This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. (...) While non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

Inference to the Best Explanation (IBE) advises reasoners to infer exactly one explanation. This uniqueness claim apparently binds us when it comes to “conjunctive explanations,” distinct explanations that are nonetheless explanatorily better together than apart. To confront this worry, explanationists qualify their statement of IBE, stipulating that this inference form only adjudicates between competing hypotheses. However, a closer look into the nature of competition reveals problems for this qualified account. Given the most common explication of competition, this qualification artificially and (...) radically constrains IBE’s domain of applicability. Using a more subtle, recent explication of competition, this qualification no longer provides a compelling treatment of conjunctive explanations. In light of these results, I suggest a different strategy for accommodating conjunctive explanations. Instead of modifying the form of IBE, I suggest a new way of thinking about the structure of IBE’s lot of considered hypotheses. (shrink)

A conjunction of two hypotheses may provide a better explanation than either one of them individually, even if each already provides a good explanation on its own. An appropriate measure of explanatory power should reflect this, but none of the measures discussed in the literature do so because they only consider how much an explanatory hypothesis reduces our surprise at the evidence – which is problematic. This chapter introduces and defends a class of coherentist measures of explanatory power, and (...) shows that one particular such measure that combines different intuitions underlying the epistemological notion of coherence overcomes the aforementioned problems of surprise reduction measures. (shrink)

In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them (...) discusses our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction. (shrink)

1. In both Benedetto Croce's and Hegel's own terminology, dialectics can be understood as dottrina degli opposti (the doctrine of the opposites – Lehre der Gegensätze).1 In the dialectical process,...

I argue that it is rational for a person to believe the conjunction of her beliefs. This involves responding to the Lottery and Preface Paradoxes. In addition, I suggest that in normal circumstances, what it is to believe a conjunction just is to believe its conjuncts.

Plurality, Conjunction and Events presents a novel theory of plural and conjoined phrases, in an event-based semantic framework. It begins by reviewing options for treating the alternation between `collective' and `distributive' readings of sentences containing plural or conjoined noun phrases, including analyses from both the modern and the premodern literature. It is argued that plural and conjoined noun phrases are unambiguously group-denoting, and that the collective/distributive distinction therefore must be located in the predicates with which these noun phrases combine. (...) More specifically, predicates must have a hidden argument place for events; the collective/distributive distinction may then be represented in the part/whole structure of these events. This allows a natural treatment of `collectivizing' adverbial expressions, and of `pluractional' affixes; it also allows a unified semantics for conjunction, in which conjoined sentences and predicates denote groups of events, much like conjoined noun phrases denote groups of individuals. (shrink)

Gonzalo Rodriguez-Pereyra (2006) argues against attempts to preserve the entailment principle (or a restriction of it) while avoiding the explosion of truthmakers for necessities and truthmaker triviality. In doing so, he both defends the disjunction thesis--if something makes true a disjunctive truth, then it makes true one of its disjuncts--, and rejects the conjunction thesis--if something makes tue a conjunctive truth, then it makes true each of its conjuncts. In my discussion, I provide plausible counterexamples to the disjunction thesis, (...) and contend that Rodriguez-Pereyra's general defence of it fails. Then I defend the conjunction thesis from Rodriguez-Pereyra's case against it. (shrink)

I put in question in this article the existence of conjunctive properties. In the second section, after having provided a characterization of conjunctive properties, I develop an argument based on the principle of ontological parsimony: if we accept that there are conjunctive properties in the universe then, ceteris paribus, our ontology turns out to be less ontologically parsimonious than if we reject them. Afterwards, in the third section, I distinguish between maximalist and non-maximalist and reductionist and non-reductionist theories of conjunctive (...) properties., as well as between reductionist and non-reductionist theories that reject conjunctive properties. Such distinctions help to clarify the options at hand when accepting or rejecting conjunctive properties. In light of these distinctions, I then tackle two objections against the argument from ontological parsimony. Finally, in the remaining sections, I deal with two arguments defended by D. M. Armstrong for the existence of conjunctive properties: the argument from infinite complexity and the argument from causal powers. I show that there are several ways to resist these arguments and their conclusion. (shrink)

The so‐called problem of irrelevant conjunction has been seen as a serious challenge for theories of confirmation. It involves the consequences of conjoining irrelevant statements to a hypothesis that is confirmed by some piece of evidence. Following Hawthorne and Fitelson, we reconstruct the problem with reference to Bayesian confirmation theory. Then we extend it to the case of conjoining irrelevant statements to a hypothesis that is dis confirmed by some piece of evidence. As a consequence, we obtain and formally (...) present a novel and more troublesome problem of irrelevant conjunction. We conclude by indicating a possible solution based on a measure‐sensitive approach and by critically discussing a major alternative way to address the problem. *Received December 2008; revised August 2009. †To contact the authors, please write to: Department of Philosophy, University of Turin, via Sant'Ottavio 20, 10124 Turin, Italy; e‐mail: [email protected] ; [email protected] or [email protected]. (shrink)

We argue against some of Reichenbach's claims about causal forks are incorrect. We do not see why the Second Law of Thermodynamics rules out the existence of conjunctive forks open to the past. In addition, we argue that a common effect rarely forms a conjunctive fork with its joint causes, but it sometimes does. Nevertheless, we think there is something to be said for Reichenbach's idea that forks of various kinds are relevant to explaining why we know more about the (...) past than about the future. And entropy turns out to play a role in the explanation, though not the determining role that Reichenbach envisions. (shrink)

The conjunction fallacy is the well-documented empirical finding that subjects sometimes rate a conjunction A&B as more probable than one of its conjuncts, A. Most explanations appeal in some way to the fact that B has a high probability. But Tentori et al. (2013) have recently challenged such approaches, reporting experiments which find that (1) when B is confirmed by relevant evidence despite having low probability, the fallacy is common, and (2) when B has a high probability but (...) has not been confirmed by relevant evidence, the fallacy is less common. They conclude that degree of confirmation, rather than probability, is the central determinant of the conjunction fallacy. In this paper, we address a confound in these experiments: Tentori et al. (2013) failed to control for the fact that their (1)-situations make B conversationally relevant, while their (2)-situations do not. Hence their results are consistent with the hypothesis that con- versationally relevant high probability is an important driver of the conjunction fallacy. Inspired by recent theoretical work that appeals to conversational relevance to explain the conjunction fallacy, we report on two experiments that control for this issue by making B relevant without changing its degree of probability or confirmation. We find that doing so increases the rate of the fallacy in (2)-situations, and leads to comparable fallacy-rates as (1)-situations. This suggests that (non-probabilistic) conversational relevance indeed plays a role in the conjunction fallacy, and paves the way toward further work on the interplay between relevance and confirmation. (shrink)

Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we (...) give the lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the notions of disjunction and iterated conditioning and we show that the usual probabilistic properties still hold. (shrink)

We show that the elimination rule for the multiplicative conjunction $\wedge$ is admissible in many important multiplicative substructural logics. These include LL$_m$ and RMI$_m$ An exception is R$_m$. Let SLL$_m$ and SR$_m$ be, respectively, the systems which are obtained from LL$_m$ and R$_m$ by adding this rule as a new rule of inference. The set of theorems of SR$_m$ is a proper extension of that of R$_m$, but a proper subset of the set of theorems of RMI$_m$. Hence it (...) still has the variable-sharing property. SR$_m$ has also the interesting property that classical logic has a strong translation into it. We next introduce general algebraic structures, called strong multiplicative structures, and prove strong soundness and completeness of SLL$_m$ relative to them. We show that in the framework of these structures, the addition of the weakening axiom to SLL$_m$ corresponds to the condition that there will be exactly one designated element, while the addition of the contraction axiom corresponds to the condition that there will be exactly one nondesignated element. Various other systems in which multiplicative conjunction functions as a true conjunction are studied, together with their algebraic counterparts. (shrink)

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X-and-Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners’ interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems. © 2004 Cognitive Science Society, Inc. All rights reserved.

We show that the rule that allows the inference of A from A ⊗ B is admissible in many of the basic multiplicative systems. By adding this rule to these systems we get, therefore, conservative extensions in which the tensor behaves as classical conjunction. Among the systems obtained in this way the one derived from RMIm has a particular interest. We show that this system has a simple infinite-valued semantics, relative to which it is strongly complete, and a nice (...) cut-free Gentzen-type formulation which employs hypersequents . Moreover: classical logic has a simple, strong translation into this logic. This translation uses definable connectives and preserves the consequence relation of classical logic . Similar results, but with a 3-valued semantics, obtain if instead of RMIm we use RMm. (shrink)

In [3] the prepositional connectives were defined in terms of the combinators K and S and the illative obs Ξ and H . Given an elimination rate for Ξ and introduction rules for H and Ξ, all the standard intuitionistic propositional calculus results could be proved provided the variables were restricted to H. The intuition behind the particular introduction rule for Ξ of [2], that was used is [3], came from a three valued truth table for implication, the values of (...) which were T, F and N. . There are in fact 4 different truth tables for implication that fit the rules for implication derived from those for Ξ. From these 4 different tables for conjunction and two for disjunction can be derived. (shrink)

Generic sentences involving phrasal conjunctions present a prima facie problem for the standard theory of generics according to which they express quasi-universal generalisations about what is characteristic for members of a particular kind. For example, the sentence ‘Elephants live in Africa and Asia’ is true, even though it is uncharacteristic for an elephant to live in both Africa and Asia. In response to this problem, theorists have recently proposed radical departures from the standard view. This paper argues that such departures (...) are unwarranted: not only do they fail to fully accommodate the data involving generic conjunctions, their scope is overly narrow, since the phenomena in question also arise in non-generic contexts. I propose a new theory of generics that aims to account for generic conjunctions in a principled manner and which sheds new light on the mereological commitments of natural language. (shrink)

It is widely believed that one should not become more confident that all swans are white and all lions are brave simply by observing white swans. Irrelevant conjunction or “tacking” of a theory onto another is often thought problematic for Bayesianism, especially given the ratio measure of confirmation considered here. It is recalled that the irrelevant conjunct is not confirmed at all. Using the ratio measure, the irrelevant conjunction is confirmed to the same degree as the relevant conjunct, (...) which, it is argued, is ideal: the irrelevant conjunct is irrelevant. Because the past’s really having been as it now appears to have been is an irrelevant conjunct, present evidence confirms theories about past events only insofar as irrelevant conjunctions are confirmed. Hence the ideal of not confirming irrelevant conjunctions would imply that historical claims are not confirmed. Confirmation measures partially realizing that ideal make the confirmation of historical claims by present evidence depend strongly on the (presumably subjective) degree of belief in the irrelevant conjunct. The unusually good behavior of the ratio measure has a bearing on the problem of measure sensitivity. For non-statistical hypotheses, Bayes’ theorem yields a fractional linear transformation in the prior probability, not a linear rescaling, so even the ratio measure arguably does not aptly measure confirmation in such cases. (shrink)

Rodriguez-Pereyra (2006) argues for the disjunction thesis but against the conjunction thesis. I argue that accepting the disjunction thesis undermines his argument against the conjunction thesis.

Are counterfactuals with true antecedents and consequents trivially true? The principle of Conjunction Conditionalization →) is highly controversial. Many philosophers view it as an attractive feature of Lewis’s semantics for counterfactuals that it can easily be modified to avoid this principle. However, Walters and Williams beg to differ. They argue that Conjunction Conditionalization is an indispensable ingredient of any Lewisian semantics, since CC is entailed by standard Lewisian theorems and a plausible semantic claim about irrelevant semifactuals. If this (...) is true, the entire tradition of revisionist counterfactual semantics is misguided, and so are many philosophical theories in which counterfactuals play a role. We argue, in defense of the revisionist tradition, that Walters and Williams’ ‘plausible semantic claim’ is in fact anything but plausible. It turns out to entail semantic principles far more controversial than Conjunction Conditionalization. (shrink)

In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, distributivity does not arise if we use the usual notion of extension between consequence (...) relations. A detailed discussion about this phenomenon, as well as some possible solutions for it, are given. (shrink)

There are two ways of understanding the notion of a contradiction: as a conjunction of a statement and its negation, or as a pair of statements one of which is the negation of the other. Correspondingly, there are two ways of understanding the Law of Non-Contradiction (LNC), i.e., the law that says that no contradictions can be true. In this paper I offer some arguments to the effect that on the first (collective) reading LNC is non-negotiable, but on the (...) second (distributive) reading it is perfectly plausible to suppose that LNC may, in some rather special and perhaps undesirable circumstances, fail to hold. (shrink)

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X‐and‐Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners' interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems.

Depending on whether we are somewhat tolerant of nearby error-possibilities or not, the safety condition on knowledge is open to a strong reading and a weak reading. In this paper, it is argued that induction and conjunction introduction constitute two horns of a dilemma for the safety account of knowledge. If we opt for the strong reading, then the safety account fails to account for inductive knowledge. In contrast, if we opt for the weak reading, then the safety account (...) fails to accommodate knowledge obtained via the method of conjunction introduction. (shrink)

ABSTRACT: The 3rd BCE Stoic logician "Chrysippus says that the number of conjunctions constructible from ten propositions exceeds one million. Hipparchus refuted this, demonstrating that the affirmative encompasses 103,049 conjunctions and the negative 310,952." After laying dormant for over 2000 years, the numbers in this Plutarch passage were recently identified as the 10th (and a derivative of the 11th) Schröder number, and F. Acerbi showed how the 2nd BCE astronomer Hipparchus could have calculated them. What remained unexplained is why Hipparchus’ (...) logic differed from Stoic logic, and consequently, whether Hipparchus actually refuted Chrysippus. This paper closes these explanatory gaps. (1) I reconstruct Hipparchus’ notions of conjunction and negation, and show how they differ from Stoic logic. (2) Based on evidence from Stoic logic, I reconstruct Chrysippus’ calculations, thereby (a) showing that Chrysippus’ claim of over a million conjunctions was correct; and (b) shedding new light on Stoic logic and – possibly – on 3rd century BCE combinatorics. (3) Using evidence about the developments in logic from the 3rd to the 2nd centuries, including the amalgamation of Peripatetic and Stoic theories, I explain why Hipparchus, in his calculations, used the logical notions he did, and why he may have thought they were Stoic. OPEN ACCESS LINK. (shrink)

Scientific realists contend that theory-conjunction presents a problem for empiricist conceptions of scientific knowledge and practice. Van Fraassen (1980) has offered a competing account of theory-conjunction which I argue fails to capture the mercenary character of epistemic dependence in science. Representative cases of theory-conjunction developed in the present paper show that mercenary reliance implies a "principle of epistemic symmetry" which only a realist can consistently accommodate. Finally, because the practice in question involves the conjunction of theories, (...) a version of realism more robust than the "entity realism" of Cartwright (1983, 1989) and Hacking (1983) is required to explain the success of theory-conjunction. (shrink)

This chapter focuses on one of the common fallacies in Western philosophy called the conjunction fallacy. It discusses a case of Linda who was deeply concerned with issues of discrimination and social justice and also participated in antinuclear demonstrations. The chapter applies the concept the present fallacy to the Linda Problem by using a Venn diagram. When one needs to determine the relative probability of different scenarios, one way to prevent himself/herself from making the conjunction fallacy is to (...) determine whether any of the options is a subset of any other. If so, he/she can conclude that the subset option is not more probable. This rule works because a specific event can never be more likely than a general event that encompasses the specific event. The chapter explains why people are so frequently drawn in by the conjunction fallacy. (shrink)

The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. Here we elaborate the suggestion (first discussed by Sides, Osherson, Bonini, & Viale, 2002) that in standard conjunction problems the fallacious probability judgements observed experimentally are typically guided by sound assessments of _confirmation_ relations, meant in terms of contemporary Bayesian confirmation theory. Our (...) main formal result is a confirmation-theoretic account of the conjunction fallacy, which is proven _robust_ (i.e., not depending on various alternative ways of measuring degrees of confirmation). The proposed analysis is shown distinct from contentions that the conjunction effect is in fact not a fallacy, and is compared with major competing explanations of the phenomenon, including earlier references to a confirmation-theoretic account. (shrink)

We show that the elimination rule for the multiplicative (or intensional) conjunction $\wedge$ is admissible in many important multiplicative substructural logics. These include LL m (the multiplicative fragment of Linear Logic) and RMI m (the system obtained from LL m by adding the contraction axiom and its converse, the mingle axiom.) An exception is R m (the intensional fragment of the relevance logic R, which is LL m together with the contraction axiom). Let SLL m and SR m be, (...) respectively, the systems which are obtained from LL m and R m by adding this rule as a new rule of inference. The set of theorems of SR m is a proper extension of that of R m , but a proper subset of the set of theorems of RMI m . Hence it still has the variable-sharing property. SR m has also the interesting property that classical logic has a strong translation into it. We next introduce general algebraic structures, called strong multiplicative structures, and prove strong soundness and completeness of SLL m relative to them. We show that in the framework of these structures, the addition of the weakening axiom to SLL m corresponds to the condition that there will be exactly one designated element, while the addition of the contraction axiom corresponds to the condition that there will be exactly one nondesignated element (in the first case we get the system BCK m , in the second - the system SR m ). Various other systems in which multiplicative conjunction functions as a true conjunction are studied, together with their algebraic counterparts. (shrink)

In 1987, Crispin Wright argued that degree-theoretic solutions to the Sorites paradox fail because the solutions do not work when the paradox is restated using a conjunctive major premise. I show that Wright is incorrect: degree-theoretic solutions also work when the paradox is stated with a conjunctive major premise.

In this paper I undermine the Entailment Principle according to which if an entity is a truthmaker for a certain proposition and this proposition entails another, then the entity in question is a truthmaker for the latter proposition. I argue that the two most promising versions of the principle entail the popular but false Conjunction Thesis, namely that a truthmaker for a conjunction is a truthmaker for its conjuncts. One promising version of the principle understands entailment as strict (...) implication but restricts the field of application of the principle to purely contingent truths (i.e. those that contain no necessary proposition at any level of analysis). But a conjunction of purely contingent truths strictly implies its conjuncts. So this version of the principle is committed to the Conjunction Thesis. The same is true of the version of the principle where entailment is understood in the sense of systems T, R, and E of relevant logic, since in these systems conjunctions entail their conjuncts. I argue that the Conjunction Thesis is false because a truthmaker is that in virtue of what a certain proposition is true and it is false that, for example, what the proposition that Peter is a man is true in virtue of is the conjunctive fact that Peter is man and Saturn is a planet (or the facts that Peter is a man and that Saturn is a planet taken together). I also argue against other versions of the principle. (shrink)

Departing from basic concepts in abstract logics, this paper introduces two concepts: conjunctive and disjunctive limits. These notions are used to formalize levels of modal operators.

In this note we sketch a decision procedure for S3.51 based on reduction to conjunctive normal form. Using the following theorem of S3.5: and its dual for M over a conjunction, any formula can be reduced by standard methods (as in S52) to a conjunction of disjunctions of the form where Í is (p ⊃ p), 0 is ∼(p ⊃ p) and α — λ are all PC-wffs (i.e. they contain no modal operators).

Argues for an assimilation of sentential and predicate conjunction to collective conjunction, based on modification of predicates by adverbs such as 'alternately'.

The knowledge account of assertion - roughly: one should not assert what one does not know - can explain a variety of Moorean conjunctions, a fact often cited as evidence in its favor. David Sosa ("Dubious Assertions," Phil Studies, 2009) has objected that the account does not generalize satisfactorily, since it cannot explain the infelicity of certain iterated conjunctions without appealing to the controversial "KK" principle. This essay responds by showing how the knowledge account can handle such conjunctions without use (...) of the KK principle. (shrink)

Consider the reasonable axioms of subjunctive conditionals if p → q1 and p → q2 at some world, then p → at that world, and if p1 → q and p2 → q at some world, then → q at that world, where p → q is the subjunctive conditional. I show that a Lewis-style semantics for subjunctive conditionals satisfies these axioms if and only if one makes a certain technical assumption about the closeness relation, an assumption that is probably (...) false. I will then show how Lewisian semantics can be modified so as to assure and even when the technical assumption fails, and in fact in one sense the semantics actually becomes simpler then. (shrink)