Reasoning with deontic and counterfactual conditionals

We report two new phenomena of deontic reasoning: (1) For conditionals with deontic content such as, “If the nurse cleaned up the blood then she must have worn rubber gloves”, reasoners make more modus tollens inferences (from “she did not wear rubber gloves” to “she did not clean up the blood”) compared to conditionals with epistemic content. (2) For conditionals in the subjunctive mood with deontic content, such as, “If the nurse had cleaned up the blood then she must have had to wear rubber gloves”, reasoners make the same frequency of all inferences as they do for conditionals in the indicative mood with deontic content. In this regard, subjunctive deontics are different from subjunctive epistemic conditionals: reasoners interpret subjunctive epistemic conditionals as counterfactual and they make more negative inferences such as modus tollens from them. The experiments show these two phenomena occur for deontic conditionals that contain the modal auxiliary “must” and ones that do not. We discuss the results in terms of the mental representations of deontic conditionals and of counterfactual conditionals.     

Social roles and utilities in reasoning with deontic conditionals

A set of experiments is reported in which a new formulation of deontic thinking is tested. This is that people represent subjective utilities inherent in conforming to or violating deontic statements, along with the social dynamics of these statements. The experiments used Wason's selection task and tested people's understanding of conditional permission. In the first two experiments, familiar scenarios referring to family interactions were used. In the third, an imaginary business content was used. In both cases it was apparent that people's thinking depended on their representation of the utilities associated with the agent of a permission statement (the party who lays down the rule) and the actor (the party whose behaviour is its target). The results are discussed as favouring an explanation in terms of mental models, rather than the schema theories which have dominated this field hitherto.     

Superordinate principles in reasoning with causal and deontic conditionals

We propose that the pragmatic factors that mediate everyday deduction, such as alternative and disabling conditions (e.g. Cummins et al., 1991) and additional requirements (Byrne, 1989) exert their effects on specific inferences because of their perceived relevance to more general principles, which we term SuperPs. Support for this proposal was found first in two causal inference experiments, in which it was shown that specific inferences were mediated by factors that are relevant to a more general principle, while the same inferences were unaffected by factors not relevant to the general principle. These results were extended to deontic inferences in two further experiments. Taken together, these findings show that unstated superordinate principles play a significant role in certain types of reasoning. Questions raised by the findings for the main theoretical approaches are discussed.     

Counterfactual and prefactual conditionals.

We consider reasoning about prefactual possibilities in the future, for example, "if I were to win the lottery next year I would buy a yacht" and counterfactual possibilities, for example, "if I had won the lottery last year, I would have bought a yacht." People may reason about indicative conditionals, for example, "if I won the lottery I bought a yacht" by keeping in mind a few true possibilities, for example, "I won the lottery and I bought a yacht." They understand counterfactuals by keeping in mind two possibilities, the conjecture, "I won the lottery and I bought a yacht" and the presupposed facts, "I did not win the lottery and I did not buy a yacht." We report the results of three experiments on prefactuals that examine what people judge them to imply, the possibilities they judge to be consistent with them, and the inferences they judge to follow from them. The results show that reasoners keep a single possibility in mind to understand a prefactual.     

A logic for deontic dilemmas

The possibility of deontic dilemmas poses a significant problem for deontic logic. Here I review some proposals to resolve this problem, and then offer a new account. This is a simple modification of standard deontic logic that enables the system to accommodate deontic dilemmas without inconsistency and without deontic explosion, while at the same time accounting for the range of genuinely valid inferences.     

Undercutting and the Ramsey test for conditionals

There is an important class of conditionals whose assertibility conditions are not given by the Ramsey test but by an inductive extension of that test. Such inductive Ramsey conditionals fail to satisfy some of the core properties of plain conditionals. Associated principles of nonmonotonic inference should not be assumed to hold generally if interpretations in terms of induction or appeals to total evidence are not to be ruled out.     

Evaluation strategies for some nonstandard conditionals during adolescence.

380 adolescents and young adults between the ages of 11 and 29 years participated in three experiments in which they were asked to evaluate both universally quantified nonstandard and standard conditionals using items of information bearing upon them. Subjects found it much easier to avoid a biconditional interpretation with the nonstandard than with the standard conditionals, which throws doubt on the explanation of desire for symmetry of biconditional conversion. It was argued, from data of other studies, that a modified version of the Piagetian view that biconditional conversion occurs as a result of a desire to avoid the complications of dealing with three factors explains most cases of such conversion in adolescence. Results also confirmed that it is more profitable to analyse performance on tasks of this kind using a two-stage model of interpretation and information use previously developed to explain performance with standard universally quantified conditionals than to view such tasks as providing truth-table values. Such an analysis was extended to the nonstandard conditionals studied in the present paper. The origins of the dramatic differences in information-use strategies adopted by adolescents for standard and nonstandard conditionals remain unclear.     

A utilitarian semantics for deontic logic

I am idebted to members of the Wellington Logic Seminar for useful discussions of work of which this essay forms part, in particular to M. J. Cresswell for comments in the earlier stages of the investigation and to R. I. Goldblatt who suggested the definition ofB _infD ^supu and made numerous other suggestions.     

Blueprint for a dynamic deontic logic

Extending the idiom of dynamic logic we outline a deontic logic in which deontic operators operate on terms rather than on formulæ. In a second step we distinguish between what we call real and deontic actions.     

Defending truth values for indicative conditionals

Philosophical Studies - There is strong disagreement about whether indicative conditionals have truth values. In this paper, I present a new argument for the conclusion that indicative conditionals...     

A deontic logic of action

The formal language studied in this paper contains two categories of expressions, terms and formulas. Terms express events, formulas propositions. There are infinitely many atomic terms and complex terms are made up by Boolean operations. Where and are terms the atomic formulas have the form = ( is the same as ), Forb ( is forbidden) and Perm ( is permitted). The formulae are truth functional combinations of these. An algebraic and a model theoretic account of validity are given and an axiomatic system is provided for which they are characteristic.The closure principle, that what is not forbidden is permitted is shown to hold at the level of outcomes but not at the level of events. In the two final sections some other operators are considered and a semantics in terms of action games.     

Reasoning with conditionals containing negated constituents.

Three experiments investigated matching bias in conditional reasoning tasks. Matching bias occurs when Ss ignore negations and match named items. Experiment 1 used an abstract and a thematic version of Evans's (1972) construction task. Results showed that matching may be due to an interaction between task demands and constructing contrast classes when interpreting negations. Experiment 2, which used Wason's (1968) selection task, introduced a manipulation to ease contrast-class construction. Confirmation plus falsification dominated over matching. Experiment 3 introduced two other manipulations to aid contrast-class construction with abstract material. Confirmation was facilitated, matching was suppressed, and falsification remained unchanged. These results suggest that matching occurs only when insufficient or ambiguous information prevents the intended interpretation of negations.     

Beliefs in conditionals vs. conditional beliefs

On the basis of impossibility results on probability, belief revision, and conditionals, it is argued that conditional beliefs differ from beliefs in conditionals qua mental states. Once this is established, it will be pointed out in what sense conditional beliefs are still conditional, even though they may lack conditional contents, and why it is permissible to still regard them as beliefs, although they are not beliefs in conditionals. Along the way, the main logical, dispositional, representational, and normative properties of conditional beliefs are studied, and it is explained how the failure of not distinguishing conditional beliefs from beliefs in conditionals can lead philosophical and empirical theories astray.