In a study in which 242 adults interpreted implicative statements by making .judgments of compatibility between sentences and pictures, three patterns of interpretation were found: conjunctive, equivalent, and implicative. There were marked differences across situations (binary or nonbinary) described by the sentences and across groups of subjects (arts or science students). From a learning viewpoint, the three patterns were hierarchically organized in the above order. Subjects gave significantly fewer conjunctive and more implicative interpretations in a transfer task. The presence of conjunctive and implicative patterns may be attributed to implicit conventions of logic and the natural languages. It is generally agreed that among the logical connectives, implication is the one that carries the most problems. Indeed, despite the number of studies that have been devoted to it, most questions remain unanswered. Braine (1978) has presented a formalization of the natural logic in which the status of the connective "if . . . then" plays a central role; in his system, "if . . . then" is the interpretation (in the axiomatic sense) of the inference line that is one of the primitive symbols of the system. According to Braine, it follows from this identification that for "ordinary users" (that is, nonlogicians) sentences of the form "if p then q" should be construed as irrelevant when p is not true because the inference just cannot be applied. This category of interpretation had been suggested earlier by Wason (1966), and its existence was later partly (Wason, 1968) or completely (Johnson-Laird & Tagart, 1969; Legrenzi, 1970) confirmed. When p and q are true the sentence is evaluated as true, and when p is true and q false it is evaluated as false. Therefore, this interpretation makes use of the three truth values (true, false, irrelevant), which is why Wason called it "defective" in reference to the two-valued truth tables of propositional logic. By deriving an inferential scheme, Braine showed that in his system "if p then q" has the same truth value as the material implica
[1]
S. E. Newstead,et al.
Language and reasoning: a study of temporal factors
,
1977,
Cognition.
[2]
J. S. Evans,et al.
Toward a Statistical Theory of Reasoning
,
1977
.
[3]
John E. Taplin,et al.
Reasoning with conditional sentences
,
1971
.
[4]
B. Shapiro,et al.
Logical Thinking in Children Ages Six through Thirteen.
,
1970
.
[5]
J. Piaget,et al.
The Psychology of the Child
,
1969
.
[6]
J. Ceraso,et al.
Sources of error in syllogistic reasoning
,
1971
.
[7]
John E. Taplin,et al.
Interpretation of Abstract Conditional Sentences in Deductive Reasoning.
,
1973
.
[8]
B. Foss.
New Horizons in Psychology 1
,
1966
.
[9]
J. S. Evans,et al.
Interpretation and Matching Bias in a Reasoning Task
,
1972
.
[10]
P. Johnson-Laird,et al.
Psychology of Reasoning: Structure and Content
,
1972
.
[11]
P C Wason,et al.
Reasoning about a Rule
,
1968,
The Quarterly journal of experimental psychology.
[12]
L. J. Chapman,et al.
Atmosphere effect re-examined.
,
1959,
Journal of experimental psychology.
[13]
J. Roberge.
An analysis of response patterns for conditional reasoning schemes
,
1971
.
[14]
Scott G. Paris,et al.
Comprehension of Language Connectives and Propositional Logical Relationships.
,
1973
.
[15]
M. Braine.
On the Relation Between the Natural Logic of Reasoning and Standard Logic.
,
1978
.
[16]
Herman Staudenmayer,et al.
Developmental changes in conditional reasoning: Linguistic or logical?
,
1974
.
[17]
Philip N. Johnson-Laird,et al.
How implication is understood.
,
1969
.
[18]
E. Peel,et al.
A method for investigating children's understanding of certain logical connectives used in binary propositional thinking.
,
1967,
The British journal of mathematical and statistical psychology.