The Mental Model Theory of Conditionals: A Reply to Guy Politzer

This paper replies to Politzer’s (2007) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the ‘paradoxes’ of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.     

Mental models and temporal reasoning

We report five experiments investigating reasoning based on temporal relations, such as: “John takes a shower before he drinks coffee”. How individuals make temporal inferences has not been studied hitherto, but we conjectured that they construct mental models of events, and we developed a computer program that reasons in this way.As the program shows, a problem of the form:

1. a before b

2. b before c

3. d while b

4. e while c

What is the relation between d and e?

where a, b, c, etc. refer to everyday events, calls for just one model, whereas a problem in which the second premise is modified to c before b calls for multiple models because a may occur before c, after c, or at the same time as c.

Experiments 1–3 showed that problems requiring one mental model elicited more correct responses than problems requiring multiple models, which in turn elicited more correct answers than multiple model problems with no valid answers. Experiment 4 contrasted the predictions of the model theory with those based on formal rules of inference; its results corroborated the model theory. Experiment 5 confirmed that a premise leading to multiple models took longer to read than the corresponding premise in one-model problems, and that latency to respond correctly was greater for multiple-model problems than for one-model problems. We conclude that the experiments corroborate the mental model theory.     

Book review

EVANS, R. M. The Perception of Color. New York: Wiley and Sons. 1974. Pp. xii + 248. £ 8.10.

ROSS, H. E. Behaviour and Perception in Strnge Enviroment. London: George Allen and Unwin. 1974. Pp. 171. £ 3.95. (Hardback), £ 1.95. (Peperback).

COOPER, J. R. BLOOM, F. E. and ROTH, R. H. The Biochemical Basis of Neuropharmacology. 2nd Ed. New York and London: Oxford University Press. 1974. Pp. 272. £ 2.50.

JOHNSON, F. N. (Ed.) Lithium Research and Teerapy. London: Acakemic Press. 1974. Pp. 570. £ 13.50.

GERGG, L. W. (Ed.) Cognition in Lerning and Memory. New York: Wiley. 1972. Pp. vii + 263. £ 5.85.

SCHIEFELBUSCH, R. L. and LLOYD, L. L. Language Perspectives-Acquisition, Retardation and Intervention. Macmillan: Baltimore, 1974. Pp 670. £ 7.95.

CHOMSKY, C. The Acquisition of Syntax of Syntax in Children form 5 to 10. Cambridge, Massa-chusetts: M. I. T. Press. 1969. Pp. 126.

Annual Review of Psychology. Vol. 25. Palo Alto, California: Annual Reviews Inc. 544 PP. $ 12.50.

HARRISON, B. Meaning and Structure: An Essay in the Philosophy of Language. New York: Harper and Row. 1972. Pp. 318. £4.65.

MACKINTOSH, N. J. The Psychology of Animal Learning. Academic Press. 1974. Pp. 730. £ 8.00.

BURES, J., BURESOVA, O. and KRIVANEK, J. The Mechanism and Application of Leao's Spreading Depression of Electroephalagraphic Activity. New York: Academic Press. 1974. Pp. 410. £ 14.15.

SOLSO, R.L. (ED.). Theories in Cognitive Psychology: The LOyola Symposium. Potomac, Maryland: Lawrence Erlbaum associates. 1974. £ 7.95.

MURDOCK, B. B. Jr. Human Memory: Theory and Data. Potomac: Erlbaum (distributed by Wiley). 1974. Pp. 362. £ 6.85.

REED, S. K. Psychological Process in Pattern Recogntion. New York: Academic Press. 1973. $ 13.95.

RABBIT, P. M. A. and DORNIC, D. (Eds). Attention and Performance V. London: Academic Press. 1975. Pp. 732. £ 16.00.     

Insight into a logical relation

Two experiments are reported which aimed to investigate factors affecting the gain of insight into the logical relation of implication. In the first experiment, subjects had to make a series of inferences about either a conditional sentence or a quantified sentence, both of which had the same underlying logical form. Under one condition the sentences had to be proved true, and under another condition, false. Proving a sentence false facilitated gain of insight, but the linguistic form of the sentence exerted no significant effect on the main dependent variable. In the second experiment, implication was not expressed as a sentence but was inherent in the structure of the task. The experimental material differed in complexity and allowed the cognitive load imposed on the subject to be varied. Results suggested that insight was not all-or-none. It was spontaneously gained when the material was simple, but temporarily lost when it was complex.     

Linguistic Context and the Priming of Semantic Information

Two experiments were carried out to demonstrate that linguistic context (in the form of a sentence) influences the interpretation of unambiguous words. Experiment I established that subjects read a sentence which primes a particular aspect of the meaning of one of the words it contains faster than they read a sentence which primes no particular aspect of the word's meaning. It also showed that subjects produce semantic characteristics of the word faster following the priming sentence than following the sentence that primes no particular semantic component. Experiment II corroborated these results using a task in which subjects read a sentence and then answered a question about the meaning of a word that occurred in it. Given a particular question, responses were faster when it followed a sentence that primed a characteristic relevant to the question than when it followed a sentence that primed no particular characteristic of the word. Responses were reliably slowest when the question followed a sentence that primed a characteristic that was not relevant to the question. Semantic priming is known to affect the identification of words and their disambiguation; the present study confirms that it also affects the specific interpretation of words.     

Shorter articles and notes the interpretation of the passive voice

It was hypothesized that sentences in the passive voice emphasize the importance of the things referred to by their grammatical subjects to a greater extent than sentences in the active voice. Each subject had to produce simple diagrams to represent two sentences, one active and one passive, and it was assumed that the size of areas in these diagrams could be taken as an index of importance. In Group EQ, the sentences specified an equivalent arrangement of colours, e.g. “Red follows Blue,” “Blue is followed by Red”; in Group CO, they specified converse arrangements, e.g. “Red follows Blue,” “Red is followed by Blue.” The predictions, that (i) the subjects of all sentences would tend to be represented as larger than the objects, and that (ii) the subjects of passives would be represented as larger than those of actives, were confirmed.     

The effects of belief on the spontaneous production of syllogistic conclusions

Two experiments examined the effects of subjects' beliefs on syllogistic inference. The first experiment showed that beliefs biased the spontaneous conclusions that subjects drew for themselves. These effects were more marked for indeterminate premises (which yield no non-trivial valid conclusions) than for determinate premises (which yield valid conclusions). There was also an effect of the nature of the beliefs: conclusions that were false by definition had a bigger effect on deductions than those that were false as a matter of fact. The second experiment replicated the finding for determinate syllogisms, using problems in moods in which the status of the valid conclusion could not be altered by conversion of the premises. Beliefs accordingly appear to affect the process of reasoning rather than the interpretation of premises.     

Reasoning from Suppositions

Two experiments investigated inferences based on suppositions. In Experiment 1, the subjects decided whether suppositions about individuals' veracity were consistent with their assertions—for example, whether the supposition “Ann is telling the truth and Beth is telling a lie”, is consistent with the premises: “Ann asserts: I am telling the truth and Beth is telling the truth. Beth asserts: Ann is telling the truth”. It showed that these inferences are more difficult than ones based on factual premises: “Ann asserts: I live in Dublin and Beth lives in Dublin”. There was no difference between problems about truthtellers and liars, who always told the truth or always lied, and normals, who sometimes told the truth and sometimes lied. In Experiment 2, the subjects made inferences about factual matters set in three contexts: a truth-inducing context in which friends confided their personality characteristics, a lie-inducing context in which business rivals advertised their products, and a neutral context in which computers printed their program characteristics. Given the supposition that the individuals were lying, it was more difficult to make inferences in a truth-inducing context than in the other two contexts. We discuss the implications of our results for everyday reasoning from suppositions, and for theories of reasoning based on models or inference rules.     

Children's creation of algorithms: simulations and gestures

Experiments showed that children are able to create algorithms, that is, sequences of operations that solve problems, and that their gestures help them to do so. The theory of mental models, which is implemented in a computer program, postulates that the creation of algorithms depends on mental simulations that unfold in time. Gestures are outward signs of moves and they help the process. We tested 10-year-old children, because they can plan, and because they gesture more than adults. They were able to rearrange the order of 6 cars in a train (using a siding), and the difficulty of the task depended on the number of moves in minimal solutions (Experiment 1). They were also able to devise informal algorithms to rearrange the order of cars when they were not allowed to move the cars, and the difficulty of the task depended on the complexity of the algorithms (Experiment 2). When children were prevented from gesturing as they formulated algorithms, the accuracy of their algorithms declined by13% (Experiment 3). We discuss the implications of these results.