In the most general terms, the Logical Connection Argument states that theory and practice are two inseparable aspects of the same thing. Every action, linguistic or otherwise, is an indivisible unity of content and the means by which it is expressed. Alternatively, we may talk of the inseparability of content and form, meaning and act of expression, goal and method or means of its realization, and so forth. The argument was meant to prove that intentions cannot be treated as (...) causes in social scientific explanation, but it did it at the cost of making any meta-analysis, and hence, critique, highly problematic. My position is that the LCA is indeed logical, and hence irrefutable. Nonetheless, we can distinguish between “raw” and “refined” versions of the argument. The refined version maintains that while ultimately and ideally, the content and means of expression presuppose one another in the sense that a content is inconceivable without a form, and vice versa, in reality there is never a perfect match between aims and methods. In typical circumstances, we do not have a precise sense of what we are doing; the meaning of our actions is gradually discovered in the course of exploratory behaviors, of which critique is an indispensable part. In this contribution, I venture to examine the problem from a neuropsychological perspective with the view to showing in exactly what sense and to what extent explorative behaviors and associated motivations preside over other activities. I argue that content is always underdetermined with respect to its form, and hence the alleged internal connection between them is not a given, but rather amounts to a regulative principle which motivates mutual adjustments. (shrink)

This is a critical discussion of the argument that since intentions are "logically connected" with their objects, Intentional actions cannot include intentions as their causes. Various versions of the argument are discussed, And it is argued that none of them shows the causal theory of intention to be inconsistent. It is argued that the causal theory is nevertheless wrong since intentions must be understood teleologically and as being, Therefore, Non-Contingently linked with actions.

Model-theoretic proofs of functional completenes along the lines of [McCullough 1971, Journal of Symbolic Logic 36, 15–20] are given for various constructive modal propositional logics with strong negation.

Logical connectives (otherwise known as 'logical constants' or 'logical particles') have seemed challenging to philosophers of language. This article gives a concise account of logical connectives.

The logical connection argument holds that factors which appear causally connected can be shown not to be so, At least when described in certain ways, If these factors are logically connected when so described. I argue that normal formulations of the logical connection argument confuse propositions and events. Moreover, When it is clarified in terms of "de re" necessity, It requires strong ontological assumptions for which no support is given and about the intelligibility of which there is reasonable (...) question. I conclude that the logical connection argument fails to give any reason for excluding any causal hypothesis. (shrink)

The logical connection argument claims that since the relation between a want and the supposedly resultant action is " logical " in nature, Whereas the relation between any cause and its effect must be contingent in nature, A want therefore cannot be the cause of an action. I consider four classical formulations of the lca, And review various objections that have been brought against them. Then I present my own formulation of the lca, Which is immune to such (...) objections. I conclude that we must abandon the idea that a person's wants cause his actions. (shrink)

An effect algebra is a partial algebraic structure, originally formulated as an algebraic base for unsharp quantum measurements. In this article we present an approach to the study of lattice effect algebras (LEAs) that emphasizes their structure as algebraic models for the semantics of (possibly) non-standard symbolic logics. This is accomplished by focusing on the interplay among conjunction, implication, and negation connectives on LEAs, where the conjunction and implication connectives are related by a residuation law. Special cases of (...) LEAs are MV-algebras and orthomodular lattices. The main result of the paper is a characterization of LEAs in terms of so-called Sasaki algebras. Also, we compare and contrast LEAs, Hájek's BL-algebras, and the basic algebras of Chajda, Halaš, and Kühr. (shrink)

1. A. Heyting (1930) introduced an intermediate logic whose semantics is based on a pair of states (‘here’ and ‘there’). This logic was axiomatized by Hosoi (1966), using the sequence of intermedia...

In this paper I will show the problems that are encountered when dealing with uniqueness of connectives in a bilateralist setting within the larger framework of proof-theoretic semantics and suggest a solution. Therefore, the logic 2Int is suitable, for which I introduce a sequent calculus system, displaying - just like the corresponding natural deduction system - a consequence relation for provability as well as one dual to provability. I will propose a modified characterization of uniqueness incorporating such a duality (...) of consequence relations, with which we can maintain uniqueness in a bilateralist setting. (shrink)

In this paper, I consider Sterba’s recent criticism of skeptical theism in context of his argument from evil. I show that Sterba’s criticism of skeptical theism shares an undesirable trait with all past criticisms of skeptical theism: it fails. This is largely due to his focus on causal connections and his neglect of logical connections. Because of this, his argument remains vulnerable to skeptical theism.

Language employs various coordinators to connect propositions, a subset of which are “logical” in nature and thus analogous to the truth operators of formal logic. We here focus on two linguistic connectives and their negations: conjunction _and_ and (inclusive) disjunction _or_. Linguistic connectives exhibit a truth-conditional component as part of their meaning (their semantics), but their use in context can give rise to various implicatures and presuppositions (the domain of pragmatics) as well as to inferences that go (...) beyond semantic/pragmatic properties (the result of reasoning processes). We provide a comprehensive review of the role of the logical connectives in language and argue that three sets of factors—semantic, pragmatic, and those related to reasoning—are separate and separable, though some details may differ cross-linguistically. As a way to showcase the argument, we present two experiments in language comprehension in Spanish wherein pragmatic content was minimised and reasoning processes neutered, thus potentially highlighting what might be the default meanings of the connectives under study. In Experiment 1 we show that the conjunctive reading of inclusive disjunction is available in positive contexts other than in syntactically intricate cases such as downward entailing and free choice contexts, contrary to what has been claimed in the literature. In Experiment 2 we show that negated conjunctions and disjunctions in Spanish can easily receive the same interpretation when contrasted against the same context and, moreover, that these interpretations match those available in English, despite claims from the literature that linguistic connectives and local negation interact differently in English and Romance languages. (shrink)

T?s?, a thirteenth century logician writing in Arabic, uses two logical connectives to build up molecular propositions: ?if-then?, and ?either-or?. By referring to a dichotomous Tree, T?s? shows how to choose the proper disjunction relative to the terms in the disjuncts. He also discusses the disjunctive propositions which follow from a conditional proposition.

Jerry Fodor argues for individualism and for narrow content by way of rejecting an argument based on the conceptual connections between reason-properties and action-properties. In this paper I show that Fodor’s argument fails. He is right that there is a New Logical Connections Argument to be made, and that it does show that water thoughts and XYZ thoughts are not different causal powers with respect to intentional properties of behaviors. However, the New Logical Connections Argument also shows that (...) they are not causal powers at all with respect to intentional properties ofbehaviors, and so Fodor’s argument to individualism and narrow content is unsound. Along the way I show that Fodor’s version of the New Logical Connections argument has serious problems of overkill. (shrink)

Logic, Logical connectives, Verbal disputes, Proof theory, Non-classical logic.

Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? (...) Much more, I argue. "If you love me, kiss me", a conditional imperative, mixes a declarative antecedent ("you love me") with an imperative consequent ("kiss me"); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three -valued imperatives which mixes declaratives with imperatives. I develop such a logic. (shrink)

Combining two thoughts into a compound mental representation is a central feature of our verbal and non-verbal logical abilities. We here approach this issue by focusing on the contingency that while natural languages have typically lexicalised only two of the possible 16 binary connectives from formal logic to express compound thoughts—namely, the coordinatorsandandor—some of the remainder appear to be entertainable in a non-verbal, conceptual representational system—alanguage of thought—and this suggests a theoretical split between the “lexicalisation” of the (...) class='Hi'>connectives and the “learnability” of invented words corresponding to unlexicalised connectives. In avisual worldexperiment aimed at tracking comprehension-related as well as reasoning-related aspects of the capacity to represent compound thoughts, we found that participants are capable of learning and interpreting a made-up word standing for logic's NAND operator, a result that indicates that unlexicalised logical connectives are not only conceptually available, but can also be mapped onto new function words, as in the case of coordinators, or connectives, a class of words that do not usually admit new coinages. (shrink)

In bilateral systems for classical logic, assertion and denial occur as primitive signs on formulas. Such systems lend themselves to an inferentialist story about how truth-conditional content of connectives can be determined by inference rules. In particular, for classical logic there is a bilateral proof system which has a property that Carnap in 1943 called categoricity. We show that categorical systems can be given for any finite many-valued logic using $n$-sided sequent calculus. These systems are understood as a further (...) development of bilateralism—call it multilateralism. The overarching idea is that multilateral proof systems can incorporate the logic of a variety of denial speech acts. So against Frege we say that denial is not the negation of assertion and, with Mark Twain, that denial is more than a river in Egypt. (shrink)

Four known three-valued logics are formulated axiomatically and several completeness theorems with respect to nonstandard intuitive semantics, connected with the notions of information, contrariety and subcontrariety is given.

I argue that james otten's attempt to revive the logical connection argument by maintaining that there is a weak logical connection between causes and effects is a failure. Claiming that the weak logical connection is only a relation between descriptions of events rather than between events themselves, I conclude that otten has repeated the same mistake of confusing properties of propositions with properties of events made by earlier advocates of the lca.

In a paper entitled ‘Reviving the Logical Connection Argument,’ James Otten attempts to revive the Logical Connection Argument, which is intended to refute the causal thesis. Otten distinguishes two versions of the causal thesis. The general causal thesis: W1 … Wn are certain of S's wants, and W1 … Wn cause A,and the restricted causal thesis:: W is S's want to perform A, and W causes A.

Some nonlinguistic systems of representation display some of the six features of a language-of-thought (LoT) delineated by Quilty-Dunn et al. But they conjecture something stronger: That all six features cooccur homeostatically in nonlinguistic thought. Here I argue that there is no good evidence for nonlinguistic deductive reasoning involving the disjunctive syllogism. Animals and prelinguistic children probably do not make logical inferences.

Natural language does not express all connectives definable in classical logic as simple lexical items. Coordination in English is expressed by conjunction and, disjunction or, and negated disjunction nor. Other languages pattern similarly. Non-lexicalized connectives are typically expressed compositionally: in English, negated conjunction is typically expressed by combining negation and conjunction (not both). This is surprising: if $$\wedge $$ ∧ and $$\vee $$ ∨ are duals, and the negation of the latter can be expressed lexically (nor), why not (...) the negation of the former? I present a two-tiered model of the semantics of the binary connectives. The first tier captures the expressive power of the lexicon: it is a bilateral state-based semantics that, under a restriction, can express all and only the distinctions that can be expressed by the lexicon of natural language (and, or, nor). This first tier is characterized by rejection as non-assertion and a Neglect Zero assumption. The second tier is obtained by dropping the Neglect Zero assumption and enforcing a stronger notion of rejection, thereby recovering classical logic and thus definitions for all Boolean connectives. On the two-tiered model, we distinguish the limited expressive resources of the lexicon and the greater combinatorial expressive power of the language as a whole. This gives us a logic-based account of compositionality for the Boolean fragment of the language. (shrink)

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...) by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

This two-volume work, first published in 1843, was John Stuart Mill's first major book. It reinvented the modern study of logic and laid the foundations for his later work in the areas of political economy, women's rights and representative government. In clear, systematic prose, Mill disentangles syllogistic logic from its origins in Aristotle and scholasticism and grounds it instead in processes of inductive reasoning. An important attempt at integrating empiricism within a more general theory of human knowledge, the work constitutes (...) essential reading for anyone seeking a full understanding of Mill's thought. Continuing the discussion of induction, Volume 2 concludes with Book VI, 'On the Logic of the Moral Sciences', in which Mill applies empirical reasoning to human behaviour. A crucial early formulation of his thinking regarding free will and necessity, this book establishes the centrality of 'the social science' to Mill's philosophy. (shrink)

This two-volume work, first published in 1843, was John Stuart Mill's first major book. It reinvented the modern study of logic and laid the foundations for his later work in the areas of political economy, women's rights and representative government. In clear, systematic prose, Mill (1806–73) disentangles syllogistic logic from its origins in Aristotle and scholasticism and grounds it instead in processes of inductive reasoning. An important attempt at integrating empiricism within a more general theory of human knowledge, the work (...) constitutes essential reading for anyone seeking a full understanding of Mill's thought. Volume 1 contains Mill's introduction, which elaborates upon his definition of logic as 'not the science of Belief, but the science of Proof, or Evidence'. It also features discussions of the central components of logical reasoning - propositions and syllogisms - in relation to Mill's theories of inductive reasoning and experimental method. (shrink)

An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, (...) all connectives defined implicitly by axiomatic extensions of the logic are explicitly definable. (shrink)

This paper is concerned with representations of belief by means of nonadditive probabilities of the Dempster-Shafer (DS) type. After surveying some foundational issues and results in the D.S. theory, including Suppes's related contributions, the paper proceeds to analyze the connection of the D.S. theory with some of the work currently pursued in epistemic logic. A preliminary investigation of the modal logic of belief functions à la Shafer is made. There it is shown that the Alchourrron-Gärdenfors-Makinson (A.G.M.) logic of belief change (...) is closely related to the D.S. theory. The final section compares the critique of Bayesianism which underlies the present paper with some important objections raised by Suppes against this doctrine. -/- . (shrink)

An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, (...) all connectives defined implicitly by axiomatic extensions of the logic are explicitly definable. (shrink)

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation (...) into conditional connectives may show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

We introduce the concept of a connected logic (over S4) and show that each connected logic with the finite model property is the logic of a subalgebra of the closure algebra of all subsets of the real line R, thus generalizing the McKinsey-Tarski theorem. As a consequence, we obtain that each intermediate logic with the finite model property is the logic of a subalgebra of the Heyting algebra of all open subsets of R.

A translation of formulas in a language L1 to formulas in a language L2 is a mapping which preserves the parameters and commutes with the substitution prefix, the propositional connectives and the quantifiers. Every translation generates a corresponding transformation of theories in L1 to theories in L2. We formulate the equiconsistency problem for such transformations and propose a variant of its solution. First, for a transformation F we find the least theory A in L1 such that its inclusion in (...) a theory T guarantees equiconsistency of F and F, then we propose axiomatizations of A for some F's. (shrink)

This is the continuation of the paper :417–446, 2010). We continue the abstract study of non-classical logics based on the kind of generalized implication connectives they possess and we focus on semilinear logics, i.e. those that are complete with respect to the class of models where the implication defines a linear order. We obtain general characterizations of semilinearity in terms of the intersection-prime extension property, the syntactical semilinearity metarule and the class of finitely subdirectly irreducible models. Moreover, we consider (...) extensions of the language with lattice connectives and generalized disjunctions, study their interplay with implication and obtain axiomatizations and further descriptions of semilinear logics in terms of disjunctions and the proof by cases property. (shrink)