If you prefer a video, click this button:

Logical Consistency Video

A set of statements is logically consistent if they can all be true at the same time. A set of statements is logically inconsistent if they cannot all be true at the same time. It may also be helpful to think of logically consistency as a set of beliefs that do not contradict each other (regardless of whether they are true).

When evaluating logical consistency, assume the statements are true and think about whether they fit together like the pieces of a puzzle. That is, consistency is about understanding the relationships between your beliefs, not proving a belief true.

Exercise

Identify the following sets of statements as logically consistent or inconsistent. Explain your reasoning.

Example: All men have blonde hair. I am a man. I have brown hair.

Answer: These three beliefs are logically inconsistent. If the first two statements are true, the third must be false. If the third is true, the first or second must be false. They cannot all be simultaneously true.

  1. I am a man. I have brown hair. You have blonde hair.
  2. All dogs are brown. Some dogs are not brown.
  3. Killing another person is always wrong. It is not wrong to kill a person in self-defense. It is also not wrong to kill people in times of war.
  4. Everyone should be tolerant because there is no way to judge another person's beliefs.
  5. Nobody is ever wrong. 2+2=4. Harry is wrong in believing that 2+2=5.
  6. This sentence is false.
  7. If God exists then Bob is mistaken. Bob is not mistaken. God exists.
  8. It is raining. It is not raining.
  9. I love beer and I hate beer.
  10. Light is simultaneously both a wave and a particle.

Answers/Discussion

  1. Logically consistent. All three statements can be true at the same time.
  2. Logically inconsistent. They are contradictory statements. If "all dogs are brown" is true then "some dogs are not brown" MUST be false.
  3. Logically inconsistent. One way out is to change “always” to “usually” in the first statement. As it stands, if the first statement is true, the next two are false and vice versa.
  4. Logically inconsistent. If there is no way to judge beliefs then how can one judge that others should hold tolerant beliefs? This one leads to interesting discussions about paradoxes, self refuting statements, and the nature of relativism.
  5. Logically inconsistent. The first statement contradicts the second two together.
  6. Logically inconsistent. If the sentence is false then it’s true; if it’s true then it’s false. It’s logically inconsistent because it’s simultaneously true and false. Perhaps we should make a rule saying that a sentence cannot be self-referential (since it leads to such paradoxes)?
  7. Logically inconsistent. If the second and third statements are true, the first must be false.
  8. Logically inconsistent. If the first sentence is written in one place or time and the second in another place or time, then they are logically consistent. However, most people interpret these two sentences as referring to the same exact place and time.
  9. Hmmmm. I believe it is logically inconsistent unless the person means they love beer until they experience the consequences, which they hate.
  10. Logically inconsistent, but why do we suppose the universe must be consistent? Where does consistency originate?

Application and Value

As you do philosophy, you will identify and evaluate many arguments. You should also evaluate the consistency of sets of beliefs/opinions. In short, logical thinking is not simply about what can be inferred from premises, it is also about the relationship between your opinions.

Since most philosophers believe truth is logically consistent, they value logical consistency because it is a tool to discover truth. Although consistency is no guarantee of truth since one could create a consistent story that is false, it seems to be a necessary condition for truth.

Of Course, some thinkers believe truth is logically inconsistent. For example, many mystics speak of God in paradoxical language because they do not believe God can be understood in logical ways. They believe logic is best used to show the limits of logic. They believe understanding your limits is the first step to transcending them. Many existentialists also argue that life is absurd, not logical. Discoveries in modern physics too seem to indicate that we can describe a paradoxical reality, but not logically understand it. Nevertheless, we still value logical consistency as a way to get at truth. Certainly, anyone who claims to be logical should take logical consistency seriously.

I am grateful to Juliana Baggini and Peter S. Fosi for their lucid chapter on consistency in The Philosopher’s Toolkit: A Compendium of Philosophical Concepts and Methods.

Return to Logic Home               Next Chapter (Ch.6, Science)