Program

Igor Douven

CNRS, University of Sorbonne, Paris, France

Title: Conditional and Inferential Connections
Summary of content to be covered in the course: Many have had the intuition that for a conditional to be true, there must be some sort of connection between its antecedent and its consequent. Plausible though the idea appears, it has proven difficult to turn into a tenable account of conditionals. This course looks at attempts to defend the idea, paying special attention to a recent proposal to understand the connection in terms of inference. Importantly, the notion of inference at play in this proposal is less strict than that of deductive inference, and comprises inductive and abductive inference as well (though is not even limited to these).

From the perspective of this proposal, we have a new look at the central questions concerning conditionals, most notably:

1. the question of what their truth conditions are (or if it have any to begin with);
2. the question of which logic they obey (so, which inferences involving conditionals are valid and which are not); and
3. the question of their probabilities.

We look at both theoretical and empirical work on 'inferentialist' approaches to the above questions.

Stefan Kaufmann

University of Connecticut, USA

1. Modals and conditionals in linguistic theory. This part covers the fundamentals of the Kratzer-style approach to conditionals, the standard in linguistics and a crucial player in contemporary debates on conditional semantics. The main ingredients are the two-parameter quantificational analysis of modality and the restrictor analysis of 'if'-clauses. We discuss some of their motivation, their relationship to other approaches, their strengths and weaknesses, and recent debates in which they figured prominently.

2. Tense and temporal reference in indicative conditionals. Most of the debates surrounding the temporal makeup of conditionals are concerned with "subjunctive" or "X-marked" conditionals. Those will be covered elsewhere in this program; here we focus on the interpretation of "indicative" conditionals. They are generally deemed less problematic (or less interesting) in terms of temporal interpretation, but we will see that the interplay between temporality and modality that they exhibit is far from trivial.

3. Variety and unity in temporal form and interpretation. We will build on the discussion of indicatives from the previous unit to discuss extensions of the framework introduced there in two directions: to different languages and to subjunctive conditionals. The focus will be on Germanic languages and on Japanese, but participants are encouraged to contribute their own data.

4. Specialty conditionals. This part covers interpretations arising with particular forms or in special contexts.  Possible topics (subject to audience requests): unconditionals; conditionalized imperatives and deontic modals; anankastic conditionals; conditional interpretations of other forms (such as expressions of temporal precedence).

John Mackay

University of Wisconsin

(1) Past Tense in Subjunctive Conditionals: Subjunctive conditionals, despite their name, are commonly marked by the presence of past tense. Yet they do not always describe past events, and at least on the surface, the difference between indicative and subjunctive conditionals does not appear to be a temporal one. We will examine different ways of explaining these phenomena. Some theorists argue that subjunctive conditionals involve a “fake” past tense that receives a modal interpretation. Others argue that it is interpreted in the standard temporal way. We will look at ways of implementing both strategies, and explore the advantages and disadvantages of both.

(2) Mood, Tense and Actuality: When an indicative clause is embedded inside a subjunctive conditional, that clause is evaluated at the actual world, rather than at the counterfactual worlds relevant to the overall conditional. In some other environments, embedded indicative clauses are not evaluated at the actual world. We will examine how tense and mood interact with actuality in conditionals. One of the central themes will be whether tense can play a role traditionally thought to be played by an actuality operator.

(3) Presupposition and Assertion: We will examine ways in which tense and mood in conditionals interact with presupposition and assertion. For example, we will look at how indicative and subjunctive conditionals have different assertoric effects, and how they interact with the context in different ways. We will consider how tense affects presuppositions in conditionals, and different theories of presupposition projection.

Readings:

David E. Over
Psychology Department, Durham University, Durham, UK

Nicole Cruz
Department of Psychological Sciences, Birkbeck, University of London, London, UK

The psychology of conditionals 

Abstract: Conditionals – indicative, counterfactual, deontic, and others – are central to the study of reasoning in linguistics, logic, philosophy, and psychology. These classes will cover the history of research on conditionals in the psychology of reasoning, and will introduce new Bayesian and probabilistic approaches, which have recently had a major impact on psychological theories about, and experiments on, human reasoning in general and conditional reasoning in particular. The new approaches recognize that most of this reasoning takes places in contexts of uncertainty. Most human inferences are not from arbitrary assumptions, but rather from uncertain premises, and lead finally to belief revision and updating. A central topic in this new research has been the hypothesis, originally proposed in logic and philosophy, that the probability of the natural language conditional, P(if p then q), is the conditional probability of q given p, P(q|p). This relationship, P(if p then q) = P(q|p), is fundamental in a Bayesian account of reasoning, and the latest research on it will be introduced and examined.

The psychology of conditional reasoning

Outline of the classes

Class 1: Introduction

Traditional psychology of reasoning studied binary reasoning from assumptions. The new Bayesian approaches are belief-based and probabilistic, and study the dynamic process of belief revision and updating.

The importance of studying conditionals in the psychology of reasoning, and the different types of conditional in natural language: indicative, counterfactual, deontic, and others.

Experiments in the psychology of reasoning will be introduced, and the material conditional of truth-functional logic.

A critical examination of the most prominent traditional accounts of the conditional in the psychology of reasoning: mental model theories of the conditional

Class 2: Significant early experiments

The reasons for taking a probabilistic approach to the study of reasoning: most human reasoning is not from arbitrary assumptions, but from uncertain premises. The premises are uncertain beliefs or are possibilities relevant to decision making, and the results are belief revision or updating, and effective decisions.

Studying Modus Ponens (MP) and Modus Tollens (MT) in the psychology of reasoning, and uncertainty and "suppression" in reasoning.

The conjunction fallacy is an example of inference from uncertain premises to uncertain conclusions.

The selection task, the most famous early experiment on conditionals, and what it tells us about them.

Class 3: Ramsey and de Finetti

The "defective" truth table and conditional assertions, and conditional bets and "void" conditionals.

The Ramsey test and the Equation, the conditional probability hypothesis, that the probability of the conditional is the conditional probability: P(if p then q) = P(q|p).

Stalnaker's theory of the conditional and Lewis's proof that the Equation must fail for conditionals of this type.

The de Finetti tables and the Jeffrey table for the conditional have "void" outcomes, or the conditional probability itself as a value.  

Class 4: Bayesian psychology of reasoning

The Equation / the conditional probability hypothesis is fundamental in Bayesian approaches to the psychology of conditionals. A conditional that satisfies the Equation has been called a "probability conditional", or the "conditional event".

The Ramsey test and the de Finetti / Jeffrey tables provide underlying support for Bayesian approaches.

Some experiments that provide support for the conditional probability hypothesis will be covered.

The Dutch book arguments as the deepest underlying justification of the Bayesian approaches.

Binary consistency will be generalized to coherence and coherence intervals, and binary validity to probabilistic validity, p-validity.

There will be a brief introduction to the possible differences between indicative and counterfactual conditionals, and students will be able to take part in an experiment on counterfactuals.   

Classes 5: More on counterfactuals

More points will be made about counterfactuals, and the results of the experiment will be presented and discussed.

Introductory readings: 

(1) Elqayam, S., & Over, D. E. (2013). New paradigm psychology of reasoning: An introduction to the special issue edited by S. Elqayam, J.F. Bonnefon, & D. E. Over. Thinking & Reasoning, 19, 249-265.

(2) Evans, J. St. B. T., Thompson, V., & Over, D. E. (2015). Uncertain deduction and conditional reasoning. Frontiers in Psychology, 6, 398.

(3) Over, D. E., & Cruz, N. (2018). Probabilistic accounts of conditional reasoning. In Linden J. Ball and Valerie A. Thompson (Eds.), International handbook of thinking and reasoning (pp. 434-450). Hove, UK: Psychology Press.