The truth doesn’t “explode” – that’s a ridiculous idea

Journalists are liars. You are now reading this statement as the first sentence of this article. Written by: journalist. But can the sentence still be true? After all, if this is true, then it is false. In short, there is an outright contradiction here. Or can a lying journalist be right and wrong?

Yes, you can, says Graham Priest (1948), professor of philosophy at the City University of New York (CUNY). It is considered a heavyweight in philosophical reasoning. at a philosophical festival the point He recently spoke in Amsterdam on his favorite topic: paradoxes and contradictions.

Since the late 1970s, Priest has advocated a very different view of truth in logic. He called his position “dialectical”, that is, the opinion that there are true and false propositions. A concept of truth that seemed at the time incompatible with established ideas in the field. But though his position in professional circles remains unorthodox, his ambivalent attitude is now resonating.

The Pastor begins “Of course we all hold to our beliefs, about the world and about politics and mores. These beliefs have consequences. After all, logic is nothing more than a formal study of its basis: what follows from what and why?” In classical logic, since Aristotle, there has been the view that sentences or self-contradictory assumptions that cannot be true, which is also known as the law of non-contradiction.Statements like “it’s raining and it’s not raining,” things that can’t be true at the same time.This seems like a reasonable assumption, but the arguments in favor of it have remained limiting The discussion has been going on for more than 2,500 years now. So it’s not that clear.”

Outside of logic, contradictions are not at all as repugnant as philosophers think

For philosophers, one of the fundamental problems with the law of non-contradiction is that it cannot be proven without invoking it – thus leading you to circular reasoning. However, the non-contradiction theorem is usually seen as irrefutable and serves as a starting point for proving other theories, which are true in their own right. It is essential to test facts, but it cannot be tested by itself. It led the philosopher and logician Wittgenstein to call all logic transcendental: it forms the basis of reasoning and reasoning, but cannot itself be explained.

Read also: Science continues to crave simplicity

According to Priest, this varies outside of philosophy: people usually have a less strong opinion about the impossibility of paradoxical propositions. The principle of non-contradiction has become familiar in logic. But outside of logic, the contradictions are not as great as philosophers think. And for good reason. In the small field of empirical philosophy—“ExPhi,” where non-philosophers are asked to give their opinion—you see, for example, that ordinary citizens are willing to hold contradictory opinions in certain circumstances, without seeing it as problematic. When it rains, many will admit that it does not rain and does not dry, or that it rains and does not rain. These seem like everyday extremes, but they are pure contradictions.”

Are ironies in general less problematic than they seem?

Paradoxes seem like party entertainment, but they are not. They arise when a contradictory or erroneous conclusion follows from all-true statements. In the early 20th century, you see such paradoxes starting to appear in basic mathematics.

Belief in true opposites will not affect everyday life. But it affects the way we view our knowledge of the world

Furthermore, until the 1990s, it was common to make another assumption in logic related to the principle of non-contradiction, also known as the “explosion” principle: if you don’t reject contradictory statements, you can too. Claim it all. There is a swell of real proposals. Everything explodes. This is a silly idea. For this reason, proponents of dialectics reject the “explosion” principle.

How then to distinguish between true and false contradictions if you want to avoid this inflation of facts?

“I think you have to broaden this question. When is it reasonable to assume that something, anything, is true? Simply put, you look at the evidence you have. It’s not as easy as it sounds, of course, but it applies to our everyday beliefs as well as to truth in general. You can also look at contradictions in the same way: you take them for granted in the relevant circumstances. This opens up new possibilities.”

Also read this review of Gödel’s biography: The wayward ghost of Hare Warum

The most famous example of this is mathematician Kurt Gödel’s “theorem of incompleteness” (1906-1978), who proved that a (mathematical) system that can prove all facts is inconsistent. Contrasts appear at the edges. The story goes that the original Czech mathematician also received opening He discovered in the United States Constitution that American democracy would be constitutionally abolished. Although it’s unclear exactly how – Gödel didn’t develop his discovery – it is assumed that it is about him Legal article refers to itself.

Priest: “We live every day with such real contradictions. Take, for example, a country in which everyone who owns land, except women, can vote – let’s say the situation in Europe, say, five hundred years ago. As long as there is no woman who owns land, This law is stable. But if we now see that women later become owners of land, you will end up with a contradiction. Then you have a woman who is entitled to vote and who is not allowed. Of course, the law can then be amended, but that does not make the contradiction any less real.” .

But isn’t that just a typo?

“In a sense, the fact that the law changed afterwards is a consequence of a contradiction that was already there. Now you could say it is a product of our minds, but such contradictions also happen in more formal areas. And often it is not up to us to decide what is ‘right’.” .

What do we get from your approach?

“The dialectical view will not affect everyday life, it is a vision of truth and a fairly specific point of view. But it does affect the way we look at our knowledge. In some cases, an inconsistent theory may be more desirable than a consistent theory. We are now witnessing the emergence of the so-called With “inconsistent” mathematics, who knows what the applications of that will turn out to be. No, hardly anyone uses it yet. But it also took science hundreds of years to find suitable applications for “complex numbers”, for example. Who knows what we can do with it in the future ?

Read also Logician and lecturer Guido van der Knaap: “It is an analytical philosophy with a rigor suitable for questions about AI and technology”

A version of this article also appeared in the July 1, 2023 issue.