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William's Journal - A great Blog entry on Tautologies

Mar. 14th, 2007

10:43 pm - A great Blog entry on Tautologies

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From http://scienceblogs.com/goodmath/2007/03/basics_tautology_with_a_free_b_1.php

Today's bit of basics is inspired by that bastion of shitheaded ignorance, Dr. Michael Egnor. In part of his latest screed (a podcast with Casey Luskin of the Discovery Institute), Egnor discusses antibiotic resistance, and along the way, asserts that the theory of evolution has no relevance to antibiotic resistance, because what evolution says about the subject is just a tautology. (I'm deliberately not linking to the podcast; I will not help increase the hit-count that DI will use to promote it's agenda of willful ignorance.)

So what is a tautology?

A tautology is a logical statement which is universally true, by nature of its fundamental structure. That is, even without knowing anything about what the statement means, you can infer that it must be true.

To make that a bit clearer, let's look at a couple of the most classic examples of tautologies.

  1. "A⇒A" - A implies A. You don't need to know what A means. You don't need to know if A itself is a true or false statement. The statement that A implies A: that is, if A is true, then A must be true - must be true.
  2. "A∨¬A" - A or not A. In classical first order predicate logic, either A is true, or A is false. So A or not A must be true. Again, we don't need to know what A means, or whether A is true or false; it doesn't matter. This statement must be true.
  3. "(A⇒B)∧A⇒B" - A implies B and A implies B. This is just a basic statement of one of the fundamental inference rules of logic. Once again, it doesn't matter what A means, or what B means; and it doesn't matter whether A or B are true or false. No matter what, by virtue of the structure of the statement, it must be true.

That third tautology is particularly important - because it's an example of a fundamental principle of logic. If you take any proof - any sequence of statements and valid inferences from those statements - and you combine all of the statements of the proof together, the resulting statement is, by definition, a tautology. The obvious implication of this is that you can take any statement which is provably true, and present it as a tautology.

And this brings us to Egnor's idiocy. It's a common tactic among idiots to criticize various scientific theories as tautological. And it's pretty much always done to mislead. Because all actual scientific theories are based on inferences from observations, and use the result of those inferences predict that future observations will match prior observations. So by taking the statement of the observation and the inference, you can derive a tautological statement from any scientific theory.

The theory of gravity? If you let go of something, it will fall - therefore, if you let go of something, it will fall.

Relativity? Light bends when it passed through a gravitational field - therefore, if I shine a light through a gravitational field, it will bend.

Evolution? The things that survive to reproduce are the things that survive to reproduce.

Tautological statements of theories don't invalidate the theories; and they don't mean that the theories are useless and have no explanatory value. The only time that a tautological statement of a theory is a problem is when it's the only statement of the theory - that is, when the theory itself consists of nothing more than a tautological structure. A theory that consisted of nothing more than the fundamental statement "A=A" isn't a theory - it's gibberish dressed up to look like a theory.

For an example of where tautological reasoning is a problem, you can do things like look at arguments presented by lazy objectivist/liberatian Ayn Rand worshippers. Please note that I'm not saying that all objectivist libertarians use this kind of nonsense - I'm describing arguments by intellectually lazy objectivist libertarians! The fundamental statement of Rand's philosophy is "A=A". But a lot of lazy objectivists take that, and use it to make ridiculous arguments. The arguments are ridiculous not because they involve a tautology, but because they use a tautology in place of an actual argument. You can find objectivists arguing that, for example, tax=theft, because tax="government taking your property away from you without your permission", and theft="someone taking your property away from you without your permission". But the real argument there isn't in the "A=A" part = it's in the definitions chosen for "tax" and "theft". To make the objectivist/libertarian argument about taxes, you need to justify the definitions - not just assert definitions, and then use the tautological equivalence of the unjustified assertions as your argument. If you read some objectivist literature, you can find some pretty good arguments about why that definition of tax is valid. But most of the time, you have people just blindly spewing the definition, and then shouting "A=A" at the top of their lungs when anyone tries to disagree with them. To repeat, the problem isn't that there's a tautology - it's that the truth of the tautological statement is used as the whole of the argument, when in fact, the argument relies on the truth of something other than the tautology. The libertarian argument about taxes is not a simple "A=A" argument. It relies on the inference that there exists an A such that taxes=A, and there exists a B such that theft=B, and that A=B, therefore taxes=theft. The step of showing the validity of defining taxes and theft as equivalent things is crucial - and omitted from the lazy version of this argument.

To return to Egnor: he asserts that the theory of evolution is irrelevant to bacterial resistance to antibiotics, because after all, all that evolution says is "If you have an antibiotic that doesn't work on a bacterium, then that antibiotic won't work on that bacterium".

Well, yeah. It does say that. But it also predicts that if you use antibiotics on some population of bacteria, and you don't kill all of them, that over time, the population of bacteria will change to become resistant to the antibiotics.

As I mentioned over at Mike's blog, this is something that's become quite personal to me, because my father has gone through a horrible medical crisis in the last few months caused by a highly antibiotic-resistant strain of staphylococcus aureus. A strain of staph that had never been observed as recently as 10 years ago, and which is dramatically different from its ancestors. A strain which is the result of an evolutionary process, where non-resistant bacteria were wiped out, and resistant bacteria filled the niche left behind. Where that simple tautological statement: "if an antibiotic doesn't kill a bacteria, then it doesn't kill the bacteria" is a precise description of how the bacteria that paralyzed my father came into being.

So remember: next time someone tries to convince you that you should ignore something just because it's a tautology, what they're really saying is, "This is true, and I can't make any argument that it isn't".

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