We present two approaches to investigate the validity of connexive principles and related formulas and properties within coherence-based probability logic. Connexive logic emerged from the intuition that conditionals of the formif not-A,thenA, should not hold, since the conditional’s antecedentnot-Acontradicts its consequentA. Our approaches cover this intuition by observing that the only coherent probability assessment on the conditional event$${A| \overline{A}}$$A|A¯is$${p(A| \overline{A})=0}$$p(A|A¯)=0. In the first approach we investigate connexive principles within coherence-based probabilistic default reasoning, by interpreting defaults and negated defaults in terms (...) of suitable probabilistic constraints on conditional events. In the second approach we study connexivity within the coherence framework of compound conditionals, by interpreting connexive principles in terms of suitable conditional random quantities. After developing notions of validity in each approach, we analyze the following connexive principles:Aristotle’s theses,Aristotle’s Second Thesis,Abelard’s First Principle, andBoethius’ theses. We also deepen and generalize some principles and investigate further properties related to connexive logic (likenon-symmetry). Both approaches satisfyminimalrequirements for a connexive logic. Finally, we compare both approaches conceptually. (shrink)

We investigate the impact of informal arguments on judgments about thought experiment cases in light of Deutsch and Cappelen’s mischaracterization view, which claims that philosophers’ case judgments are primarily based on arguments and not intuitions. If arguments had no influence on case judgments, this would seriously challenge whether they are, or should be, based on arguments at all—and not on other cognitive sources instead, such as intuition. In Experiment 1, we replicated Wysocki’s (Rev Philos Psychol 8(2):477–499, 2017) pioneering study on (...) a Gettier-style case, and we confirmed that the informal arguments used by him had no significant effect. However, we also included an improved argument for ascribing knowledge, which did have a significant effect even in Wysocki’s original design. We therefore followed up with Experiment 2 on three Gettier-style cases, where we used a more natural dialogical format for presenting both case descriptions and informal arguments. Overall, we found a clear impact of prima facie good pro and con arguments on case judgments. The issue of argument impact is thus no obstacle to arguing about thought experiments. (shrink)

In this paper, a novel experimental task is developed for testing the highly influential, but experimentally underexplored, possible worlds account of conditionals (Stalnaker, 1968; Lewis, 1973). In Experiment 1, this new task is used to test both indicative and subjunctive conditionals. For indicative conditionals, five competing truth tables are compared, including the previously untested, multi-dimensional possible worlds semantics of Bradley (2012). In Experiment 2, these results are replicated and it is shown that they cannot be accounted for by an alternative (...) hypothesis proposed by our reviewers. In Experiment 3, individual variation in truth assignments of indicative conditionals is investigated via Bayesian mixture models that classify participants as following one of several competing models. As a novelty of this study, it is found that a possible worlds semantics of Lewis and Stalnaker is capable of accounting for participants’ aggregate truth value assignments in this task. Applied to indicative conditionals, we show across three experiments, that the theory both captures participants’ truth values at the aggregate level (Experiments 1 and 2) and that it makes up the largest subgroup in the analysis of individual variation in our experimental paradigm (Experiment 3). (shrink)

While Classical Logic (CL) used to be the gold standard for evaluating the rationality of human reasoning, certain non-theorems of CL—like Aristotle’s and Boethius’ theses—appear intuitively rational and plausible. Connexive logics have been developed to capture the underlying intuition that conditionals whose antecedents contradict their consequents, should be false. We present results of two experiments (total n = 72), the first to investigate connexive principles and related formulae systematically. Our data suggest that connexive logics provide more plausible rationality frameworks for (...) human reasoning compared to CL. Moreover, we experimentally investigate two approaches for validating connexive principles within the framework of coherence-based probability logic (Pfeifer & Sanfilippo, 2021). Overall, we observed good agreement between our predictions and the data, but especially for Approach 2. (shrink)

We present an interdisciplinary approach to argumentation combining logical, probabilistic, and psychological perspectives. We investigate logical attack principles which relate attacks among claims with logical form. For example, we consider the principle that an argument that attacks another argument claiming A triggers the existence of an attack on an argument featuring the stronger claim A ∧ B. We formulate a number of such principles pertaining to conjunctive, disjunctive, negated, and implicational claims. Some of these attack principles seem to be prima (...) facie more plausible than others. To support this intuition, we suggest an interpretation of these principles in terms of coherent conditional probabilities. This interpretation is naturally generalized from qualitative to quantitative principles. Specifically, we use our probabilistic semantics to evaluate the rationality of principles which govern the strength of argumentative attacks. In order to complement our theoretical analysis with an empirical perspective, we present an experiment with students of the TU Vienna ( n = 139) which explores the psychological plausibility of selected attack principles. We also discuss how our qualitative attack principles relate to well-known types of logical argumentation frameworks. Finally, we briefly discuss how our approach relates to the computational argumentation literature. (shrink)

Habilitation thesis in psychology. The book consists of a collection of reasoning studies. The experimental investigations will take us from people’s reasoning about probabilities, entailments, pragmatic factors, argumentation, and causality to morality. An overarching theme of the book is norm pluralism and individual differences in rationality research.

In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval [0,1]. We examine the iterated conditional (B|K)|(A|H), by showing that A|H p-entails B|K if and only if (B|K)|(A|H) = 1. Then, we show that a p-consistent family F={E1|H1, E2|H2} p-entails a conditional event E3|H3 if and only if E3|H3= 1, or (E3|H3)|QC(S) = 1 for some nonempty subset S (...) of F, where QC(S) is the quasi conjunction of the conditional events in S. Then, we examine the inference rules And, Cut, Cautious Monotonicity, and Or of System P and other well known inference rules (Modus Ponens, Modus Tollens, Bayes). We also show that QC(F)|C(F) = 1, where C(F) is the conjunction of the conditional events in F. We characterize p-entailment by showing that F p-entails E3|H3 if and only if (E3|H3)|C(F) = 1. Finally, we examine Denial of the antecedent and Affirmation of the consequent, where the p-entailment of (E3|H3) from F does not hold, by showing that (E3|H3)|C(F) is not equal to 1. (shrink)

The purpose of this paper is to show that if one adopts conditional probabilities as the primitive concept of probability, one must deal with the fact that even in very ordinary circumstances at least some probability values may be imprecise, and that some probability questions may fail to have numerically precise answers.

It is widely held that there are important differences between indicative conditionals (e.g. “If the authors are linguists, they have written a linguistics paper”) and subjunctive conditionals (e.g. “If the authors had been linguists, they would have written a linguistics paper”). A central difference is that indicatives and subjunctives convey different stances towards the truth of their antecedents. Indicatives (often) convey neutrality: for example, about whether the authors in question are linguists. Subjunctives (often) convey the falsity of the antecedent: for (...) example, that the authors in question are not linguists. This paper tests prominent accounts of how these different stances are conveyed: whether by presupposition or conversational implicature. Experiment 1 tests the presupposition account by investigating whether the stances project – remain constant – when embedded under operators like negations, possibility modals, and interrogatives, a key characteristic of presuppositions. Experiment 2 tests the conversational-implicature account by investigating whether the stances can be cancelled without producing a contradiction, a key characteristic of implicatures. The results provide evidence that both stances – neutrality about the antecedent in indicatives and the falsity of the antecedent in subjunctives – are conveyed by conversational implicatures. (shrink)

This paper investigates whether empirical findings on how humans evaluate arguments in reinstatement cases support the ‘fewer attackers is better’ principle, incorporated in many current gradual notions of argument acceptability. Through three variations of an experiment, we find that (1) earlier findings that reinstated arguments are rated lower than when presented alone are replicated, (2) ratings at the reinstated stage are similar if all arguments are presented at once, compared to sequentially, and (3) ratings are overall higher if participants are (...) provided with the relevant theory, while still instantiating imperfect reinstatement. We conclude that these findings could at best support a more specific principle ‘being unattacked is better than attacked’, but alternative explanations cannot yet be ruled out. More generally, we highlight the danger that experimenters in reasoning experiments interpret examples differently from humans. Finally, we argue that more justification is needed on why, and how, empirical findings on how humans argue can be relevant for normative models of argumentation. (shrink)

In this paper we show that axiomatic extensions of H. Wansing’s connexive logic $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ ) are algebraizable (in the sense of J.W. Blok and D. Pigozzi) with respect to sub-varieties of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ )-algebras. We develop the structure theory of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ )-algebras, and we prove their representability in terms of twist-like constructions over implicative lattices (Heyting algebras). As a consequence, we further clarify the relationship between the aforementioned classes. Finally, taking advantage of (...) the above machinery, we provide some preliminary remarks on the lattice of axiomatic extensions of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ ) as well as on some properties of their equivalent algebraic semantics. (shrink)