Talk:Proof (truth)/Archive 1

Archive 1

Archive 2

VP

This is the "truth" half of my split of the old dab page for proof into two main parts, the other being Proof (quality). --Vaughan Pratt (talk) 06:26, 6 July 2010 (UTC)

Sources needed

The entire article is unsourced. Sources are required in order to comply with verifiability policy and to demonstrate that the article does not constitute original research. The tag should not be removed until the issue is addressed. --Moonriddengirl ^(talk) 18:10, 6 July 2010 (UTC)

I think you're misreading WP:V, which says "in practice not everything need actually be attributed. This policy requires that anything challenged or likely to be challenged, including all quotations, be attributed to a reliable source in the form of an inline citation, and that the source directly support the material in question." Until you challenge something there is nothing that needs sourcing in this article, and therefore no issues remaining to be addressed. --Vaughan Pratt (talk) 18:51, 6 July 2010 (UTC)

WP:V also says:

Articles should be based on reliable, third-party (independent), published sources with a reputation for fact-checking and accuracy; this avoids plagiarism, copyright violations, and unverifiable claims being added to articles. Sources should directly support the material as it is presented in an article, and should be appropriate to the claims made.

WP:NOR says:

This means that all material added to articles must be attributable to a reliable published source, even if not actually attributed.... To demonstrate that you are not adding original research, you must be able to cite reliable published sources that are directly related to the topic of the article, and that directly support the material as presented.

and:

Research that consists of collecting and organizing material from existing sources within the provisions of this and other content policies is fundamental to writing an encyclopedia. The best practice is to write articles by researching the most reliable sources on the topic and summarizing what they say in your own words, with each statement in the article attributable to a source that makes that statement explicitly.

I am requesting that you cite your sources accordingly to demonstrate so that our readers may verify that the material is reliable and that it is not original research. This is good practice on Wikipedia. If you want to discuss the policy in principle - including when it is appropriate to remove a request for sources from an article that has none - we should take that up at a central discussion point. --Moonriddengirl ^(talk) 19:24, 6 July 2010 (UTC)

But sources for what? There is no such thing as a source for a whole article, there are only sources for claims made within an article. What claim or fact in the article do you feel could turn out to be false, or to fall under the heading of "original research," or any other ground for challenge? Citing again from the lead in WP:V (italics mine), "Anything that requires but lacks a source may be removed, and unsourced contentious material about living persons must be removed immediately." I don't see anything at all controversial in the article that would require a source. Apparently you do, but what is it (or them)? Help me here. --Vaughan Pratt (talk) 20:45, 6 July 2010 (UTC)

Incidentally for perspective take a look at the section Dialog#Modern_period_to_the_present, which is of a size comparable to my whole article, and compare them for number of assertions that might turn out to be false. Then compare them for number of sources. If that section is acceptably sourced then mine must certainly be. --Vaughan Pratt (talk) 20:57, 6 July 2010 (UTC)

(edit conflict) All right, what's the source for your definition? Who says that the role of proof in epistemology, jurisprudence, and theology is played by the notion of justification? Where can we go to confirm that the ancient Greeks took the shadow cast on the moon by the earth during a lunar eclipse as proof of the proposition that the earth was round? Who says that there is no absolute threshold of sufficiency at which evidence becomes proof? Where can readers verify that "Formal logic provides the main exception, where the criteria for proofhood are ironclad and it is impermissible to defend any step in the reasoning as 'obvious.'"? Provide sources for these things, and it will no longer be true that the article is unsourced.

You have written an article which you may be very qualified to write, but our readers do not know this. One of the purposes of providing sources for articles is so that they can see that the content is based on something other than your own opinions or observations. Wikipedia is a tertiary source, not a primary one. We are here to "summarize secondary sources". We need to identify the secondary sources that we are summarizing.

As to your later note, see "other stuff exists". While drafted to address deletion debates, the principle applies: the condition of another article has no bearing on this. Nobody has said that article is perfect; however, I'll note that it includes "references" nevertheless. --Moonriddengirl ^(talk) 21:08, 6 July 2010 (UTC)

Ok, from your questions I see a couple of things I can tighten up, thanks for that. In general however it seems to me that any nonobvious facts about the various topics the article touches on are covered in the articles I link to, and I was unable to come up with any external sources that would be more helpful. Let me illustrate this in terms of your questions.

• What's the source for your definition? A glib answer would be http://dictionary.com, whose first entry for "proof" happens by chance to be essentially the one I gave. However it was not the source I used when I wrote the article, and I was actually pleasantly surprised that the dictionary had essentially my definition. The problem is that "proof" has a score of definitions, but there is a pattern to them in which some fall more naturally under "truth" and some under "quality" (and some arguably in between, for example proof as "an arithmetical operation serving to check the correctness of a calculation"). My definition was intended to serve as a convenient catch-all that accommodates all variants of the "truth" notion in order to give more structure to that portion of the original dab page for proof, so you can think of my article as a sort of cross between a dab page and a proper article (one reason why it's so short given the scope of the material covered). The vague requirement of sufficiency is essential here in order to accommodate all the variants that were on the original dab page, which vary widely in what they regard as sufficient and what forms evidence may take. As such my definition is neither true nor false but rather defines the scope of this article as an approach to tying parts of an earlier dab page together with some noncontroversial connective tissue. A lot of Wikipedia articles have benefited from having their editors find more coherent ways of packaging material that is not controversial (witness the many links) and therefore not in need of additional sourcing beyond that found within the components being packaged in this way. That said, I could certainly give http://dictionary.com as a source for my definition as being one of the many dictionary definitions of the word, but do Wikipedia readers need to be told where to look for dictionary definitions?
• Who says that the role of proof in epistemology, jurisprudence, and theology is played by the notion of justification? I was just going with the original dab page for proof, which listed the first two; I tended to agree with their inclusion even though I don't have a specific source in mind to defend it. Clicking on the link for justification takes you to a dab page the first three links of which take you to respectively epistemology, jurisprudence, and theology, each a huge subject whose practitioners would find your question as strange as "who says arithmetic is about numbers?" However now that you point it out I do see a problem with my links for epistemology, jurisprudence, and theology, which should instead take the reader directly to theory of justification, justification (jurisprudence), and justification (theology) respectively. I'll fix that, thanks for bringing it to my attention.
• Where can we go to confirm that the ancient Greeks took the shadow cast on the moon by the earth during a lunar eclipse as proof of the proposition that the earth was round? Nothing in the article depends on whether this is true or false, since even if false it still serves to illustrate the point of the statement it appears in, that proofs need not be verbal. If you prefer I can replace it with "Before Galileo people took the apparent motion of the Sun across the sky as proof that the Sun went round the Earth," or perhaps you have an even better example in mind, which I'd be happy to use. Bear in mind that Wikipedia's target audience is the well educated adult, for whom sourcing universally known and accepted facts should be unnecessary, especially when only serving as an illustration of something else.
• Who says that there is no absolute threshold of sufficiency at which evidence becomes proof? This should be self-evident to every well educated adult, but just in case I took the precaution of illustrating it with two familiar examples. Are you suggesting that this claim still might turn out to be false, these examples notwithstanding, and hence require a source to back it up? There's a limit to what's reasonable to question the truth of. While I have no idea where one would source such an obvious statement, I also can't imagine anyone seriously challenging its truth. It's not the sort of statement that should require sourcing.
• Where can readers verify that "Formal logic provides the main exception, where the criteria for proofhood are ironclad and it is impermissible to defend any step in the reasoning as 'obvious.'"? In the article formal logic linked to by that statement. However a better link might be formal proof, and I could elaborate on the statement by quoting "For a well-formed formula to qualify as part of a proof, it must be the result of applying a rule of the deductive apparatus of some formal system to the previous well-formed formulae in the proof sequence." from the lead of formal proof.

When links are used to propagate questionable information to other articles, they should be replaced with external sources to blunt accusations of circularity. However when they are used to develop a high-level topic hierarchically in terms of lower-level topics of a more fundamental nature, they are more convenient for the Wikipedia reader than external sources, and there is no risk of circularity as long as the hierarchy is respected.

Many thanks for your thoughtful comments, which have improved the article. --Vaughan Pratt (talk) 01:04, 7 July 2010 (UTC)

WP:NOR: "Wikipedia articles may not be used as tertiary sources in other Wikipedia articles, but are sometimes used as primary sources in articles about Wikipedia itself." "See also" links do not suffice. However, perhaps the articles you've linked to would provide sources that you might use. Adding reliable sources to meet Verifiability policy would be the improvement I suggest. If you don't want to, though, we can leave the tag; somebody will probably add them eventually. --Moonriddengirl ^(talk) 01:19, 7 July 2010 (UTC)

Fine by me. It's a true tag ("This article does not cite any references or sources"), whether or not they're needed. Maybe the tag should be phrased to allow for articles containing no material in need of sourcing (independently of whether this article is one). --Vaughan Pratt (talk) 01:31, 7 July 2010 (UTC)

That would be a question to raise at the appropriate community board, perhaps WT:V. --Moonriddengirl ^(talk) 01:33, 7 July 2010 (UTC)

Disambig page

Despite its new title, this "article" is clearly not about the concept of proof in logic. It reads like a verbose and rambling version of a disambiguation page. This made me wonder what was on the proof page - where I discovered that Vaughan Pratt (talk · contribs) had recently removed most of the disambig links from that page. I have restored the disambiguation page proof to its former, more complete, version, which I believe now makes this new page redundant. Gandalf61 (talk) 10:19, 7 July 2010 (UTC)

The new title is wrong. The article is about the first of the dictionary definitions for "proof" at dictionary.com, namely "sufficient evidence for the truth of a proposition." This notion arises in a number of contexts, of which logic is only one. Hence whatever Michael Hardy thought was the problem with "Proof (truth)" is only made worse by his renaming to "Proof (logic)". "Proof" with the meaning treated here is broader than that, but not so broad as to encompass for example proof spirit and galley proofs, making "Proof" on its own an inappropriate title. If "Proof (truth)" can be improved I'm all for that, but "Proof (logic)" is not an improvement.

The article does two things.

1. It lists the areas in which this notion of proof arises, gives the name used for the notion in each area (e.g. justification in epistemology, evidence in law), and gives links to articles on its use in each area.

2. It expands on the concept of "sufficient evidence" by making the obvious points that (a) evidence need not be verbal and (b) sufficiency is context-dependent, with examples of each point.

These two things are more appropriately done in an article on the broad notion of proof encompassed by its primary dictionary definition than in each of the articles targeting specific areas in which this notion of proof arises. At the same time it ties those area-dependent uses of "proof" together in a way that exposes and develops their common elements. The dab page by itself does not accomplish those things.

If the article is verbose and/or rambling then it should be tightened up, but I thought I'd gotten 1 and 2 reasonably tight already. Could you be more specific about what you mean by "verbose," and by "rambling?" --Vaughan Pratt (talk) 13:17, 7 July 2010 (UTC)

wikt:Verbose: "Abounding in words, containing more words than necessary".

wikt:Rambling: "A long meandering talk with no specific topic or direction".

This page lists a number of uses of the word "proof" in different contexts - logic, philosophy, rhetoric, jurisprudence - which are hardly connected, except by the word itself. They have few "common elements", as the very disjointed style of this page demonstrates. Your notion that the meanings of "proof" can be neatly divided into "truth" and "quality" appears to be your own invention, and is completely bogus - the concept of "proof" in logic and mathematics, for example, fits neither of your categories. A disambiguation page (like proof itself) should simply list articles that have similar names, with at most a short, one-sentence description of each, and let the reader choose which article they wish to read. Gandalf61 (talk) 13:47, 7 July 2010 (UTC)

The point of a dab page, I would have thought, is to collect the different meanings of a term in one place. The dictionary meaning of proof as sufficient evidence for the truth of a proposition is a single meaning and should therefore not need a dab page. You can say that the concept of "proof" in logic and mathematics is something other than "sufficient evidence for the truth of a proposition" but if this is what editors on Wikipedia generally believe I'd be happy to consult representative bodies of logicians and mathematicians to see if they agree.

Your statement that I came up with the division is contradicted by the original dab page, which already made that division (though obviously Proofing (baking technique) should have gone under "Various kinds of testing"). I merely noticed that the first ten items were not different meanings of proof but the same meaning, the dictionary meaning, arising in different settings. Ordinarily when this happens Wikipedia has an article on the general concept with links to its various specialized uses. That's what should have happened here but did not due to the failure of previous editors to recognize the commonality of meaning of "proof" here and instead treating them as unrelated meanings of the word "proof." The only genuine ambiguity is between the two uses of proof dealing respectively with proofs of facts vs. testing and measuring. I am not wedded to any given title for either of those two meanings, the more appropriate the better though as I said "Proof (logic)" doesn't seem at all appropriate. --Vaughan Pratt (talk) 17:45, 7 July 2010 (UTC)

There is no "commonality of meaning". Proof in mathematics is not based on "sufficient evidence" - it is based on logical deductions from axioms. It is an entirely different concept from proof in rhetoric, law and philospohy. "The unique feature that sets mathematics apart from other sciences, from philosophy, and indeed from all other forms of intellectual discourse, is the use of rigorous proof"; Stephen Krantz, The History and Concept of Mathematical Proof. And the concept of "truth" in mathematics is also entirely different from "truth" in law or philosophy. "Mathematical truths, if they exist, aren't a matter of experience. Our only access to them is through reasoned argument."; Richard Bornat "Proof and Disproof in Formal Logic". Gandalf61 (talk) 19:52, 7 July 2010 (UTC)

Ah, thank you, your quote from Krantz is a good source for the article's sentence Formal proof provides the main exception, where the criteria for proofhood are ironclad and it is impermissible to defend any step in the reasoning as "obvious". The only catch is that Krantz is really talking about formal logic here, and seems unaware that proofs as arising in mathematical practice invariably lack rigor and can only be said to be rigorous in the sense you and Krantz seem to have in mind by virtue of being potentially formalizable. This is an interesting and very important distinction between mathematics as a practical art and its idealization via formal logic.

Bornat's point about the provenance of evidence would be a good addition to the article, which currently says nothing about where evidence comes from. As it stands nothing in the article contradicts Bornat's point that mathematical evidence comes from postulates while other evidence comes from experience. But even though there is nothing inaccurate in the article in that regard the point is still well worth making in the article. --Vaughan Pratt (talk) 20:30, 7 July 2010 (UTC)

Incidentally you've rather messed up the structure of what I've put together here by removing the link to the article from the page Proof. I hope you won't mind if I put it back. And in view of the obvious inappropriateness of "Proof (logic)" as the title I'll also change that back, though if someone has a better suggestion please do implement it. --Vaughan Pratt (talk) 20:32, 7 July 2010 (UTC)

Good. We agree that "Proof (logic)" is the wrong title for this article, and that the concept of formal proof in mathematics and logic is different from the concept of evidence-based and persuasive proof in law, philosophy and rhetoric. I have moved the article to "Proof (informal)" and removed the irrelevant material about formal mathematical and logical proof - these concepts are covered in other articles. Gandalf61 (talk) 22:21, 7 July 2010 (UTC)

I'm sorry but I've given sound reasons to keep that material and you haven't. All you've done is quote sources that say the same thing in effect as the article does about mathematical and logic, namely that they set a higher standard of sufficiency, and that their evidence does not come from experience, which the article did not claim. So far you have quoted nothing that warrants that deletion. I don't believe it's appropriate--in fact I would say it was at least bad manners--to unilaterally delete material that is actively being debated merely because you happen to be on one side of that debate. --Vaughan Pratt (talk) 22:42, 7 July 2010 (UTC)

Moreover the article did not restrict itself either to formal proof (as implied by Michael Hardy's "Proof (logic)") or to informal proof. The notion of "sufficient evidence" does not distinguish between formal and informal argument, and the article is not about informal proof per se but about proof. Please either strengthen your argument so that it makes your point or revert your change (but don't use either logic or informal in the title, please). --Vaughan Pratt (talk) 22:45, 7 July 2010 (UTC)

Meanwhile I reverted the change myself so that others would have a chance to judge the original and draw their own conclusions. By all means re-delete it if and when a consensus in your favor has had a chance to form. --Vaughan Pratt (talk) 03:27, 8 July 2010 (UTC)

I think the problem here is that it is difficult for non-mathematicians to grasp the concept of mathematical evidence (which is error-free). Karl Popper has written extensively about this as well as Vienna Circle and other philosophers in the first half of twentieth century. Let me give two examples of sufficient evidence one in math and one in biology: to prove that there is a white raven, it is sufficient to find a white raven (and some evidence that that raven is white which is obvious here), and this white raven will be the sufficient evidence for the truth of "There is a white raven". Similar to this, to prove that "There is a natural number that is equal to sum of its proper factor" one only needs to come up with a number with this property and give the evidence showing that it is indeed equal to sum of its divisors (which will be just summing them up and comparing the sum with the number). In this sense the number 6 (together with "1,2,3 are the only proper divisors of 6" and "1+2+3=6") is a sufficient evidence for the truth of the mathematical sentence. I hope that it is clear up to here. Now, the problem in other sciences is that most of interesting propositions are universal, and therefore not affirmable (a proposition is affirmable if and only if its negation is refutable in Popper's sense), and as a result they almost never have sufficient evidence for truth of a proposition, i.e. most of arguments in other sciences give evidence for the truth of the proposition but not sufficient to establish its truth without error. Even physics which is one of the closet sciences to mathematics has this problem as history has shown that what is claimed to be truth about nature keeps changing. Vienna circle supported a positivist view which meant that any proposition which is not affirmable/verifiable is meaningless. Popper's solution was to allow refutable propositions as long as they are not refuted. To sum up, the dispute here seems to stem up out of impossibility of providing sufficient evidence to establish the truth of most of the propositions, which at the end results in arguments which are not proofs, while it is possible in mathematics to give those sufficient evidences. If we go to the level that other sciences are capable of providing sufficient evidence (affirmable propositions similar to the one I mentioned above) one can see that the notion of proof is the same for mathematics and other sciences. (Apologies if I diverged from what is being argued over here.) rdt (talk) 07:41, 8 July 2010 (UTC)

Obviously I agree with you here, and thank you for your support. However it may be worth noting that computer science has updated the notion of mathematical proof well beyond what the Vienna Circle and Popper had to work with. In particular interactive proof systems generalize traditional proof systems analogously to how alternating computation and probabilistic computation generalize nondeterministic computation. Probabilistic proof systems allow for the possibility of a very small but nonzero chance of incorrectly accepting an unsound proof or rejecting a sound one, in return for much less effort of checking. Hence even though we have not left the fictive realm of mathematics we have learned how to buy efficiency of proof by abandoning the perfection that was formerly the touchstone of mathematical proofhood. --Vaughan Pratt (talk) 08:09, 8 July 2010 (UTC)

Thank you. I did not have interactive/probabilistic proofs in my mind when I wrote the above comment, but now that you have mentioned them, I agree with you. It seems to me that they are closer to what is used in Law, so maybe there is also a similarity between these interactive/probabilistic notions of proofs and the notion of proof used in other sciences. Maybe the correspondence holds not only for affirmable propositions, but also for other propositions. rdt (talk) 05:19, 9 July 2010 (UTC)

Gandalf61 writes "Proof in mathematics is not based on "sufficient evidence" - it is based on logical deductions from axioms." As a mathematician, I must disagree. Gandalf's statement is a version of the formalist philosophy of mathematics, but most mathematicians are not formalists. According to the platonist philosophy of mathematics, mathematics is definitely about truth, and one has sufficient evidence for a mathematical proposition precisely when one has a logical deduction of it from manifestly true axioms, that is a proof. (I am anti-platonist myself, but many mathematicians, if not most, disagree with me.) In mathematical logic, "proof" is more of a term of art; you don't care whether the axioms are true or not and consider only logical deductions from axioms. (And as Vaughn Pratt points out, most proofs in mathematics are not proofs in the sense of mathematical logic, although in principle the former could be made into examples of the latter and might be regarded as abbreviations or summaries.) But even there, the term derives from the meaning of "proof" as evidence for truth, only the notion of truth has been abstracted away and we are only looking at what provides sufficient (mathematical) evidence for what. (And then, of course, there is logic that is not mathematical logic and even logic that is not deductive, although it gets short shrift these days.) —Toby Bartels (talk) 16:56, 9 July 2010 (UTC)

Meat puppetry

User Vaughan Pratt is doing meatpuppetry at the mailing list FOM (Foundations of Mathematics) [see here http://www.cs.nyu.edu/pipermail/fom/2010-July/014869.html] Thoraeton (talk) 17:35, 9 July 2010 (UTC)

I do not think it qualifies as meatpuppetry because he signed his own name in the open, and there was nothing concealed there. I think he just wanted comments. I see no sinister covert intentions there. History2007 (talk) 17:42, 9 July 2010 (UTC)

Who said that meatpuppetry has to be concealed or sinister? As a rule you should "not bias discussions by asking for supporters from other places". It is very possible that he didn't know that he was doing wrong but that doesn't mean that the fault was not committed. Thoraeton (talk) 18:11, 9 July 2010 (UTC)

To make a long story short, I do not think it is worth making a big deal of this. History2007 (talk) 18:14, 9 July 2010 (UTC)

But in Wikipedia "I" doesn't matter. This discussion about proof (and incidentally about truth) is a delicate one. With that email, maybe not intentionally, Pratt has shifted this discussion by recruiting members of a list that will support certain points of view above others. In this case, the views of professionals from areas of mathematics and philosophy is going to and is being favored (who knows if as a consequence of that email). In any case, there is already no way to revert the damage but, at the very least, the possibly unintentional meatpuppetry should be pointed out such that it consequences are understood and to avoid it happening again. Thoraeton (talk) 18:30, 9 July 2010 (UTC)

So there actually are people who want to prevent experts from contributing to Wikipedia. I wouldn't have believed it if I hadn't seen this. What, pray tell, is the rationale for such a position? False vacuum (talk) 21:50, 9 July 2010 (UTC)

In my view this was not. But there are public relation agents who work together to position articles about celebrities, companies, products, etc. and they coordinate behind the scenes. That is meatpuppery. History2007 (talk) 21:53, 9 July 2010 (UTC)

As far as I see, Vaughan Pratt has only asked for opinion of experts in the area (both con and pro) and for references, he has not asked them to support him. I don't think meatpuppetry forbids talking about what is being discussed on Wiki anywhere else. It would count as meatpuppetry only if he asked them to come and support him in the discussion on this page which does not seem to be the case. rdt (talk) 22:05, 9 July 2010 (UTC)

If anybody wants to keep track, I came here because of a message that Vaughn sent to a mailing list. Because of the way he phrased it (which anybody can read at the FOM post linked above), I did not interpret it as a call for support. Also, I do not believe that I would have bothered to come if I were not already a Wikipedian, and recruiting other Wikipedians' opinions is perfectly kosher. Finally, while I agreed with Vaughn here, I've disagreed with him at Talk:Proof. In short, despite my disclosure, I hope that people will accept my input. —Toby Bartels (talk) 02:42, 10 July 2010 (UTC)

Request for expert respect

Hi, first, Dr Pratt, what a pleasant surprise. Nice to see you, although I shall remain anon. Now, I came upon this page by pure, pure chance, but I would hereby like to encourage everyone to be very very nice to Dr Pratt, so he will continue to contribute to Wikipedia, because he is what Wikipedia needs in terms of top level expertise. This man could write a book on logic (or 20 different topics for that matter) in his sleep. I will not involve myself in the discussion here, except to say that with experts of this class, Wikipedia has hopes of becoming a serious encyclopedia. Cheers. History2007 (talk) 17:53, 7 July 2010 (UTC)

Being a bona-fide, gold plated, expert does not exempt any editor from the provisions of WP:Verifiability and WP:Reliable sources. Welcome Dr. Pratt, whoever you are. Roger (talk) 18:31, 7 July 2010 (UTC)

Yes, but a community which respects its experts prospers. Believe me, Wikipedia is lucky to have him edit at all, see Vaughn Pratt. So please help him nicely to provide the benefit of what he knows. Many Wikipedia pages need help from experts, and the least the Wikipedia community can do is be nice to them, and help them as much as possible. Else, this page will get edited by an undergrad student who knows the rules, but not the topic. Personally, I do not bother to edit logic or computing pages that often, because I have to debate too much - gets me upset, e.g. see Randomness that is in deep trouble, needs help but I can not be bothered any more. Now I write articles on art! A topic I know nothing about. I do not want the same to happen to him. He has done 3,000 edits and I would hope to see those increase, not stop because he gets frustrated. The man deserves to be treated well - he has done a lot for science. Now, Dr. Pratt would you like to fix the page on Randomness? It needs help. Cheers. History2007 (talk) 18:56, 7 July 2010 (UTC)

@History2007, while your hero worship might be admirable, it makes no difference to the problems this article has. You and Dr Pratt would really help this article by simply slapping a few citations on it. I'm pretty sure the good doctor wouldn't dream of submitting an article to an academic journal without a bibliography - why do so here? I simply don't get why there is so much argument against citing sources? Have you actually read and understood Argument from authority? Roger (talk) 19:36, 7 July 2010 (UTC)

Sorry Roger, I must be too dumb to follow your logic. You figure it out, you must be smarter than me. I am going to work on art topics from now. Good luck. History2007 (talk) 19:42, 7 July 2010 (UTC)

Thank you, History2007, and I hope I've always remained within not just the letter but the spirit of all the many Wikipedia guidelines, especially those such as WP:V. These represent the consensus view of the many editors who've taken an active interest in the day-to-day governance of Wikipedia and who continue to converge on a workable collection of guidelines within the overall framework of Wikipedia, itself an evolving entity to a lesser extent.

That said, Wikipedia as a whole should be open to input from experts in an area concerning disputes over specific points as they arise. As Jimmy Wales wrote in his [April 2005 letter from the founder, "Attracting and retaining academic specialists is one of our goals." As a retired professor with a wider-than-usual range of interests I have more than the usual amount of pro bono time for worthwhile community projects, among which Wikipedia is hard to beat, and I'm very happy to have this opportunity to work with the Wikipedia community on improving Wikipedia. --Vaughan Pratt (talk) 19:51, 7 July 2010 (UTC)

Regarding "I'm pretty sure the good doctor wouldn't dream of submitting an article to an academic journal without a bibliography - why do so here?" the answer is simple: there is no original research in this article and as such one could never get it accepted by any academic journal, which would reject it on the ground that it contains nothing not already known by every well-educated high school senior. There simply is nothing to source other than to say that the first sentence can be verified by anyone in doubt by going to dictionary.com. On Conservapedia it might be necessary to tell people where to find dictionary definitions, but on Wikipedia? Wikipedia's target audience is the well-educated adult. Anyone who disagrees and feels that it's appropriate to source a dictionary for the dictionary definition of a word can always add that source, I don't own this article. --Vaughan Pratt (talk) 19:58, 7 July 2010 (UTC)

You are being nice now. Let them be nice to you. Anyway, good to see you here. History2007 (talk) 20:11, 7 July 2010 (UTC)

Good heavens, I hope I didn't say something that could be construed as not nice. Granted it's impolite to contradict someone, but in this case since the contradiction began with Gandalf61 I'm not sure how to avoid the appearance of contradicting him back when I defend my position. --Vaughan Pratt (talk) 20:35, 7 July 2010 (UTC)

No, you are being very polite. Long & short of it: to get things done in Wikipedia, here is the algorithm:

• Decide on the facts. It is easy if you know the topic.
• Find some reference on Google books that says roughly the same thing.
• Just add twice as many references as you need
• Make sure the argument flows.

The SAD fact is the pie chart of talk page vs real edits. It is best to avoid talk pages and follow that algorithm first. I sometimes sneak in and do a little technical article once in a while if no one is looking, but usually avoid technical topics just because I have to argue with people who miss the basic point. The real problem is that Wikipedia policies give all editors the same weight. Anyway, it is best to add a lot of references first before editing, that way no one will question it. And it takes less effort that way, because once they start questioning it, then that unfortunate term called pride gets in and logic takes a back set. So the basic algorithm in Wikipedia is the opposite of "shoot first ask questions later", it is: "Add references first, don't answer questions later". It always works that way. History2007 (talk) 20:57, 7 July 2010 (UTC)

@Vaughan Pratt: I believe you are mistaken when you say the target audience is educated adults - you should see how heavily high school students rely on this site for their work!

There was some discussion in Wikipedia some years ago on who to target Wikipedia articles to, where it was stated that articles should be readable by well educated adults. Unfortunately I can't seem to locate the relevant page so perhaps that view has changed since, so I'll stop promoting it. I don't see "Who is Wikipedia for?" in either WP:FAQ or WP:FAQ/Editing, which I would think would be the most obvious places to address that question. --Vaughan Pratt (talk) 22:37, 7 July 2010 (UTC)

@History2007 "Wikipedia policies give all editors the same weight" is not a problem, it is one of WP's most valuable virtues. I suspect you do not fully grok the fallacy of Argument from authority. The fact that any 8th grader is free to request a Nobel laureate to substantiate their claims is IMHO one of the greatest advantages this site has over its peers.

Its way past bedtime in my timezone, goodnight all! Roger (talk) 21:21, 7 July 2010 (UTC)

Wait, wait. There's something illogical here. First you say authorities can't wield their authority on Wikipedia, then you seem to say they can. Is the difference that one must be a Nobel Laureate before one is permitted to substantiate a claim on their own recognizance, or that it must first be vetted by an 8-th grader? Sorry, I parsed your statement incorrectly, I thought "their" was referring to the 8-th grader looking to the Nobel laureate to endorse the 8th grader's contribution, but you meant the 8-th grader could hassle the Nobel Laureate. Well, you may think that's wonderful, but if you multiply the number of 8-th graders in the world by the proportion of them that like to tweak their betters purely for the fun of it (witness the number of acts of vandalism per minute on Wikipedia), you've created a force for evil capable of bringing the expert contributions to Wikipedia to a grinding halt. I won't let them do this unless they overwhelm me, but given the small percentage of my time left to me these days to generate actual Wikipedia content as opposed to fighting what I've been unable to distinguish from obvious stupidity (perhaps due only to my own stupidity) I must say I'm starting to feel overwhelmed. --Vaughan Pratt (talk) 00:22, 8 July 2010 (UTC)

I can assure you from my side there is/was no intent to "hassle" anyone. I happen to think this is a very useful article and now that it is well sourced its in compliance with the editorial policies of WP. The advantage of having non-experts asking (in good faith) the experts to substantiate what from the experts pov may seem to be a self evident truth is one of the cornerstones of WP. Vandalism is the downside of such openness but I don't believe it substantially detracts from the value of the verifiability policy. Roger (talk) 10:42, 8 July 2010 (UTC)

No comment. History2007 (talk) 21:28, 7 July 2010 (UTC)

Thanks for the tips, History2007. Actually this is the first time I've been seriously challenged about references in a situation where I thought none were needed (a common situation when stating the obvious, such as the fact that hands normally have five fingers which was challenged for four days, which Short Brigade Harvester Boris (talk) drew my attention to). However I see what you mean. As long as there are editors on Wikipedia with a trigger-finger for reference tags I guess you're right about putting references on even universally known statements regardless of whether they're needed according to the rules, so as to avoid getting bogged down arguing that the rules have been met. There is no requirement that Wikipedia editors make challenges in good faith, which creates a problem for statements everyone knows to be true yet remain vulnerable to bad-faith challenges made for the sake of being able to point to the challenge itself as proof that a citation is needed. --Vaughan Pratt (talk) 21:40, 7 July 2010 (UTC)

I think we have a new law of "conservation of wiki-energy" here. It takes less energy to add twice as many references beforehand than talk and talk about it afterwards. Can I get the semi-Nobel prize for that? But things are not always challenged. As I have noted elsewhere Number of references for Britney Spears = 173 Number of references for Statistical physics = 0. I am deliberately not fixing the Statistical physics page to keep that joke alive. However, Hilbert Space is actually a well written page. So quality in Wikipedia is at the moment very spotty. Gradually, gradually it may improve after the new WP:Pending changes system gets going. In the early days Wikipedia was content hungry and anyone should have been allowed to do anything. Now, Wikitimes are a-changing. History2007 (talk) 23:42, 7 July 2010 (UTC)

Interesting idea, though you may have a better shot at the Ignoble prize. I will take care not to brag about pages I've written or contributed to that I'm particularly proud of, for fear of the editors who are now going round challenging sentences everyone knows are true for no apparent reason other than to be mean to those who rub them the wrong way. Naturally they'll start in on the ones I'm most proud of, and Wikipedia seems to offer no recourse. It's kind of sad. I would switch to Wikiversity if I thought anyone read it: experts in their field don't get hounded by 8-th graders there, but they don't get any audience either that I can tell. --Vaughan Pratt (talk) 00:12, 8 July 2010 (UTC)

I am actually not a prize collector. I just do this for fun really. Regarding page, in time the dynamics of challenges change. After a page has been stable for some time, it usually stays that way. Science pages are more stable in fact. The current affair pages are another story. History2007 (talk) 00:30, 8 July 2010 (UTC)

I see what you mean. Better articles are Random sequence and Algorithmically random sequence, which cover the main notions of randomness in the modern literature (though Uspensky's contributions are unfortunately omitted). The Randomness article is about random sequences (see the first sentence) and therefore I would think should be merged with Random sequence since it's about the same subject. --Vaughan Pratt (talk) 00:03, 8 July 2010 (UTC)

Actually, I fixed Random sequence, and it was really bad before that. I am not happy with it. It still needs work, but after writing History of randomness, I got bored. It is more fun writing things from scratch - instead of debating. The Randomness article should really cover more than sequences given that physical and biological systems are discussed. It is a key topic, and it is a REALLY terrible article as is. If you can pay attention to that it will be great. History2007 (talk) 00:15, 8 July 2010 (UTC)

One point of confusion I see in the Randomness article is that it uses "sequence" (an infinite list) interchangeably with "string" (a finite list) without comment. This misses the whole point of Kolmogorov randomness, that it's entirely about finite strings. Instead the article jumps back and forth between finite strings and infinite sequences as though there were no difference. On the other hand the treatment of randomness in QM is spot on, albeit brief. Biology is different from QM in that whereas QM is pure randomness, the need for mutations to be random as opposed merely to exhibit some level of complexity is much less clear. Well, there's a lot more to say on that but this is the wrong venue. --Vaughan Pratt (talk) 00:49, 8 July 2010 (UTC)

Yes, not the right venue, but my entire obvious strategy was to get you to think of that topic instead of the pedestrian discussion here that is upsetting at best. The deep articles need help rather than this one. And maybe, just maybe my strategy will work. You are, of course right about the finite/infinite problem there. That article needs a unified approach, at the moment is a collage of errors. History2007 (talk) 01:05, 8 July 2010 (UTC)

Anyway, signing off now, for a while. Again, a nice surprise to see you. History2007 (talk) 01:28, 8 July 2010 (UTC)

Mainly time-consuming, only upsetting to the extent of my thinking wishfully about the time I could have spent doing more useful things. --Vaughan Pratt (talk) 03:36, 8 July 2010 (UTC)

I have nothing much to contribute to this specific discussion other than to voice support for the idea that proofs in mathematics are "based on sufficient evidence" (the sufficient evidence is the sequence of deduction steps). The other point I want to make is that as an expert in logic and theoretical computer science I stopped contributing to Wikipedia a long time ago because clueless editors too often destroyed everything of value I added by quoting various Wikipedia guidelines on me. I never say a guideline that says "if you're an editor and you don't understand the content, just revert the changes". When an expert makes a change, you should not revert it because he failed to follow a guideline. You should help him fix it. In the present situation an editor is using two puny references against a lifetime expertise of an expert mathematician on a topic that is not even discussed in such an explicit form in the literature. It is blindingly obvious to a professional logician that "formal proof" is a form of "evidence". Some people set formal proofs apart from other kinds of proofs because formal proofs have qualities that other proofs do not have, and that's where the editor has confused a distinction in quantity as a distinction of quality. Frege (talk) 11:34, 8 July 2010 (UTC)

Amen my friend. You are right. Your statement that "I stopped contributing to Wikipedia a long time ago because clueless editors too often destroyed everything of value I added" expresses a very familiar sentiment. That was why I asked people to treat Vaughn Pratt carefully - not that they listened. I think all experts should declare their own Bill of Rights. As is, many seem to be on "Expert Strike". I am also on semi-strike, in a way. An encyclopedia by the people for the people is good, but an encyclopedia by the amateurs for the amateurs has to stop at Britney Spears products. History2007 (talk) 11:48, 8 July 2010 (UTC)

Fortunately I have a thick skin as regards my own feelings, and try to keep a thin one for others, which so far hasn't led to my seeing any reason to stop contributing to Wikipedia. But I've been contributing for several years now and this is the first run-in I've had with source challenges. Perhaps the problem is that proof is on the one hand one of my central interests (so I've built up a deeper-than-average perspective) and on the other a concept many feel on top of, albeit not always with the same perspective. When I write about Planck radiation or residuated lattices it tends not to draw any flak. --Vaughan Pratt (talk) 01:09, 9 July 2010 (UTC)

Additional input requested

I have mentioned this article and discussion at Wikipedia talk:WikiProject Mathematics. Input from other Wikipedia mathematicians may help to establish consensus on whether the definition "sufficient evidence for the truth of a proposition" applies to the concept of formal proof in mathematics and logic. Gandalf61 (talk) 08:35, 8 July 2010 (UTC)

OK I'm somewhat confused now. Are we discussing the best naming for various proof articles or are we discussing the content of this article? As far as the term in quotes goes that is imho a correct description, however as usual the with such general description, they may have different individual interpretations. In particular it depends on what you read into the term "sufficient" since its exact meaning depends on the field. Sufficient in math or logic is somewhat different from sufficient in law or social sciences.--Kmhkmh (talk) 09:25, 8 July 2010 (UTC)

It's not clear whether this article is about proof in logic, proof in mathematics, proof in science, or forensic proof: it should probably be more specific in focus. At the moment, the article is a really an essay hanging largely on a single e-dictionary definition [1]. Most references are either unreliable, or else apply to formal proof, which the article is not about. However, there's much here that is excellent, and I feel there's a fantastic article here trying to get out. -- Radagast3 (talk) 09:28, 8 July 2010 (UTC)

Maybe we need a visual index Radagast. Last one you did was very nice. This should only take a month! History2007 (talk) 09:42, 8 July 2010 (UTC)

I'm not sure exactly where this article should go, given the confusing relationship to the dab page Proof. I think the author was aiming for a top-level overview, perhaps a little like Discrete mathematics, but such an overview is hard to write for this particular concept. I've tagged the article as an orphan, but I'm not quite sure where it should fit into the Wikipedia network in its present form. -- Radagast3 (talk) 09:55, 8 July 2010 (UTC)

Why not turn this article into a general overview article on proof in general and link it prominently on the dab page? In that context the sourcing issue can be seen slightly more relaxed, since overview article can to some degree rely on sources given the specialized articles it summarizes and links to.--Kmhkmh (talk) 10:06, 8 July 2010 (UTC)

This article has evolved considerably since I last looked at it ~12hours ago, for one its a lot shorter. It was in fact a more general overview as originally written but someone has narrowed it down quite drastically. I'll continue watching its development with interest. Roger (talk) 10:47, 8 July 2010 (UTC)

Let me say again what my original purpose was. I saw a dab page for proof pointing off to ten different pages all dealing with what I would now call instances of the concept of proof as it arises in argumentation (as distinct from quality control, the remaining items on that dab page), and viewed it as odd. It was odd because usually when a single concept arises in a wide variety of areas, an article is written about that concept at a level of generality not overly specialized to any of those areas, and then it enumerates each area with a heading followed by "main article" linking to the main article for that area, and says a little about that area for the benefit of those who prefer to read a single article giving shallow coverage of several areas, possibly with relationships between those areas, rather than being obliged to dive into each area separately the way a dab page forces one. It didn't seem to me that the first half of the dab page was consistent with how Wikipedia treats the corresponding situation for other topics. In the meantime Gandalf61 has reverted the dab page to its original form, rather undermining the structure I had in mind for it. --Vaughan Pratt (talk) 03:33, 9 July 2010 (UTC)

Two valued mentality

Before things get cast in stone, since this may be a good time to look at the bigger picture (pun comes later) let me comment that much of the discussion of logic in Wikipedia has a two valued mentality. That should really change. In fact, the article on fuzzy logic is so bad, if poor Zadeh ever sees that he will drop his camera and break it. History2007 (talk) 10:59, 8 July 2010 (UTC)

Logicians generally prefer intuitionistic logic over fuzzy logic when objecting to the law of excluded middle (sorry, Lotfi). I plan to incorporate material along these lines when I get a break from fighting these fires, including the French point of view led by Jean-Yves Girard on the abstract essence of proof, which became a hot topic in computer science after Girard spoke about it at LICS'86 in Boston. (Much of my own research during the 1990's was devoted to the connection between Girard's linear logic and concurrency, with my two research associates Dominic Hughes and Rob van Glabbeek solving in 2003 the problem of incorporating Girard's additive connectives into proof nets, which had been open since Girard invented the concepts in the 1980's; previously only the multiplicative connectives had been adequately dealt with.) Even more abstract than Girard's notion of proof net is the idea that a proof is simply any morphism in a category endowed with suitable structure conferring proof-like qualities on every morphism, a point of view developed in considerable detail in the recent book "Proof-Theoretical Coherence" by Kosta Došen and Zoran Petrić (340 pp., 2004). --Vaughan Pratt (talk) 15:24, 8 July 2010 (UTC)

Yes, that was partly why I joked about "putting in the two two guilders" below - I guess too obscure a joke. I fully agree that a proof is best represented on morphisms. But I think most Wiki-readers will find those concepts just too hard to grasp. The fuzzy approach is best known among readers - most of whom think MacLane was a song writer, not a working mathematician. So the presentation needs to be much simpler - before the man breaks his camera. History2007 (talk) 16:09, 8 July 2010 (UTC)

Fuzzy logic seems to make sense at first: what could be more natural than real numbers serving as truth values? It breaks down in application when you define "very true" so as to make "it is very true that John is tall" logically equivalent to "John is very tall" as proposed by Zadeh, which few if any linguists would agree with.

As an axiomatic system of logic intuitionistic logic is no harder than Boolean algebra (NB not the article Boolean logic which is far worse than either the Randomness or fuzzy logic articles and has been in violation of WP:OWN for quite a while now) once you understand that both logics define AND, OR, TRUE, and FALSE the same way but differ in that they define NOT and IMPLIES in the opposite order.

• Boolean logic defines NOT so that P AND NOT P is FALSE while P OR NOT P is TRUE. It then defines P IMPLIES Q to be NOT P OR Q.
• Intuitionistic logic defines P IMPLIES Q to be the weakest proposition that renders sound the inference rule Modus Ponens, from P and P IMPLIES Q infer Q. It then defines NOT P to be P IMPLIES FALSE.

That's the difference. --Vaughan Pratt (talk) 04:21, 9 July 2010 (UTC)

That discusses the merits of one approach vs another - and I guess was prompted by my leap to select fuzzy as the ambassador of inexactness - just because it has more tabloid press attention. However, that aside, reading not just this article, but others in Wikipedia, I get the feeling that the primary focus is exact methods. That was why I suggested looking at "proof of risk" as a case study below. In practice, foundations aside, many less than exact proofs involve weights of one type or another that get manipulated, and the actual "proof" has a different flavor than straight deduction, just as different programming languages have different "tastes" although in the end they can be viewed in very abstract terms.

On that notes, again since this article is stepping outside the safe mathematical territory, it would be good to mention that most people (e.g. jury members, investors, voters, etc.) who are to be "convinced" have a less than consistent understanding of logic and proofs (in court rooms, banks and political debates) rely on that. And phrasing is another issue ala Kahneman and Tverski, etc. so the same "predicate" phrased differently may convince or not. I have come to think that this is a very wide topic now.

Regarding "worst article awards" let me nominate Semantic Reasoner, Inference engine and Knowledge base as well, now that we are on this topic.

Finally, let me point out that in Roman_Catholic_Dogma#Theological_certainties there are 7 truth values to choose from in theological proofs. Most people are not aware of that and the Institute for Mathematical Theology has not addressed the issue yet. History2007 (talk) 05:55, 9 July 2010 (UTC)

"Evidence"

Some kinds of proof are what might be called "evidence-based", such as those in law enforcement and the sciences, and others are not, such as those in mathematics. The first sentence, therefore, doesn't quite seem appropriate to the content of the article, which encompasses both the evidence-based and non-evidence-based proofs. So as I see it there are two ways forward. First, make the article just about the evidence-based notion of proof. In that case, we should consider how the current article fits with the closely related article evidence; a merge may even be appropriate. Second, change the first sentence to something that more accurately reflects the content of the article. Here there may be a problem with original research. What we need is an authoritative source that systematically examines various notions of proof in the way that the article attempts to do. Sławomir Biały (talk) 12:13, 8 July 2010 (UTC)

Proof by contradiction.... I wonder what Brouwer might say if tried to put in two guilder. History2007 (talk) 12:22, 8 July 2010 (UTC)

Interesting, but for the most straightforward interpretation of evidence, mathematical proof (including proof by contradiction) simply is not evidence-based. As a working mathematician, I can say that a mathematician does not gather evidentiary facts together until something is demonstrated to be true on the weight of those facts. Rather we typically gather evidence until we believe that something is true, and then we try to prove our belief. The proof is typically totally independent of the evidence gathered. Now it has already been argued here that in a mathematical proof, the "evidence" that constitutes the proof is the sequence of steps that constitute the proof. But this interpretation requires a debauched construal of the term evidence. Sławomir Biały (talk) 12:39, 8 July 2010 (UTC)

Congratulations on your status: working mathematicians are rare these days. Most have sold their souls to Wall Street these days and are now quants. Now, that brings about another interesting point: how does one "prove the risk level" of an item? Shall I also mention the dreaded term GC or Proof, what proof? By the way, a nice set of articles you wrote, I had read some and liked them before. History2007 (talk) 12:52, 8 July 2010 (UTC)

Agree with Sławomir Biały. That pretty much sums up my concerns also. Gandalf61 (talk) 12:49, 8 July 2010 (UTC)

Well, it's obvious that the premises in a step of a mathematical justify the step, is it not? Or would you say that premises constitute neither evidence nor justification? --Vaughan Pratt (talk) 14:45, 8 July 2010 (UTC)

Your definition of proof does not mention justification - oh wait a minute - now it does. Gandalf61 (talk) 15:29, 8 July 2010 (UTC)

Right. Merely because I don't agree with you needn't be taken to imply that I think you're wrong. :)  I can see the point being argued either way, so to be on the safe side I expanded "evidence" to "evidence or justification." --Vaughan Pratt (talk) 15:37, 8 July 2010 (UTC)

So you are just playing mind games here - that's nice. Anyway, your new definition is an improvement. A formal proof is a logical justification of the truth of its conclusion. A legal proof is an evidence-based justification of the truth of an accusation. So if you take out the reference to "evidence", leaving "a proof is a justification of the truth of a proposition", then I can agree that this is a definition of proof that applies to both formal and informal proofs. We will still, of course, need a source for this definition. Gandalf61 (talk) 15:49, 8 July 2010 (UTC)

I would have thought that the stickler who insists on drawing a hard line between "justification" and "evidence" on at best murky grounds was the one playing the mind game. It is clear from the variation in interpretation of the two words between areas that no such hard line can be drawn in an area-independent way. In epistemology evidence supports justification, which plays roughly the role of proof. In law evidence refers to affidavits and exhibits and is judged for its admissibility, whereas justifications are more in the nature of exceptions to prohibitions, as in justifiable homicide. In these two areas one seeks to use either evidence or justification or both as appropriate to the area in the course of fulfilling respectively the philosophic or legal burden of proof. Other areas vary yet again, for example mathematics as you've noted, or at least claimed. In light of the variability and interchangeability of these terms I seriously doubt that the dictionary writer intended the sort of fine distinction you're insisting on here. Personally I was quite satisfied with leaving the definition the way I had it originally.

In that regard, bear in mind that my original training was in mathematics and physics and much of my research has been in logic, yet despite my heavy mathematical background I did not even think to consult a dictionary when I began the article with "A proof is sufficient evidence for the truth of a proposition." Had someone suggested adding "or justification" I would have questioned its necessity prior to your aggressive editing. (Your style seems to be to edit first and ask questions later, the opposite of mine.) It was not until challenged for a source that I did so, and I will confess that I was surprised (pleasantly of course) to see essentially my definition as the first entry when I googled "proof dictionary."

While I have no objection to expanding "evidence" to "evidence or justification," the only need I see for this is for those claiming the existence of a universal distinction. I don't believe the existence of such people justifies removing what for those who see no hard line between the two will be a perfectly good source. The fine line that dictionary writers must observe is not that one but rather the line between too little and too much respect for nuance, witness "or to produce belief in its truth" in the dictionary.com definition, which barely scratches the surface of the possible nuances the dictionary writer could have covered. One can imagine the dictionary publisher insisting as a matter of style on a limit on the number of disjunctions permitted in any one entry. --Vaughan Pratt (talk) 17:17, 8 July 2010 (UTC)

A further observation would be that "evidence for the truth of a proposition" is correct but "justification for the truth of a proposition" is not. A proposition or its assertion can be justified but its truth cannot be; its truth can however be established or defended. I'm sure we all have access to dictionaries; I prefer the OED myself, though I rarely need to consult it for the meanings of such common words. So in case there's any doubt, what I'm saying in this comment is that the sentence with "evidence" is fine, and that the sentence with "evidence or justification" is not. False vacuum (talk) 18:12, 8 July 2010 (UTC)

Sorry, I meant to say also that the relationship between "evidence" and "justification" is that evidence that a proposition P is true is (some) justification for asserting P. And I certainly do agree "that the premises in a step of a mathematical [proof] justify the step", and furthermore that this intuitive idea is embraced by saying that the premises in a (correct) derivation of P constitute "sufficient evidence" that P is true. False vacuum (talk) 18:49, 8 July 2010 (UTC)

Since there seems to some doubt here as to the necessity of "or justification" that I inserted merely to satisfy Gandalf61, I would like to restore the definition to the one I came up with originally, which seems ok to at least some subset of the mathematical community that's weighed in here so far. When I originally wrote "A proof is sufficient evidence for the truth of a proposition" it never occurred to me either to consult a dictionary or to doubt the suitability of "evidence." Since "or justification" complicates the definition in what now appears to be an unnecessary way, and since the difference in area-dependent usage conventions between "evidence" and "justification" is so broad as to make any generic distinction meaningless, I propose to remove "or justification" so as to restore the definition to what I originally wrote. This has the additional advantage of not having to search endlessly for a dictionary that includes "justification" as an alternative to "evidence" when sourcing the definition, which is likely to fail since dictionary writers seem not to have seen any need to draw that distinction. Any strenuous objections? --Vaughan Pratt (talk) 03:33, 9 July 2010 (UTC)

The OED offers this definition: "Something that proves a statement; evidence or argument establishing a fact or the truth of anything, or belief in the certainty of something; an instance of this." I'm still uncomfortable with the bare use of the word "evidence" here. I've changed it from "or justification" to "or argument". Hopefully this will satisfy everyone. Sławomir Biały (talk) 12:38, 9 July 2010 (UTC)

Thanks. I think we are so close to the payoff point on the asymptote here that we should just agree to move on. History2007 (talk) 13:11, 9 July 2010 (UTC)

Thank you, thank you, thank you, Sławomir. It had occurred to me yesterday to make exactly that change myself, but as one of the primary disputants I felt it would be more of a conflict of interest for me to do it than for someone further from the eye of this particular hurricane. "Evidence or argument" should take care of Gandalf61's concern while matching the OED nicely (should have thought of the OED myself).

One impact of this change however is that it tends to undermine the appropriateness of "Proof (argument)" as the most appropriate title for the page, by raising the question, wouldn't "Proof (evidence)" serve equally well? Since the point of a proof of this sort (as distinct from say a galley proof) is to establish truth of a proposition (pace the extreme formalist purists who argue that proof is mere uninterpreted symbol pushing), I will change the title back to what it was when I first wrote the article, namely "Proof (truth)". --Vaughan Pratt (talk) 16:02, 9 July 2010 (UTC)

Except that this will require administrative assistance, since moves are not easily undone. The problem is that a move does not delete the original page but redirects it. The original page then blocks the attempt to move the article back, and an administrator then needs to step in to delete the blocking page. Moves are easier for non-administrators to do than to undo. --Vaughan Pratt (talk) 17:24, 9 July 2010 (UTC)

Test drive section for article

I think the definition is getting better - but perhaps not perfect yet. Now how about a test drive? I think on the mathematical front, things will probably be solid soon, but how about the real world "informal proof" cases to which the article also aims to apply. How about a scenic test drive with lots of different scenes. May I suggest the fascinating "formal and informal proofs" provided by David X. Li's work to convince people as test cases? In the end that is as big an impact mathematics has had in recent years. I think it would be good if different editors tried that, e.g. 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? My apologies if there is no religious proof angle here, but that might be too much to ask, unless Mr Li suddenly converts and provides proof of repentence and forgiveness. But seriously, a few test cases and examples will be nice eventually. And as you note this example has a built in inexact angle. I thought that will be good to see too. And I almost forgot: "how did the proofs go wrong? Proof is one thing, correct is another. History2007 (talk) 19:42, 8 July 2010 (UTC)

Fact flag removal

Exactly what facts are being disputed here now? I would like to see a list of such disputed facts. The article does NOT seem inaccurate to me. It is clinical, but accurate. It can do with examples and drama that can teach people things, but that is not the subject of a fact flag. I am hereby invoking WP:Needs proof now to ask for proof of the factual inaccuracy. I see no inaccuracies therein - the need for examples, yes, but overall it addresses the topic. Examples can be added later anyway. The basic idea is VERY simple: an informal proof is a set of justifications to fool someone, excuse me, convince someone, about something. And the article says that. No need for a dispute here at all. We need to move on. History2007 (talk) 11:36, 9 July 2010 (UTC)

I didn't put the tag there, but I presume it applies to the last few unsourced sentences: "Suitably incriminating evidence left at the scene of a crime may serve as proof of the identity of the perpetrator. Conversely a verbal entity need not assert a proposition to constitute a proof of that proposition. A signature constitutes direct proof of authorship; less directly, handwriting analysis may be submitted as proof of authorship of a document. Privileged information in a document can serve as proof that the document's author had access to that information; such access might in turn establish the location of the author at certain time, which might then provide the author with an alibi."

My main problem is that the article is called Proof (informal), but over a third of the article is about formal proof in mathematics. Perhaps this article should be merged with Evidence? -- Radagast3 (talk) 13:28, 9 July 2010 (UTC)

I do not think merge with evidence makes sense. The article needs expansion, but a merge will open another Pandora's box. If there are unsourced items that needs an unsourced flag therein, not a blanket condemnation at the top. And this article does have a formal twist, and we are discussing informal items, e.g. 7 truth values in theology, so we should just let it grow organically, before subjecting it to over-regulation. Anyway, to address your "need for non-math" I just started adding Aristotle, Augustine, etc. to add philosophy, religion, etc. I am looking for something with more life e.g. Lewinski's "proof" of knowing Clinton, or Obama's proof with his birth papework etc. That might be fun to add too. History2007 (talk) 13:34, 9 July 2010 (UTC)

It was originally called "Proof (truth)." It was first moved to "Proof (logic)" by Michael Hardy, who misunderstood the article as being about logic, and then to "Proof (informal)" by Gandalf61 who misunderstood it as being about informal proof. Unfortunately moving an article leaves the original page behind with a redirect to the new name, which then blocks undoing the move because only an administrator can delete the original page. I've accordingly requested administrative help with undoing these moves. --Vaughan Pratt (talk) 17:16, 9 July 2010 (UTC)

Ok, but whatever the name may be, the flag needs to come off. There is nothing incorrect here, as far as I can see except the application of the flag itself. And there are 20 references for 2 pages of text. That is even an overkill. There is no need for a fuss here. The flag needs to come off. History2007 (talk) 17:21, 9 July 2010 (UTC)

I hate to say it, but as a procedural matter the flag should remain on until the incorrect title has been fixed by undoing that move, which has been requested at Proof (truth). We are currently waiting for an administrator to either delete the Proof (truth) page so a non-administrator can move this page back there, or to do both steps (but it may be cleaner not to involve administrators in the second step). --Vaughan Pratt (talk) 17:28, 9 July 2010 (UTC)

Ok, move accomplished and flag removed accordingly. --Vaughan Pratt (talk) 21:14, 9 July 2010 (UTC)

What an amazing waste of time for all the great minds involved here. The W in Wikipedia stands for ... I hope not wasted time....? Now, back to content. 21:37, 9 July 2010 (UTC)

Unfortunately it's not over yet, there are still people undoing the larger structure that this article was designed to support even as I work on it -- the rug keeps on being pulled out from under my feet by people who imagine there's a problem and revert my work yet are incapable of communicating the nature of the problem they claim to see. See below. --Vaughan Pratt (talk) 02:27, 10 July 2010 (UTC)

Well, good luck. I have wasted enough time here. I will look back after a few days, by then all involved must be worn out and a solution through fatigue will set in. But the general topic has now interested me, and I will think about it. I think when you are personally discussing the mathematical angle, you are doing fine, but the moment you step outside that border I see problems appearing almost by the nano-second. For the record, I do not think the general issue of proof (as a uniform solution both inside and outside of mathland) has been addressed in the literature outside anyway, and this is in effect a nice attempt to do it by flying over the barriers of WP:OR. Any lawyer will tell you that proof / convincing is a different game than that presented here. And the words "convince" or "argue" are just unclear anyway. Until you have a "model of discourse" that defines interaction between the parties, the solution presented is a 5% proof solution anyway. History2007 (talk) 07:52, 10 July 2010 (UTC)

Actually there is an extensive literature on the notion of proof independent of the provenance of its evidence, brought to my attention by subscribers to the Foundations of Mathematics mailing list. Aristotle regarded his development of syllogistic logic as formalizing everyday argument rather than mathematical argument per se, and Lewis Carroll's series of syllogisms published as a weekly feature of a newspaper adhered to Aristotle's perspective by having no mathematics whatsoever in any of the syllogisms.

On the other hand the Stanford Encyclopedia of Philosophy does not have an article on proof. I've been meaning to bug Ed Zalta about this but keep forgetting to do so whenever I bump into him, though that might be my subconscious warning me that if I bring that up with Ed he'll ask me to write it. (I'm the author of the SEP article on algebra, the fourth article that pops up when you Google encyclopedia algebra. It took a lot of work and needs a lot more that I ran out of time for.)

Hopefully someone will contribute a paragraph to Proof (truth) about interactive proofs, which would address the notion of proof understood by lawyers and just about anyone generating a proof in real time in discourse, the court room, etc. The article does not say that proof as a perlocutionary speech act must follow the form of a published proof, which should be pointed out in any treatment of interactive proof in the article (but then someone is going to demand a source, as though they could imagine that this could be false---I am astonished at the vivid imaginations of some of the people demanding sources for statements I can't imagine being false). --Vaughan Pratt (talk) 17:43, 12 July 2010 (UTC)

No, I can not agree that you have it nailed. I see no proof of that. In fact, the article on Mathematical proof has done a better job of bringing in the notion of community standards to refer to the discourse. It says: a convincing demonstration (within the accepted standards of the field) which is lacking in this article. The issue here is not really proof, but truth masquerading as proof. An argument has to meet specific standards of sanity or insanity before it can be considered a proof - no mention of that here. Proofs are inherently dependent on the social environment within which they are presented. And any good lawyer will tell you that the color of his tie/suit is as important as anything he says - as is his tone of voice, eye contact, etc. etc. And key issues about the existence of multiple proofs and hence their impact on "truth, whatever it might be" is not discussed. There are currently at least 12 proofs of who shot JFK that are not considered totally insane, and 1,200 that are considered insane. Which one is a proof, and what is truth? Who knows? I have no idea. And arguments or proofs about the value of Renminbi that would be accepted in the US would be immediately rejected in China and result in the "re-education" of the proof provider. That was why I wanted to see if you could even attempt to approach the key case in which mathematical proofs have impacted the world in recent memory: the Gaussian copula and David X. Li. But obviously that is too hard for the framework presented here. In my mind, if you want to "prove" that you have nailed it, you will deal with Mr Li and the non mathematical aspects of proof of risk, derived from mathematical proofs. Until then, this is still an article by the mathematicians, for the mathematicians. History2007 (talk) 21:01, 14 July 2010 (UTC)