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Neil deGrasse Tyson makes a bad philosopher

Dr. at the November 29, 2005 meeting of the NA...

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.

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12 Responses to “Neil deGrasse Tyson makes a bad philosopher”

  1. Internet Math Guy says:

    There’s also something very wrong in his complaint about labels as such.

    Surely, Mr Tyson thinks that people are arrangements of smaller particles and that you could (theoretically) describe their interactions mathematically. I mean, I’m just basing this on him being a scientist, but it seems a fair presumption.

    Mathematics is just the application of reasoning using labels to represent inclusion in to a group and deriving consequences from membership (or alternatively, specialized memberships from multiple general memberships incident on a single thing – that multiple labels correctly apply, so we can make a new and accurate label).

    If people are mathematical, then Mr Tyson literally disbelieves his own point: labels are a legitimate way to reason about people – that is, which groups they belong to is a legitimate way to reason about them – as long as you’re using the actual properties for group membership.

    The solution to the bad reasoning is not to launch an assault on the use of labels in reason, as such, but rather to teach people how to actually use them and stop making bad inferences based on them. Which is what he really objected to.

    I just feel, that in this whole video, he takes exactly the opposite of his usual stance: spreading ignorance and sloppy thinking on a topic.

    • Thanks for the comment. Your points seem reasonable, but correct me if I’m wrong: you seem to be responding to his original reluctance of describing himself as an atheist, whereas I was complaining about him using his own poor understanding of philosophy as a basis for critiquing philosophers.

      • Internet Math Guy says:

        I was actually lamenting that as part of describing himself as an atheist, he butchered math, for about the same reasons he did philosophy in his reply.

        It seemed topical enough to add in; sorry if that’s not the case. (And I felt included by his reference to logicians, since this part of mathematics has a great overlap with logic. The question of how reasoning works is in both domains, even if they use slightly different terminology to describe their answers.)

        • Internet Math Guy says:

          Not an atheist*

        • No need to apologise. I was just making sure I understood you correctly. And I agree it’s topical. You’re also absolutely right that there’s an overlap between logicians and mathematicians. It’s practically the same thing, really.

        • Saying “you can’t prove a negative” in logic is a bit like saying “you can’t use calculus to arrive at a negative result” in mathematics.

    • John Morales says:

      Yes, the law of non-contradiction* is a classic theorem in propositional logic, but in this case there are implicit assumptions in the claim that a negative can’t be proven.

      This issue is closely related to the burden of proof — specifically, in those cases where an existence claim implies evidence should be available yet such cannot be adduced, the burden of proof falls onto the claimant rather than the proposer.

      Consider, for example, Russell’s Teapot — a canonical example where absence of evidence doesn’t disprove the claim — in comparison to Philolaus’ Antichthon, for which the absence of evidence does disprove the claim.

      (In short, where evidence is to be expected by the very nature of an existence claim, the absence of such evidence is indeed evidence of the non-existence of that which is claimed)

      * Perhaps you are familiar with the principle of explosion, too.

      • What you said is completely correct. And yes, I am familiar with the principle of explosion. It’s a side-effect (so to speak) of validity. An argument is valid iff its conclusion cannot be false while its premises are true without incurring contradiction. However, that entails that arguments with contradicting premises are always valid simply because any conclusion with any truth-value will incur a contradiction. This lets you validly (albeit not soundly) deduce anything. Hence ‘explosion.’ If a contradiction is true, everything is true.

        • Tom says:

          Strictly speaking it’s only a “side-effect” (as you put it) of Classical validity. There are plenty of paraconsistent logics in which the principle of explosion doesn’t hold, yet all have working notions of validity and logical inference.

          Nice point on the article, however. Philosophers do say some stupid things, but usually not what scientists accuse them of.

  2. Matt says:

    When folk say “you can’t prove a negative”, what they mean is “you can’t prove an unbound negative”.

    However, there is only a single statement that is truly unbounded, that being that X “has never, does not, and will never” Y “anywhere in the universe”.

    For example: unicorns “have never, do not, and will never” exist “anywhere in the universe”, or in folk-speak, “unicorns do not exist”.

    Only by leaving time and space unbound is any negative unprovable in principle, but most are unprovable in practice. The looser the time/space binding, the more in-practice provable the statement becomes.

    So “there are now unicorns on Earth this year” may be in-practice unprovable, but is eminently more provable than “there have never been any unicorns in the Milky Way galaxy”. In the other direction “there are no unicorns in this room right now” becomes easily provable.

    Note that even the unbound state of non-specific time and position are not certainly in-principlly unprovable: like everything, that depends entirely on metaphysics. Think of what an MWI version of quantum mechanics would do.

    • Surely you mean that unbound negatives are empirically unprovable? We could still prove that unicorns have never, do not, and never will exist if we conclude it validly from premises we agree upon. If, for instance, we could show that unicorns are self-contradictory, and we agree on the premise that nothing self-contradictory has ever, does not, and will never exist, then…well, you see where I’m going.

      Thanks for the comment.

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