Abstract
In this paper, the meaning and processing of the German conditional connectives (CCs) such as wenn ‘if’ and nur wenn ‘only if’ are investigated. In Experiment 1, participants read short scenarios containing a conditional sentence (i.e., If P, Q.) with wenn/nur wenn ‘if/only if’ and a confirmed or negated antecedent (i.e., P/not-P), and subsequently completed the final sentence about Q (with or without negation). In Experiment 2, participants rated the truth or falsity of the consequent Q after reading a conditional sentence with wenn or nur wenn and a confirmed or negated antecedent (i.e., If P, Q. P/not-P. // Therefore, Q?). Both experiments showed that neither wenn nor nur wenn were interpreted as biconditional CCs. Modus Ponens (If P, Q. P. // Therefore, Q) was validated for wenn, whereas it was not validated in the case of nur wenn. While Denial of the Antecedent (If P, Q. not-P. // Therefore, not-Q.) was validated in the case of nur wenn, it was not validated for wenn. The same method was used to test wenn vs. unter der Bedingung, dass ‘on condition that’ in Experiment 3, and wenn vs. vorausgesetzt, dass ‘provided that’ in Experiment 4. Experiment 5, using Affirmation of the Consequent (If P, Q. Q. // Therefore, P.) to test wenn vs. nur wenn replicated the results of Experiment 2. Taken together, the results show that in German, unter der Bedingung, dass is the most likely candidate of biconditional CCs whereas all others are not biconditional. The findings, in particular of nur wenn not being semantically biconditional, are discussed based on available formal analyses of conditionals.
Highlights
Conditionals (e.g., If it rains, the streets get wet.) are one of the most studied topics in cognitive science
We started with Denial of the Antecedent (DA) instead of Affirmation of the Consequent (AC) inferences, as DA (i.e., If P, Q. not-P. // not-Q; see (2d)) reserves the temporal or causal relation between the antecedent and the consequent proposition in the given conditionals, but we will show later with Experiment 2 and 5 that the experimental results based on them are comparable, at least in the current study
The results revealed that wenn und nur wenn, while being rarely used in German, is a biconditional connective
Summary
Conditionals (e.g., If it rains, the streets get wet.) are one of the most studied topics in cognitive science. B. Arguably biconditional CCs (i.e., those that might convey P as a sufficient and necessary condition for Q): vorausgesetzt, dass ‘provided that’, unter der Voraussetzung, dass ‘provided that’, unter der Bedingung, dass ‘on condition that’, nur wenn ‘only if’. Biconditional CCs (i.e., those that might convey P as a sufficient and necessary condition for Q): vorausgesetzt, dass ‘provided that’, unter der Voraussetzung, dass ‘provided that’, unter der Bedingung, dass ‘on condition that’, nur wenn ‘only if’ These CCs differ in syntactic properties in that some contain single connectives and some are verbal or prepositional phrases. We will deal with their semantic and pragmatic contributions, focusing on the question of whether they express semantic biconditionals or not Being conditional connectives, they bear some relation to the logical connective of material implication or conditional if ( ?) and the logical connective of material biconditional iff (if and only if, $) in first-order logic
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