Changes

The usage of the terms '''''logical implication''''' and '''''material conditional''''' varies from field to field and even across different contexts of discussion.  One way to minimize the potential confusion is to begin with a focus on the various types of formal objects that are being discussed, of which there are only a few, taking up the variations in language as a secondary matter.

The usage of the terms '''''logical implication''''' and '''''material conditional''''' varies from field to field and even across different contexts of discussion.  One way to minimize the potential confusion is to begin with a focus on the various types of formal objects that are being discussed, of which there are only a few, taking up the variations in language as a secondary matter.

The main formal object under discussion is a logical operation on two logical values, typically the values of two [[proposition]]s, that produces a value of <math>\operatorname{false}</math> just in case the first operand is true and the second operand is false.  By way of a temporary name, the logical operation in question may be written as <math>\operatorname{Cond}(p, q),</math> where <math>p\!</math> and <math>q\!</math> are logical values.  The [[truth table]] associated with this operation appears below:

The main formal object under discussion is a logical operation on two logical values, typically the values of two propositions, that produces a value of <math>\operatorname{false}</math> just in case the first operand is true and the second operand is false.  By way of a temporary name, the logical operation in question may be written as <math>\operatorname{Cond}(p, q),</math> where <math>p\!</math> and <math>q\!</math> are logical values.  The [[truth table]] associated with this operation appears below:

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