Project „Logical Connectives in Natural Languages”
The research project concentrates on the natural-language counterparts of logical connectives (“if-then”, “or”, “and”) and it aims to develop a complementary semantic theory of these connectives. We believe that such a theory should account for the variety of uses of these connectives, their particular senses, and at the same time provide a unitary semantic analysis for each of them.
The first general task is to explain mutual inferential relations of the aforementioned connectives. On one hand, the connectives under investigation behave like their logical counterparts as they license various inferences corresponding to appropriate tautologies of classical logic:
(1) “Either p or q. Hence if not-p, then q.”
(2) “It is not both the case that p and q. Hence either not-p or not-q.”
(3) “It is not both the case that p and not-q. Hence either not-p, or not not-q. That is, either not-p or q.
(4) “Either not-p or q. Hence, if p, then q.”
These inferences are intuitively valid and this feature apparently depends on the meanings of the embedded connectives. The simplest explanation of it is to assume that “if-then”, “or”, “and” has the meanings of ⊃, ∧, ∨ respectively. On the other hand, not all patterns of classical logic are intuitively valid (e.g., “If p, then if q, then p”, “p and q. Hence, q and p”) and, more generally, the assumption that the connectives under investigation are truth functional does not explain the intuitive validity of some other inferences, e.g.,
(5) Either p, or q. Hence it is possible that p.
(6) If p, then not-q. Hence it cannot be the case that p and q.
The question is then what kind of inferences with the connectives are actually valid and in what extent, their meanings overlap with the meanings of the truth functional connectives. Although most controversies concern the relation between “if-then” and ⊃ (see: Bennett 2003, Edgington 2007), there also some theorists who deny that “or” has the semantic contribution of ∨ (e.g., Geurts 2005) and that “and” has the semantic contribution of ∧ (e.g., Txurruka 2003.)
The second task is to explain various more specific senses which the sentences of the form “If p, then q”, “p or q”, “p and q” may express in a context. For instance, “and” may convey a temporal or a causal relation between the constituent clauses; “if-then” may convey a causal, evidential, analytical, and many other types of relations between the antecedent and the consequent of a conditional, e.g.,
(7) If the indicator is red, then we have acid in the jar.
(8) If Jones killed Smith, then he is a murderer!
(9) If you are eighteen, you are allowed to buy alcohol.
(10) If you are hungry, there are some biscuits in the kitchen.
How these meanings are generated? Do they belong to the level of semantics or pragmatics? Or are they somewhere in between?
The third task is to explain the relevance condition which a felicitous utterance of a connective sentence should fulfill. The condition states that an utterance of the form “If p, then q”, “p or q”, “p and q” is felicitous once p and q are somehow related to each other. In other words, it is infelicitous in a case when p is completely unrelated to q, e.g.,
(1) If the Earth orbits the sun, then two plus two equals four.
(2) Either the Earth orbits the sun, or two plus two equals four.
(3) The Earth orbits the sun and two plus two equals four.
Most philosophers assume that the relevance condition is genuinely pragmatic and can be accounted for and justified by Gricean theory of communication, in particular, it can be derived from the Cooperative Principle (see: Grice 1989, Simmons 2001). However, this view has been recently questioned in the case of conditionals by Björnsson (2008, 2011) who claims that the connection between the antecedent and the consequent is a part of the truth conditional content of a sentence – and thus it is semantically significant. In our project, we aim to examine and develop Björnsson’s proposal.
Bennett, J., 2003, A Philosophical Guide to Conditionals, Oxford: Clarendon Press.
Björnsson, Gunnar, (2008), “Strawson on ‘If’ and Hook”, South African Journal of Philosophy 27(3): 24-35
Björnsson, Gunnar, (2011), “Towards a Radically Pragmatic Theory of If-Conditionals”, in K. Turner (ed.) Current Research in the Pragmatics/Semantics Interface. Making Semantics Pragmatics, vol. 24., Brill Academic Publishers
Edgington, D., 2007, “On Conditionals” in D.M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd Edition, Volume 14: 127–221.
Geurts, B., 2005, “Entertaining Alternatives: Disjunctions as Modals”, Natural Language Semantics 13: 383-410.
Grice, H., P., 1989, Studies in the Way of Words, Cambrigde MA: Harvard University Press.
Simmons, M., 2001, “Disjunction and Alternativeness”, Linguistics and Philosophy 24(5): 597-619.
Txurruka, I., G., 2003, “The Natural Language Conjunction ‘and’” Linguistics and Philosophy 26,(3): 255-285