Connexive Logic - Connecting Antecedent To Consequent

Connecting Antecedent To Consequent

The objection that is made to the truth-functional definition of conditionals is that there is no requirement that the consequent actually follow from the antecedent. So long as the antecedent is false or the consequent true, the conditional is considered to be true whether there is any relation between the antecedent and the consequent or not. Hence, as the philosopher Charles Sanders Peirce once remarked, you can cut up a newspaper, sentence by sentence, put all the sentences in a hat, and draw any two at random. It is guaranteed that either the first sentence will imply the second, or vice versa. But when we use the words "if" and "then" we generally mean to assert that there is some relation between the antecedent and the consequent. What is the nature of that relationship? Relevance (or Relevant) logicians take the view that, in addition to saying that the consequent cannot be false while the antecedent is true, the antecedent must be "relevant" to the consequent. At least initially, this means that there must be at least some terms (or variables) that appear in both the antecedent and the consequent. Connexivists generally claim instead that there must be some "real connection" between the antecedent and the consequent, such as might be the result of real class inclusion relations. For example, the class relations, "All men are mortal," would provide a real connection that would warrant the conditional, "If Socrates is a man, then Socrates is mortal." However, more remote connections, for example "If she apologized to him, then he lied to me," (suggested by Bennett) still defy connexivist analysis.