What is the law of the excluded middle?

Answer  
  

The Bible affirms the existence of absolute truth, contrasting with contemporary worldviews such as [postmodernism](postmodernism-dangers.html), which deny it. For example, truth is an attribute of God (Numbers 23:19; Romans 3:3–4\), a characteristic of the Bible (Psalm 119:160; John 17:17\), and embodied in the person of Jesus Christ (John 1:17; 14:6\). The evaluation of truth claims is necessary to determine their validity, and the rules of logic offer a framework that serves this purpose. Among these rules, the law of the excluded middle (LEM) is a fundamental principle historically attributed to the Greek philosopher [Aristotle](Aristotelianism.html). The law states that a declarative proposition—a statement that asserts or denies something—is either true or its negation is true, thereby eliminating a third option.  
  

To illustrate the law of the excluded middle, consider the statement “the sun is hot,” symbolized by the variable *P*. The law states that either *P* is true, or its negation is true, i.e., “the sun is not hot,” symbolized by the variable *\~P*. (The \~ symbol is called the “tilde” and represents negation in logic.) The phrase *excluded middle* comes from the principle that there is no middle ground between an assertion being true or false, eliminating the possibility of a third option.  
  

For further clarity, in practical terms, the negation of the proposition in the example “the sun is hot” (*P*) does not necessarily mean that “the sun is cold.” While cold is commonly thought of as the opposite of hot, the negation of the proposition merely indicates that the sun is not hot (*\~P*). This implies that the sun could be any temperature other than hot, such as warm.  
  

The law 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 (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](Christian-logic.html) a valuable tool to understand, explain, and defend one’s beliefs (e.g., 1 Peter 3:15\). Although it’s impossible to please God without faith (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.  
  

