Basic Logical Principles Required for Apologetic Endeavors

June 25, 2002 by Doug Groothuis

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Winfried Corduan only very briefly mentions three related principles of logic—identity, contradiction, and excluded middle—in his excellent apologetics text, No Doubt About It.¹ I will provide a bit more clarification concerning these principles and introduce one more closely related logical principle in order to fathom better their meaning in relation to apologetics. All four of these principles trade on the idea of antithesis and identity.

These principles of logic are not deduced or inferred from other principles that are more basic or more certainly known. These principles must be presupposed or assumed in order to communicate intelligibly. As such, we might borrow a term from Immanuel Kant (without endorsing his whole philosophy) and call them transcendental preconditions for knowledge. That is, if there is to be knowledge at all, these principles must be in place. These principles stand behind all rational thought and language. They are not arbitrary or whimsical, as are some other principles or ideas that people gratuitously adopt (such as, “I just know in my knower—without need of any outside evidence—that I was abducted by aliens."). They are fundamental principles or laws of thought, not groundless speculations or ad hoc notions. They are neither Eastern nor Western, neither male nor female, nor are they pigmented. They are eternal and essential principles by which our minds were created by God to function. They are rooted in the perfect reason and comprehensive knowledge of God himself.

1. The principle (or law) of identity simply states that something is what it is: “A=A.” Something is itself and nothing other than itself. If we say, “You’re not yourself today!” we don’t violate the principle of identity. We mean, rather, that someone is acting out of character, acting strangely or unexpectedly. The person is still identical to herself even if she is acting strangely.

2. The principle (or law) of contradiction is, rather paradoxically, also sometimes called the principle of non-contradiction. This is not a contradiction, but simply two ways of looking at the same logical operation of antithesis. Aristotle put it this way: “The same attribute cannot at the same time belong and not belong to the same subject in the same respect” (Metaphysics 1005 b19-20). Or: “A is not non-A.” Put another way: a proposition and its denial or negation cannot both be true. Those who deny the principle (or law) of contradiction, appropriately enough, contradict themselves. Consider: “The law of contradiction is false.” If so, the opposition of this claim—that the law of noncontradiction is true—must be reckoned false. Thus, the principle of contradiction is affirmed. The principle is inescapable and incorrigible if we intend to state anything meaningful about reality. It’s not just a good idea; its a law of thought and a law of being.

3. The principle (or law) of excluded middle states that “either A or non-A"; any middle option is excluded. That is, it is not the case that “A and non-A,” nor is it the case that “neither A nor non-A.” Put more technically, given any meaningful proposition A, the proposition “either A or not-A” is necessarily true. For example, “There is either a building over two hundred stories high or it is not the case that there is such a building.” Or: “Jesus is Lord or Jesus is not Lord.” This should not be confused with the similar principle (or law) of bivalence.

4. The principle (or law) of bivalance affirms that any meaningful proposition is either true or false. “Douglas Groothuis is half Italian” 2is either true or false; not both true and false, not neither true nor false. Every proposition has a truth value, and there are only two truth values—true and false. To distinguish this from the principle (or law) or excluded middle we should note that: “The law of excluded middle is a logical law operating at the level of the object language, whereas the principle of bivalance is a semantic principle, one governing the interpretation of the language to which it is applied.” 3In other words, the law of excluded middle relates to the state of things or being: “Either there is a pro-life Democrat at Denver Seminary or there is not a pro-life Democrat at Denver Seminary.” The principle (or law) of bivalance relates to the nature of statements (semantics): “There are no pro-life Democrats at Denver Seminary” is either true or false. Of course, these semantic statements about pro-life Democrats at Denver Seminary do refer to things outside of themselves, so the semantical content is related to objects outside of semantics, given the correspondence view of truth. The proposition, “Hell exists,” is either true or false and is made true or false in relation to states of affairs outside of the proposition itself.