What is the law of the excluded middle?

Answer

The Bible confirms the existence of absolute truth, in contrast to modern worldviews like postmodernism, which reject it. For instance, truth is a quality of God (Numbers 23:19;Romans 3:3-4), a characteristic of the Bible (Psalm 119:160;John 17:17), and manifested in the person of Jesus Christ (John 1:17;John 14:6). Assessing truth claims is essential to establish their validity, and the principles of logic provide a framework for this purpose. Among these principles, the law of excluded middle (LEM) is a foundational concept traditionally credited to the Greek philosopher Aristotle. This law asserts that a declarative statement—a statement that affirms or denies something—is either true or its negation is true, leaving no room for a third possibility.

To demonstrate the law of excluded middle, let’s take the statement “the sun is hot,” represented by the variable P. According to the law, either P is true, or its negation is true, i.e., “the sun is not hot,” represented by the variable ~P. (The ~ symbol is known as the “tilde” and signifies negation in logic.) The term excluded middle originates from the concept that there is no intermediate position between a statement being true or false, ruling out the existence of a third alternative.

To provide further clarification, in practical terms, negating the proposition in the example “the sun is hot” (P) does not necessarily imply that “the sun is cold.” While cold is commonly viewed as the opposite of hot, the negation of the proposition simply indicates that the sun is not hot (~P). This suggests that the sun could be any temperature other than hot, such as warm.

The lLaw of the excluded middle can help Christians understand and defend the Bible’s teachings. For example, in John 17:17, Jesus said to the Father, “Your word is truth” (ESV). Using the law of the excluded middle, the Bible is either true, P, as Jesus asserted, or not true, ~P. The law reveals that Scripture can’t be true and not true at the same time. Thus, there is no middle ground such as the Bible being true for one reader but not true for another one.

Furthermore, the law of the excluded middle applies equally to assertions that deny a proposition. For instance, the Bible asserts that God does not lie, which is a negation «in hope of eternal life, which God, that cannot lie, promised before the world began; », (Titus 1:2). According to the law of the excluded middle, this proposition—“God does not lie,” ~P—is either true, or its affirmation—“God does lie,” P—is true. The law states that every declarative statement, regardless of being phrased negatively or positively, must be either true or false, with no middle ground.

The law of the excluded middle doesn’t only pertain to direct statements in which an assertion is made but can also be used to assess narrative claims. For example, the Gospels teach that Jesus rose from the dead three days after His crucifixion (e.g., Luke 24:2-8). In this case, the declarative proposition that Jesus rose from the dead, P, can only be true or false. If P is true, then its negation, i.e., “Jesus did not rise from the dead,” ~P, is false. According to the law, there is no middle alternative between P and ~P.

The Bible encourages believers to use reason within the context of their faith (e.g., Isaiah 1:18; James 3:17), making logic a valuable tool to understand, explain, and defend one’s beliefs «but sanctify the Lord God in your hearts: and be ready always to give an answer to every man that asketh you a reason of the hope that is in you with meekness and fear: », (e.g., 1 Peter 3:15). Although it’s impossible to please God without faith «But without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him. », (Hebrews 11:6), logic is a valuable tool for Christians. Jesus is an example of this since He often used logic to explain faith and encourage people to follow Him (e.g., Luke 14:28-32). Accordingly, the law of the excluded middle is a significant asset to Christianity as it helps believers articulate and analyze truth claims.