{"id":717,"date":"2008-12-15T11:07:54","date_gmt":"2008-12-15T11:07:54","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2008\/12\/15\/once-again-egnor-and-tautologies\/"},"modified":"2008-12-15T11:07:54","modified_gmt":"2008-12-15T11:07:54","slug":"once-again-egnor-and-tautologies","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2008\/12\/15\/once-again-egnor-and-tautologies\/","title":{"rendered":"Once again, Egnor and Tautologies"},"content":{"rendered":"

As you’ve probably heard from other ScienceBlogger’s, that paragon of
\narrogant ignorance, Dr. Michael Egnor, is back at it again – and he’s abusing
\nthe language of logic in a way that really frustrates me. I’ve written
\nabout this before, but the general topic recently came up in comments, so
\nI thought I’d bump it up to the top, along with another slap aimed at Egnor.<\/p>\n

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
\nstatus as an accomplished brain-surgeon to try to boost the bullshit spewing out of DI. <\/p>\n

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”.<\/p>\n

You see, what Egnor keeps doing, over and over again, is arguing that
\nevolution is just a tautology, and that therefore it’s meaningless. He
\ndefines 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.<\/p>\n

Leave aside for the moment the fact that he mis-states<\/em> the key premise of evolution. That’s a huge, obvious, and deliberate<\/em> 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<\/em> a tautology? And does
\ncriticizing something as “just a tautology” actually make any sense?<\/p>\n

<\/p>\n

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<\/em> 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.<\/p>\n

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.<\/p>\n

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<\/em> true, by the definitions of the basic elements of the propositional logic in which it’s written.<\/p>\n

Now, for what appears to be a change in course: What is a proof?<\/p>\n

A proof in a particular logic L is a set of basic statements (axioms), a
\nsequence of inferred steps<\/em>, 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.<\/p>\n

That sounds a bit hairy, so let’s pick it apart a bit. A logic is a
\nsystem which (loosely speaking) consists of three parts. First, it has
\na syntax – that is, a system of rules for describing how you can form
\nvalid statements in that logic. Second, it has a set of inferrence rules – rules
\nthat describe how to use true statements to produce other true statements; each
\nproduction of a new true statement from a set of known statements is called
\nan inference<\/em>. Finally, the logic has semantics<\/em> – that is, a
\nway of assigning meaning to statements within the language.<\/p>\n

What does an inference rule look like? Put extremely simply, an inference rule
\nconsists of a structural pattern<\/em> which says given a set of true
\nstatements that match the patterns, you can produce a new true statement.
\nFor example, a classic inference rule of propositional logic is (in an unfortunately awkward syntax, due to the limitations of HTML):<\/p>\n