Dr. at the November 29, 2005 meeting of the NASA Advisory Council, in Washington, D.C. (Photo credit: Wikipedia)

A couple of days ago there was a minor kerfuffle between Hemant Mehta, the Friendly Atheist, and Neil daGrasse Tyson, the equally friendly astrophysicist, over the correct usage of the term ‘atheist.’ It wasn’t very interesting to me. Neil can call or refrain from calling himself whatever he wants. To me anyone who lacks a belief in gods is an atheist, but that’s how I choose to use the word. Some people use it differently. That’s fine. If they object to be called an atheist, I will respect their wishes even if I personally happen to think they are one. I share Neil’s disdain for arguing semantics. If both parties have clearly defined their terms from the outset, then it shouldn’t be a problem. Good on you, Neil, for wanting to focus on real issues instead of trivial semantics.

However, that is not what woke me from my slumber. Rather, it was the following paragraph from Neil deGrasse Tyson’s elaboration in the comments after Hemant’s blog-post:

The concept that you can’t prove a negative is often applied to “you can’t prove God does not exist”.  This notion, while strictly true in logic and philosophy, is simply rubbish to the practicing scientists. That’s why logicians and philosophers, in modern times, make bad scientists.  We prove negatives all the time.

I know it might seem petty and needlessly nitpicky of me to criticise a man as awesome as Neil for something he probably wrote in all due haste in a comment to a blog-post – hey, I’ll confess that I’m not always as lucid and deliberated in internet communications as I could be – but Neil managed to touch upon no less than two of my pet peeves with pin-point precision: namely the condescension of many academics towards philosophers and the oft-repeated misapprehension that ‘philosophy’ or ‘logic’ somehow prohibits the proving of a negative. What follows is the response I made to Neil in the comments:

I’m sorry, Neil. I’m a big fan. I really am. But rather than supporting that philosophers make bad scientists, that paragraph supports that scientists such as yourself make bad philosophers. I’m actually astounded that a person like you, who usually has such an immense depth of knowledge would say something so profoundly ignorant of philosophy and logic.

First of all, qualifications out of the way: I’m almost done with my MA in philosophy, but any other philosopher worth their salt will also tell you what I’m about to tell you: no, it’s decisively not true – strictly or otherwise – in either logic or philosophy that you can’t prove a negative. That’s complete nonsense. In fact, if that were the case, how on Earth would you know, since “you can’t prove a negative” is itself a negative statement? Not to mention that any positive statement is a negative statement of a negative statement. ‘(p & not-q)’ is truth-functionally equivalent to not-not-(p & not-q) which again is truth-functionally equivalent to not-not-not-not-(p & not-not-not-q) and so on. There is no profound logical difference between a positive and a negative proposition, which lets you philosophically prove the former but inhibits you from proving the latter.

There are various forms of philosophical argumentation, but let’s go with simple deduction. A deductive argument is valid if and only if the conjunction between its premises and the negation of its conclusion results in a logical contradiction. That is, the concept of validity is itself founded upon the law of non-contradiction, which is the negative statement that “it’s not the case that p and not-p.” Which, wouldn’t you know it, can be proven formally as follows:

1) (A & ~A) [Proposition]

2) A [Conjunction elimination from 1]

3) ~A [Conjunction elimination from 1]

4) ~(A & ~A) [Reductio, 1 - 3]

You’re a great man, Neil. But, please, in the future refrain from saying that philosophers are bad scientists simply because you don’t understand philosophy.

Yours truly,
Heini Reinert

Post-edit: I should have mentioned that I borrowed my law of non-contradiction argument from here, since I didn’t feel like reinventing the wheel.