In this paper we propose to present from a new perspective some loci comunes of traditional logic. More exactly, we intend to show that some hypothetico-disjunctive inferences (i.e. the complex constructive dilemma, the complex destructive dilemma, the simple constructive dilemma, the simple destructive dilemma) and two hypothetico-categorical inferences (namely modus ponendo-ponens and modus tollendo-tollens) particularize two more abstract inferential structures: the constructive n-lemma and the destructive nlemma.

Conceptual change and its connection to the development of new seien tific theories has reeently beeome an intensively discussed topic in philo sophieal literature. Even if the inductive aspects related to conceptual change have already been discussed to some extent, there has so far existed no systematic treatment of inductive change due to conceptual enrichment. This is what we attempt to accomplish in this work, al though most of our technical results are restricted to the framework of monadic languages. We (...) extend Hintikka's system of inductive logic to apply to situations in which new concepts are introduced to the original language. By interpreting them as theoretica1 concepts, it is possible to discuss a number of currently debated philosophical and methodological problems which have previously escaped systematic and exact treatment. For instance, the role which seientific theories employing theoretical con cepts may play within inductive inference can be studied within this framework. From the viewpoint of seientific realism, sueh a study gives outlines for a theory of what we call hypothetico-induetive inference. Some parts of this work which are based on Hintikka's system of in ductive logic are fairly technical. However, no previous knowledge of this system is required, but, in general, acquaintance with the basic ideas of elementary logic and probability theory is suffieient. This work is part of a project, originated by Professors Jaakko Hintikka and Raimo Tuomela, concerning the role of theoretical concepts in science. (shrink)

Many philosophers have claimed that Bayesianism can provide a simple justification for hypothetico-deductive inference, long regarded as a cornerstone of the scientific method. Following up a remark of van Fraassen, we analyze a problem for the putative Bayesian justification of H-D inference in the case where what we learn from observation is logically stronger than what our theory implies. Firstly, we demonstrate that in such cases the simple Bayesian justification does not necessarily apply. Secondly, we identify a set of (...) sufficient conditions for the mismatch in logical strength to be justifiably ignored as a "harmless idealization''. Thirdly, we argue, based upon scientific examples, that the pattern of H-D inference of which there is a ready Bayesian justification is only rarely the pattern that one actually finds at work in science. Whatever the other virtues of Bayesianism, the idea that it yields a simple justification of a pervasive pattern of scientific inference appears to have been oversold. (shrink)

Hypothetico-deductivists have struggled to develop qualitative confirmation theories not raising the so-called tacking by disjunction paradox. In this paper, I analyze the difficulties yielded by the paradox and I argue that the hypothetico-deductivist solutions given by Gemes (1998) and Kuipers (2000) are questionable because they do not fit such analysis. I then show that the paradox yields no difficulty for the Bayesian who appeals to the Total Evidence Condition. I finally argue that the same strategy is unavailable to (...) the hypothetico-deductivist. (shrink)

Although inference to the best explanation is ubiquitous in science and our everyday lives, there are numerous objections to the viability of IBE. Many of these objections have been thoroughly discussed, however, at least one objection to IBE has not received adequate treatment. We term this objection the “Disjunction Objection”. This objection challenges IBE on the grounds that it seems that even if H is the best explanation, it could be that the disjunction of its rivals is more likely to (...) be true. As a result, IBE appears to license accepting a hypothesis that is more likely than not to be false. Despite these initial appearances, we argue that the Disjunction Objection fails to impugn IBE. (shrink)

We provide a new link between deductive and probabilistic reasoning fallacies. Illusory inferences from disjunction are a broad class of deductive fallacies traditionally explained by recourse to a matching procedure that looks for content overlap between premises. In two behavioral experiments, we show that this phenomenon is instead sensitive to real-world causal dependencies and not to exact content overlap. A group of participants rated the strength of the causal dependence between pairs of sentences. This measure is a near perfect (...) predictor of fallacious reasoning by an independent group of participants in illusory inference tasks with the same materials. In light of these results, we argue that all extant accounts of these deductive fallacies require non-trivial adjustments. Crucially, these novel _indirect_ illusory inferences from disjunction bear a structural similarity to seemingly unrelated _probabilistic reasoning_ problems, in particular the conjunction fallacy from the heuristics and biases literature. This structural connection was entirely obscure in previous work on these deductive problems, due to the theoretical and empirical focus on content overlap. We argue that this structural parallelism provides arguments against the need for rich descriptions and individuating information in the conjunction fallacy, and we outline a unified theory of deductive illusory inferences from disjunction and the conjunction fallacy, in terms of Bayesian confirmation theory. (shrink)

Alleged counter-examples deployed in Park [Erkenntnis 60: 229–240] against the account of selective hypothetico-deductive confirmation offered in Gemes [Erkenntnis 49: 1–20] are shown to be ineffective. Furthermore, the reservations expressed in Gemes [ibid] and [Philosophy of Science 62: 477–487] about hypothetico-deductivism are retracted and replaced with the conclusion that H-D is a viable account of confirmation that captures much of the practice of working scientists. However, because it cannot capture cases of inference to the best explanation and cases (...) of the observational confirmation of statistical hypotheses, it is concluded that H-D cannot supply a complete theory of confirmation. (shrink)

In medical diagnostic examination three main stages may be distinguished: (a) initial exploration, (b) hypothesis-directed investigation, and (c) final diagnosis making. The purpose of this work is to study some methodological problems concerning the second of the above stages of the diagnosis and to prepare a background for a mathematical model [30] of this process.In diagnostic problem solving, the reasoning proceeds along the main lines traced by some initial suggestions and passes through various intermediate elements which are connected with one (...) another forming ramifying chains and nets of inferences and hypotheses. Such a complex mental construction is based on laws which form medical knowledge and reflect various regularities and relations, causal, structural, functional, and others. (shrink)

Sentences with disjunction in the scope of a universal quantifier, Every A is P or Q, tend to give rise to distributive inferences that each of the disjuncts holds of at least one individual in the domain of the quantifier, Some A is P & Some A is Q. These inferences are standardly derived as an entailment of the meaning of the sentence together with the scalar implicature that it is not the case that either disjunct holds of (...) every individual in the domain of the quantifier, \Every A is P &\Every A is Q. As we show, this derivation faces a challenge in that distributive inferences may obtain in the absence of plain negated inferences. We address this challenge by showing that on particular assumptions about alternatives, a derivation of distributive inferences as scalar implicatures can be maintained without in fact necessitating plain negated inferences. These assumptions accord naturally with the grammatical approach to scalar implicatures. We also present experimental data that suggest that plain negated inferences are not only unnecessary for deriving distributive inferences, but might in fact be unavailable. (shrink)

The paper explores the disjunctive riddle for induction: If we know the sample Ks to be P, we also know that they are P or F. Assuming that we also know that the future Ks are non-P, we can conclude that they are F, if only we can inductively infer the evidentially supported P-or-F hypothesis. Yet this is absurd. We cannot predict that future Ks are F based on the knowledge that the samples, and only they, are P. The (...) ensuing challenge is to account for the unprojectibility of the disjunctive hypothesis. I provide an explanation in terms of epistemic dependence. The P-or-F hypothesis is unprojectible because the evidence supporting it depends epistemically on the evidence for the defeated P-hypothesis. The paper also shows that the disjunctive riddle covers the essence of Goodman's infamous grue-problem, which, therefore, can be resolved by the same means: In contrast to the green-hypothesis, the grue-hypothesis is unprojectible because the grue-evidence depends on the evidence for a defeated hypothesis. (shrink)

Plausibly, an inference is an act of coming to believe something on the basis of something else you already believe. But what is it to come to believe some- thing on the basis of something else? I propose a disjunctive answer: it is either for some beliefs to rationally cause another—where rational causation is understood as causation that is either actually or potentially productive of knowledge—or for some beliefs to “deviantly” cause another, but for the believer mistakenly to come (...) thereby to believe that the former have rationally caused the latter. The result, I argue, is both a theoretically satisfying account of the act of inferring and a demonstration of the power of a knowledge-first approach to the philosophy of mind. (shrink)

With any structural inference rule A/B, we associate the rule $${(A \lor p)/(B \lor p)}$$, providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( $${\lor}$$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a $${\lor}$$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the $${\lor}$$ -extension of each admissible rule is admissible. We prove that (...) any structural finitary consequence operator (for intermediate logic) can be defined by a set of $${\lor}$$ -extended rules if and only if it can be defined through a set of well-connected Heyting algebras of a corresponding quasivariety. As we exemplify, the latter condition is satisfied for a broad class of algebraizable logics. (shrink)

The validity of argument by disjunctive syllogism has been denied by proponents of relevant and paraconsistent logic. DS is stigmatised for its role in inferences — most notably C.I. Lewis's derivation of that fallacy of irrelevance ex falso quodlibet — that involve both it and other rules of inference governing disjunction, or, to speak more precisely, other rules of inference taken to apply to the very same disjunction that obeys DS. In avoiding these inferences the road less (...) travelled is to deny the identity rather than to deny DS: what follows is, then, an exercise in disjoining disjunctions. (shrink)

We present evidence that preschool children oftentimes understand disjunctive sentences as if they were conjunctive. The result holds for matrix disjunctions as well as disjunctions embedded under every. At the same time, there is evidence in the literature that children understand or as inclusive disjunction in downward-entailing contexts. We propose to explain this seemingly conflicting pattern of results by assuming that the child knows the inclusive disjunction semantics of or, and that the conjunctive inference is a scalar implicature. We (...) make two assumptions about implicature computation in the child: that children access only a proper subset of the adult alternatives, and that children possess the adult capacity to strengthen sentences with implicatures. As a consequence, children are expected to sometimes not compute any implicatures at all, but in other cases they are expected to compute an implicature that is different from the adult implicature. We argue that the child’s conjunctive strengthening of disjunctive sentences realizes the latter possibility: the adult infers that the conjunction is false but the child infers that the conjunction is true. This behaviour is predicted when our assumptions about child development are coupled with the assumption that a covert exhaustive operator is responsible for strengthening in both the child and the adult. Specifically, children’s conjunctive strengthening is predicted to follow from the same mechanism used by adults to compute conjunctive free choice implicatures in response to disjunctive permission sentences. We furthermore argue that this parallel between the child and the adult extends to disambiguation preferences. In particular, we present evidence that children prefer to strengthen disjunctions to conjunctions, in matrix and embedded positions ; this result mirrors previous findings that adults prefer to compute free choice, at the root and under every. We propose a disambiguation strategy that explains the preference for conjunctive strengthening – by both the child and the adult – even though there is no general preference for exhaustification. Specifically, we propose that the preference for a conjunctive strengthening follows from a pragmatic preference for a complete answer to the Question Under Discussion. (shrink)

Williamson's influential anti-luminosity argument aims to show that our own mental states are not “luminous,” and that we are thus “cognitively homeless.” Among other things, this argument represents a significant challenge to the idea that we enjoy basic self-knowledge of our own occurrent mental states. In this paper, I summarize Williamson's anti-luminosity argument, and discuss the role that the notion of “epistemic basis” plays in it. I argue that the anti-luminosity argument relies upon a particular version of the basis-relative safety (...) condition on knowledge. This commitment is significant because basic self-knowledge seemingly lacks any kind of distinct epistemic basis, such as inference, observation, testimony, etc., despite representing a genuine kind of knowledge of contingent matters of fact. I consider a disjunctivist account, according to which true basic self-beliefs indeed lack an epistemic basis in any kind of epistemic method, yet are still epistemically grounded in the mental states they concern. I argue that this account of self-knowledge is compatible with standard understandings of the basis relative safety condition on knowledge, but rejects the particular version required by the anti-luminosity argument. (shrink)

Upward monotonic semantics for necessity modals give rise to Ross’s Puzzle: they predict that □φ entails □(φ ∨ ψ), but common intuitions about arguments of this form suggest they are invalid. It is widely assumed that the intuitive judgments involved in Ross’s Puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from □(φ ∨ ψ), interpreters infer that the truth of each disjunct (φ, ψ) is compatible with the relevant set of worlds. I introduce two pieces (...) of data that this analysis fails to explain. Analyzing this data, I argue, suggests that necessity modals with embedded disjunctions license ‘Independence’ inferences: from the truth of □(φ ∨ ψ), interpreters infer that φ-without-ψ and ψ-without-φ are each compatible with the relevant set of worlds. I outline a bilateral inquisitive semantics for necessity modals that predicts the validity of the Independence inferences. I then argue that the resulting theory should be understood as one on which disjunctions denote pluralities of propositions, and necessity modals behave like collective predicates applied to these pluralities. (shrink)

Disjunctive Syllogism, that is, the inference from 'not-A or B' and 'A', to 'B' can lead from true premises to a false conclusion if each of the sentences 'A' and 'not-A' is a statement of a partial truth such that affirming one of them amounts to denying the other, without each being the contradictory of the other. Such sentences inevitably occur whenever a situation which for its proper precise description needs the use of expressions such as 'most probably true' (...) and so forth, is described (less precisely) by sentences not containing such expressions. (shrink)

Perception can’t have disjunctive content. Whereas you can think that a box is blue or red, you can’t see a box as being blue or red. Based on this fact, I develop a new problem for the ambitious predictive processing theory, on which the brain is a machine for minimizing prediction error, which approximately implements Bayesian inference. I describe a simple case of updating a disjunctive belief given perceptual experience of one of the disjuncts, in which Bayesian inference (...) and predictive coding pull in opposite directions, with the former implying that one’s confidence in the belief should increase, and the latter implying that it should decrease. Thus, predictive coding fails to approximately implement Bayesian inference across the interface between belief and perception. (shrink)

A bounded formula is a pair consisting of a propositional formula φ in the first coordinate and a real number within the unit interval in the second coordinate, interpreted to express the lower-bound probability of φ. Converting conjunctive/disjunctive combinations of bounded formulas to a single bounded formula consisting of the conjunction/disjunction of the propositions occurring in the collection along with a newly calculated lower probability is called absorption. This paper introduces two inference rules for effecting conjunctive and disjunctive (...) absorption and compares the resulting logical system, called System Y, to axiom System P. Finally, we demonstrate how absorption resolves the lottery paradox and the paradox of the preference. (shrink)

Since the appearance of Prior’s tonk, inferentialists tried to formulate conditions that a collection of inference rules for a logical constant has to satisfy in order to succeed in conferring an acceptable meaning to it. Dummett proposed a pair of conditions, dubbed ‘harmony’ and ‘stability’ that have been cashed out in terms of the existence of certain transformations on natural deduction derivations called reductions and expansions. A long standing open problem for this proposal is posed by quantum disjunction: although its (...) rules are intuitively unstable, they pass the test of existence of expansions. Although most authors view instabilities of this kind as too subtle to be detected by the requirement of existence of expansions, we first discuss a case showing that this requirement can indeed detect instabilities of this kind, and then show how the expansions for disjunction-like connectives have to be reformulated to rule out quantum disjunction. We show how the alternative pattern for expansions can be formulated for connectives and quantifiers whose rules satisfy a scheme originally developed by Prawitz and Schroeder-Heister. Finally we compare our proposal with a recent one due to Jacinto and Read. (shrink)

Philosophical discussions on causal inference in medicine are stuck in dyadic camps, each defending one kind of evidence or method rather than another as best support for causal hypotheses. Whereas Evidence Based Medicine advocates the use of Randomised Controlled Trials and systematic reviews of RCTs as gold standard, philosophers of science emphasise the importance of mechanisms and their distinctive informational contribution to causal inference and assessment. Some have suggested the adoption of a pluralistic approach to causal inference, and an inductive (...) rather than hypothetico-deductive inferential paradigm. However, these proposals deliver no clear guidelines about how such plurality of evidence sources should jointly justify hypotheses of causal associations. We here develop such guidelines by first giving a philosophical analysis of the underpinnings of Hill’s viewpoints on causality. We then put forward an evidence-amalgamation framework adopting a Bayesian net approach to model causal inference in pharmacology for the assessment of harms. Our framework accommodates a number of intuitions already expressed in the literature concerning the EBM vs. pluralist debate on causal inference, evidence hierarchies, causal holism, relevance, and reliability. (shrink)

When a proposition is cumulatively entailed by a finite setA of premisses, there exists, trivially, a finite subsetB ofA such thatB B entails for all finite subsetsB that are entailed byA. This property is no longer valid whenA is taken to be an arbitrary infinite set, even when the considered inference operation is supposed to be compact. This leads to a refinement of the classical definition of compactness. We call supracompact the inference operations that satisfy the non-finitary analogue of the (...) above property. We show that for any arbitrary cumulative operationC, there exists a supracompact cumulative operationK(C) that is smaller thenC and agrees withC on finite sets. Moreover,K(C) inherits most of the properties thatC may enjoy, like monotonicity, distributivity or disjunctive rationality. The main part of the paper concerns distributive supracompact operations. These operations satisfy a simple functional equation, and there exists a representation theorem that provides a semantic characterization for this family of operations. We examine finally the case of rational operations and show that they can be represented by a specific kind of model particularly easy to handle. (shrink)

Participants acting as mock jurors made inferences about whether a person was a suspect in a murder based on an expert's testimony about the presence of objects at the crime scene and the disclosure that the testimony was true or false. Experiment 1 showed that participants made more correct inferences, and made inferences more quickly, when the truth or falsity of the expert's testimony was disclosed immediately after the testimony rather than when the disclosure was delayed. Experiment (...) 2 showed no advantage for prior disclosure over immediate disclosure. Experiment 3 showed that the pattern of inferences when there was no disclosure mirrored the pattern when it was disclosed that the expert's testimony was true rather than false. Participants made more correct inferences from true conjunctions than disjunctions, and from false disjunctions than conjunctions. We discuss the implications for theories of the mental representations and cognitive processes that underlie human reasoning. (shrink)

We present a number of puzzles arising for the interpretation of modified numerals. Following Büring and others we assume that the main difference between comparative and superlative modifiers is that only the latter convey disjunctive meanings. We further argue that the inference patterns triggered by disjunction and superlative modifiers are hard to capture in existing semantic and pragmatic analyses of these phenomena (neo-Gricean or grammatical alike), and we propose a novel account of these inferences in the framework of (...) bilateral state-based modal logic defining a first order extension of Aloni (Semant Pragmat 15:5-EA, 2022. https://doi.org/10.3765/sp.15.5)’s. (shrink)

This paper argues that in mathematical practice, conjectures are sometimes confirmed by “Inference to the Best Explanation” as applied to some mathematical evidence. IBE operates in mathematics in the same way as IBE in science. When applied to empirical evidence, IBE sometimes helps to justify the expansion of scientists’ ontological commitments. Analogously, when applied to mathematical evidence, IBE sometimes helps to justify mathematicians' in expanding the range of their ontological commitments. IBE supplements other forms of non-deductive reasoning in mathematics, avoiding (...) obstacles sometimes faced by enumerative induction or hypothetico-deductive reasoning. Both platonist and non-platonist interpretations of mathematics ought to accommodate explanation in mathematics and ought to recognize IBE in mathematics, though these interpretations disagree on the ontological commitments that mathematicians ought to have. This paper offers an inductive account of why mathematical IBE tends to lead to mathematical truths. (shrink)

This discussion note aims to show that Moti Mizrahi does not make clear whether the proponents of the semantic view of scientific progress reject or accept the inference rule of Addition. If they reject the rule, then it does not make sense that Mizrahi contrives different types of disjuncts ‘on behalf of’ proponents of the semantic view. If they accept the rule, then the characterisation of the semantic view that Mizrahi discusses has nothing to do with the supposedly arbitrariness of (...) scientific progress, as Mizrahi contends. (shrink)

This paper presents experimental data relevant to understanding the modal free choice effect (Kamp, 1973) when there are more than two disjuncts under the relevant modal operator. The results suggest that speakers' willingness to draw free choice inferences is correlated with whether the embedded disjuncts are *modally separable*, in a sense brought into focus by considering cases within which the relevant propositions fail to be pairwise redundant but are redundant as a set.

People reject ‘paradoxical’ inferences, such as: Luisa didn't play music; therefore, if Luisa played soccer, then she didn't play music. For some theorists, they are invalid for everyday conditionals, but valid in logic. The theory of mental models implies that they are valid, but unacceptable because the conclusion refers to a possibility inconsistent with the premise. Hence, individuals should accept them if the conclusions refer only to possibilities consistent with the premises: Luisa didn't play soccer; therefore, if Luisa played (...) a game then she didn't play soccer. Two experiments corroborated this prediction for three sorts of ‘paradox’, including a disjunctive paradox. (shrink)

In sentences with internal negation, Free Choice Inferences (FCIs) are cancelled (Chierchia 2013). The present study investigated the possibility that FCIs are negated, not cancelled, by external negation. In previous research, both Mandarin-speaking children and adults were found to license FCIs in affirmative sentences with a modal verb and the disjunction word huozhe ‘or’ (Zhou, Romoli & Crain 2103). The present study contrasted internal versus external negation in sentences that contained all the ingredients needed to license FCIs. Four experiments (...) were conducted using the Truth Value Judgment Task (Crain & Thornton 1998). Experiment 1 tested Mandarin-speaking children and adults using sentences with internal negation, a modal verb and disjunction. As expected, children did not license FCIs; rather, they assigned a ‘neither’ interpretation to disjunction. Also as expected, adults analyzed disjunction as taking scope over internal negation, yielding a ‘not both’ interpretation (Jing, Crain & Hsu 2005). Experiment 1 provided the benchmarks for sentences with external negation in Experiments 2-4. Experiment 2 confirmed that English-speaking adults distinguish between internal and external negation in sentences with disjunction. In Experiment 3, external negation was conveyed by the focus adverb zhiyou ‘only’. External negation eliminated the between-group differences observed in Experiment 1. Both children and adults analyzed external negation as taking scope over disjunction. Experiment 4 tested the effect of external negation on the computation of FCIs. The test sentences only differed from Experiment 1 by using external negation, rather than internal negation. Again, children and adults interpreted the test sentences in the same way. Most importantly, in contrast to Experiment 1 (with internal negation), both groups analysed external negation as negating, rather than cancelling, FCIs. The findings support the distinction between internal and external negation. (shrink)

An approach to inference to the best explanation integrating a Popperianconception of natural laws together with a modified Hempelian account of explanation, one the one hand, and Hacking's law of likelihood (in its nomicguise), on the other, which provides a robust abductivist model of sciencethat appears to overcome the obstacles that confront its inductivist,deductivist, and hypothetico-deductivist alternatives.This philosophy of scienceclarifies and illuminates some fundamental aspects of ontology and epistemology, especially concerning the relations between frequencies and propensities. Among the most (...) important elements of this conception is thecentral role of degrees of nomic expectability in explanation, prediction,and inference, for which this investigation provides a theoretical defense. (shrink)

An approach to inference to the best explanation integrating a Popperianconception of natural laws together with a modified Hempelian account of explanation, one the one hand, and Hacking's law of likelihood (in its nomicguise), on the other, which provides a robust abductivist model of sciencethat appears to overcome the obstacles that confront its inductivist,deductivist, and hypothetico-deductivist alternatives.This philosophy of scienceclarifies and illuminates some fundamental aspects of ontology and epistemology, especially concerning the relations between frequencies and propensities. Among the most (...) important elements of this conception is thecentral role of degrees of nomic expectability in explanation, prediction,and inference, for which this investigation provides a theoretical defense. (shrink)

People reject ‘paradoxical’ inferences, such as: Luisa didn't play music; therefore, if Luisa played soccer, then she didn't play music. For some theorists, they are invalid for everyday conditionals, but valid in logic. The theory of mental models implies that they are valid, but unacceptable because the conclusion refers to a possibility inconsistent with the premise. Hence, individuals should accept them if the conclusions refer only to possibilities consistent with the premises: Luisa didn't play soccer; therefore, if Luisa played (...) a game then she didn't play soccer. Two experiments corroborated this prediction for three sorts of ‘paradox’, including a disjunctive paradox. (shrink)

In this paper, I focus on the so-called "tacking by disjunction problem". Namely, the problem to the effect that, if a hypothesis H is confirmed by a statement E, H is confirmed by the disjunction E v F, for whatever statement F. I show that the attempt to settle this difficulty made by Grimes 1990, in a paper apparently forgotten by today methodologists, is irremediably faulty.

This paper in revised form appears in Facta Philosophica 5:1 (2003) 49­75. It addresses some problems about intensional transitives raised by Moltmann and Zimmerman, corrects some oversights in my paper in The Proceedings of the Aristotelian Society (S.V. for 2002), and adds new material on binary vs. tripartite construals of “relational/notional”, bridge inferences, weakening inferences, and the relevance problem. Its other sections are, like the PASS paper, concerned with the conjunctive force of disjunctive NP complements of intensional (...) transitive verbs: “Smith needs a good lawyer or a friendly judge” on its normal reading implies both “a good lawyer could help him” AND “a friendly judge could help him”. The reading on which “Smith needs a good lawyer or a friendly judge” is implied just by “Smith needs a good lawyer” (and so doesn’t imply a friendly judge could help him) is much less preferred, except when the disjunction is followed by a coda such as “and he doesn’t care which”. (shrink)

The mental model theory predicts that reasoners normally represent what is true, but not what is false. One consequence is that reasoners should make "illusory" inferences, which are compelling but invalid. Three experiments confirmed the existence of such illusions based on disjunctions of disjunctions. They also established a successful antidote to them: Reasoners are much less likely to succumb to illusions if the inferences concern disjunctions of physical objects (alternative newspaper advertisements) rather disjunctions of the truth values of (...) assertions. The results shed light both on the cause of the illusions and on the current controversy among different theories of reasoning. (shrink)

Causal Modeling Semantics (CMS, e.g., Galles and Pearl 1998; Pearl 2000; Halpern 2000) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual (A ∨ B) > C at a causal model M as a (...) weighted average of the probability of C in those submodels that truthmake A∨ B (Briggs 2012; Fine 2016, 2017). The weights of the submodels are given by the inverse distance to the original model M, based on a distance metric proposed by Eva, Stern, and Hartmann (2019). Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined. (shrink)

Relevantism, as a matter of definition, rejects classical logic as incorrect and adopts instead a relevant logic as encapsulating correct inference. It rejects classical logic on the grounds that the rule of Material Detachment, from A and not A or B to infer B,, sometimes leads from truth to falsity. Relevantism — although promoted by some relevant logicians, and an integral part of ultralogic — has recently encountered heavy, but interesting, criticism from relevance logicians themselves.

Principles of communication allow the listener to infer (upon hearing (1) that unless the speaker believed that (1alt) were false, the speaker would have uttered (1alt).

According to mental model theory, illusory inferences are a class of deductions in which individuals systematically go wrong. Mental model theory explains them invoking the principle of truth, which is a tendency not to represent models that falsify the premises. In this paper we focus on the illusory problems based on conditional sentences. In three experiments, we show that: (a) rather than not representing models that falsify the conditionals, participants have a different understanding of what falsifies a conditional (Experiment (...) I); (b) specifically, participants think that a conditional with an impossible antecedent or consequent is false (Experiment 2); (c) if the domain of the conditionals in the illusory problems are expanded to show that their antecedents and consequents are possible, the participants find it easy to reach the correct conclusions (Experiment 3). According to our results, the illusory inferences based on conditional premises, differently from those based on disjunctive premises, are caused by a difference between the understanding of natural language factual conditionals and the truth table of the factual implication; the principle of truth is not necessary to explain them. (shrink)

The article approaches cut elimination from a new angle. On the basis of an arbitrary inference relation among logically atomic formulae, an inference relation on a language possessing logical operators is defined by means of inductive clauses similar to the operator-introducing rules of a cut-free intuitionistic sequent calculus. The logical terminology of the richer language is not uniquely specified, but assumed to satisfy certain conditions of a general nature, allowing for, but not requiring, the existence of infinite conjunctions and disjunctions. (...) We investigate to what extent structural properties of the given atomic relation are preserved through the extension to the full language. While closure under the Cut rule narrowly construed is not in general thus preserved, two properties jointly amounting to closure under the ordinary structural rules, including Cut, are. -/- Attention is then narrowed down to the special case of a standard first-order language, where a similar result is obtained also for closure under substitution of terms for individual parameters. Taken together, the three preservation results imply the familiar cut-elimination theorem for pure first-order intuitionistic sequent calculus. -/- In the interest of conceptual economy, all deducibility relations are specified purely inductively, rather than in terms of the existence of formal proofs of any kind. (shrink)

This paper describes in some detail a pattern of justification which seems to be part of common sense logic and also part of the logic of scientific investigations. Calling this pattern “abduction,” the paper lays out an “abduction-prediction” model of scientific inference as an update to the traditional hypothetico-deductive model. According to this newer model, scientific theories receive their claims for acceptance and belief from the abductive arguments that support them, and the processes of scientific discovery aim to develop (...) theories with strong abductive support. It is suggested that the study of diagnosis presents a good opportunity for studying abduction under somewhat simpler and more reproducible conditions than occur in scientific discovery. A computer-based diagnostic system is described which provides a small-scale validation of the abduc-tion-prediction model by showing that a version of it can be made precise enough to be implemented and to perform correctly for diagnosis. (shrink)

Denić ( 2018, 2019, To appear ) observes that the availability of distributive inferences—for sentences with disjunction embedded in the scope of a universal quantifier—depends on the size of the domain quantified over as it relates to the number of disjuncts. Based on her observations, she argues that probabilistic considerations play a role in the computation of implicatures. In this paper we explore a different possibility. We argue for a modification of Denić’s generalization, and provide an explanation that is (...) based on intricate logical computations but is blind to probabilities. The explanation is based on the observation that when the domain size is no larger than the number of disjuncts, universal and existential alternatives are equivalent if distributive inferences are obtained. We argue that under such conditions a general ban on ‘fatal competition’ (Magri 2009a, b, Spector 2014 ) is activated, thereby predicting distributive inferences to be unavailable. (shrink)

In this paper we address the modelling of reasoning processes in natural agents. We focus on a very basic kind of non-monotonic inference for which we identify a simple and plausible underlying process, and we develop a family of logical models that allow to match this process. Partial worlds models, as we call them, are a variant of Kraus, Lehmann and Magidor’s cumulative models. We show that the inference relations they induce form a strict subclass of cumulative relations and tackle (...) the issue of providing sound and complete sets of rules to characterise them. Taking inspiration from the work of Gabbay and Schlechta, we analyse the question in terms of definable sets of partial worlds and conclude that completeness is probably unreachable using a standard propositional language. This brings us to enrich our language with an additional connective, which makes it possible to distinguish between two kinds of disjunction in the partial worlds context. Within this renewed framework, we provide two representation theorems: one for inference relations induced by precisification-free smooth models, and the other for inference relations induced by precisification-free ranked models. Finally we give an aperçu of how partial worlds models lend themselves to the modelling of learning. (shrink)