Blackwell Reference Online

Extract

Whenever one asserts a claim of any kind, one engages in a commitment not just to that claim itself, but to a variety of other claims that follow in its wake, claims that, as we tend to say, follow logically from the original claim. To say that Smith and Jones are both great basketball players is to say something from which it follows that Smith is a great basketball player, that someone is a great basketball player, that there is something at which Smith is great, and so on. This general fact, that certain claims follow logically from others, is the central concern of a theory of logical consequence. Logical consequence is just the relation that connects a given claim or set of claims with those things that follow logically from it; to say that B is a logical consequence of A is simply to say that B follows logically from A. All of ordinary reasoning turns on the recognition of this relation. When one notices, for example, that a certain prediction follows from a given theory, that a particular view is a consequence of some initial commitments, that a collection of premises entails a given conclusion, and so on, one is engaged in reasoning about logical consequence. The other logical properties and relations whose recognition is central to ordinary reasoning are closely related to, and can be defined in terms of, logical consequence: • An argument is valid iff (if and ... log in or subscribe to read full text