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. 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; it’s 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” is 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.” In 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.
 Winfried Corduan, No Doubt About It (Nashville, TN: Broadman, Holman, 1997), 26-27.
 This statement is true. My father was half-Dutch, my mother is fully Italian.
 “Principle of Bivalence,” Dictionary of Philosophy, revised second edition, edited by Anthony Flew (New York: St. Martin’s Press, 1984), 46.
Monday, August 29, 2005
Basic Logical Principles Required for Apologetics
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These principles are the grounding of modernism and basically disregarded in postmodernism. But a postmodernist must use them in order to state anything meaningful at all about postmodernism. Is it fair then to say that postmodernism is self-refuting? How would a think postmodernist object to his notion?
These principles explain how our minds work when they are working according to the divine design plan. No one can communicate anything meaningfully or rationally without presupposing these principles. In this sense, they are transcendental: they are necessary conditions for intelligibility. This is true in every age, however we dice them up--premodern, modern, postmodern, post-postmodern, or anything else.
I don't consider myself a "post-modernist" by any stretch -- not sure what that means, and not sure if it solidly means anything ...
But I'll have to say that most things aren't "A" -- most things are harder to define than that, and the rough edges of our definitions make for the more interesting arguments.
And I'd have to ask: If it's 100% true that "you're 50% Italian", does that make it 50% true that "you're Italian"? Depends on how the categoies sit, whether that bivalence holds steadily.
I actually commented on my blog (weekendfisher.blogspot.com), but the scope of that post just started with this as a springboard; it also gets into whether logic is really the only useful tool in our bag for understanding the world, and whether it is always the best one.
Take care & God bless
The question of the identity of "A" is a question of meaning. But once we stipulate what "A" is, the laws kick in flawlessly.
You cannot place percentages on truth value. A clear indicative sentence (and the proposition it expresses) is either true or false, with no middle ground. Certainty, however, can be ticed up according to a spectrum or even by percentages (although this seems artificial for most philosophical interesting things). Those of you into Baysian calculations will not like my last remark!
Good stuff, thanks.
I would suggest that pomo is self-defeating, partly because the statement "all truth is relative" is absolute. Basically, if you try and operate as though these rules of logic don't apply, then any sort of meaningful communication becomes impossible. Postmodernism only works if we get rid of the idea of linguistic meaning - and that fails to correspond with how we understand the universe.
Unfortunately, the greater proportion of adherents to a post-modern world view don't have the patience to think out the implications of their beliefs - and the smaller proportion in ivory towers expect too much to have their pronouncements taken as authoritative to realise the paradox that is inherent in this.
Have you seen and/or reviewed Brian Flemming's "The God Who Wasn't There?"
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