Talk:Proof (truth)

Inexact Truth

Vacuum, there is useful logic there, but it was long, really too long to be used. But as a start, although the use of "probability" is controversial around some parts of Berkeley, and you need to change that, that issue is good to add. And you need to say what makes proof different from convincing in far fewer words. And the moment we mention inexact and language Kahneman and Tversky should be mentioned. My suggestion: fix Fuzzy logic 1st to deal with fuzzy truth, then build fuzzy proof and convoncing therefrom. History2007 (talk) 14:40, 5 September 2010 (UTC)

I certainly agree that heuristics and biases are a central topic in any general, encyclopedic treatment of epistemology, which is what you seem to want this article to become (I'm not sure I disagree, but as Vaughan says above, there are limits to what can be covered in any given article). Of course, if you had read what I wrote above, you'd probably have noticed that I've already strongly implied—well, signalled—that I consider that stuff relevant to our discussion. If you had read what I wrote above, you would probably also have noticed that I don't think truth is a fuzzy notion at all (and that fuzzy logic has nothing directly to do with epistemology). I know very little about fuzzy logic, though, so I'm probably the wrong person to fix that article, and if what you imply is true, maybe I'd better not even read it. I'd also appreciate clarification about the Berkeley comment.

Finally, if you had read what I wrote above, you would have seen that I did "say what makes proof different from convincing" in very few words. I'll quote myself:

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.

I made a mistake here, and then later mindlessly copied it, thus magnifying it. I should have followed my own advice, and read what I wrote. See below. False vacuum (talk) 05:52, 6 September 2010 (UTC)

My last post was only intended to clarify what I inferred from your last post might still be unclear. Hence the length and discursiveness. Also I rather enjoyed writing it. False vacuum (talk) 15:14, 5 September 2010 (UTC)

So the distinction is the truth of the conclusion? Do you have a few references for that? And in theology how does one establish the truth of the conclusion? I am not really comfortable with this, need to think about it. But the word inexact needs to come in somehow with a margin of use. History2007 (talk) 15:28, 5 September 2010 (UTC)

Actually, no. I don't think the distinction is simply the truth of the conclusion. I've never thought anything of the sort (as is pretty clear from reading the rest of what I wrote—I hope) and didn't mean to say it. The distinction concerns both the truth of the conclusion and the validity of the conclusion-producing or -establishing process (of course). As more than one of us (including me) has said several times now, a proof of something (in the natural-language sense) is a process that establishes something, i.e. establishes that something is true. (I'll call attention again to the fact that explicit references to the concept of 'truth' may be elided without obscuring the meaning). Again, my apologies for this trivial mistake, and for not noticing and correcting it sooner. False vacuum (talk) 05:52, 6 September 2010 (UTC)

So do I take it that your suggested definition is that proofs and convincing defer on the "validity" of both the conclusion and the argument? Is that the shorthand definition? Do you have a few references for this assertion? History2007 (talk) 06:41, 6 September 2010 (UTC)

Again, the definition of 'proof' does not need to mention 'convincing'. The 'ought to convince a suitably idealised reasoner' formulation I mentioned once was not a proposed definition; it was just another way of putting what I think is generally agreed to be the same concept. I agree with the standard definition that a proof is that which establishes the truth of its conclusion. Let me amplify that this is just a definition; by calling this the definition of the word 'proof' we are making no empirical claims. Discussions of what the standards of proof should be, what constitutes a valid proof, and what evidence or arguments should suffice to convince us of various things are entirely germane, but they are not relevant to the definition of the word 'proof'. I have asserted above (and linked to a justification for this assertion) that they are not relevant to the definition of 'truth', but perhaps I have been insufficiently explicit about this distinct point. False vacuum (talk) 21:31, 6 September 2010 (UTC)

Well, against my own advice I've started looking at the fuzzy logic article, and I'm glad I have. Thanks for attracting my attention to it. I'd be curious to know whether you think its approach is fundamentally flawed, or just that it's disorganised and doesn't explain a lot of the material in a remotely accessible way. But that's probably not appropriate for this talk page. False vacuum (talk) 15:45, 5 September 2010 (UTC)

Fuzzy logic is actually simpler, in my view than many others. The fuzzy logic page was just written by some unknown editor in a hurry and is a mess. As to the flaws of Zadeh's concepts, or their merits, that is the subject of international debate, some love fuzzy, some do not. But the average reader can digest fuzzy if presented right. That is why I think fuzzy proof is a good way of presenting things. History2007 (talk) 15:51, 5 September 2010 (UTC)

While the mathematics of fuzzy logic is not problematic, Zadeh insists on applying it to natural language in naive ways. For example he wants to use composition of functions to infer from "It is very true that John is tall" that "John is very tall." This is not the sort of thing you can get a lot of linguists to line up behind. He's been bugging me about this the last couple of months, whether in connection with this article or not I have no idea. --Vaughan Pratt (talk) 08:07, 12 September 2010 (UTC)

What is the "inexactness" that History2007 is complaining about here? This sounds like Original Research. Unless you can source this, the "generalize" tag has no place here. --Vaughan Pratt (talk) 00:58, 4 October 2010 (UTC)

Examples?

There are abstract claims in this article about the representation of proofs in inexactness, law and religion, but not one solid example is provided of an inexact proof or a religious proof. Not one. I think there is need for at least one solid example in law and one in religion that , instead of all this abstract talk, else those need to be withdrawn. And of course, there is no example of an inexact proof here. That is also needed, else that claim needs to be withdrawn. History2007 (talk) 08:28, 6 September 2010 (UTC)

I just checked, and there is no mention of inexactness of proofs in the article; the closest thing I can find is the claim that there is "no absolute threshold of sufficiency at which evidence becomes proof." Would you care to rephrase/reconstruct your objection in light of this (as I argue above) important distinction? False vacuum (talk) 21:16, 6 September 2010 (UTC)

That yudkowsky site does not pass WP:Reliable and can not be used. And much of what you assert is based on your own "intuition" as you said. Again, that has the problem of WP:OR. And of course there is no mention of inexactness: that is a shortcoming of the approach presented in the article. And again: law, etc. is not dealt with at all. I added the example of Augustine from theology myself, but that does not fit into your formalism. So the inexact issue is unresolved. And "no absolute threshold of sufficiency at which evidence becomes proof" is a roundabout way of talking about inexact thresholds. This article is begging for a few flags. History2007 (talk) 22:07, 6 September 2010 (UTC)

This is finally beginning to seem pointless, unfortunately. I'm not sure what problem you have with Yudkowsky; I'd argue about his reliability as a source if it were actually relevant, but I wasn't using or proposing to use that article as a source for anything. I was commending it to the attention of you and anyone reading this discussion, as well as explaining what my own position on 'truth' is. In fact, as I have said several times now, my position is that the article should not discuss the concept of 'truth'; if this position carries the day, we certainly will not need a citation to support it. Furthermore, I expressed my ideas about 'proof' and 'truth' in general because you specifically, repeatedly asked about them, and they are interlarded with adumbrations as to which portions correspond to what I claim are standard usage. You have not responded in a way that suggests that you have read and understood what I said about defeasibility, the difference between vagueness and uncertainty, und so weiter. And in any case, your position is certainly no less idiosyncratic than mine. For example, the contention that "no mention of inexactness[...] is a shortcoming of the approach presented in the article" is your own opinion, with which I disagree on the grounds that (1) there is nothing about "the approach presented in the article" that precludes the introduction of appropriate treatments of 'inexactness'; (2) if 'inexactness' has to do with the "threshold of sufficiency at which evidence becomes proof", then it is mentioned (and we both agree that there is room for expansion; look here for assistance); and (3) if 'inexactness' has to do with the nature of truth itself as opposed to processes that discover or verify it, then... well, let's just say if that's what you're really arguing then you've got a lot of 'splainin' to do. However, in the final analysis, we are supposed to be talking about the article here, and while I agree with you that it could use some more examples, I'm not the person to write up detailed analysis of legal or (God forbid!) theological 'proof'. I'd much rather go and learn some more about fuzzy logic. False vacuum (talk) 03:57, 7 September 2010 (UTC)

However, the claim that "[t]his article only describes one highly specialized aspect of its associated subject" is patently absurd. Is that really the tag you wanted? Also, having re-read the article, I see how the paragraph about contradictory theological 'proofs' tends a little too much toward rhetorically undermining the idea that 'proofs' are any good at all; n.b. that just because somebody called something a 'proof' hundreds of years ago doesn't mean it is uncontroversially classified as a 'proof' today (just as Aristotle's Physics wouldn't be classified as 'physics' today)—and, for that matter, just because somebody calls something a 'proof' (or presents an argument that convinces people) today doesn't mean it actually is a proof, or that you could call it a 'proof' without scare quotes and not get slapped with a tag. False vacuum (talk) 04:08, 7 September 2010 (UTC)

Is there a "needs inexact logic" tag? And are you beginning to see the problems in the article? History2007 (talk) 05:50, 7 September 2010 (UTC)

I hope not (but the tag you applied is still false nonetheless), and no (except for the one I just mentioned). The article does not assert that proofs must be "exact", whatever that might mean, and therefore is, even by your lights, no worse than incomplete, it would seem (again, except for that paragraph). Do you disagree with the general definition of proof I've stated several times? The one that's in the article? False vacuum (talk) 05:51, 9 September 2010 (UTC)

I am sorry, but I am finding it hard to extract the exact definition of proof you propose. Please state it again in one sentence here, with WP:Reliable refs to support it. Thanks. If you mean the one that is there, i.e. "A proof is sufficient evidence or argument for the truth of a proposition" I would object to "the truth" and would suggest something like "a, possibly inexact, truth value". And I would say that sufficient needs a qualifier as in the Mathematical proof article, e.g. within the standards of a given cultural framework, at a given time. History2007 (talk) 07:00, 9 September 2010 (UTC)

How about just deleting "the truth of"? Since I don't mind either one, you'll have to discuss this with others. --Vaughan Pratt (talk) 08:11, 12 September 2010 (UTC)

It will be somewhat telegraphic, and will again run away from the inexact issues, but is vague enough to end this discussion maybe - although it will not teach the reader that much. But the issue of what the Mathematical proof article says, e.g. within the standards of a given cultural framework, will still hang around. Anyway, if the definition is made vague enough the objections will gradually go away, as will the value. History2007 (talk) 12:14, 12 September 2010 (UTC)

(edit conflict)

History2007: The "finding it hard to extract" comment seems a bit gratuitous; I said "[t]he one that's in the article[.]" And in any case, which of the things I've said about the meaning of 'proof' do you feel contradicts the definition in the article, and why? As for your two suggestions:

• I disagree that 'sufficient' needs a qualifier in the definition, and I disagree with any intended implication that the article begs any questions about what is, in fact, sufficient as it stands. The use of the word 'sufficient' in the definition does not indicate a standard of sufficiency, and the article says little or nothing—positive or negative—about standards of sufficiency except that they may vary ("The concept arises in a variety of areas, with both the nature of evidence and the criteria for sufficiency being area-dependent." That sentence has been there almost from the beginning.) Again, it can be expanded, but it's not wrong (not even by reason of excessive narrowness).
• I disagree that "a, possibly inexact, truth value" is any less controversial or POV than plain old "the truth". History2007, you disclaimed being a fuzzy-logic partisan above, but I'm starting to wonder. Do I actually need to point out that there are ways of dealing with uncertainty and ambiguity without resorting to 'degrees of truth'? Vaughan already explained why 'degrees of truth' don't model the natural-language or common-sense picture of truth: "John is very tall" doesn't mean the same thing as "it is very true that John is tall".

Finally, I suppose I'll repeat that in my opinion there's no need to mention 'truth' at all. It is however a perfectly good word, the existence of which allows more felicitous linguistic constructions; the dictionary editors write "for the truth of a proposition" instead of just "for a proposition", not to express a metaphysical view, but because (they think) it sounds better—clearer, even. False vacuum (talk) 14:56, 12 September 2010 (UTC)

Simpler question: Does the Mathematical proof article need to have standards of the field removed from 1st parag? History2007 (talk) 15:10, 12 September 2010 (UTC)

No. Why do you ask? False vacuum (talk) 15:28, 12 September 2010 (UTC)

This page should be a generalization of that page and Legal proof and Religious proof and.... by induction. History2007 (talk) 15:31, 12 September 2010 (UTC)

Hi, History2007. Since no one but you seems to feel that some sort of generalization of this article is needed, and since you haven't suggested any direction for or details of such generalization in the three months since you requested such, I'm now going to time out and remove your generalize tag until some concrete progress is made in that direction beyond merely tagging articles for the sake of tagging them.

Do let us know if this is problematic for you. --Vaughan Pratt (talk) 06:36, 17 December 2010 (UTC)

No worries I will not lose any sleep over it. But, it will take up a day after Christmas for me to go and fix the article. Overall, I think the non-mathematical items need fixing, e.g. proof in criminal vs civil cases where the standard of reasonable doubt is different; proof presented to a single individual vs a group; proofs that can have a demarcation criterion (e.g. in physics) vs those that can not ((e.g. in religion), etc. etc. etc. It should also be mentioned that some fields (such as mathematics) disallow inexact proofs (of theorems) while others such as law expect them. I have, in the background been computing these definitions in the back of my mind, now I can write it up later. It should also be mentioned that proofs may be automatic, etc. I think it is also fun to mention that some university is now selling proofs and theorems therein named after people, etc. I think what would be fun would be if you would actually write a paragraph or two on the more mathematical parts as a separate section where you summarize the idea of walking over nodes in some abstract structure such as a category and then another section will deal with legal proofs and another with ... whatever. In the meantime I conjecture that many of the nonmathematical proofs will then get absorbed into the walk-over nodes paradigm, but that the inexact cases will not be that intuitive when mapped. I think by the time that is done it will be spring and then we can take a springbreak. History2007 (talk) 10:21, 17 December 2010 (UTC)

Shorter definition?

While I'm fine with the present definition, it occurred to me that "proof" could be defined even more simply as "demonstration of truth." This of course is the content of QED: quod erat demonstrandum, which can be loosely translated as "This completes the demonstration." You prove something by demonstrating its truth.

As asked above, where does buying the judge fit into that? History2007 (talk) 19:47, 19 September 2010 (UTC)

History2007 and False vacuum have put a lot of energy into arguing over the longer definition, which might be mitigated by the instant on effect of this shorter definition: as explained in the relevant article, a false vacuum is unstable to instanton effects that may tunnel to a lower energy state. --Vaughan Pratt (talk) 18:37, 19 September 2010 (UTC)

Regarding: false vacuum is unstable to instanton effects that may tunnel to a lower energy state do you have "a proof" of that? More importantly has the issue of argument vs proof been settled? Does a proof have to be of something that is true? Whatever true may mean? History2007 (talk) 19:23, 19 September 2010 (UTC)

The article is about that meaning of "proof" for which the purpose of proof is to establish truth. Certainly "proof" has other meanings, which should join those already in the dab page.

I still would like to see this be made the primary article and the dab page be linked to from a hatnote in the primary article, as typically done in these situations. Would anyone object if I did this? --Vaughan Pratt (talk) 05:17, 10 January 2011 (UTC)

I do not see this as "ready for prime time" yet. It needs much work really. I will get to it, I will get to it. History2007 (talk) 09:17, 10 January 2011 (UTC)

2012-8-7 - semiprotected

There has been a slow edit war for a while where unregistered editors (and a few registred ones) reverse the order of the first sentence. I have semiprotected the article for two week. Please use the talk page to discuss the wording and find some consensus, rather than just reverting back and forth. — Carl (CBM · talk) 01:52, 8 August 2012 (UTC)

I don't know for certain but I believe the reason for the edits may be in reference to the mouse-over text of an old XKCD comic. http://xkcd.com/903/ It says that from any page on Wikipedia, by following the first link on every page that is not in brackets, bold, or italicised, that you will eventually reach the Philosophy page. This holds for most pages if from Proof(truth) you go via Argument but creates a loop without Philosophy if you go through Evidence. Incidentally, Munroe's Proposition is still not true regardless of the state of this page for some pages lead to loops not going anywhere near Philosophy, but I cannot remember the example I found. -Xotame 12:46 22/10/2012 — Preceding unsigned comment added by 141.163.66.130 (talk) 11:47, 22 October 2012 (UTC)

Update, Coffee and Drip brew Loop around eachother. This talk page doesn't seem awfully often frequented and I think the most common viewers are probably the people involved in the "edit war" which is clearly ongoing. For that reason, I'm going to add any other pages I find that don't redirect to Philosophy in this comment. — Preceding unsigned comment added by 141.163.66.130 (talk) 10:38, 20 November 2012 (UTC)

Someone recently made the word sufficient the first link. While it might appear that this solves the problem, the link does eventually lead to Philosophy. On an unrelated note: Is anyone even reading this? — Preceding unsigned comment added by 141.163.66.131 (talk) 11:28, 30 January 2013 (UTC)

Oh and someone changed a link in Drip brew such that it now leads to philosophy. I have no idea where I stand in this edit war.

The article was created in July 2010. By the end of that month the "sufficient evidence or argument for" part of the first sentence had stabilized to agree in content with (i) the body of the article, which has a lot to say about sufficient evidence, (ii) the four supporting sources, and (iii) the following online dictionary definitions, some of which settle for "sufficient evidence" alone without bothering with "argument".

Oxford Dictionaries: 1. evidence or argument establishing or helping to establish a fact or the truth of a statement.

Random House: 1. evidence sufficient to establish a thing as true, or to produce belief in its truth.

American Heritage Dictionary: 1. The evidence or argument that compels the mind to accept an assertion as true.

Merriam-Webster: 1a : the cogency of evidence that compels acceptance by the mind of a truth or a fact.

MacMillan: 1. information or evidence that shows that something is definitely true or definitely exists

Cambridge Dictionaries Online: a fact or piece of information that shows that something exists or is true.

What has been lacking in the edit summaries for the various changes to this sentence is sufficient evidence or an argument for departing from the stable version. Vaughan Pratt (talk) 20:31, 23 January 2014 (UTC)

Move to primary topic?

As the article seems to have stabilized pretty well since 2010, and no one seems to be arguing that any of the other meanings of "proof" are just as primary as this one, are there any objections to making this article primary by moving Proof to Proof (disambiguation) (which is currently just a redirect to Proof) and Proof (truth) to Proof? Vaughan Pratt (talk) 20:44, 23 January 2014 (UTC)