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Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions and argument flow. Compound propositions are formed by connecting propositions by logical connectives. The propositions without logical connectives are called atomic propositions.
"What the Tortoise Said to Achilles", written by Lewis Carroll in 1895 for the philosophical journal Mind, is a brief allegorical dialogue on the foundations of logic. The title alludes to one of Zeno's paradoxes of motion, in which Achilles could never overtake the tortoise in a race. In Carroll's dialogue, the tortoise challenges Achilles to use the force of logic to make him accept the conclusion of a simple deductive argument. Ultimately, Achilles fails, because the clever tortoise leads him into an infinite regression.
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In propositional logic, transposition is a valid rule of replacement that permits one to switch the antecedent with the consequent of a conditional statement in a logical proof if they are also both negated. It is the inference from the truth of "A implies B" the truth of "Not-B implies not-A", and conversely. It is very closely related to the rule of inference modus tollens. It is the rule that:
Relevance theory is a framework for understanding utterance interpretation first proposed by Dan Sperber and Deirdre Wilson and used within cognitive linguistics and pragmatics. It was originally inspired by the work of H. Paul Grice and developed out of his ideas, but has since become a pragmatic framework in its own right. The seminal book, Relevance, was first published in 1986 and revised in 1995. The impact of their work is seen by the fact that Google Scholar lists over 21,000 citations of this book.
Laurence Robert Horn is an American linguist. He is Professor Emeritus of Linguistics in the Department of Linguistics at Yale University with specialties in pragmatics and semantics. He received his doctorate in 1972 from UCLA and formerly served as Director of Undergraduate Studies, Director of Graduate Studies, and Chair of the Yale Department of Linguistics.
In pragmatics, scalar implicature, or quantity implicature, is an implicature that attributes an implicit meaning beyond the explicit or literal meaning of an utterance, and which suggests that the utterer had a reason for not using a more informative or stronger term on the same scale. The choice of the weaker characterization suggests that, as far as the speaker knows, none of the stronger characterizations in the scale holds. This is commonly seen in the use of 'some' to suggest the meaning 'not all', even though 'some' is logically consistent with 'all'. If Bill says 'I have some of my money in cash', this utterance suggests to a hearer that Bill does not have all his money in cash.
In philosophy, a razor is a principle or rule of thumb that allows one to eliminate unlikely explanations for a phenomenon, or avoid unnecessary actions.
Explicature is a technical term in pragmatics, the branch of linguistics that concerns the meaning given to an utterance by its context. The explicatures of a sentence are what is explicitly said, often supplemented with contextual information. They contrast with implicatures, the information that the speaker conveys without actually stating it.
Logical consequence is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises? All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth.
Logic is the systematic study of the forms of inference, the relations that lead to the acceptance of one proposition, the conclusion, on the basis of a set of other propositions, the premises. More broadly, logic is the analysis and appraisal of arguments. The premises may or may not support the conclusion; when they do not, the relation is characterized as a fallacy.
In the Neo-Gricean approach to semantics and pragmatics championed by Yale linguist Laurence Horn, the Q-principle is a reformulation of Paul Grice's maxim of quantity combined with the first two sub-maxims of manner. The Q-principle states: "Say as much as you can ." As such it interacts with the R-principle, which states: "Say no more than you must ."
References
- ↑ Horn, Laurence (1989). A Natural History of Negation. Chicago, IL: The University of Chicago press. pp. 193–203.
- 1 2 "Implicature" in the Stanford Encyclopedia of Philosophy.
- ↑ "The Gricean Model" in the Encyclopedia of Cognitive Science.
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