A question about Tautology

A while ago I was looking up Falsifiability and came upon the word [url=http://en.wikipedia.org/wiki/TautologyTautology].
So now, I have some stupid questions.

  1. Are tautological statements scientific?

2 If not, why?

If so

  1. Can a belief or theory be tautological?
    For example, say person A says to person B, “You’re beliefs are unscientific because they’re not falsifiable” and person B responds “They don’t have to be, they’re tautological.”
    Now, going into more detail than person A just saying “Oh yeah, then prove it.” what could person A say in repose that would prove person B wrong?

I hope my questions make sense, thanks.


A tautology is a statement that is true for logical reasons rather than because of its correspondence to the real world. Like, “If Bigfoot is both large and hairy, then Bigfoot is hairy.” This statement, taken as a whole, must be true, regardless of whether or not Bigfoot exists or what characteristics Bigfoot possesses. You wouldn’t use scientific means to go about proving this statement true, the way you would with statements like “Bigfoot exists” or “Bigfoot is hairy,” that could be either true or false.

Tautologies aren’t necessarily as useless or redundant as that link seems to imply. In more complicated cases, it may take a bit of logical analysis to determine whether something is, in fact, tautological. In fact, for an argument to be logically valid means that “If (the premeses) are all true then (the conclusion) must be true” is a tautology.

I understand, thanks.

They can be, although they needn’t be.

In essence all that a statement requires to be scientific is that it be falsifiable. If I claim “All members of the cat family are cats” that’s certainly a tautology, but it’s also scientific. It can be readily falsified by looking at all the species’ physical characteristics or their genetics if you want to get real fancy. It would be totally redundant to do so of course since the original statement was tautological, but that doesn’t make it any less possible.

And of course the obvious corollary is that not all tautological statements are scientific.

Yep. Darwin’s theory of “Survival of the Fittest” is the classic example of a tautological theory.

The theory states that the individuals that are best able to survive to reproduce are the fittest. And fitness is defined as those that are best able survive and reproduce. So the theory really says that those individuals best able to survive to reproduce are those that are best able to survive to reproduce. It’s an utter tautology, but nonetheless true, and one the most important scientific theories of all time.

You can simply point out that the defining characteristic of [Popperian] science is that something be falsifiable. Any belief does indeed need to be falsifiable to be scientific. Person B can’t simply respond that they don’t; need to be, that’s just an argument from assertion and it’s worthless.

But bear in mind that there are numerous standards of ‘science’, not all of which rely in falsifiability. What you really need to do is agree on what definition you are using and see whether the beliefs meet that standard. I’m unaware of any definition of science that states that simply being true and logical qualifies a belief as scientific though.

A political science professor of my acquaintance describes tautologies as “No sh–” statements.

How would you falsify that? There isn’t a possible experiment you could design that would show that a cat is not a member of the cat family.

Falsification in science doesn’t mean that you ever actually show something is wrong. Obviously all accepted theories have never actually been falsified. But they are all open to falsification.

It’s quite easy to state falsification criteria for the tautology I gave. All we need to do is define “cat”. The all we need to do is examine any designated member of the cat family and see if it meet those criteria. If it doesn’t meet those criteria then my tautology will have been falsified. Or alternatively we can define “cat family” and examine individual cats and see if they met the criteria for inclusion. Either way works just as well.

As I said, in practice this is totally redundant. We already know that all cats are members of the cat family and vice versa. That’s why it’s tautology. Nonetheless the theory is open to falsification. There are tests which can be done that could prove the claim false even though we know beforehand that they won’t.

That can be true even of the most blatant tautologies. If I theorise “A tomato is defined as a fruit, therefore all tomatoes are fruit” that’s pretty blatant. I can go out and test all tomatoes and if one tuns out to be a penguin I can claim to have falsified the tautology. Of course because it’s tautological we know that it never will be falsified, but nonetheless it remains open to testing falsification.

I think the thing to realise is that falsification in science means that the originator states a workable method by which it can be proven wrong. It doesn’t mean that he believes it actually might be proven wrong or that anyone is ever actually going to show it to be wrong by the method proposed. It simply means that if the theory was wrong then that method could demonstrate it.

Well no, if you define cat as anything other than “a member of the cat family” then it no longer becomes a tautology, you could conceivably find a cat thats not in the cat family. If you do define cat as “a member of the cat family”, then there is no conceivable way to ever falsify that statement because it would lead to a logical paradox. Either way, it’s either a tautology or a scientific statement but it can’t be both.

Where tautology gets the odor of inauthenticity is in rhetoric, as in politics, policy, and other debates, although tautologies in scientific research can also yield misleading-to-meaningless findings.


Poster 1: "Well, I don’t think trolls should be banned from the Straight Dope boards. Everyone says they are disruptive to the community, but really, if you control for incoherence and abrasiveness, trolls are no more disruptive than anyone else. "

Poster 2: “I disagree. Trolls are a real problem, especially the newbies. Our real problems come from newbies: if you correlate trollishness with the extent to which posters are newbies, you see that newbies cause most of the disruptions on this board. We should come down tougher on newbies who step over the line.”

The first poster is stating an obvious tautology because incoherence and abrasiveness are very much bound up in the definition of “troll” as we use the term on this board. The second poster is using a slightly sneakier one: trolls tend to get banned, most often early on, and therefore do not tend to get beyond newbiehood with posting privs intact, so a higher proportion of newbies are trolls, but as a consequence of banning trolls. Coming down harder on newbie infractions would not only fail to fix the problem, it would most likely make it statistically worse.

This latter type of tautology —where one variable under consideration is a causal or definitional component of another in unacknowledged ways — can make mathematically legitimate studies effectively lies in terms of not saying or demonstrating what they purport to say or demonstrate. You can, for instance, often “show” that there is no discrimination on the basis of race in situation “X” when you control for socio-economic status and education, but depending on what situation “X” is that can be like saying there is no discrimination on the basis of sex when you control for number of testicles.

In political rhetoric, tautology is quite common. I say my administration has balanced the budget after having done so much interesting definitional work on the budget that I’ve effectively defined it as balanced, or have defined “a balanced budget” as the one we’ve got. Or I state that our enemies are terrorists while defining terrorists as anyone who is our enemy in a war on terrorism in which anyone who is not with us is against us. Or I say that I didn’t have sex with that woman as long as we define “sex” as something I didn’t do with that woman. Etc.

I agree with Shalmanese against Blake. A statement of the form “All members of this group satisfy these criteria” is not a tautology—unless your criterion is simply “being a member of the group in question,” in which case your statement is a tautology, but it’s not something you can check; it’s true by definition.

If a statement really is a tautology, there is no way it can possibly be false.

The “opposite” of a tautology would be a contradiction: a statement that, logically, cannot possibly be true (like, one that asserts that both P and not-P are true). Mathematicians often use “proof by contradiction” to prove that something is true by showing that the assumption that it’s not true leads to a contradiction.

I do like Blake’s “survival of the fittest” example. That is, or at least can be worded so as to be, a tautology. But there’s more to Darwin’s theory than that tautology. (In fact, I think the “survival of the fittest” idea predates Darwin.)

The first thing I thought of as an example of a tautological belief like the OP asked for is Anselm’s ontological argument for the existence of God. Roughly, it says that God is the being than which no greater can be imagined; but a God that exists is greater than a God that doesn’t; hence God must exist. If you accept the argument—and that’s a big if (see the link)—the existence of God is tautological.

What you guys are overlooking is that just because something is true by definition that doesn’t mean you can’t also check it. This is a point I stressed above. You can check most statements that are true by definition. Of course the check will always confirm that it is true but that doesn’t mean that it is any less true. It just makes checking redundant because we know in advance what we will reveal.

Are you honestly saying that I can’t check whether an animal is a cat or not?

Shalmanese you apparently still don’t quite understand the difference between falsify and falsifiability. As I stressed above, you can never falsify anything that is true. That doesn’t mean that everything that is true is unscientific. Falsifiability simply means that something is potentially open to being falsified, not that it ever actually will be or even can be falsified.

A tautology is necessarily true, and true by definition. If it were not true it wouldn’t be a tautology. Nonetheless you can attempt to falsify a tautology. I can attempt to prove that an ocelot is not a cat despite being a member of the cat family. I know in advance that I will fail because it must by definition be a cat but nonetheless a way exists in which I can try. And if the tautology were not true (i.e. it were not a tautology) it would be revealed. That is all that is required for a theory to be science. A theory doesn’t have to actually be falsified to be science. It simply needs ot be falsifiable. That’s a very important distinction.

I agree with Blake. Obviously, it’s impossible to find a cat that isn’t a cat, but so what? No true statement can be proven false. Falsifiability doesn’t mean you need to be able to find a case where the statement isn’t true, only that there’s some sort of test you can do for which a certain result would prove the statement to be untrue. If the statement is true (whether because it’s a tautology or otherwise) you just won’t ever get that result.

Let’s choose an even simpler example than “All cats are cats.” Suppose we said “All red objects are red objects.” This is clearly a tautology. It would be a tautology whether we had defined the term “red object” or not. However, as it happens “red object” does have a definition beyond “the class of things which are red objects.” Specifically, its meaning is related to what frequencies of light the object reflects. We can then take a red object, shine a beam of light on it, measure the frequencies of the reflected light, and confirm that it indeed satisfies the definition of red. If we took a red object and did this and it turned out it wasn’t red, then we’d have disproven the statement “all red objects are red objects” (assuming we haven’t made any experimental errors). Of course, it is impossible to get such a result, but that’s not because the statement is a tautology, it’s just because the statement is true. It’s impossible to disprove any true statement.

Contrast that to a statement like “God exists.” That statement isn’t falsifiable, not because no experiment would ever give the result “God doesn’t exist”, but rather because no experiment could even be proposed for which a certain result would show that God doesn’t exist. The problem isn’t that a certain outcome to the test can’t possibly occur, but that the test itself can’t possibly exist.

Now wait a minute! It seems that one of us—either Blake or myself—doesn’t quite know what we’re talking about. I wonder which one it is.

[Bear of very little brain] Think… think think… think think think… [/Bovlb]

Hmm. Maybe Blake does have a point! Consider this example from my own home turf of mathematics: All even numbers are divisible by 2. That is a tautology, true by definition, but I can check it: just pick an even number and try to divide it by 2. It will, of course, but it’s still something that can be checked. Okay, Blake, I concede your p—

Hey, wait a minute! Not so fast! How did I “just pick an even number” in the first place? How did I know the number I picked was even? It may be “obvious” to me which ones are even, thanks to long familiarity, but doesn’t it really boil down to the fact that, when I picked an even number, I was picking one that I knew, in the back of my mind, to be divisible by 2?

Or take tim314’s example:

How can you “take a red object” unless you know, somehow, that it is a red object? If it turned out that it wasn’t red, it wouldn’t mean you’d disproven the statement; it would mean that you hadn’t really picked a red object at all.

If you’re picking a red object and then testing to see if it satisfies the definition of red, or if you’re picking an even number and seeing if it’s divisible by 2, aren’t you really just performing the same test twice in a row, and seeing if what passed the test the first time passes it the second time?

But, but, but what if you were using some other definition of “even,” some other way of knowing whether the number you picked was an even number—one that was logically/mathematically equivalent to being divisible by 2 but was formulated differently. Certainly you could check specific examples to see whether the two definitions were consistent. If that was what we were doing, would that count as attempting to falsify a tautology?

I’m confused. Can some other Doper, preferably one trained in logic, come in and get this straightened out?

The obvious problem I’m having with that post Thudlow is that you say that you are saying that any attempt at falsification has to hinge upon preselection of the subjects. You have to pick and even number, you have to select a red object, you have to select a cat.

Of course that’s not true. You can select random animals or random objects or random numbers. You can then test them to see if they meet the criteria for red or the criteria for cat or the criteria for even. Of course they always will do so if they are cats or red or even. But that didn’t prevent you for checking. Nor did you ever need to select your sample based on the pre-existing characteristic.

You didn’t even need to know what the pre-existiing characteristic was. An assistant with no preconcieved notions at al could have collected the data and handed it to you after the fact and you would still have the same results to analyse. The analysis will inevitably show that red objects reflect at frequency X and that cats have genotype Y and that een numbers aredivisible by 2, but the collector of the data never selected the smaplee based on those traits. She need not have selecte d the samples based on an traits at all.

But how do you know which of the objects selected are the red objects, or which are the cats, or which are the even numbers, etc.?

By checking whether they meet your criteria for being red, or cats, or even. Whether you are dealing with a tautology or not that is always the case. You need to deifne all the terms in the statement and see whether your samples do or don’t meet that deifntion.

In the case of a tautology the criteria used for determining ‘evenness’ or ‘redness’ or ‘catness’ are exactly the same ones that place an object into the category of ‘cat’ or ‘red’ or ‘even’ with 100% overlap. But that doesn’t make it impossible to check that an object in fact meets those criteria. It just makes it pointless to do so.

That’s an excellent point and helps answer part of my OP, thank you.

The point is that in order for a statement to be falsifiable, there has to be some set of circumstances that make it false. Any statement that is not falsifiable is a tautology. Some are trivial–all cats are cats, every even number is divisible by 2, etc.–and some are not–the sum of the angles of any triangle in the Euclidean plane is 180[sup]o[/sup], all finite simple groups are classified, etc.

Cite please.

By that standard of falsifiable no true statement is falsifiable. Obviously there is never a circumstance in which a true statement can be made false. That’s inherent in the definition of true. So if we apply that standard no true statement is falsifiable and hence no true statement can ever be scientifically valid. That’s obviously nonsense.
Now if we look at the standard of scientific falsification applied by father of the term, Karl Popper, we see that it simply means that the “The theory is incompatible with certain possible results of observation”. Note that it never mentions that it has to actually be false under any circumstances, simply that there has to exist a possibility of being proven false. I think Tim paraphrased it best: “The problem isn’t that a certain outcome to the test can’t possibly occur, but that the test itself can’t possibly exist.” So long as it is potentially possible to obtain an observation that is incompatible with the statement then the statement is falsifiable.

That is also not true. “The Judaeo-Christian God exists” is the classic example of an unfalsifiable statement. It is in no way tautological. The same is true for statements concerning the afterlife or, as Popper noted, most of Freudian psychology. There is an entire universe of statements that are unfalsifiable and yet in no way tautological.

Do you have any references to support the contention that Any statement that is not falsifiable is a tautology. It seems to be obviously untrue.