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What is the liar’s paradox?

liar’s paradox

“The liar’s paradox” refers to a statement that inescapably leads to a logical contradiction—it appears to be both true and false at the same time. The simplest example would be the declaration “this statement is false.” There have been many versions of the liar’s paradox and many attempts to solve it. This idea was even used for rhetorical effect in the Bible, by Paul in his letter to Titus. Though there is no universally accepted solution to the liar’s paradox, it is not considered a challenge to our sense of reality.

Confusion arises over what the liar’s paradox represents. The problem is entirely about language, communication, and abstract representation of ideas. The paradox exists because we struggle to express truth in a form immune to apparent contradiction. In other words, we have difficulty expressing truth with no ambiguity.

Logicians and philosophers do not respond to the liar’s paradox by jettisoning the law of non-contradiction. That would be impossible: to do so would require use of that law itself. “This statement either violates non-contradiction, or it does not.” The puzzle is in explaining how to resolve the breakdown in our understanding. This focuses almost exclusively on grappling with how we use language to express truth.

The liar’s paradox has been around for thousands of years. Some of the most brilliant minds in philosophy have worked on it. Entirely “solving” it is not a reasonable expectation, especially in an article of this length. However, it is possible to understand how and why the paradox is unique and why it doesn’t suggest anything controversial about reality itself. Proposed solutions are the subject of intense debate. But, so far as the real world goes, there are ways to deal with such a conundrum.

Perhaps the simplest response is to say expressions of a liar’s paradox are not meaningless; rather, they are irrelevant. The liar’s paradox forms a circular loop of logic. Therefore, that specific statement cannot—by definition—have any logical or meaningful connection to anything outside itself. Since the statement refers only to itself and is dependent only on itself, it’s the equivalent of its own logical universe. If the truth or falsehood of the statement can be tied to something outside itself, then it’s not actually a liar’s paradox. But if it really is a liar’s paradox, then by definition it has absolutely zero connection to the rest of reality—or to any other logical statement.

In that sense, one can see the liar’s paradox as a statement that cuts itself off from the rest of reality. So far as the rest of the universe is concerned, it might as well not exist. The reason we can’t draw conclusions from it is that it’s not connected to anything but itself.

Resolutions for other specific instances of the liar’s paradox include suggesting the statement is not even a paradox; it is simply gibberish. That might be due to improper use of grammar or hidden contradictory premises. For example, the question “can God make a rock so heavy He cannot lift it?” is an example of self-contradictory premises.

Philosophers have explored the idea of adapting language to avoid certain forms of the liar’s paradox. Some have even suggested simply ignoring it and avoiding creation of such logical loops whenever possible.

Ultimately, the liar’s paradox is an example of how human understanding is limited. Our powerful, God-given ability to learn and reason is nothing compared to omniscience and omnipotence (Isaiah 55:8–9). Whether it’s shortcomings in our language, our logic, or our perspective, we cannot expect to have an infallible understanding of all things (Psalm 63:1; Proverbs 3:5). Accepting our finiteness, even as we seek to expand our knowledge (Psalm 19:1), is key to recognizing our place and purpose in reality.

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What is the liar’s paradox?
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This page last updated: January 4, 2022