Talk:Proof (truth)/Archive 2

Archive 1

Archive 2

Dab page

I have moved this discussion to Talk:Proof. Everybody who has taken part in the discussion here is strongly encouraged to check it out there! —Toby Bartels (talk) 02:38, 10 July 2010 (UTC)

It occurs to me that the opinions that came in on my proposal for a different way of treating the dab page for Proof were initially in favor, but that that was back when the question was in this talk page (the one for Proof (truth)). Those opinions were as follows.

Strongly support this proposal. There are two basic meanings of "proof", as above. The OED agrees, by the way. False vacuum (talk) 22:10, 9 July 2010 (UTC)

Support but let us not give the Overdosed Edict of the Dons too much control over things. History2007 (talk) 22:18, 9 July 2010 (UTC)

But then Radagast3 and Toby Bartels objected and Toby moved the whole discussion to the talk page for Proof. When I asked what policy on dab pages I'd violated Radagast3 answered, "We have policies on dab pages: both Gandalf61 and I are maintaining the original structure of Proof" and explained that dab pages shouldn't have dab pages.

While I'm fine with their maintaining the dab page, it seemed to me everyone could be accommodated simply by renaming Proof (truth) and Proof to respectively Proof and Proof (disambiguation). With that formulation of my original proposal, the question boils down to which of these two pages should be the primary one for "Proof" and therefore does not need qualification. The problem with moving the discussion to the article that already has that benefit, namely the dab page, is that it biases the discussion to favor the status quo, because users of the dab page are more likely to visit its talk page than users of this page.

To even things up a bit, for the benefit of visitors to this talk page who might not realize there is a question relevant to them at Talk:Proof (since all details of the question were moved out of this page), do you have any opinion either way on whether to make the dab page or this article the primary topic for "Proof"? The dab page would be the logical choice if there is no clearly leading candidate among the topics on the dab page. The examples of Straw, Drill, Count etc. appear at the end of the section Talk:Proof#Reorganisation to illustrate how this sort of thing has been handled elsewhere. --Vaughan Pratt (talk) 23:27, 10 July 2010 (UTC)

I'm still keen to see this article become the primary one for "proof," given that neither alcoholic proof (an obsolete concept now superseded by alcohol by volume) nor proofreading seem as central, and the other meanings of "proof" are rarely encountered. Do people still think these other meanings are sufficient reason not to make this article the primary topic for "Proof"? --Vaughan Pratt (talk) 17:13, 4 September 2010 (UTC)

Yes, an article about the general concept of proof is certainly what should be found at proof. I have less sympathy than some for the idea that the primary purpose of an online encyclopedia should be to minimise the number of clicks and amount of reading required to get to the Proof (rapper) page. False vacuum (talk) 18:43, 4 September 2010 (UTC)

In fact, I hold the heretical view that it's good if people accidentally learn things—especially important things. And apparently I'm not afraid to admit it! Well, I am pseudonymous. ...I'm also very tired. False vacuum (talk) 19:15, 4 September 2010 (UTC)

Time for a nap?  :) --Vaughan Pratt (talk) 07:39, 12 September 2010 (UTC)

RfC: Perlocutionary speech acts

Should the article claim that a proof qua performative utterance is "a perlocutionary speech act intended to persuade a hearer or reader of the truth of a proposition" or "a perlocutionary speech act which persuades a hearer or reader of the truth of a proposition"? The criterion of being "intended to persuade" does not seem sufficient; do we want to say that e.g. an incompetent lie could qualify as a "proof"? On the other hand, "which persuades" may be too strong a criterion; I agree with User:History2007 that "a proof may be presented, but may not persuade, even if correct", but I'm not sure this objection uses the same sense of "proof" as the "performative speech act" one. I'm actually not sure I believe that any perlocutionary speech act qualifies as a proof. This is perhaps an idiosyncrasy of my own, however; I should like to retain distinctions between proofs and such things as e.g. successful convincings. ...Unfortunately, Google can't find the word "proof" in How to Do Things With Words. So, um. Comments? False vacuum (talk) 01:11, 2 September 2010 (UTC)

In my view a "general definition" of proof is far more complicated than the simple treatment within this article has even approached. This is a mathematician's over-simplified view of the real world. So just changing that part will be a small band-aid on a terminal patient, which most physicians have abandoned. Not worth the debate in my view. History2007 (talk) 04:26, 2 September 2010 (UTC)

Hmm. For what it's worth, I don't think the general concept of proof is all that complicated: it's basically just a demonstration that should convince an idealised reasoner, although there's lots of scope for making that vague notion more precise in various directions. Anyway, it would be fun to have that conversation, but this one is just about what the perlocutionary concept of proof is (if there even is one). False vacuum (talk) 03:11, 4 September 2010 (UTC)

Question 1: Are you even suggesting that the presentation here approaches adequacy? This page does not even include the word "inexact", and is written with a 2 valued mindset. So there is a long way to go - and that is just a minor starter. Above, I suggested a test drive: the "formal and informal proofs" provided by David X. Li's work to convince people as test cases:

What type was the proof that the Gaussian copula is mathematically correct? What type was the proof that it was applicable? What type was the informal proof that people should bet money on it? How is the legal proof going to work in court? How will the lawyers prove their fees were reasonable, while holding back their laughter?

As you see there are different types of proofs therein. Would you like to handle that and present an analysis for us here?

And how does your definition handle the 12 "proofs" (or shall I say 120) as to who did JFK? Again, one can not discuss proof without establishing the concept of "truth" first, and in the non-mathematical world, truth can be a slippery item. Now, in your definition the question of who decides "should" is missing. As stated above, arguments or proofs about the value of Renminbi that "should" be accepted in the US would be immediately rejected in China and result in the "re-education" of the proof provider. SO teh should makes that definition as vague. How does one measure "should"? As for Perlocutionary act (an article in even more need of an ambulance than this one) they just deal with "words". Words are just a part of a proof in the real world - tone, context, distraction, authority, etc. all have an impact.

So one needs to define truth first, before defining proof. Of course, the presence of an Ultimate Truth Authority or a Formal Truth Authority within a region of the world does make a difference to what truth is, but that is a local phenomenon in many cases. History2007 (talk) 04:18, 4 September 2010 (UTC)

Let me take issue with several things here. First, I disagree that the article was "written with a 2 valued mindset." I wrote the original article from a Heyting algebra or intuitionistic point of view, and no editor in the meantime has added anything to suggest that truth is 2-valued or even Boolean, or that the law of excluded middle must be accepted in every proof (though there is no harm taking it as an axiom provided one makes it clear one is doing so).

Second, perhaps the concept of "encyclopedic coverage" is being taken too literally here. Every subject can be developed further, hence any finite treatment of it must stop somewhere. No one is saying that the present article is now complete, so pointing out that it is not is a strawman argument.

Regarding truth, if that must be defined before defining proof, then "sufficient" must be defined before as well, along with "argument" and "evidence." Insisting on that sort of thing when people already have their own reasonably reliable intuitions about the meanings of those concepts makes the article unreasonably unwieldy. --Vaughan Pratt (talk) 16:48, 4 September 2010 (UTC)

Addressing the original question of this section, I wrote "intended to persuade" because that's how proofs are written or otherwise presented. However it is very reasonable to argue that a proof found unpersuasive by its audience is not much of a proof, just as someone who fires into a crowd with intent to kill but hits no one is not much of a killer. Would replacing "a perlocutionary speech act intended to persuade" by "a persuasive perlocutionary speech act" improve matters? --Vaughan Pratt (talk) 17:01, 4 September 2010 (UTC)

I like that. It's a little more ambiguous, but 'persuasiveness' could be taken as just the property in virtue of which the speech act in question is a proof; certainly it isn't a proof in virtue of either the speaker's intention or the effect on the hearer (at least, on any particular hearer). That's my intuition, anyway. I've written some more below; it started as a response directly to History2007. False vacuum (talk) 18:35, 4 September 2010 (UTC)

Since nobody else has done it, I've made another try at fixing that sentence. I still regard the original question as somewhat open, however. False vacuum (talk) 14:17, 5 September 2010 (UTC)

Okay. I'll take a break from battling the forces of darkness over at Unruh temperature (now that it probably won't be deleted) and indulge myself with this. For History2007 and hypothetical others sharing a similar orientation, here's what I think:

• On whether the article even begins to be adequate: Well, it's an overview, not a detailed treatment of everything there is to say about the word 'proof' (even in its 'truth-related' senses only)—there are individual articles for that—but, yeah, I think it adequately conveys the basic idea. There's more that could be said, but nothing that makes what's already there wrong, not even slightly. In particular, claims that e.g. arbitrary resources might be required to specify what constitutes "sufficient evidence or argument" in general or in any or all specific cases detract not one whit, in themselves, from the viability of that definition.

• On two-valuedness, fuzziness, etc.: I'll skip that for the moment. But eventually there should be good intuitive explanations of such things as the difference between ambiguity and uncertainty, and the proper use of probability and Bayes' rule in epistemology; Heyting algebras and the topos-theoretic picture are nice too, though. And modal logics! But, clarity first.

• On History2007's various specific examples: These are all about convincing, not proof. I'm getting the sense that History2007 and I have divergent intuitions about what the (natural-language) word 'proof' means, after all. People believe all sorts of things; to me, it sounds clearly wrong to say that "P was proved to X" when all that is meant is "X was convinced of P". Those two constructions refer to distinct situations, and the difference between them is precisely this matter of truth. P has to be true in the first case; in the second, it doesn't matter.

This is wrong. I wasn't paying enough attention here. The difference between them is not merely the truth of P, but also that the convincing is in the former case, and in the latter case not, such as to be successful if and only if P is true. False vacuum (talk) 05:52, 6 September 2010 (UTC)

• On the supposed need to define truth: I don't see it. I mean, it has to be defined at some point, but no matter what it means, it factors out of this particular definition. "Sufficient evidence or argument for [some undefined property I'll look up later] of a proposition."

• On the supposed ambiguities in the concept of truth, and authorities making a difference to what truth is: the obvious first approximation to a response is this.

False vacuum (talk) 18:35, 4 September 2010 (UTC)

Well, I think the statement "I wrote the original article from a Heyting algebra or intuitionistic point of view" is proof of what I have said N times (with N getting very large), namely that this is a "mathematician's view" of proof, yet the article suggests the concepts used even apply to real world topics such as law and religion.

Regarding proof vs convincing, could you please provide an exact definition of the natural-language word 'proof' Vaccum? Does a lawyer prove things to a jury or convince the jury? Does a theologian prove things to a novice, or convince the novice? Did the risk analysts prove the safety of CDOs within a given risk margin or convince people about them? Did the convincing rely on mathematical proofs? Please provide examples of proof in law and religion as well. Thanks. History2007 (talk) 20:10, 4 September 2010 (UTC)

By the way, let us just look at our conversation, step back, then smile. We have 3 mathematicians talking with each other, and discussing if the presentation extends beyond "math land". Terms used include Heyting algebra, topos theory, etc. I rest my case. This is a mathematical article, discussed by mathematicians. We are deep in the middle of math-land here, far from a court room or the Holy Office. This discussion is pretty much like 3 Cardinals standing around a corner in the Vatican, discussing Islam, and debating if their joint mindset captures the subtleties of the Islamic viewpoint. It will not. They are far from Mecca. History2007 (talk) 20:26, 4 September 2010 (UTC)

I'm finding this discussion entertaining, but I believe it is also important. And I think it's particularly important to counter not only the idea that mathematicians, philosophers, or any kind of academic specialists are any less qualified to discuss matters outside their areas of speciality than anyone else (the denial of which should be utterly uncontroversial), but also the idea that mathematicians, scientists, and philosophers in particular do not, in fact, have special expertise concerning problems of epistemology, truth, and proof—even though such expertise can be useful and important outside of what are usually considered the sciences. That having been said, this conversation is of course open to everyone, and in fact I am probably not a mathematician sensu stricto. But my answer (informed by whatever expertise I may happen to possess) to History2007's questions above is that those are all instances of convincing but that in itself does not make them instances of proof. People can be convinced of things either implicitly or explicitly, and either with or without proof (for present purposes I'm going to completely avoid the issue of religious belief, or belief in belief). Psychology is complicated. Even mathematical psychology is complicated—there might be all sorts of factors contributing to the choices one makes as to which subjects and ideas to attend to, what derivations to perform, what problems to investigate, and in general what to learn; and this will profoundly affect what proofs one reads and understands, how one views various aspects of them, and of course what proofs one produces and how they proceed. But none of these psychological factors affect the validity of proofs in any way, and they have no implications for the nature of proof. The essential idea I'm arguing for here is precisely that there are objective standards for what qualifies as a proof, even if no-one knows what they are. And I am further arguing that this idea is in fact included in the natural-language sense of 'proof', which is, more or less, that (a) proof of P is "sufficient evidence or argument for the truth of P"; whatever P is, someone who believes P will perhaps believe that P has been "proved" or perhaps merely that it has been established as probably true (the latter being the more epistemologically-well-informed position, especially outside of mathematics [although it is important to understand that even though mathematical statements can follow with certainty from other mathematical statements, our knowledge that they do can never be absolutely certain]), and will have a more or less accurate understanding of what are good standards for proof of, or of what constitutes good evidence for, that particular proposition or sort of proposition—but no-one, or at least no-one sane, believes "the fact that I believe P constitutes proof of P".

Looking back over what I've written above, I notice that there is still a potential ambiguity as to whether I am arguing that proof of P is that which is sufficient to establish (the truth of) P with probability 1 or that which is sufficient to establish (the truth of) P with appropriately high probability. This is due to the absence of this subtle distinction from the understanding reflected in natural languages. Thus the appropriate formulation leaves off the probability-qualifier altogether: that which is sufficient to establish (the truth of) P. To comment a bit more on the philosophy: If, as is common in the mathematical case, a proof is conceived as a purely abstract object, then there is nothing to say about probabilities; the proof simply leads from premisses to conclusion (using whatever logic it uses), and epistemology only comes in in connection with verifying the proof. This verification process involves the usual sorts of defeasibility, which entail among other things that one can never achieve probability 1 that the proof is valid, i.e. that it conforms to whatever standard it is being held to—here we are ignoring the defeasibility of knowledge, understanding, and operational correctness of the standard itself; that involves further complications, but they can also be handled if necessary. The question of validity of the proof is—epistemically—distinct from the question of whether its conclusion is true; the criteria for validity of the proof are intended to be such that the conclusion of a valid proof is true, but these criteria are also the outcome of a defeasible (epistemic) process.

It's worth noting that the detailed, precise analysis of these matters—indeed, the science of epistemology itself—only becomes possible after one stops worrying about what truth is. False vacuum (talk) 14:02, 5 September 2010 (UTC)

Also, I meant to point out that all the references to specifically mathematical notions like Heyting algebras and topoi (on this talk page) are serving mainly to signal our expertise to each other (and anyone reading the talk page); in particular, I'm pretty sure Vaughan Pratt only meant that he didn't write the article in a way that presupposes two-valued logic (I certainly don't disagree). False vacuum (talk) 15:14, 5 September 2010 (UTC)

And if I weren't not an intuitionist, that wouldn't necessarily mean I agree. Fortunately, I am (not). False vacuum (talk) 15:48, 5 September 2010 (UTC)

Indeed. And I also wouldn't dispute that the bulk of the article was informed by mathematics, since I'm informed by mathematics and I wrote the bulk of the article. (But that would also prove that the article was informed by computer science, electrical engineering, and physics.)

What puzzles me however is the idea that when you convince somebody of P, you haven't necessarily proved P to their satisfaction. This seems to contradict the article's definition of "proof" as "sufficient evidence or argument for the truth of a proposition." Sufficient for whom? Does the article not say enough about the dependence of the notion of proof on the audience? An argument can be obvious to one hearer but not to another. --Vaughan Pratt (talk) 07:51, 12 September 2010 (UTC)

If I convince Sarah Palin of something, she may (or may not) believe I've proved it, but that doesn't mean I have. For that matter, 'convincing X that I've proved P' isn't the same as 'proving P to X's satisfaction'. That's why the definition isn't "sufficient evidence to convince an audience of the truth of a proposition", but just "sufficient evidence for the truth of a proposition". (I'm leaving out the 'or argument' since it's redundant.) I suggested at one point that the intuitive distinction between proof and mere convincing is that a proof is what would be sufficient to convince a suitably idealised reasoner, but of course this is vague. Everyone here agrees that there is a distinction between proof and convincing, right? False vacuum (talk) 14:56, 12 September 2010 (UTC)

Apology and Request for Someone to Fix This Mess

I just checked to see if there was anything going on here, and I discovered that my most recent comment and a large initial segment of the discussion on this page had mysteriously disappeared. Naturally I looked at the history, and the first thing I noticed was that my own last edit was what had supposedly removed most of the other content. Needless to say, I was rather horrified by this. It looks as though the damage was undone by User:History2007, by reverting that edit (that's why my comment disappeared). But then there are two more edits in the history with summaries that refer to archiving "old" threads, and the net result seems to be that they're gone again (leaving much of what remains impossible to make sense of). I'm not even seeing any links to archives. Can anyone fix this? Does anyone agree with me that that stuff shouldn't even be archived yet (let alone deleted)? Can anyone help me figure out how I screwed up the page? (I'm using Firefox 3.6.9 on Ubuntu, if that helps.) False vacuum (talk) 17:49, 16 September 2010 (UTC)

It's nothing you did, there is a bot that archives old topics when talk pages get too big. I placed an "Archive box" at the top of the page that contains a link to the archive. Roger (talk) 20:07, 16 September 2010 (UTC)

No no, I'm not that confused. But perhaps my explanation was less than clear. Two ostensibly separate things happened: (1) It seems that I, or rather some unfortunate conjunction of elements of the software on my computer, deleted most of this talk page a few days ago, and (2) by the time I discovered that this had occurred, it had further transpired that (User:History2007 had fixed it and then subsequently) User:Dodger67 (Roger) had invoked a bot to archive a smaller portion of the talk page, but neglected to create a link to that archive (which has now also been rectified), so that it still looked as though a large portion of the page was missing. (I did have the notion that there might have been some indirect connection between these two events; as improbable as it seems, I now realise there may not have been.) So my comment above was intended to explain that I didn't vandalize the talk page deliberately, for the benefit of anyone who saw it in that intermediate state or who examines the history; but it was also intended to request the repatriation of that material. Now that I see it has indeed been archived and linked to, I'll change that to a request that this unilateral (and non-obligatory) act of archiving be reversed (unless User:Vaughan Pratt, User:History2007, and others are content with the present situation). False vacuum (talk) 21:02, 16 September 2010 (UTC)

Oh I see! So the archive actually missed out a part that was accidentally deleted before. The best option would be to undo the archive then look into the history and recover the deleted content. Once that is done the Archive procedure can be re-instated. Archiving is not at the discression of an elite clique of editors (See WP:OWN), it is a standard practice across the entire Wikipedia, see Help:Archiving a talk page. This page has an unfortunate history of claiming exemption from the normal rules and procedures of Wikipedia - see the struggle it took to just get a few citations put in it. Roger (talk) 07:54, 17 September 2010 (UTC)

Your new interpretation is still wrong (in case anyone else is in doubt, there's nothing missing from the archive; I've probably checked at least twice now), you personally chose to archive the content in question (there being no policy which mandated such an act at that point—certainly not WP:OWN, which is completely irrelevant), and your various accusations are baseless and offensive. However, this isn't worth discussing any more. False vacuum (talk) 07:14, 19 September 2010 (UTC)

Let it be

Vacuum, There is no need for an apology, you clicked a wrong button, but the world has not ended. Just let it be and move on.

But as far as the article is concerned, I still see problems. Going back to law, the reliance on "evidence" as "legal proof" is not exactly right and assumes a tilt towards criminal law, rather than say commercial law cases. It also seems that the tone of both articles on Legal proof and this article is (quite understandably) informed by common law rather than Civil law (legal system). I agree with the "I am informed by mathematics" comment above, and I would also say that this article is more informed by common law than civil law for it was written with a US-law tone.

And again, to go back at real examples, just take a current case: As we type these during September 2010, there are attorneys out there constructing "legal proof"] whether Mark Hurd should join Oracle Corporation. Much of the "proofs" on both sides will rely on the peculiar features of California law (specially anti-competition issues) rather than Perry Mason-like evidence of a monogrammed handkerchief left at the HP boardroom. And please note that much of the debate will be about events in the future which have not taken place yet, e.g. Hurd's disclosure of specific competitive items to Oracle 3 month's from now. So there is no evidence for those yet. That is also a shortcoming of redirecting "Legal proof" to "evidence" in the first place.

So here both sides will present "arguments" in Hurd's case. Based on the definition here, is only one of them a proof? Is the difference between a proof and argument is whether the judge buys it? Or in some other societies (California excepted, of course) whether one buys the judge? Here a proof is distinguished from an argument by the decision of the judge. Hence any payments made to judges to influence them are actually part of the factors that influence if something is just a "legal argument" or a "legal proof". This is unlike logical proof where the existence of a path between two points is almost independent of human judgement.

Anyway, many cases of contract and commercial law, "legal proof" relies as much on digging up suitable sections of law than it does on finding evidence hidden in a desk drawer. And in many cases, "legal proofs" used in law of obligations cases in civil law may use technicalities that have little to do with evidence as such. So the legal proof part of this article is weak and narrow. History2007 (talk) 08:01, 17 September 2010 (UTC)

I appreciate this clarification, and will get back to you shortly (after I have time to do a bit of research). False vacuum (talk) 07:16, 19 September 2010 (UTC)