scholarly journals Conditional Reasoning Part I

2020 ◽  
pp. 95-118
Author(s):  
Peter Langland-Hassan
Keyword(s):  
Mental Models ◽  
Formal Logic ◽  
Conditional Reasoning ◽  
Apparent Difference ◽  
Truth Conditions ◽  
Indicative Conditional ◽  
Counterfactual Conditional ◽  
Alternative Proposal ◽  
Normative Standards

Three types of conditional are distinguished: the material conditional, indicative conditional, and subjunctive/counterfactual conditional. The apparent difference in truth conditions of each is suggestive of different psychological procedures used in the evaluation of each. The psychology of the material conditional is then examined. Despite procedures in formal logic that are suggestive of sui generis imaginative states (e.g., “assuming” a proposition for conditional proof, or for reductio), we need not countenance the use of such states within the psychological procedures used to carry out the inferences. Further, work in psychology has long suggested that humans do not, as a rule, reason in accordance with normative standards appropriate to the material conditional. A popular alternative proposal in psychology is that conditional reasoning involves the use of mental models (Johnson-Laird & Byrne, 2002). The use of mental models is shown to be consistent with conditional reasoning involving only sequences of beliefs.

¿Razonamos en función de nuestro conocimiento general? Un estudio de las interacciones entre el procesamiento de la información y la inferencia lógica

2015 ◽  
pp. 33
Author(s):  
Miguel López Astorga
Keyword(s):  
Information Processing ◽  
Teaching And Learning ◽  
Learning Processes ◽  
Formal Logic ◽  
Conditional Reasoning ◽  
General Knowledge

RESUMENEn este trabajo, analizamos un experimento sobre el razonamiento condicional de Staller, Sloman y Ben-Zeev (2000). En dicho experimento, los sujetos parecen manifestar un comportamiento contrario a las prescripciones de la lógica formal. Nosotros lo revisamosy descubrimos todas las variables que es preciso atender en los procesos de enseñanza y aprendizaje, variables que no siempre son consideradas por los docentes.Palabras clave: condicional, conocimiento general, inferencia, procesamiento de la información, representación mental.DO WE REASON ACCORDING TO OUR GENERALKNOWLEDGE? A STUDY ABOUT INTERACTIONSBETWEEN INFORMATION PROCESSING AND LOGICALINFERENCEABSTRACTIn this paper, I analyze an experiment about conditional reasoning presented by Staller,Sloman and Ben-Zeev (2000). In that experiment, the subjects’ behavior seems contradictory to prescriptions of formal logic. I check it and I discover all the variables that we need to deal with them in teaching and learning processes, despite that such variables are notalways checked by the teachers.Keywords: conditional, general knowledge, inference, information processing, mentalrepresentation.

Conditionals and Abduction

2020 ◽  
pp. 161-166
Author(s):  
Timothy Williamson
Keyword(s):  
Past Tense ◽  
Indicative Conditionals ◽  
Cognitive Differences ◽  
Indicative Conditional ◽  
Counterfactual Conditional ◽  
Counterfactual Conditionals ◽  
The Past ◽  
Testing Of Hypotheses ◽  
New Evidence

The chapter gives a preliminary sketch of some cognitive differences between indicative conditionals and counterfactual conditionals relevant to the testing of hypotheses by experiment. They especially concern cases where the indicative conditional can be decided without new evidence while the counterfactual conditional cannot. They also show that the antecedent of a ‘counterfactual’ conditional need not be presupposed to be false. Differences connected with the past tense morphology of ‘would’ are explored. Cases are given where the morphology should be understood as expressing a ‘fake past’, modal rather than temporal.

On the Mental Representation of Conditional Sentences

1996 ◽  
Vol 49 (4) ◽  
pp. 1086-1114 ◽  
Author(s):  
Jonathan St. B. T. Evans ◽  
Charles E. Ellis ◽  
Stephen E. Newstead
Keyword(s):  
Mental Models ◽  
Research Methods ◽  
Mental Representation ◽  
Conditional Reasoning ◽  
Strong Tendency ◽  
Inference Rules ◽  
Counter Example ◽  
First Finding ◽  
Blue Triangle ◽  
Conditional Statements

Four experiments are reported which attempt to externalize subjects’ mental representation of conditional sentences, using novel research methods. In Experiment 1, subjects were shown arrays of coloured shapes and asked to rate the degree to which they appeared to be true of conditional statements such as “If the figure is green then it is a triangle”. The arrays contained different distributions of the four logically possible cases in which the antecedent or consequent is true or false: TT, TF, FT, and FF. For example, a blue triangle would be FT for the conditional quoted above. In Experiments 2 to 4, subjects were able to construct their own arrays to make conditionals either true or false with any distribution of the four cases they wished to choose. The presence and absence of negative components was varied, as was the form of the conditional, being either “if then” as above or “only if”: “The figure is green only if it is a triangle”. The first finding was that subjects represent conditionals in fuzzy way: conditionals that include some counter-example TF cases (Experiment 1) may be rated as true, and such cases are often included when subjects construct an array to make the rule true (Experiments 2 to 4). Other findings included a strong tendency to include psychologically irrelevant FT and FF cases in constructed arrays, presumably to show that conditional statements only apply some of the time. A tendency to construct cases in line with the “matching bias” reported on analogous tasks in the literature was found, but only in Experiment 4, where the number of symbols available to construct each case was controlled. The findings are discussed in relation to the major contemporary theories of conditional reasoning based upon inference rules and mental models, neither of which can account for all the results.

scholarly journals Dynamic Probabilistic Entailment. Improving on Adams' Dynamic Entailment Relation

2021 ◽  
pp. 1-26
Author(s):  
Robert Van Rooij ◽  
Patricia Mirabile
Keyword(s):  
Original System ◽  
Modus Ponens ◽  
Behavioral Experiment ◽  
Truth Conditions ◽  
Indicative Conditionals ◽  
Indicative Conditional ◽  
Entailment Relation ◽  
New Information ◽  
General Relevance ◽  
Hypothetical Syllogism

The inferences of contraposition (A ⇒ C ∴ ¬C ⇒ ¬A), the hypothetical syllogism (A ⇒ B, B ⇒ C ∴ A ⇒ C), and others are widely seen as unacceptable for counterfactual conditionals. Adams convincingly argued, however, that these inferences are unacceptable for indicative conditionals as well. He argued that an indicative conditional of form A ⇒ C has assertability conditions instead of truth conditions, and that their assertability ‘goes with’ the conditional probability p(C|A). To account for inferences, Adams developed the notion of probabilistic entailment as an extension of classical entailment. This combined approach (correctly) predicts that contraposition and the hypothetical syllogism are invalid inferences. Perhaps less well-known, however, is that the approach also predicts that the unconditional counterparts of these inferences, e.g., modus tollens (A ⇒ C, ¬C ∴ ¬A), and iterated modus ponens (A ⇒ B, B ⇒ C, A ∴ C) are predicted to be valid. We will argue both by example and by calling to the results from a behavioral experiment (N = 159) that these latter predictions are incorrect if the unconditional premises in these inferences are seen as new information. Then we will discuss Adams’ (1998) dynamic probabilistic entailment relation, and argue that it is problematic. Finally, it will be shown how his dynamic entailment relation can be improved such that the incongruence predicted by Adams’ original system concerning conditionals and their unconditional counterparts are overcome. Finally, it will be argued that the idea behind this new notion of entailment is of more general relevance.

Reasoning with three Types of Conditional: Biases and Mental Models

1993 ◽  
Vol 46 (4) ◽  
pp. 653-677 ◽  
Author(s):  
Thomas C. Ormerod ◽  
Kenneth I. Manktelow ◽  
Gregory V. Jones
Keyword(s):  
Mental Models ◽  
Internal Structure ◽  
Temporal Order ◽  
Conditional Reasoning ◽  
Rule Generation ◽  
Differential Effects ◽  
Evaluation Task ◽  
Abstract Rule ◽  
Pattern Of Performance ◽  
Rule Evaluation

Two experiments are reported which compare conditional reasoning with three types of rule. These consist of two types of rule that have been widely studied previously, if p then q and p only if q, together with a third type, q if p. In both experiments, the p only if q type of rule yields a different pattern of performance from the two other types of rule. Experiment 1 is an abstract rule-evaluation task and demonstrates differential effects of temporal order and of suppositional bias. Experiment 2 investigates rule generation, rephrasing, and comparison, and demonstrates differential effects of temporal order and of thematic content. An analysis of the results is offered in terms of biases and mental models. Effects of rule form and context can be explained as reflecting the different sequences in which mental models are created for each rule form. However, it is necessary to consider the internal structure of individual mental models to account for effects arising from temporal ordering of rules.

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