1. The Law of Identity
The Law of Identity states that if any statement is true, then it is true; or, every proposition implies itself: A implies A. This may appear to be trivial, but as Gordon Clark notes, what a strange world it would be if it were not the case, for it would be a world without the concept of identity or sameness.
2. The Law of Excluded Middle
The Law of Excluded Middle states that everything must either be or not be; or, everything is A or not-A. That is to say, for example, a rock is either hard or not-hard, or either at rest or not-at rest.
What can be said of a passenger in an airplane en route to a far-away place? Is he at rest or not at rest? Both at rest and not at rest? Not at all, for you cannot have it both ways at the same time, place or respect, where the words have the identical meaning, as a bit of reflection will show. (For example, the passenger, if seated, is at rest in respect to the aircraft, but in motion with respect to the earth).
An example of this law in practice is seen in the statement "It is snowing" as it is either snowing or not snowing, there is no alternative besides these two options. So what it does is exclude any middle alternative between something being either true or false. Jesus makes use of the Law of the Excluded middle in Luke 11:23 - Anyone who is not with me is against me. Jesus leaves no another option: for Him or against Him.
3. The Law of Noncontradiction
The Law of Contradiction (Noncontradiction) states that no statement can be both true and false; or, A and not-A is a contradiction -- always false. Thus, the Law states not both A and not-A. Nothing can both be and not be at the same time and at the same place. Aristotle's formulation of this law states that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect: Not both A and not-A. Again, every statement of the form A and not-A is false. Every such compounded statement is contradictory.
For example:
"Therefore, there is now no condemnation for those who are in Christ Jesus" (Romans 8:1) cannot be both true and false. To assert that the statement and its denial are both true, or both false at the same time and in the same respect is to fall into contradiction and absurdity.
What this means is that a statement such as "God exists" cannot be true and false at the same time. He either exists or he does not he cannot simultaneously exist and not exist. A further example is the statement "It is raining"; this cannot be true and false in the same sense at the same time. It could be raining in London but not raining in Birmingham but the Law of Non Contradiction shows us that it cannot be raining and not raining in the same space at the same time.
The law of contradiction is supreme; it encompasses the other two. Its formulation as Not both A and not-A assumes the Law of Identity in that the proposition "A" univocally implies itself (A implies A). As a disjunction, it expresses the Law of Excluded Middle, A or not-A. Moreover, the Law of Contradiction is necessary for any meaningful discourse, for without it, the distinction between truth and falsity disappears and with it meaning.
John Robbins nails it thus:
"The law of contradiction means something more. It means that every word in the sentence 'The line is straight' has a specific meaning. The does not mean any, all, or no. Line does not mean dog, dandelion, or doughnut. Is does not mean is not. Straight does not mean white, or anything else. Each word has a definite meaning. In order to have a definite meaning, a word must not only mean something, it must also not mean something. Line means line, but it also does not mean not-line, dog, sunrise, or Jerusalem. If line were to mean everything, it would mean nothing; and no one, including you, would have the foggiest idea what you mean when you say the word line. The law of contradiction means that each word, to have a meaning, must also not mean something."(John W. Robbins. "Why Study Logic," Trinity Review, Jul/Aug 1985, No. 44)
The laws of logic are rooted in God's nature and, therefore, God acts in a logical way and cannot behave illogically for this would be against His very nature. In John 1:1, he writes that in the beginning was the word [logos - rational and divine mind]. (The Greek word logos is the origin of our word for logic.)
The Laws of Logic are not arbitrary, but necessary for discourse, communication, and worship. The Laws of Logic are universal, without them no communication with anyone – ever. No matter the culture, people know that 5 items are 5 items and not 24, that a tree is a tree and not anything else, and that if it is raining where they are, it cannot be raining in the same space at the same time!
The Laws of Logic are not only necessary and universal, but immaterial and unchanging. Nash provides the following summary of his discussion of logic and the law of contradiction:
Logic and Significant Human Thinking
It should be obvious how the previous comments lead to another conclusion: If the denial of the law of noncontradiction precludes significan speech and behavior, significant human thinking also becomes impossible. When students find themselves taking a course, any course, taught by a professor who thinks in this illogical way, a consistent professor (note the implicit logical presence here) would have to admit there is no difference between a good exam and a bad one, between a good grade and a bad one. Unless such a professor cheats, it seems difficult to see how he could avoid giving all students the same grade. (Ronald H. Nash, Life's Ultimate Questions, ©1999 Ronald Nash, Zondervan, Grand Rapids, MI, 49530, p. 198.)
It is no surprise that we are logical beings since we are created in the very Image of God our creator who, by his very nature, is logical. So, these laws are understood to apply not only to the unambiguous, precise terms contained in the propositions of arguments, but also to all meaningful discourse.
Without the first, identity or sameness is lost; without the second, confusion begins; and without the last, nonsense is in full residence. Without them intelligible discourse is impossible.
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