## Dealing with Idiots

I’ve lately come to remember why I don’t read or respond to mtraven, owner of the Omniorthogonal blog. In short: he’s a fool.

See this post and its associated comments. Consider particularly this bit:

*The essential difference between mathematics and the natural sciences is that theorems of mathematics can be proved, whereas theories of natural science can only be disproved. You would not say that mathematics was empirical if you understood the nature of proof.*

Both statements are wrong. Disproof is equivalent to proof of its negation; if it were not possible to prove statements about natural science, disproof would be equally impossible. If mathematical statements could not be disproven, they couldn’t be proven either.

‘Proof’ as it is meant in mathematics means that a stated derivation of an assertion has been generated through application of logical operation from more rudimentary operations, and this derivation has been evaluated as valid by analysis. It is fundamentally empirical.

As for ‘social construction’, see the Stanford Encyclopedia of Philosophy on the concept. mtraven is utterly and completely wrong about what it means to say that a thing is socially constructed. The Wikipedia entry on the subject is perfectly acceptable, although mtraven rejects it out of hand.

August, 2010 at 3:56 am

“I’ve lately come to remember why I don’t read or respond to mtraven”

Yet isn’t that just what you are doing in this very post?

Do you have any response to this critic of yours?

August, 2010 at 2:42 pm

I had previously made a note not to read or respond to him, but had forgotten why over time. After reading his post – and his responses to my points – I established a whole new set of reasons not to respond to him.

As for this post, it’s not so much a response to him as a critique of the stuff he says. It neither expects nor invites feedback on his part, and I would in fact prefer it if he did not.

Basically, I used a language shortcut because I didn’t feel like typing out a rigorous description of what I was doing. Sloppy, but commonly understood.

August, 2010 at 4:34 am

He is wrong to use the term “proof” only in its mathematical sense even when talking of the empirical sciences. However, you are at least as wrong in claiming that mathematics is empirical, when what you accurately describe as “proof” in mathematics is, quite simply,

notwhat empirical is. Empirical means using a trial and error method and going by experience.To illustrate the difference, you may be interested in the empirical and

shaggy-doggish “engineer’s proof” that all numbers are factors of

120:-

1 is a factor of 120.

2 is a factor of 120.

3 is a factor of 120.

4 is a factor of 120.

5 is a factor of 120.

6 is a factor of 120.

7 is a factor of 120 with a small experimental error…

It has been said that mathematics is an art used in the service of science. It is not a coincidence that the older universities (such as Cambridge, where I got my mathematics BA) do not give BScs in mathematics but BAs – it is an art, not a science.

August, 2010 at 2:45 pm

And that is precisely what is done with mathematical proofs. It’s just like any other experimental result – it’s just that the experiment is (generally) neurological in nature.

August, 2010 at 6:30 pm

The quote that melendwyr included was not written by me, but my an anonymous commenter on my blog. Presumably we can get attributions straight if nothing else.

I’m actually closer than not to melendwyr’s position on mathematics.

Re social construction, he is simply stuck on a definition of it that makes it de facto ridiculous. But the proponents of it obviously don’t think they are being ridiculous, so therefore they mean something else. I suggest reading the first chapter of Latour’s book Pandora’s Hope where he addresses these misunderstandings directly.

August, 2010 at 10:13 pm

– mtraven

You’ve made your position clear. Now go elsewhere.

August, 2010 at 10:16 pm

But the proponents of it obviously don’t think they are being ridiculous, so therefore they mean something else.

See? And that’s what he puts forward as ‘logic’.

People who believe ridiculous things generally don’t believe that their beliefs are ridiculous. That has no bearing on whether they are or not.

August, 2010 at 9:50 pm

And also for your consideration:

“In studying a philosopher, the right attitude is neither reverence nor contempt, but first a kind of hypothetical sympathy, until it is possible to know what it feels like to believe in his theories, and only then a revival of the critical attitude, which should resemble, as far as possible, the state of mind of a person abandoning opinions which he has hitherto held…. Two things are to be remembered: that a man whose opinions and theories are worth studying may be presumed to have had some intelligence, but that no man is likely to have arrived at complete and final truth on any subject whatever. When an intelligent man expresses a view which seems to us obviously absurd, we should not attempt to prove that it is somehow true, but we should try to understand how it ever came to seem true. This exercise of historical and psychological imagination at once enlarges the scope of our thinking, and helps us to realize how foolish many of our own cherished prejudices will seem to an age which has a different temper of mind.”

— Bertrand Russell, A History of Western Philosophy

I’ve been saying pretty much the same thing for years, but just found this quote from Russell, who I’m guessing carries more weight.

August, 2010 at 11:11 pm

OK, I’m gone. You have some nerve coming onto my blog to argue, then retreating to your own to insult me, and expecting me to be silent. But I guess I can survive.

One thing I like about Latour is how much he infuriates the mediocre. Probably that’s a character flaw.

August, 2010 at 9:47 pm

I see no reason to give idiots an opportunity to censor me.

Don’t let the door hit you on the way out.

December, 2010 at 9:21 pm

According to Kant, mathematics and logic are analytical and a priori, whereas natural sciences are synthetic and a posteriori. That is what the passage you quoted is saying. Mathematical proof does not require the gathering of evidence, experimentation, or observation, i.e., empirical methods. It refers back to premises and determines the validity of the conclusion drawn from them by the application of first principles. These are not empirical methods.

December, 2010 at 9:27 pm

Wrong, wrong, wrong.

If you construct a mathematical model of the weather, and then refer to it to determine whether it will likely rain tomorrow, that’s theoretical. But to find out what the model says, you have to gather evidence, experiment, and observe – to determine what IT is. This is empirical.

Every use of theory is founded upon empiricism, without exception. To determine whether an assertion follows from premises, we make observations and predictions; we submit data to parts of our minds, observe the results, and draw conclusions about other instances of the query – both across time, in future interrogations of ourselves, and across individuals, if they will agree.

December, 2010 at 9:49 pm

When we speak of mathematical proof, we are BIT speaking about mathematical models of weather. That’s merely an application of mathematics to the physical sciences in a manner familiar since the time of Newton. It is not pure mathematics, which is entirely analytic and aprioristic.

What is meant by mathematical proof is, for example, how we demonstrate the 47th problem of Euclid by reference solely to Euclidean postulates and axioms. No evidence-gathering or experimentation is necessary. And, once proved, such a theorem is not susceptible of disproof.

The physical sciences obviously differ. In them, a theory is true only until further notice. The Ptolemaic theory of the universe, the phlogiston theory of Becher and Stahl, and the existence of a fluid medium called aether as necessary to the propagation of light waves were all once considered valid theories, and all have now been disproved.

It might bolster your argument if you could disprove a theorem of Euclid’s by experiment or observation in the same manner. I suspect we shall wait till the Greek kalends before you do so.

December, 2010 at 10:16 pm

Wrong, and wrong.

Each and every act of computation performed to determine whether the conclusion follows from the arguments preceding it constitutes an experiment; each observation of the result of said computations constitutes gathering evidence.

And every time we generate an evaluation of the theorem, we’re checking to see if it’s valid, which means we can potentially be required to discard it as invalid. Humans make errors, such errors can and have been found in assertions previously considered valid, and the underlying logic behind the theorem can change.

The fact that said logic is so stable that no exception has ever been found is irrelevant. Just because the sun has always risen, it doesn’t follow that it will always do so. Deductive logic is just inductive logic with the uncertainty filed down.