Willard spotted this in the New York Times and asked me to pass it along for your consideration:

This is as good (or bad) as it gets, the closest thing to causation and a smoking gun that we will see. (To prove “scientific” causality you’d have to completely control the diets of thousands of people for decades. It’s as technically impossible as “proving” climate change or football-related head injuries or, for that matter, tobacco-caused cancers.) And just as tobacco companies fought, ignored, lied and obfuscated in the ’60s (and, indeed, through the ’90s), the pushers of sugar will do the same now.

I think it over-reacts a bit, but it’s germane. The notion of “proof” is seriously misplaced in public discourse. “Proof” is a property of mathematics, not of science. You can only prove things about your models.

I used to feel that way about "proof."

But don't we have a useful colloquial notion of "proof" in public discourse (as in, say, "burden of proof" or "prove you can do it!")?

"Prove" in the colloquial sense of "demonstrate to someone's satisfaction."

“If you ask me as a person, do I think the Russian heat wave has to do with climate change, the answer is yes,” said Gavin Schmidt, a climate researcher with NASA in New York. “If you ask me as a scientist whether I have proved it, the answer is no — at least not yet.” (August 2010)

http://www.nytimes.com/2010/08/15/science/earth/15climate.html?_r=0

I'm interested how your headline refers to: http://en.wikipedia.org/wiki/Alcohol_proof and

http://en.wikipedia.org/wiki/Denial_of_Peter

I mean, one can use 100% proof in science, though it's obsolete and likely inefficient regarding the intended use of 100% alcohol (extracting DNA), but I can't understand how the other one relates to the issue at hand. No offense intended.

The problem with these kind of discussions is that "proof" is simply a word. Words are things which evolve in their meaning and are also transferred into new contexts, so you can get separate evolutionary paths for the same word.

For example, the etymologically- equivalent verb for 'to prove' in Spanish is 'probar' which is literally translated as 'to try', 'to test' or

'to probe'. If you wanted to try on clothes in a Spanish store you would enter los probadores, which literally would be something like 'The proving rooms'. Maybe some would disagree but I doubt many Spanish people think they have mathematically proven the correctness of their clothing.I think there's enough room in the word to allow a distinction between scientific proof and mathematical proof, and a number of other forms of proof. Of course, there's also room for confusion concerning this distinction, especially in an area such as climate change where some people seem to crave confusion.

These are fair enough answers, but they aren't bulletproof. When someone who doesn't want to believe "X" demands proof of said "X" in belligerent tones, you can be pretty sure that whatever you come up with will not be seen as a proof.

Heck, I suppose a sufficiently talented denier could deny Pythagoras.

Prior to presenting information you could ask what they mean by "proof" - what standards would they adopt for judging whether or not "X" could be considered proven.

They might return a non-answer, in which case they can be dismissed as a troll. They might give an answer, and you can judge their standards against various general items of scientific "knowledge", and whether those are proven according to the commenter's standards - i.e. are the standards reasonable?

Mathematical proofs are not what they seem to be either:

> Some understanding of the notion of proof is necessary for any mathematician, if for nothing else, then at least for the communicability of mathematical results: publication rests on the understanding that proofs can be made as explicit as to be routinely checkable for correctness. However, proof theory has so far not become a practical tool for the working mathematician; the applications in mathematics have been rather isolated cases. Recent work on formalizing mathematical proofs with computerized systems, called proof editors, may gradually change this picture.

http://plato.stanford.edu/entries/proof-theory-development/

Coincidentally, I discovered how Mark Bittman recycles spring-fold pan used for cakes:

http://www.youtube.com/watch?v=W7Yh6R0wvyU

And for good measures, notice how Mark Bittman and Jamie Oliver sell the incentives to learn cooking at the end of this video:

http://www.youtube.com/watch?v=AmY3A_BzBWk

Seems that Mark Hoofnagle is unimpressed:

> Bittman has actually just said “obesity doesn’t cause diabetes”, and now has proven himself a deluded fool.

http://scienceblogs.com/denialism/2013/02/28/no-its-not-the-sugar-bittman-and-motherjones-have-overinterpreted-another-study

Yet another blogger with an attitude [1].

Reading Hoofnagle's post makes me predict the creation of a new website: dietaudit.org.

[1] http://neverendingaudit.tumblr.com/post/12239577107

Good suggestions, however it is best in careful work to restrict 'proof' to deductive logic (and by extension, mathematics). There are exceptions; for example the court will explain to the jury the standard of legal proof required.

"de Nier's Last Theorem"

-- by Horatio Algeranon

I have discovered

A marvelous proof

Global warming is bunk,

A mammoth goof!

But alas, this blog

Is simply too small

To contain the proof

So... that is all.

— Pierre de Nier

Marvelous.

David,

That might work for your own case, but I don't think we should expect the word "proof" to be used in the field of logic alone.

***

In the public discourse, arguments are sometimes seen as a law-abiding process. If we believe the work of Stephen Toulmin, rationality in general can be modelled that way. So the notion of proof is here to stay.

Even if we would not use the word "proof", we use other very strong concepts. Take causality, which has surfaced in Bittman's op-ed and in Hoofnagle's post. Bittman talks for instance about the Bradford Hill criteria:

> The study controlled for poverty, urbanization, aging, obesity and physical activity. It controlled for other foods and total calories. In short, it controlled for everything controllable, and it satisfied the longstanding “Bradford Hill” criteria for what’s called medical inference of causation by linking dose (the more sugar that’s available, the more occurrences of diabetes); duration (if sugar is available longer, the prevalence of diabetes increases); directionality (not only does diabetes increase with more sugar, it decreases with less sugar); and precedence (diabetics don’t start consuming more sugar; people who consume more sugar are more likely to become diabetics).

http://opinionator.blogs.nytimes.com/2013/02/27/its-the-sugar-folks/

Bittman refers to this resource for the concept, which I find quite interesting:

http://changingminds.org/disciplines/argument/types_reasoning/bradford_hill.htm

I'm not sure the study satisfied this criteria. The only concept I found was Granger-causality:

> e also performed Granger-causality tests, which use the temporal nature of the data to test whether high sugar availability preceded an increase in diabetes (“precedence”) or whether high diabetes prevalence preceded high sugar availability.

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0057873

This ain't bad, since climate science might have a tough time living up to this standard. But it's only orthogonal to the Bradford Hill. Worse, and more to the point, a population study can't claim to have real causality unless there's a very good story at the individual level. This story, in our case, is quite contentious. Even worse, it might be unethical to even establish such stronger causal relationship!

Let's look at it this empirically. I went on that thread to tell Hoffnagle that "obesity causes diabetes" does not sound right. First, it presumes causal *states*, wherewas in "smoking causes cancer", smoking is an *activity*. Second, obesity is a concept that is defined by the BMI, which makes sense only at the population level, a level where causality is quite abstract, to say the least. And I got dissed.

willard --- It is quite tedious to establish in each and every case the standard or method of 'proof' that is to obtain. This is often conflated with the 'weight of the evidence'; certainly so in court cases. But in science one should really be careful not to do that.