections. Recent work has done much to elucidate Bolzano's conceptions, but his notion of a sum has proved stubbornly resistant to complete understanding. This paper offers a new interpretation of Bolzano's concept of a sum. I argue that, although Bolzano's presentation is defective, his conception is unexceptionable, and has important applications, notably in his work on the foundations of arithmetic.     

Remarks on Bolzano's Conception of Necessary Truth

This essay presents a new interpretation of Bolzano's account of necessary truth as set out in §182 of the Theory of Science. According to this interpretation, Bolzano's conception is closely related to that of Leibniz, with some important differences. In the first place, Bolzano's conception of necessary truth embraces not only what Leibniz called metaphysical or brute necessities but also moral necessities (truths grounded in God's choice of the best among all metaphysical possibilities). Second, in marked contrast to Leibniz, Bolzano maintains that there is still plenty of room for contingency even on this broader conception of necessity.     

Assertion, inference, and consequence

In this paper the informativeness account of assertion (Pagin in Assertion. Oxford University Press, Oxford, 2011) is extended to account for inference. I characterize the conclusion of an inference as asserted conditionally on the assertion of the premises. This gives a notion of conditional assertion (distinct from the standard notion related to the affirmation of conditionals). Validity and logical validity of an inference is characterized in terms of the application of method that preserves informativeness, and contrasted with consequence and logical consequence, that is defined in terms of truth preservation. The proposed account is compared with that of Prawitz (Logica yearbook 2008. pp. 175?C192. College Publications, London, 2009).     

Functional explanation,consequence explanation,and Marxism

I argued in Karl Marx's Theory of History that the central claims of historical materialism are functional explanations, and I said that functional explanations are consequence explanations, ones, that is, in which something is explained by its propensity to have a certain kind of effect. I also claimed that the theory of chance variation and natural selection sustains functional explanations, and hence consequence explanations, of organismic equipment. In Section I I defend the thesis that historical materialism offers functional or consequence explanations, and I reject Jon Elster's contention that game theory can, and should, assume a central role in the Marxist theory of society. In Section II I contrast functional and consequence explanation, thereby revising the position of Karl Marx's Theory of History, and I question whether evolutionary biology supports functional explanations. Section III is a critique of Elster's views on functional explanation, and Sections IV and V defend consequence explanation against metaphysical and epistemological doubts. A concluding section summarizes my present understanding of the status of historical materialist explanations.     

From constants to consequence, and back

Bolzano??s definition of consequence in effect associates with each set X of symbols (in a given interpreted language) a consequence relation ${\Rightarrow_X}$ . We present this in a precise and abstract form, in particular studying minimal sets of symbols generating ${\Rightarrow_X}$ . Then we present a method for going in the other direction: extracting from an arbitrary consequence relation ${\Rightarrow}$ its associated set ${C_\Rightarrow}$ of constants. We show that this returns the expected logical constants from familiar consequence relations, and that, restricting attention to sets of symbols satisfying a strong minimality condition, there is an isomorphism between the set of strongly minimal sets of symbols and the set of corresponding consequence relations (both ordered under inclusion).     

Conversation,relevance, and argumentation

This paper deals with the explanation the maxim of relevance provides for the way utterances in argumentative discourse follow each other in an orderly and coherent fashion. Several senses are distinguished in which utterances can be considered relevant. It is argued that an utterance can be considered relevant as an interactional act, as an illocutionary act, as a propositional act, and as an elocutionary act. These four kinds of relevance manifest the rational organization of discourse, which is aimed at bringing about mutual alignment between the participants, enabling them jointly to work out certain interactional outcomes that are acceptable to both of them.     

Command and consequence

Philosophical Studies - An argument is usually said to be valid iff it is truth-preserving—iff it cannot be that all its premises are true and its conclusion false. But imperatives (it is...     

Divine determinism,human freedom,and the consequence argument

In this paper I consider the view, held by some Thomistic thinkers, that divine determinism is compatible with human freedom, even though natural determinism is not. After examining the purported differences between divine and natural determinism, I discuss the Consequence Argument, which has been put forward to establish the incompatibility of natural determinism and human freedom. The Consequence Argument, I note, hinges on the premise that an action ultimately determined by factors outside of the actor’s control is not free. Since, I argue, divine determinism also entails that human actions are ultimately determined by factors outside of the actors’ control, I suggest that a parallel argument to the Consequence Argument can be constructed for the incompatibility of divine determinism and human freedom. I conclude that those who reject natural compatibilism on the basis of the Consequence Argument should also reject divine compatibilism.     

Audiences,relevance, and cognitive environments

This paper discusses the fundamental sense in which the components of an argument should be relevant to the intended audience. In particular, the evidence advanced should be relevant to the facts and assumptions that are manifest in the cognitive environment of the audience. A version of Sperber and Wilson's concept of the cognitive environment is applied to argumentative concerns, and from this certain features of audience-relevance are explored: that the relevance of a premise can vary with the audience; that irrelevant premises can be made relevant; that evidence can be relevant by degrees; and that this notion of relevance will assist the argumentation analyst in the identification and assessment of hidden premises.     

Contextualism,safety and epistemic relevance

The paper discusses approaches to Epistemic Contextualism that model the satisfaction of the predicate ‘know’ in a given context C in terms of the notion of belief/fact-matching throughout a contextually specified similarity sphere of worlds that is centred on actuality. The paper offers three counterexamples to approaches of this type and argues that they lead to insurmountable difficulties. I conclude that what contextualists (and Subject-Sensitive Invariantists) have traditionally called the ‘epistemic standards’ of a given context C cannot be explicated in terms of a contextually specified similarity sphere that is centred on actuality. The mentioned accounts of epistemic relevance and thus the corresponding accounts of the context-sensitivity (or subject-sensitivity) of ‘knows’ are to be rejected.

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The variety of consequence,according to Bolzano

Contemporary historians of logic tend to credit Bernard Bolzano with the invention of the semantic notion, of consequence, a full century before Tarski. Nevertheless, Bolzano's work played no significant rôle in the genesis of modern logical semantics. The purpose of this paper is to point out three highly original, and still quite relevant themes in Bolzano's work, being a systematic study of possible types of inference, of consistency, as well as their meta-theory. There are certain analogies with Tarski's concerns here, although the main thrust seems to be different, both philosophically and technically. Thus, if only obliquely, we also provide some additional historical perspective on Tarski's achievement.     

Combining classical logic, paraconsistency and relevance

We present a logic with has both a simple semantics and a cut-free Gentzen-type system on one hand, and which combines relevance logics, da Costa's paraconsistent logics, and classical logic on the other. We further show that the logic has many other nice properties, and that its language is ideal from the semantic point of view.     

Ideal evidence, relevance and second-order probabilities

Conclusion The concepts of supportive evidence and of relevant evidence seem very closely related to each other. Supportive evidence is clearly always relevant as well. But must relevant evidence be defined as evidence which is either supportive or weakeking? In an explicit or implicit manner, this is indeed the position of many philosophers. The paradox of ideal evidence, however, shows us that this is to restrictive. Besides increasing or decreasing the probability attached to some hypothesis, evidence can alter or interact with the background assumptions underlying the hypothesis.In most circumstances, the (post hoc) relevance of evidence can indeed be judged by its effect on the confidence one attaches to hypotheses. Occasionally, as in the circumstances described by Example I, and more generally called the Paradox of Ideal Evidence, the relevance of evidence to an hypothesis can only be understood by appeal to a broader sense.In Memory of My Father. Yehoshua Bar-HillelThe author wishes to thank Haim Gaifman for a most thoughtful and constructive review of an earlier draft of this paper.