As you’ve probably heard from other ScienceBlogger’s, that paragon of

arrogant ignorance, Dr. Michael Egnor, is back at it again – and he’s abusing

the language of logic in a way that really frustrates me. I’ve written

about this before, but the general topic recently came up in comments, so

I thought I’d bump it up to the top, along with another slap aimed at Egnor.

For those who don’t know, Dr. Egnor is a brain surgeon at SUNY Stonybrook – an excellent school, and Dr. Egnor is, from all information I’ve heard, an outstanding surgeon. In his free time, he blogs for the Discovery Institute, using his

status as an accomplished brain-surgeon to try to boost the bullshit spewing out of DI.

One of Dr. Egnor’s favorite attacks in his anti-evolution screeds always makes me think of a line from one of my favorite movies: “Hello, my name is Inigo Montoya, you killed my father, prepare to die”. Oops, no, not that one. (Sorry, couldn’t resist.) The real line is “You keep using that word. I do not think it means what you think it means”.

You see, what Egnor keeps doing, over and over again, is arguing that

evolution is just a tautology, and that therefore it’s meaningless. He

defines evolution as the statement “that which survives, survives”. He almost never gets through one of his posts without that accusation in one form or another: evolution is a tautology, and that implies that it’s meaningless and worthless as an explanation of anything.

Leave aside for the moment the fact that he *mis-states* the key premise of evolution. That’s a huge, obvious, and *deliberate* mistake, but let’s just ignore it for now. Instead, I’d like to just look at the problem with his statement about tautologies. What exactly *is* a tautology? And does

criticizing something as “just a tautology” actually make any sense?

In logic, a tautology is a statement which is inevitably true solely by virtue of its structure. Alternatively, it’s a logical statement which is true for *any* binding of its variables – that is, the structure of the statement means that it’s true, regardless of the meanings assigned to its basic elements.

For example, “A ⇒ A” – that is, “If A is true, then A is true.” It doesn’t matter what meaning you assign to A, the statement “If A is true, then A is true” will always, inevitably, be true.

For a slightly more complex example, “A ∧ (A ⇒ B) ⇒ B” – in english, “If A is true, and it’s true that if A is true, then B is true, then B must be true.” It doesn’t matter what A and B are; it doesn’t matter whether A and B themselves are true or false. The statements above will always be true. It cannot possibly be anything *but* true, by the definitions of the basic elements of the propositional logic in which it’s written.

Now, for what appears to be a change in course: What is a proof?

A proof in a particular logic L is a set of basic statements (axioms), a

sequence of *inferred steps*, and a conclusion, such that the conclusion can produced from the axioms by the application of a series of inferrence rules defined by L, where each inferrred rule produces a new fact using one of the inferrence rules of L.

That sounds a bit hairy, so let’s pick it apart a bit. A logic is a

system which (loosely speaking) consists of three parts. First, it has

a syntax – that is, a system of rules for describing how you can form

valid statements in that logic. Second, it has a set of inferrence rules – rules

that describe how to use true statements to produce other true statements; each

production of a new true statement from a set of known statements is called

an *inference*. Finally, the logic has *semantics* – that is, a

way of assigning meaning to statements within the language.

What does an inference rule look like? Put extremely simply, an inference rule

consists of a *structural pattern* which says given a set of true

statements that match the patterns, you can produce a new true statement.

For example, a classic inference rule of propositional logic is (in an unfortunately awkward syntax, due to the limitations of HTML):

**Given:**“A” and “A ⇒ B”**Infer:**“B”

That is, for any value of A and B, if you have the statements that

match the patterns “A” and “A ⇒ B”, then you can infer “B”.

An inference rule is entirely syntactic (which is to say, structural). It doesn’t

rely on meaning *at all*. Without knowing what any of the statements in an

inference step mean, you can apply the inference, so long as you have the correct

structural elements.

So – a proof is a series of inference steps which lead from a set of axioms to a

conclusion. Hopefully, you should be starting to see where this is going: a proof is a

series of applications of structural rules that lead from its axioms to its

conclusion.

If the common logics that we use for most scientific studies (that is, propositional logic and first-order predicate logic), you can take *any* proof, and turn it into a single, massive logical statement. How? Take the axioms, and join them with logical ands. For each application of an inference rule, write a version of that inference as a logical implication, and join that implication to the proof with a logical and. Then add the result of the implication as a new statement, again joined

with logical and.

Let’s take an example – one of the old classics. Our axioms:

- All men are mortal: “∀m: IsAMan(M) ⇒ IsMortal(M)”.
- Socrates is a man: “IsAMan(Socrates)”.

Our desired conclusion is “Socrates is mortal”; in logical syntax, “IsMortal(Socrates)”. We’ll do the proof in first order predicate logic.

There’s one inference in the proof – the application of logical implication. Written as an implication itself, that works out to “IsAMan(Socrates) ∧ (IsAMan(Socrates) ⇒ IsMortal(Socrates)) ⇒ IsMortal(Socrates)”.

So let’s join it all up:

(∀m: IsAMan(M) ⇒ IsMortal(M)) &land; (IsAMan(Socrates)) ∧

*(the axioms)*

(IsAMan(Socrates) ∧ (IsAMan(Socrates) ⇒ IsMortal(Socrates)) ⇒ IsMortal(Socrates)) ⇒ IsMortal(Socrates) ∧

*(the inferrence)*

IsMortal(Socrates)

*(The result of the inference, and also the conclusion)*.

There it is – the full proof as a single logical statement? What did we do by translating the proof into a statement this way? We produced a tautology. *Every* proof can be stated as a tautology. And therefore, *every provably true statement* can be stated as a tautology.

All of math is, ultimately, nothing but a set of tautologies.

The theory of relativity is nothing but a tautology.

The entire practice of science-based medicine is nothing more than the application

of a mass of tautologies.

“Just a tautology” isn’t a meaningful criticism of an idea – because all provable ideas are “just” tautologies.

If he wants to claim that evolution is vacuous, then he should say that; but he deliberately appropriates and abuses the language of logic in order to

make his argument *sound* more serious, just like he uses his

medical credentials to make his bogus arguments sound more credible.

Finally, a brief mention of what’s wrong with Dr. Egnor’s statement of the

tautology of evolution: it leaves out a crucial element of the theory – a part

without which the theory loses all of its explanatory value.

You see, tt’s true that evolution says that those that survive, survive. But

evolution says more than that. Evolution says that children aren’t exactly the same as

their parents, and those changes can be inherited by *their* children.

A properly complete (if reductionist) statement of the theory of evolution is:

“Children are heritably different from their parents, and those that survive and

reproduce, survive and reproduce children which are heritably different from themselves”. This statement of evolution is still tautological in the same way as Dr. Egnor’s statement, but it’s is a *vastly* different and more meaningful

statement that Dr. Egnor’s vacuous one. Why, do you suppose, does Dr. Egnor constantly

leave out that key bit, about children being heritably different from their

parents?

Do I even need to answer that question? I think not.

*
*

* A personal note here; if you’re not interested in personal ramblings, feel
free to skip this. I’ve been asked why I give Egnor and friends so much attention. There is a good reason for it. I’ve got a serious emotional stake in the effects of
the way that people like Egnor – a *

*teacher*at a medical school – deny the importance of evolution in medical education.

My father died a year and a half ago. What finally killed him was pneumonia. But what *caused* his death was the stupidity and ignorance of an asshole

doctor. My father died of an antibiotic resistant infection. His doctor was,

unfortunately, a fundamentalist christian, but for some reason, my dad trusted him.

This doctor watched as a series of infections ravaged my father’s body, and

at pretty much every step, he did the wrong damned thing. The reasoning

behind his errors relates directly to the kind of argument Egnor makes: antibiotic

resistance isn’t the production of *new traits*; it’s merely the selection

of existing traits in a population. So he prescribed antibiotics in a way that

anyone with a damned clue about how bacteria evolve would have *predicted* would increase the antibiotic resistance of the bacteria.

What’s going to happen in you take a staph infection, and give it penicillin? There’s a good chance you’ll kill the infection. What if the penicillin doesn’t? Then you know you’re dealing with a resistant infection. What’s the right thing to do next? My dad’s doctor gave him more beta-lactam antibiotics with the addition of clavulanic acid, which is an agent that defeats the most common mechanism of penicillin resistance. When that didn’t work, he *gradually* increased the dose of clavulanic acid – the *perfect* thing to do to help the bacteria evolve increased resistance. Then he put him into a room with a patient with antibiotic resistant pneumonia. After all, they both had antibiotic resistant infections.

The guy’s pig-ignorance of how bacteria evolve led him to follow a

treatment plan that could almost have been *designed* to create deadly

strains of resistant bacteria. (And that same doctor prescribes antibiotics

like candy. Got a sniffle? Here, have some antibiotics. They probably won’t do anything, since it’s probably a viral infection, but what’s the harm in being sure? Dumb bastard.)

It’s incredibly important that doctors understand this stuff. Not just

understand that antibiotic resistance *exists*, but understand

how it *develops*, and how that development can be enabled

by inappropriate treatment decisions. Egnor argues vehemently that

discussions of evolution absolutely do *not* belong in medical

education – that any discussion of the process of evolution is, at best,

a waste of time for medical students. Attitudes like that cost lives. And

to me, that cost isn’t abstract at all.