Coding the Liar Paradox

As a software developer with a philosophy degree, I often find myself being asked how my degree is relevant to my work. While to me it’s clear that my philosophy studies have been invaluable for my development skills, I find it hard to explain to others. Unlike a computer science graduate whose studies have a very obvious impact on their work, as a philosophy graduate I need to show how dealing with metaphysics, ethics, or logic questions adds value to my day-to-day work as a software developer.

I can try and argue that both fields require analyzing problems, critical thinking, and problem-solving skills, but I think a better approach would be to demonstrate how close these fields are by examining a famous philosophy question. In this article, I will present the classical logic exercise of the Liar Paradox and analyze it using code implementation. By doing this, I hope that I can, on the one hand, get software developers interested in philosophy, and on the other hand, provide a better answer to a question I am often asked.

As a philosophy student, one of the topics that intrigued me the most was paradoxes of self-reference. A paradox of self-reference is a statement that, by referring to itself, causes a paradox — meaning, the conclusion of this statement will go beyond our common beliefs.

A self-reference statement can have a truth value (true or false):

There are more complex statements that include self-contradiction, like:

Let’s examine the above statement: If it’s true that every rule has an exception, including the rule presented in this statement, the exception of this rule states that there is a rule that can’t have an exception. Therefore, this statement contradicts itself and can’t be true. However, the negation of this statement — “there is such a rule that has no exception” is a true statement, since we can show the existence of such a rule. For example — “all even numbers are divisible by 2.”

The most interesting form of self-reference statements, however, is the one that leads to a paradox, and the most famous one is the Liar Paradox. This is one of the paradox’s definitions, as explained in Wikipedia:

This unique and short statement (A) has very powerful consequences. If A is true it must be false but if it’s false it must be true. In other words, we see that statement (A) can’t have a defined truth value. This is an irregular conclusion that contradicts the fact that all statements must have a truth value. Although it’s a very short argument, I think you will agree that it’s a bit confusing. To make it best understood for software developers, I decided to “translate” the paradox into code. I chose to implement the Paradox with Ruby as a boolean function in hope to catch the essence of statement (A). We need to pass a boolean parameter to the function to indicate if it’s TRUE or FALSE — the same practice we have in investigating statement (A).

The output of running this code would be:

At this point, I hope that bringing the Paradox into the realm of code helped you to understand the idea behind the Liar Paradox. However, does it really demonstrate the essence of the paradox? Did the transfer of the statement into code help us understand the problematic conclusion that statement (A) does not have any truth value? Probably not — yet.

For example, the following statement (B) is grounded.

B. The next statement is a lie

B1. The next statement is a lie

B2. The next statement is a lie

B4. Today is Friday

As we can see, statement (B) has a truth value that will be set (eventually) from the fact that today is or isn’t Friday. Although the statement “the next statement is a lie” has no truth value by itself, when it is part of a series of statements like the one presented here it could be grounded if, at some point, the series of statements is fixed on a claim about the world. So, if today is Friday then (B2) is false, (B1) is true, and (B) is false. But on any other day, (B) is true! Although the truth value of (B) is changeable, it is grounded and no matter what the day is today, statement (B) has a truth value.

In contrast, the next statement © is ungrounded:

C. (C) is true

Is (C)true? Well, if (C) is true then (C) is true. But (C) is true if (C) is true. Can you see where I’m going with this? Although (C) is not paradoxical, it can’t produce a truth value. In that sense, (C) is an ungrounded statement since it has nothing to say about the world we can use to determine its truth value.

I want to emphasize this idea by implementing the last two statements. A grounded statement could be transformed into the below function. I added a made-up stop condition with a depth parameter to simulate example (B) when we have a series of four statements:

This will yield the following output on Friday:

While an ungrounded statement will transform into something like this:

This will yield:

For the grounded statement (B), we could “manually” set the (B3) “Today is Friday” statement so that it will say something about the world and by that enable (B) to achieve its truth value. The Liar Paradox, however, is a statement that is “too focused” on itself, and even when it’s trying to say something about the world (“everything I say is false”) it will always fail to ground itself and will result in a pursuit that will never end (at least until the stack is exceeded).

After introducing and implementing the Liar Paradox with code, we can see the similarities between the paradox and the ungrounded sentences presented within this article. I won’t argue that this solves the paradox, but I think we can conclude that this approach strengthens the idea that the Liar Paradox shares some common properties with ungrounded statements. This, I hope, helps to understand the paradox and what a possible solution could look like.

More than that, I hope I have been able to demonstrate a connection between philosophy and software development and spark an interest in philosophy for software developers who are unfamiliar with the field in general and with the Liar Paradox in particular.

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