Talk:Logical implication

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[edit] Material implication

What the hell is the difference between Logical implication and the Material conditional ????? I propose a merge. Fresheneesz 07:35, 11 October 2006 (UTC)

A logical implication is a valid material implication (or material conditional). These are two different but often confused notions. The pages should remain separate, but the page on logical implication needs to be updated so as to reflect this distinction. 128.112.210.248 22:29, 7 November 2006 (UTC)

Actually both pages are a mess. Nortexoid 06:04, 10 December 2006 (UTC)

[edit] Introduction

The introduction of the article had been changed to read:

Logical implication is not to be confused with material implication (AKA material conditional).

In ordinary language, material implication is often expressed by sentences of the following form:

• If P then Q.

Here P and Q are propositional variables that represent propositions in a given language. In a statement of the form "if P then Q", the first term, P, is called the antecedent and the second term, Q, is called the consequent; and the statement as a whole is called a conditional. Assuming that the conditional is true, then the truth of the antecedent is a sufficient condition for the truth of the consequent, while the truth of the consequent is a necessary condition for the truth of the antecedent.

A sentence is valid (not to be confused with the property of an argument being valid) if and only if it is true on every interpretation. (See also logical truth, tautology.)

A logical implication is a valid material implication.

The rest of this article appears to be about material implications.

I found this introduction confusing, since it looks like discussion of the article rather than an introduction to the article. So I replaced the introduction with an earlier version. The above introduction is probably salvageable if it is modified to stop talking about what shouldn't be confused and start talking about what is to be understood. Michael Slone (talk) 23:52, 9 December 2006 (UTC)