Tautological Definition Fallacy

The fallacy of using a definition that seems to be sharp and crisp, but is in fact tautological (but this is hidden, mostly unintentionally).

The problem: the point at which a definition that was useful and very sharply defined becomes tautological is often not easily seen.

But when this happens, everything seems to fit the definition (obviously once one discovers its tautology).

In discussions this may happen by driving some definition to its extreme, e.g. to make its intent clear to the listeners. But in its extreme the definition suddenly loses all its utility by becoming tautological.

Examples:

Pattern:

The opposite of NoTrueScotsman, where conditions are added until the intent is restored, here conditions are removed or generalized until truth remains only.

-- GunnarZarncke

Removing conditions until only truth remains will not of itself produce a fallacy; you have to then use the definition as if it had additional conditions as well. -- JamesKeogh

Yes, I thought I made that clear in the first lines. -- .gz


Sometimes the tautology is obvious. AynRand built an entire philosophy on the expression of an empty tautology, A=A.

I would say rather, that she built her philosophy on the idea that reality is logical, as proven by the fact that the reader (or listener in her novels) understands that A=A has meaning, and is not "empty" as you put it. A=A was first realized by MrPlato.

A=A has meaning, yes. So does goofleblort=goofleblort and fwengza=fwengza. How this manages to support any kind of argument requires a sort of intellectual dishonesty that essentially boils down to "I like what she's saying, therefore it's logically correct".

Her point is that if A=A has no meaning, then logical arguments would not exist and "intellectual dishonesty", not to mention everything on this page, this wiki etc. would have no meaning either. In her novels, the antagonists are portrayed as intellectually dishonest because they espouse policies which will lead to a world without meaning, all the while denying that they are doing so. The protagonists cleverly use "A=A" to stop them.

'A=A' has meaning, no. But 'A' does. Or rather 'A' may have, and arguments based on that meaning on 'A' have too. But I guess, that saying 'A=A' or longer 'A is just A' is just colloquial speech for emphasizing, that 'A' is taken or assumed to be an axiom.

Um, maybe we have different meanings for "meaning" (see LaynesLaw), but A=A is a starting point for logic and math, and the concept of a taulolgy exists because we instantly recognize that A=A, which is what every tautology devolves to anyway, so it is no more "empty" than any other. To say it has no meaning is to refute a lot more than just "A=A has meaning".


Definitions are not logical statements so I'm having some difficulty seeing how a definition could ever be tautological. Recursive definitions with fixpoints are perfectly legal (e.g. 'define A = node:T->* | tree:(A,A)->*'; 'define A = {first:*->T,rest:*->A}'). There are even definitions that describe nothing outside themselves ('define A = A', as discussed above), but even this definition is by no means 'tautological'. It's circular, yes, but it still gives you both the conditions for recognizing an A and for determining the properties of an A... based, in this case, entirely on the presence or absence of terminal symbol 'A'.

Linguistically, 'define A = A' indicates that A is a terminal... 'A' possess no more intrinsic meaning than in its presence or absence. It may still possess extrinsic or contextual meaning. Consider the definition of 'the'. You can describe 'the' by its use (to indicate uniqueness of an object described by a noun phrase) and its class (article), but these do not define 'the'. In particular, they do not provide you a mechanism to recognize 'the' or to analyze a 'the' except by recognition that the word 'the' is in use or is absent. (Not entirely true... you can recognize a situation where 'the' could have been used... but usually only as a contextual transformation from one of the other articles (a unique x => the x; one of the x => an x).)

'True' and 'False' are similar in nature. The meaning of 'true' is defined only by its use in the logics that provide 'true' as an answer to a proposition. You cannot define 'true' without describing a logic and the whole context in which the 'true' is used, and even then the internal definition of 'true' is that 'true = true' and 'true != false'.

The fallacy described here should not be called the 'tautological definition' fallacy. I think what is intended here is the use of conveniently choosing one's own definitions to sidestep relevant issues, or to better enforce one's own rhetoric, consciously or otherwise.

[abortion example extracted to DefinitionWithAgenda]

The only way to properly counter their sophistry is to enter a debate over definitions (which won't be well accepted by the person depending on loaded words to defend his or her position). And LaynesLaw doesn't even really apply... until the definitions are hammered out, the argument hasn't even started. That said, I've noticed several people on this Wiki incant 'LaynesLaw' to better defend positions like those described here, essentially to prevent challenge to their questionable or loaded definitions.

I, unfortunately, lack a better name for this fallacy... but the current name irks me a little. Maybe 'DefinitionWithAgenda'?

I agree that tautological definition is problematic - it's too short. But "Fallacy of defining something by hiddenly employing a tautology" is just too long :-) It's not the definition that is tautological, but the condition in the thing matched by the definition. Like in your def A = A, which matches everything but in that case that is obvious and intended. More problematic is something like def A = f(A, B, C) where f looks very complex on the onset, but actually is just id(A).

I disagree with your DefinitionWithAgendaFallacy?. Not that that wouldn't be a fallacy too - and one I recognize very well - it's just not this fallacy. Have a look at the examples. This is really about a lack of rigor in ones definitions that makes them useless (because obvious tautological). Or maybe not - after we always agree if we reach a sufficient close agreement about our common reality (like: humans behave like the humans we recognize each other to be).

-- .gz

I'm not sure that what you're describing is actually a fallacy. If a definition turns out to cover every object in the domain, then any results from using that definition would then apply to every object. No harm done. (Unless you committed other fallacies on the way, such as assuming that there are things that don't meet the definition.)

'define A = A' applies only to the name 'A'. It is not the same as the set: {x such that x = x}. If you wanted that, you'd need to use 'define A = {x such that x = x}'. Definitions circumscribe and finite one word, not a whole domain. In gz's example 'define A = f(A,B,C)', 'f' appears to be incredibly complex (e.g. say a complex word problem) that just happens to evaluate back to 'A' (the name for the word problem) or to A (the word problem itself). I'd argue that this is no less a valid definition of A. It's much like a quine. It is not tautological or fallacious (definitions are neither arguments nor rhetoric), and not necessarily useless (the determination that 'f(A,B,C)' to evaluates to 'A' can be of great utility whether or not A is a fixpoint 'f(A,B,C)'). What I believe you must intend to describe as a fallacy is not the circular definition, but rather some sort of fallacious or misleading use of this definition to further one's argument, where the arguer takes the complex definition of 'A' and makes it appear to apply to something more than it does, or appear to have more or fewer properties than it does.

I think I see. You're describing the creation of a definitional maze to hide the 'actual' definition.


Extracted discussion around abortion rhetoric to DefinitionWithAgenda.


Related to DogmaticFallacy, NoTrueScotsman, BeggingTheQuestion

See FallaciousArgument


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