Talk:Hypothetico-deductive model

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This statement in the current article is incorrect:

"This problem is related to the problem of induction, and arrises because it is logically invalid to infer a general case – a hypothesis – from any series of specific observations."

Induction cannot be "logically invalid" because induction is non-logical it has nothing to do with logic which is deductive by definition. B 23:10, Dec 11, 2003 (UTC)

Garr. I've gone on a wild goose chase, around and around, and back to the start. Indeed, Bayes does solve this "paradox" which is no paradox.

We solve it by saying "certainly if you show me a non-white thing, and I see it is not a swan, it actually does increase the validity of my hypothesis, just that a swan being white inncreases the validity a lot, and a non-white thing being a non-swan increases the validity of my hypothesis an almost-insignificant amount."

Read the article on the Raven paradox to see how easily it's solved using modern logical and statistical method. —Preceding unsigned comment added by PhiloVivero (talk • contribs)

Did you take a look at the talk page for raven paradox? Banno 11:34, Jun 11, 2004 (UTC)

I would submit that this "paradox" is poorly based on the Method in the first place- at least for the scientifically minded. Philosophers may decide to debate other aspects of the method that are decidely less used. For scientific usage, a hypothesis is: hy·poth·e·sis Audio pronunciation of "hypothesis" ( P ) Pronunciation Key (h-pth-ss) n. pl. hy·poth·e·ses (-sz)

  1. A tentative explanation for an observation, phenomenon, or scientific problem that can be tested by further investigation.

(The American Heritage® Dictionary of the English Language, Fourth Edition)

Thus, "All Swans are white" is not a hypotheis. It is a statment of generality of observations. Statements or obbservations alone do not provide a structure for prediction and experimentation - i.e. an Method. With out a method, we are aimless. No? —Preceding unsigned comment added by 132.198.177.222 (talk • contribs)

The statement "all swans are white" is only logically equivalent to "all non-white things are not swans" if it is a double implication, i.e.

Swan <-> White is equivalent to NOT(Swan) <-> NOT(White).

So if your hypothesis is

Swan -> White (which I think is more common), this is actually not equivalent to Not(Swan) -> Not(White).

An observation of a non-white thing will not (dis)prove anything if I'm correct. —Preceding unsigned comment added by 130.37.30.222 (talk • contribs)

Wrong. A basic premise of classical logic is 'modus tollens', which is as follows:

1. A -> B 2. therefore -B -> -A

Or, if A implies B, then not-B implies not-A. Think about it in terms of set-theory, if you prefer. Imagine a Venn diagram; if A implies B (eg. if X is a swan, then X is white), then set A will be a subset of set B--the A circle will be completely inside the B circle. Therefore if an object is not B (ie. outside the larger B circle), it is not A (ie. cannot be inside the smaller A circle): if it is not-white, it is not a swan. So the paradox holds. Capiche? —Preceding unsigned comment added by 149.169.167.138 (talk • contribs)

It will suffice to simply point out where someone is in error, without taking on a tone of superiority. Besides, you are describing the law of transposition. Modus tollens says that if you have (A > B) and you know (~B) then you know (~A). You should probably be certain that you are correct before you make a fool of yourself trying to point out an error. Jaggerblade 16:36, 23 October 2006 (UTC) [forgot to sign before - time is wrong]

Not all swans ARE white. "Swan" is not a species, but rather is a collection of a few Genera. Even in the genus "Cygnus" do we see the Australian Black Swan as well. We could state that all Mute Swan or all Whooper Swan or all Trumpeter Swan are white. —Preceding unsigned comment added by 70.57.233.2 (talk • contribs)

Umm... I believe that you are wrong by assuming that all A are an element of B implies that all B are A. For example, all pigs are animals is true, but all animals are pigs is not true. We are dealing with set theory, not propositional logic. Also, modus tollens is "if p implies q,and p is false, then q is false", not "if p implies q, and q is false, p is false". And yes, not all swans are white:) —Preceding unsigned comment added by 69.169.233.206 (talk • contribs)
Modus tollens, as I pointed out above, is the denial of a hypothetical following the asserted denial of its consequent. You do indeed deny the consequent, and not the other way around, as you have written. Denying the antecedent is fallacious, because its truth or falsity has no bearing on the truth or falsity of the conditional. That's why the truth-table for two-value conditionals is written as follows:
p  >  q

T (T) T
T (F) F
F (T) T
F (T) F
Notice that a conditional is always considered true, despite its antecedent being false. You can also see very easily from this truth table how modus tollens works out: if you know that the conditional itself is true, and you spot that the consequent is false, you can look at the two cases where the consequent is false (lines 2 and 4) and see that the truth of the conditional will only be preserved if the antecedent is also false (line 4).
I don't know what you mean by set theory exactly, but in terms of logic, we are dealing with Aristotelian logic, also known as categorical logic. All Swan is White being transformed into All non-White is non-Swan is indeed a legal move, and is preserved in modern logic by the law of transposition. It really makes perfect sense if you think about it. If you know that every swan is going to be white, then you also know that any time you see something that isn't white, it is not a swan.
Also, I would encourage anyone who doubts my claim about modus tollens to simply consult an introductory logic textbook. This arguing is just silly, because modus tollens is an accepted formula, and is therefore a verifiable fact. Someone here is obviously right and the other obviously wrong. There is no need for continued discussion: anyone who wants to see who is correct can go straight to the source. Here's a net source that may clear things up: [Discussion of Conversion, Obversion, & Contraposition], [Discussion of Elementary Propositional Rules of Inference] Thanks. Jaggerblade 16:36, 23 October 2006 (UTC)


Contents

[edit] Popper

The Hypothetico-deductive method is the name given to Popper's philosophy of science. Although a few other philosophers had similar ideas, it was Popper who developed the logic of falsification. Go back to the version before the interference of Jon Awbrey (talk · contribs), who is now banned, and you will see that the article once supported this view.[1] Falsification and Hypothetico-deductive method are not mentioned in Charles Peirce. Or to put the same point in another way, the statements that Aristotle, Peirce and Hemple all knew about hypothetico-deductive method - well, shall we say that they need supporting citations? Banno 22:37, 20 October 2006 (UTC)

[edit] Re-direct?

The logic and philosophy here are pretty shallow. Perhaps it should just be re-directed to the much more complete Falsification article. Banno 22:37, 20 October 2006 (UTC)

[edit] Sign your comments, please

For some reason, most users on this particular talk page do not find it necessary to sign their comments. Please do not forget your four tildes! Simões (talk/contribs) 19:12, 21 October 2006 (UTC)

[edit] Is 2nd paragraph of the article now a straw man?

I believe that, with the current revision, the 2nd paragraph is now a straw man. The implied hypothesis of the 2nd paragraph is that all ravens are black. Use of an empty (thus nonstringent) test is not "corroboration" of the hypothesis, merely because it does not and cannot refute the hypothesis. We only count as a test those elements that could conceivably falsify the hypothesis. Then the 2nd paragraph seems polntless. --Thomasmeeks 00:19, 12 March 2007 (UTC)

The first para. has been further tightened to remove ambiguity. The 2nd and 3rd para. appear to be irrelevant to the formulation in the first paragraph. On that basis, there is no reason to retain them. The Falsifiability article avoids the same problem similarly. Comments welcome. --Thomasmeeks 22:42, 22 March 2007 (UTC) (Proofreading fix.) Thomasmeeks 18:30, 25 March 2007 (UTC)

Rather than delete the 2nd and 3rd paragraphs of the article (suggested above), I have attempted to strengthen them in the current Edit, adding responses of advocates for the hypothectico-deductive method. --Thomasmeeks 21:07, 25 March 2007 (UTC) (sp.) Thomasmeeks 10:52, 8 April 2007 (UTC)

[edit] "Logically equivalent to.."

There is a line in the article that says "'All ravens are black' is logically equivalent to 'all non-black things are non-ravens' ". Since when was this a logical equivalence!? One statement does not imply the other. Roberdin 20:12, 14 May 2007 (UTC)

Same statement is in Raven paradox. Blackburn's Dictionary of Philosophy affirms it (Hempel's paradox entry, p. 173). One way to picture it is with a Venn diagram as: ravens a subset (whether proper or not) of black things, which are in turn a subset of all things. --Thomasmeeks 00:31, 15 May 2007 (UTC)
They certainly do imply one another. If you're familiar with first-order logic, you can quickly prove the biconditional relation of the following:
  1. ∀x(Rx→Bx)
  2. ∀x(~Bx→~Rx)
Simões (talk/contribs) 00:38, 15 May 2007 (UTC)
Providing one assumes the Law of excluded middle. Pgr94 08:01, 15 May 2007 (UTC)
They have to assume the law of non-contradiction, too, but this all goes without saying. Everyone assumes these laws unless they're explicitly talking or writing about non-classical logics. Simões (talk/contribs) 00:36, 16 May 2007 (UTC)
Translation of the above notation and terminology:
For all objects x such that x is a Raven, x is Black.
For all objects x such that x is not a Raven, x is not Black.
Biconditionality means logical equivalence. The equivalence of the 2 statements agrees with Blackburn and Simões. ("For all objects [x] such that," called a 'universal qualifier', is often written as an upside-down A.) --Thomasmeeks 22:22, 26 June 2007 (UTC)

[edit] Popper and Hypothetico-deductive approach

The article presents Popper as the popularizer of the hypothetico-deductive approach. This is obviously complete nonsense. Popper was an opponent of the existence of any approach that infers something from evidence (or that even holds that evidence exists), be it a hypothetical inference or any other. Popper also clearly held that no corroboration in the sense used in the article exists. As Miller correctly says in his Crtitical Rationalism, Popper's approach is a hypothetico-destructive, not a hypothetico-deductive one. And Popper went further and held that scientific method does not exist, but that the hypothetico-destructive approach is universal and applies to anything at all; not in any way restricted or special to science. --rtc (talk) 01:30, 26 November 2007 (UTC)

At least one citation from Popper with page numbers, to back up your statement, is in order here. Since the term 'hypothetico-destructive' is so distinctive, Popper would have included it, if he espoused it. If he originated the school of thought, but did not name it then we need an article with a link to this one. --Ancheta Wis (talk) 11:37, 26 November 2007 (UTC)
It is right at the beginning of chapter 6 in said book Crtitical Rationalism. The reference given to the index in Conjectures and Refutations in this article point to places that talk about hypothetico-deductive systems, not about a hypothetico-deductive method, and Popper does not talk about his own position, but about historical theories. --rtc (talk) 02:49, 27 November 2007 (UTC)