Trivial. Redundant. Dogmatic. Useless.
That’s what people really mean when they say, “Oh, your argument is just a tautology.” Indeed, one of the quickest ways to dismiss an idea is to label it “tautological” and, therefore, empty of content.
The standard philosophic position goes like this, “Tautologies are merely true by definition and cannot teach us anything about the world.”
I couldn’t disagree more strongly with this line of reasoning. Not only is it mistaken to dismiss tautologies, it’s completely backwards. For three distinct reasons, tautologies are foundational for critical reasoning; they are the building blocks for an accurate worldview.
A Bad Reputation
First of all, we need to understand what tautologies are and why they are so frequently dismissed. A tautology is a proposition that is true in all possible circumstances – sometimes people say, “true by definition” or “self-evidently true”. The central idea is that it has no possibility of being false.
Consider the sentence “All fish are fish”. Is there any possibility of this sentence being false?
No; therefore, it’s a tautology. If a fish is a fish, then it’s a fish. Therefore, all fish are certainly fish. There’s no exceptions. If we abstract one degree, we can see the structure of the proposition:
“All X are X”.
Clearly, no possible X could ever not be an X – regardless of what X is. So, we might say this abstract proposition is true in all possible circumstances. But does it tell us anything useful?
The standard criticism of tautologies goes like this: because of the the fact that tautologies are necessarily true, they do not tell us anything new about the world. They cannot possibly be wrong; therefore, they do not add to our knowledge. They are redundancies, and they ultimately do not need to be stated.
“A fish is a fish” is trivial and doesn’t tell you anything you didn’t already know. Some people have even called tautological reasoning “circular”, or claim it’s merely begging the question.
This is all wrong. Tautologies are arguably the most important propositions in all of philosophy. They cannot be dismissed without throwing out a foundational tool for critical thinking.
The first mistake is simple: not all tautologies are created equal. Some are trivial; it’s true. “A fish is a fish”, by itself, doesn’t tell you anything useful. But some tautologies are far more profound.
So here are three major reasons why the conventional thinking regarding tautologies is mistaken.
Deny, Restate, and Accept
First of all, most obviously, tautologies become important when people deny their truth. In a peculiar combination, many ideas get dismissed as tautological, while simultaneously being denied as true. The law of identity, for example, is foundational – that “A is A”, or “a thing is a thing” – and yet huge numbers of people deny its truth.
In an ideal world, law of identity might never need to be stated because it’s self-evident. But that’s not the world we live in, and swathes of people deny the truth of the law of identity. I call these people “irrationalists”, and they usually appeal to flawed interpretations of quantum physics or the liar’s paradox to justify their rejection of the law of identity.
The same phenomenon happens in economics. As I will explain in a future post, the foundations for sound economic theory are logically deducible, necessary truths that all follow from the simple premise that “humans act”.
Because the theory is tautological, people are quick to dismiss the ideas as “trivially true”. Yet, in the same breath, those same people will turn around and deny the truth of the tautology – by arguing for price floors or ceilings, for example.
You cannot have it both ways. If the tautology is trivially true, then it mustn’t be denied. If it’s denied, then it’s obviously worth re-stating.
Second – and heretical to philosophic orthodoxy – tautologies can actually teach us something new about the world. Lots of things, in fact.
Consider an idea I recently wrote about in The Metaphysics of Logic. Even if an omnipotent God exists, he certainly did not create the laws of logic. Those laws bind everything in existence, without exception, including any omnipotent gods. This conclusion is not hypothetical; it’s logically necessary and tautological.
Yet, billions of people on the planet probably believe otherwise. A standard theological idea is that “God created everything, including the laws of logic.” But this is mistaken.
Understanding why God could never “create logic” is neither trivial nor redundant. It’s new information that can only be revealed after a deliberate exercise in logical reasoning. It tells you something new about the universe that you wouldn’t know otherwise.
Or, consider an even larger set of truths: mathematics. Mathematics is fundamentally tautological. “2 + 2 = 4” is true in all possible circumstances. Yet, nobody would conclude, “therefore mathematics is useless and doesn’t tell you anything about the world”.
Math tells you all kinds of profound truths about the world, and few things are more concretely practical. This is because mathematical truths are fundamentally grounded in logical (tautological) reasoning.
Even though careful mathematical reasoning can lead to absolutely certain conclusions, it isn’t “merely” self-evident. Consider the equation: “962 x 2231 = N”.
Go ahead and use simple logic to find the answer.
It’s not so easy.
The answer is “N = 2,146,222”, and it couldn’t be anything else. Does that mean the solution is trivial? Of course not. Just because something is necessarily true doesn’t mean it’s irrelevant or worthy of dismissal. And it certainly doesn’t mean you know the conclusion beforehand.
The Most Profound Truth
Third, and perhaps most importantly, if we grant that tautologies are necessarily true, we must ask a simple question: why? Why are tautologies necessarily true – why can you know with certainty that “a fish is a fish”?
In other words, what gives tautologies their necessary quality?
You might be tempted to answer, “Well, it just has to be that way!”
And that’s precisely correct.
So not only are tautologies useful, they point to the very foundations of our epistemology. Nothing is more important or fundamental for somebody interest in truth. Logic puts the “tautological-ness” into tautologies. It’s what all self-evident truths appeal to. It’s why certain propositions can be “true by definition”.
Certainly not Circular
One more confusion I want to clarify. Some people insist that tautologies are useless because they are examples of “circular reasoning” (more precisely called “begging the question”). Colloquially, circular reasoning is where you assert your conclusion as a premise. For example:
“Judy is the tallest girl in the class because she is the tallest girl in the class.”
This proposition merely states its conclusion as a premise. To some, this might look like a tautology – “A because A”. But crucially, this is not a tautology; there is an obvious circumstance in which the conclusion is false: if Judy is not the tallest girl in the class – a possibility which doesn’t entail any logical contradiction. This is what differentiates circular reasoning from tautologies.
Contrast this to the proposition, “All of the students in class are students”.
This is a proper tautology; there’s no possible circumstance in which it isn’t true. Negating the conclusion would imply a contradiction – i.e. that “some of the students in class are not students”.
So no, tautologies are not circular. They are simply true in all circumstances. Or you might say “they are not false in any circumstance.” Being necessarily true is a poor reason to dismiss an idea as trivial or redundant.
Overall, it’s a grave error to overlook the usefulness and profundity of tautologies. Not only should we examine them, we should embrace them and incorporate them into the foundations of our ideas.
Discovering tautologies is exciting, and it’s literally synonymous with discovering truth. Not to mention: any sound deductions that follow from tautologies are also necessarily true. If we construct theories that are founded on necessarily-true premises, we can built a robust worldview that is justified all the way to its foundations.