# Tautology

#### wegs

##### Matter and Pixie Dust
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How can a formula or assertion always be true, given any interpretation? Is that basically what tautology is?

I'd like a better understanding of this, and I've read up on it recently, and it's not making sense. It's the interpretation part that is throwing me off.

How can a formula or assertion always be true, given any interpretation? Is that basically what tautology is?

I'd like a better understanding of this, and I've read up on it recently, and it's not making sense. It's the interpretation part that is throwing me off.
If A is always unique then A is never B.

I'm not a big fan of formal logic or philosophy with its epistemology, tautology or whatever. I think in philosophy it's not such a technical subject that it requires anything other than "common language".

I think tautology in philosophy just refers to true but useless statements.

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Okay, thanks. So, we can tell something is an example of tautology if all interpretations lead to the same true statement?

I've read this though as an example: The ball is purple, or the ball is not purple.

The ball would obviously be either/or, so why state it in those terms, I wonder.

I've read this though as an example: The ball is purple, or the ball is not purple.
I would not call that a tautology. It serves a purpose to point out that X (in this case, ball colour) is binary.

A tautology, as I understand it, is where the assertion is true because it is defined to be true as part of the assertion:

"All purples balls are purple."

I don't find the usefulness in this. How does this differ from say a ''valid argument?'' The opposite of a tautology is a contradiction, but I can't think of any viable examples (of a contradiction to a tautology), without it looking like I'm completely opposing the initial statement.

I don't find the usefulness in this. How does this differ from say a ''valid argument?'
Sorry, can you specify what 'this' is? I'm having trouble following you.

Sorry, can you specify what 'this' is? I'm having trouble following you.

Sorry. ''This'' = a tautology

Sorry. ''This'' = a tautology
Well, a tautology isn't useful.
I mean, it may be, but I see them essentially as a type of logical flaw - almost indistinguishable from 'begging the question' (assuming your conclusion in your premise).

Right, okay. Tautology isn't the same thing as redundancy, even though a tautology seems repetitive.

I'm obsessed with tautology right now, and trying to figure this out!

Right, okay. Tautology isn't the same thing as redundancy, even though a tautology seems repetitive.

I'm obsessed with tautology right now, and trying to figure this out!
If you read almost anything Jan Ardena writes, you'll see a lot of tautologies.
He generally asserts that God must exist because how could the universe come into being except by the creation of some greater essence. That sort of thing.
It doesn't have to be repetitive; it simply has to be self-validating (it uses its own conclusion to validate its premise. In other words, begging the question).

Oh no! Then, I'm guilty of tautology-speak, too.

Whenever I've posted ''Personally, I...'' That's a tautology! I don't need to say, personally because the *I* assumes that it's personal.

I'm even more obsessed now!

Oh no! Then, I'm guilty of tautology-speak, too.

Whenever I've posted ''Personally, I...'' That's a tautology! I don't need to say, personally because the *I* assumes that it's personal.

I'm even more obsessed now!
Heh. No that's not a tautology, unless the personally and the I are a premise-conclusion construct.
That's just a garden-variety redundant redundancy.

I looked it up, it's a tautology. :=}

Probably not a big deal when we're using them in everyday conversation, but in formal writing, they should be avoided.

I looked it up, it's a tautology. :=}
Huh. You learn something new every day...

Probably not a big deal when we're using them in everyday conversation, but in formal writing, they should be avoided.
Yeah. Strunk & White and Stephen King agree.

How can a formula or assertion always be true, given any interpretation?

"Interpretation" is being used in a technical way. It isn't talking about interpretations of passages in natural or poetic language in which text might have literal or figurative meanings. In logic, it's talking about the Frege-Russell truth-functional theory upon which most of modern formal logic is based, in which every proposition receives a truth-value restricted to T (true) or F (false). That truth assignment is what's referred to as its 'interpretation'.

(A or not-A) is an example of a tautology. Let's look at that.

'A' can be interpreted in the linguistic sense to mean any sentence we like, but in the logical sense "interpreting" it means that (whatever 'A' means) we are assigning 'A' a truth value of either T or F, so that 'A' can be either

T
F

'~A' (not-A) will have the opposite truth value from 'A', namely F or T. (That's just from how these things are defined, the 'not-' operator reverses the truth value.)

F (if A is T, then ~A is F)
T (if A is F, then ~A is T)

'or' is a logical connective that connects two propositions. In truth-functional logic it has its own truth value which is determined by the truth values of what it's connecting (that's why it's called truth-functional). 'Or' is T if either one (or both) of its components is T. It's only F if both of the things connected by the 'or' are F. (That's just from how 'or' is defined in formal logic.)

These definitions of logical terms don't always correspond to how the same words are used in everyday speech, which leads to problems like the 'paradoxes of material implication' in which the commonly accepted logical definition of the 'if-then' relation leads to some very counter-intuitive results. Contemporary logic is working on making formal logic more congruent with natural language (typically by adding new logical operators for things like time, belief or possibility). This is where many of the controversies among professional logicians arise.

Returning to our example tautology (A or ~A)...

We have these two alternatives depending on what truth value we give 'A'

1. A is T, so ~A is F, so (A or ~A) is T because A is T (and the definition of 'or')
2. A is F, so ~A is T, so (A or ~A) is T because ~A is T (and the definition of 'or')

The "interpretation" is our truth value assignment to the simplest components (A and ~A in this case). In the case of a tautology, the larger compound statement is always going to be T regardless of the interpretation, in other words, it will always be T regardless of what T or F values the simpler components receive.

The opposite of a tautology is a contradiction. Contradictions will always be F, regardless of how the component parts are interpreted (the T or F values they receive).

To illustrate that, we can do precisely what we did above with 'or', except with 'and' this time. 'And' is defined so that it can only be true if both of the things it connects are T. (One of them no longer suffices.)

So

1. A is T, so ~A is F, so (A and ~A) is F because ~A is F (and the definition of 'and')
2. A is F, so ~A is T, so (A and ~A) is F because A is F (and the definition of 'and')

This stuff illustrates something else: why formal logic is "formal".

If (A or ~A) is always T, regardless of whether we interpret 'A' as T or F, and even regardless of what 'A' actually stands for in real life language, then the fact that (A or ~A) is a tautology is revealed to be a purely formal property, arising from the form of the expression and not its content.

The same thing is true of the contradiction (A and ~A). It doesn't matter what 'A' means or whether we interpret it as T or F, it's a contradiction simply on account of its form.

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To digress slightly, my favourite tautology in language, as opposed to philosophy, is - perhaps inevitably - from a sports commentator, who opened his remarks by saying: "Let me recapitulate back to what I said previously".

To digress slightly, my favourite tautology in language, as opposed to philosophy, is - perhaps inevitably - from a sports commentator, who opened his remarks by saying: "Let me recapitulate back to what I said previously".
Aw! lol

I'm coming to the realization that nearly everything I've ever uttered, is a tautology. Must work to correct this!

Aw! lol

I'm coming to the realization that nearly everything I've ever uttered, is a tautology. Must work to correct this!
You mean, "In my opinion, nearly everything I've ever uttered, is a tautology". Not to lecture, or anything.

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My mean, "In my opinion, nearly everything I've ever uttered, is a tautology". Not to lecture, or anything.
You... lecture? Nah.

Have you ever considered repeating a meaning in a sentence may serve some aesthetic function like emphasis or clarity of description? Alliteration uses the same first letters of words. Maybe tautology serves a purpose like that.

Example: "Let me recapitulate back to what I said previously".