August 27 - 28, 2020
The workshop brings together new developments in theoretical and experimental investigations on conditionals and reasoning in the areas of philosophy, psychology, logic, and probability theory. Its specific emphasis is on exploring relations between qualitative and quantitative approaches to conditionals––logical (broadly construed) and probabilistic––and their application to the empirical analysis of human reasoning. The event is part of the project “Qualitative and Quantitative Approaches to Reasoning and Conditionals” (DFG Project Nr. 272903199) in collaboration with the project "Logic and Philosophy of Science of Reasoning under Uncertainty" (BMBF Project Nr. 01UL1906X) at the chair of Prof. Hans Rott in Regensburg.
For a workshop report see: Michel, C., Pfeifer, N., Rott, H. (2020): "If ifs and ands were pots and pans...": Qualitative and Quantitative Approaches to Reasoning and Conditionals, 27-28 August (Workshop Report).
Thur. AUG 27
10:00 - 10:55 Edgington
"Conditionals, indeterminacy, probability and truth"
"A theory of conditionals"
"Gibbardian collapse and trivalent conditionals"
"Negating conditionals, connexively"
Virtual Tour & Open Microphone
Fri. AUG 28
"The probability conditional and inferentialism"
"Inference strength (still) predicts the probability of
conditionals better than conditional probability"
"Conditionals and the hierarchy of causal queries"
"Inference tickets and the asymmetry between modus ponens
and modus tollens"
"Compound and iterated conditionals in the setting of
"Aristotle's logical thinking probabilized: from qualitative to
quantitative reasoning and back"
Nicole Cruz (UNSW Sydney)
Dorothy Edgingtion (University of Oxford)
Paul Egré (CNRS/ENS, PSL University Paris)
Shira Elqayam (De Montfort University)
Mario Günther (Australian National University)
Christoph Michel (Universität Regensburg)
Hitoshi Omori (Ruhr-Universität Bochum)
Niki Pfeifer (Universität Regensburg)
Hans Rott (Universität Regensburg)
Giuseppe Sanfilippo (Università degli Studi di Palermo)
Niels Skovgaard-Olsen (Georg-August-Universität Göttingen)
The probability conditional and inferentialism
Psychological research on reasoning has recently advanced from an earlier approach based on binary classical logic to Bayesian, or probabilistic, theories. Our version of the new developments is grounded in what has been called "the Equation", P(if p then q) = P(q|p). We will call a conditional that satisfies the Equation a probability conditional. There is a large body of theoretical and empirical work in support of the Equation, but it has recently been challenged by research on inferentialist accounts of conditionals. These accounts have used counterintuitive missing-link conditionals to argue for the importance of an inferential relation between p and q, similar to an inference ticket, which ensures that P(q|p) > P(q|not-p). We will briefly outline our probabilistic approach to conditionals and alternative proposals from inferentialism. We will then discuss logical, conceptual, and empirical arguments against some inferentialist positions, and propose an alternative account of missing-link conditionals, which draws on pragmatics and on the distinction between singular and general conditionals.
Conditionals, Indeterminacy, Probability and Truth
Many conditionals whose antecedents turn out to be false are not merely uncertain but indeterminate. Nevertheless, I argue, they may be assessed probabilistically. For instance, given the proportions, it’s 90% likely that if I had picked a red ball it would have a black spot; but typically, there is no fact of the matter about which red ball I would have picked, if I had picked a red ball. Thus, probabilities apply even when there is no fact of the matter. I relate these ideas to a different kind of indeterminacy, the case of vagueness. I also relate this to work by Richard Bradley (Phil. Review 2012), where he argues that conditionals (a) are assessed by conditional probability, (b) are not (ordinary) propositions, but a more complex semantic entity, and (c) can nevertheless be given truth conditions such that the probability of their truth is the conditional probability of consequent given antecedent.
Gibbardian Collapse and Trivalent Conditionals
This paper discusses the scope and significance of the so-called triviality result stated by Allan Gibbard for indicative conditionals, showing that if a conditional operator satisfies the Law of Import-Export, is supraclassical, and is stronger than the material conditional, then it must collapse to the material conditional. Gibbard's result is taken to pose a dilemma for a truth-functional account of indicative conditionals: give up Import-Export, or embrace the two-valued analysis. We show that this dilemma can be averted in trivalent logics of the conditional based on Reichenbach and de Finetti's idea that a conditional with a false antecedent is undefined. Import-Export and truth-functionality hold without triviality in such logics. We unravel some implicit assumptions in Gibbard's proof, and discuss a recent generalization of Gibbard's result due to Branden Fitelson.
Inference strength (still) predicts the probability of conditionals better than conditional probability
Hypothetical Inferential Theory, or HIT, postulates that conditionals are evaluated by the strength of the inferential connection from antecedent to consequent. In this talk, we extend HIT for the first time to include the Ramsey test. The popular interpretation of the Ramsey test is the Equation, suggesting that the probability of the conditional is based on its conditional probability. In contrast, HIT suggests an interpretation based on the strength of inferential connection from antecedent to consequent. We pitted the two interpretations against each other empirically by giving participants fifty everyday causal conditionals repeated across three different tasks: judging the probability of the conditionals, the strength of inference from antecedent to consequent, and the probabilistic truth-table task. As predicted, we found inference strength to be a much stronger predictor of the probability of conditionals relative to conditional probability, thus supporting HIT and the inference-based interpretation of the Ramsey test. Similarly, an individual differences analysis found that the majority of participants conformed to an inference-based pattern, with a very small minority conforming to conditional probability. A second experiment extended these results by increasing the sample of conditionals to include negative inference and missing-link conditionals. We replicated and extended the results, finding again inference strength to be a much stronger predictor of the probability of conditionals relative to conditional probability. The results extended to negative and missing conditionals as well as positive inference conditionals. We conclude with thoughts on the New Paradigm.
A Theory of Conditionals
Philosophers dream of a theory according to which (1) conditionals have truth conditions, (2) the truth conditions for subjunctive and indicative conditionals are uniform but sufficiently different, (3) we can assign probability to conditionals, (4) we have a model for when to believe a conditional, and (5) a model for what to learn from a conditional. In this talk, we let the dream come true. If time permits, we outline some ramifications of the proposed theory. When are the inference schemes Or-to-If and Im/Export valid? How does the theory deal with nested conditionals? Can the theory accommodate the difference between would- and might-conditionals?
Inference Tickets and the Asymmetry between Modus Ponens and Modus Tollens
Departing from Ryle's original suggestion that inferences apply conditionals, I introduce a conception of indicative conditionals as inference tickets in order to analyse human reasoning. A valid inference ticket essentially requires the truth of a contextually strict conditional, amended by a preference regarding revisions of belief states. These preferences are inherently parts of epistemic contexts and permit for a parsimonious explanation of the observation that Modus Tollens inferences are drawn less readily than Modus Ponens inferences. In addition, I shall demonstrate how the account explains a well-known experimental-psychological result concerning the suppression of Modus Ponens inferences.
Aristotle's logical thinking probabilized: from qualitative to quantitative reasoning and back
Aristotle's probably most elaborated logical thinking handed down to us is presented in his Analytica Priora, which contains the famous syllogisms. Syllogisms are deductive argument forms about categorical propositions. Categorical propositions express whether some or all members of one category (denoted by the subject term S) are included in another category (denoted by the predicate term P). They are qualitative in the sense that they either form an affirmation (e.g., Some S is P) or a denial (e.g., No S is P). In my talk, I present a probabilistic semantics for Aristotelian syllogisms which allows for quantitative reasoning (Pfeifer & Sanfilippo, submitted). By suitable interpretations of categorical propositions in terms of conditional probability and respective concepts of validity, all traditionally valid syllogisms can be rationally reconstructed within coherence-based probability logic. I explain how this quantitative framework also allows for going back to qualitative reasoning, for example, via the notions of defaults and negated defaults. I also show how Aristotle's intuition---that conditionals with contradictory antecedents and consequents should be false (which also matches people's intuitions; Pfeifer, 2012)---can be framed within coherence-based probability logic. Among other instances of contradictions and conditionals, Aristotle's intuition has been investigated within connexive logic in recent years. While connexive logic is qualitative, I show how basic connexive principles can be interpreted quantitatively. Finally, I discuss how interactions among qualitative and quantitative approaches foster our understanding of conditionals.
This talk explores conditionals expressing that the antecedent makes a difference for the consequent. A 'relevantised' version of the Ramsey Test for conditionals is employed in the context of the classical theory of belief revision. The idea of this test is that the antecedent is relevant to the consequent in the following sense: a conditional is accepted just in case (i) the consequent is accepted if the belief state is revised by the antecedent and (ii) the consequent fails to be accepted if the belief state is revised by the antecedent's negation. The connective thus defined violates almost all of the traditional principles of conditional logic, but it obeys an interesting logic of its own. If there is time, I will also compare difference-making conditionals with 'evidential conditionals' or 'contraposing conditionals' as studied recently by Crupi & Iacona and Raidl.
Compound and iterated conditionals in the setting of coherence.
In our approach, the probability of a natural language conditional, P(if A then C), is interpreted by the subjective probability of the conditional event C|A. The conditional event is, in de Finetti’s sense, a three-valued logical entity. Its probability coincides with the conditional probability of C given A, i.e. P(C|A). An objection to identifying P(if A then C) with P(C|A) was that it appeared unclear how to form compounds and iterations of conditionals by preserving the usual probabilistic properties and by avoiding Lewis' Triviality.
In this talk, I illustrate how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations.
Specifically, based on Gilio and Sanfilippo (2014, 2019, working paper), I discuss logical operations among conditional events in a coherence-based approach, where the compound and iterated conditionals are conditional random quantities which go beyond the three-valued logic of conditional events. I show that in this "algebra" of conditionals De Morgan’s Law and the usual probabilistic properties are preserved and Lewis' Triviality results are avoided. I also give a characterization of p-consistency and p-entailment, with applications to several inference rules in probabilistic nonmonotonic reasoning. Then, I illustrate two methods which allow to turn not p-valid inference rules into p-valid ones.
Moreover, in analogy to the Deduction Theorem, I show that a conditional event E|H is p-entailed by a p-consistent family of two conditional events A|H and B|K if and only if the prevision of the iterated conditional (E|H)|((A|H)&(B|K)) is constant and equal to 1 (Gilio, Pfeifer, Sanfilippo, 2020). I also explain how to formalize latent information by iterated conditionals. I conclude my talk with some remarks on the supposed “independence” of two conditionals, and I interpret this property as uncorrelation between two random quantities (Sanfilippo, Gilio, Over, and Pfeifer 2020).
Conditionals and the Hierarchy of Causal Queries
In a series of experiments, we test the hypothesis that causal relations require multiple conceptual dimensions (prediction, intervention, and counterfactual dependence), which are differentially encoded in indicative and counterfactual conditionals. Our results indicate that the acceptance of indicative and counterfactual conditionals can become dissociated (Experiments 4, 5), and that the acceptance of both is needed for accepting a causal relation between two co-occurring events (Experiment 2). The implications that these findings have for the hypothesis above and recent debates at the intersection of the psychology of reasoning and causal judgment are discussed.
The Workshop will be held online. Participation is free but the number of participants is limited. We therefore kindly ask you to register via email under email@example.com. Once registered as a participant you will receive information and instructions for how to participate.
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