Reasoning strategies for suppositional deductions

Subtracting “ought” from “is”: Descriptivism versus normativism in the study of human thinking

We propose a critique ofnormativism, defined as the idea that human thinking reflects a normative system against which it should be measured and judged. We analyze the methodological problems associated with normativism, proposing that it invites the controversial “is-ought” inference, much contested in the philosophical literature. This problem is triggered when there are competing normative accounts (the arbitration problem), as empirical evidence can help arbitrate between descriptive theories, but not between normative systems. Drawing on linguistics as a model, we propose that a clear distinction between normative systems and competence theories is essential, arguing that equating them invites an “is-ought” inference: to wit, supporting normative “ought” theories with empirical “is” evidence. We analyze in detail two research programmes with normativist features – Oaksford and Chater's rational analysis and Stanovich and West's individual differences approach – demonstrating how, in each case, equating norm and competence leads to an is-ought inference. Normativism triggers a host of research biases in the psychology of reasoning and decision making: focusing on untrained participants and novel problems, analyzing psychological processes in terms of their normative correlates, and neglecting philosophically significant paradigms when they do not supply clear standards for normative judgement. For example, in a dual-process framework, normativism can lead to a fallacious “ought-is” inference, in which normative responses are taken as diagnostic of analytic reasoning. We propose that little can be gained from normativism that cannot be achieved by descriptivist computational-level analysis, illustrating our position with Hypothetical Thinking Theory and the theory of the suppositional conditional. We conclude that descriptivism is a viable option, and that theories of higher mental processing would be better off freed from normative considerations.

On some limits of hypothetical thinking

Faced with extreme demands, hypothetical thinking runs the danger of total failure. Paradoxical propositions such as the Liar ("I am lying") provide an opportunity to test it to its limits, while the Liar's nonparadoxical counterpart, the Truthteller ("I am telling the truth"), provides a useful comparison. Two experiments are reported, one with abstract materials ("If I am a knave then I live in Emerald City") and one with belief-laden materials (a judge says: "If I am a knave then I enjoy pop music"). In both experiments, conditionals with Truthteller-type antecedents were "collapsed" to responses of conditional probability closely resembling estimates of control items. Liar-type antecedents, in contrast, dramatically weakened belief in conditionals in which they were embedded. The results are discussed in the framework of the theory of hypothetical thinking.

A quantitative model of the human-machine interaction and multi-task performance: a strategy function and the unity model paradigm

A human-machine-interaction (HMI) model is developed for the human operator (HO) performing five simultaneous tasks and characterized by a strategy function. Five levels of total machine-initiated baud rate (B(IN)) are generated by the multi-attribute task battery (MATB) and five HO baud rates (B(O)) are then recorded. Total baud ratio (B ) is defined as the ratio of B(O) to B(IN). Results indicate that with increasing B(IN) levels: (1) there is an overall increase in B(O), and (2) there is an overall decrease in B . These results are due to a decreasing HMI performance and divergence of the strategy function from a unity model paradigm.

The heuristic-analytic theory of reasoning: Extension and evaluation

An extensively revised heuristic-analytic theory of reasoning is presented incorporating three principles of hypothetical thinking. The theory assumes that reasoning and judgment are facilitated by the formation of epistemic mental models that are generated one at a time (singularity principle) by preconscious heuristic processes that contextualize problems in such a way as to maximize relevance to current goals (relevance principle). Analytic processes evaluate these models but tend to accept them unless there is good reason to reject them (satisficing principle). At a minimum, analytic processing of models is required so as to generate inferences or judgments relevant to the task instructions, but more active intervention may result in modification or replacement of default models generated by the heuristic system. Evidence for this theory is provided by a review of a wide range of literature on thinking and reasoning.

Conditionals: a theory of meaning, pragmatics, and inference

The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals.

Mental models and deduction

According to the mental-model theory of deductive reasoning, reasoners use the meanings of assertions together with general knowledge to construct mental models of the possibilities compatible with the premises. Each model represents what is true in a possibility. A conclusion is held to be valid if it holds in all the models of the premises. Recent evidence described here shows that the fewer models an inference calls for, the easier the inference is. Errors arise because reasoners fail to consider all possible models, and because models do not normally represent what is false, even though reasoners can construct counterexamples to refute invalid conclusions.

Are conjunctive inferences easier than disjunctive inferences? A comparison of rules and models

We report four experiments investigating conjunctive inferences (from a conjunction and two conditional premises) and disjunctive inferences (from a disjunction and the same two conditionals). The mental model theory predicts that the conjunctive inferences, which require one model, should be easier than the disjunctive inferences, which require multiple models. Formal rule theories predict either the opposite result or no difference between the inferences. The experiments showed that the inferences were equally easy when the participants evaluated given conclusions, but that the conjunctive inferences were easier than the disjunctive inferences (1) when the participants drew their own conclusions, (2) when the conjunction and disjunction came last in the premises, (3) in the time the participants spent reading the premises and in responding to given conclusions, and (4) in their ratings of the difficulty of the inferences. The results support the model theory and demonstrate the importance of reasoners' inferential strategies.

The temporality effect in counterfactual thinking about what might have been

When people think about what might have been, they undo an outcome by changing events in regular ways. Suppose two contestants could win 1,000 Pounds if they picked the same color card; the first picks black, the second red, and they lose. The temporality effect refers to the tendency to think they would have won if the second player had picked black. Individuals also think that the second player will experience more guilt and be blamed more by the first. We report the results of five experiments that examine the nature of this effect. The first three experiments examine the temporality effect in scenarios in which the game is stopped after the first contestant's card selection because of a technical hitch, and then is restarted. When the first player picks a different card, the temporality effect is eliminated, for scenarios based on implicit and explicit negation and for good outcomes. When the first player picks the same card, the temporality effect occurs in each of these situations. The second two experiments show that it depends on the order of events in the world, not their descriptive order. It occurs for scenarios without preconceptions about normal descriptive order; it occurs whether the second event is mentioned in second place or first. The results are consistent with the idea that the temporality effect arises because the first event is presupposed and so it is immutable; and the elimination of the temporality effect arises because the availability of a counterfactual alternative to the first event creates an opposing tendency to mutate it. We sketch a putative account of these effects based on characteristics of the mental models people construct when they think counterfactually.

Deductive reasoning with factual, possible, and counterfactual conditionals

We compared reasoners' inferences from conditionals based on possibilities in the present or the past (e.g., "If Linda had been in Dublin then Cathy would have been in Galway") with their inferences based on facts in the present or the past (e.g., "If Linda was in Dublin then Cathy was in Galway"). We propose that people construct a richer representation of conditionals that deal with possibilities rather than facts: Their models make explicit not only the suppositional case, in which Linda is in Dublin and Cathy is in Galway, but also the presupposed case, in which Linda is not in Dublin and Cathy is not in Galway. We report the results of four experiments that corroborate this model theory. The experiments show that reasoners make more inferences from conditionals based on possibilities rather than on facts when the inferences depend on the presupposed case. The results also show that reasoners generate different situations to verify and falsify conditionals based on possibilities and facts.

DEDUCTIVE REASONING

This chapter describes the main accounts of deductive competence, which explain what is computed in carrying out deductions. It argues that people have a modicum of competence, which is useful in daily life and a prerequisite for acquiring logical expertise. It outlines the three main sorts of theory of deductive performance, which explain how people make deductions: They rely on factual knowledge, formal rules, or mental models. It reviews recent experimental studies of deductive reasoning in order to help readers to assess these theories of performance.