Talk:Validity

From Wikipedia, the free encyclopedia

Socrates
Philosophy Portal
This article is within the scope of the WikiProject Philosophy, which collaborates on articles related to philosophy. To participate, you can edit this article or visit the project page for more details.
Stub This article has been rated as Stub-Class on the quality scale.
Top This article has been rated as Top-importance on the importance scale.

Contents

[edit] Disputed

The content of this article is contradicted by an authority. See Talk:Logical_argument#RV_20040302.27s_edit for details. ---- Charles Stewart 13:02, 28 Oct 2004 (UTC)

I read the linked article regarding the dispute. Different sources may provide different definitions for validity and soudness (and adequacy and correctness). It is generally accepted that valid statements are true under every interpretation. Wittgenstein 1921 calls such statements 'tautologous' or 'tautologies'. The same applies to sets of statements (i.e. arguments). If all the members of S are true under every interpretation, S is a valid argument. Or you could simply say that an argument is valid iff its corresponding statement is true under every interpretation. I.e. {P->Q, P, Q} is valid iff P->Q->P->Q (or [(P->Q)&P]->Q) is true under every interpretation (is valid). Statements aren't said to be 'sound'.
I've seen in numerous texts soundness being applied to informal arguments - arguments that are interpreted. They are not called 'valid' because they are not true under every interpretation. They are sound, however, because i)the premises are true; ii)the conclusion is true; iii)the premises and conclusion are relevantly related; in other words, they do not commit any informal fallacy. Soudness may also be applied to theories. Nortexoid 04:01, 11 Nov 2004 (UTC)
"The same applies to sets of statements (i.e. arguments). If all the members of S are true under every interpretation, S is a valid argument."
This is wrong. A valid argument is not a set of tautologies (think how useless this would be); it is a set of statements where the conclusion necessarilly follows from the premises.
You took the quote out of context. Notice that I was talking about tautologies as valid. And then notice that I was talking about arguments as conditional statements, in which case S would be taken to be a set of arguments (which explains the parenthetical part). Nortexoid 12:00, 6 November 2007 (UTC)

It's a Larry's Text page. It might be better to start again from scratch. Charles Matthews 10:28, 22 Nov 2004 (UTC)

[edit] Fixed

I struck some text but kept what read properly to me. You are invited to improve it. Ancheta Wis 04:09, 28 Feb 2005 (UTC)

Do not remove the definition of 'valid formula'. It is as primary a use of 'valid' as that applied to arguments.Nortexoid 02:17, 2 Mar 2005 (UTC)

[edit] Corrections

I made a few corrections. First, it was said that a valid formula is true under every valuation. In model theory, a valuation is a part of an interpretation (or model or structure), but it is not the whole thing. A valid formula is true under every interpretation. (In sentential logic, a valuation is an assignment of truth values to sentence letters. Here valuation and interpretation are the same. But the concept of validity is not restricted to sentential logic.) Second, tautologous was cited as synonymous with valid. But tautology is a term of sentential logic. Again, this is too restrictive.

I also added a bit on the relation between valid argument and valid formula. I suppose that expands a bit on the Fixed comment above by Charles Matthews. --JMRyan 00:20, 12 August 2005 (UTC)

An atomic valuation and an interpretation amount to the same thing in predicate logic. An interpretation will induce a unique atomic valuation. Conversely, an atomic valuation v (on a domain D) will have an associated interpretation which defines each relation (or property) P as the set of n-tuples <a1,...,an> from D such that P(a1,...,an) is true under v. It doesn't really matter how it's phrased unless someone is unaware of their equivalence. Nortexoid 05:44, 12 August 2005 (UTC)

[edit] Models of Propositional Calculus

Presumably any model of propostional calculus would consist of a truth assignment to each atomic proposition (and then to every wff using the standard semantics of ^,v,¬ etc.) such that the axioms hold. Is this right?


[edit] A better definition

Here's the current definition of a valid argument: "An argument is said to be valid if, in every model in which all premises are true, the conclusion is true."

Under this definition it's ambiguous whether an argument is valid when it contains a self-contradictory premise (since there would be no model in which all the premises are true). At least the way I learned it, we want such arguments to be considered valid. So a better definition would be:

"An argument is valid if and only if it is impossible for all the premises to be true and the conclusion false."

It's not ambiguous. If an argument has an inconsistent set of premises then it is vacuously true that "an argument is valid if, in every model in which all premises are true, the conclusion is true". Note that the antecedent of that conditional fails in the case of inconsistent premises, and so the conditional will be "vacuously" true.
Your definition invokes these strange locutions involving impossibility that we'd be better off without. Nortexoid 19:10, 21 December 2005 (UTC)
Okay, whatever. I'm fine with the other definition... but if there are inconsistent premises, are you sure "the conclusion is true in every model in which all premises are true" would be false? To me it makes just as much sense to call that true, if there are no models in which all premises are true.
That is precisely what was said. If there is no model for the premises taken together, then it is vacuously true that "the conclusion is true in every model in which all the premises are true". Is is not false. Nortexoid 02:17, 23 December 2005 (UTC)

[edit] Appeal to authority

I'd like a second opinion in the discussion at Talk:Appeal to authority...I could be wrong, or arguing poorly... NickelShoe 15:46, 2 February 2006 (UTC)

[edit] Nortexoid Edit Undone

I have reverted Nortexoid's major edit of the validity article for a few reasons. I preface these reasons with the note I did not see anything wrong with the content of what was in that edit. I think that things might well proceed in the direction introduced, but the context of the article as a whole should be acommodated. In particular, (a) the term 'valid' as used in the broad subject of logic should initially be characterized for the general reader, not as used specifically in formal logic (as the Nortexoid edit presents it). To begin the argicle in this way immediately puts the term, and the concept, in the ball-park of formal logic, which isn't the only place the term/concept occurs in logic generally. (b) It also invokes concepts of models and interpretations that have not been spelled out for the uninitiated reader--so that he/she comes to the article, reads the first sentence, and has no idea what is meant. There are other various reasons for looking more carefully at the edit--there is some redundancy (which can be OK, but in this case appeared to me at least somewhat awkward), and again at the end of the article the concept of validity is put into the category only of formal model theory--which underdetermines the scope of logic. There are little things, too, which might better be discussed. For example, Nertexoid adds the parenthetical "partial" to that remark that assignment of Socrates, men and mortals to the terms in the partly formalized argument comprise an interpretation of the argument. This is of course technically right--in mathematical logic, an interpretation needs to interpret the whole language--but attendance to that bit of formal correctness isn't necessary for conveying to the general reader the basic concepts for understanding validity. (I note, too, that interpreting the quantifiers and connectives isn't usually what is meant in logic by "an interpretation"--although we do talk of non-standard models of (e.g.) arithmetic, where the domain isn't the reals (or whatever) and where we interpret, say, the symbol '+' as indicating a different operation than addition, etc. By noting this, I don't mean that what is said is wrong, but that it is perhaps somewhat misleading to have it here in the article, as it skews the discussion in the direction of a more specific, rather than a more general, discussion of the article's subject.) Again, these remarks aren't about the edit author's (obvious) competence in the subject, but about the best approach to an article for non-specialists (which could certainly contain links to more specialized treatment, even within Wikipedia).--jbessie 15:42, 4 May 2007 (UTC)

I didn't see this before. Personally I don't care how the article reads, or what is pedagogically best for a general audience (though I do not think what is there now is best), but I thought Wikipedia was an encyclopedia, not a dictionary. If people want lay-definitions of the term 'valid' as it is used by people who misuse it, then they would consult a dictionary, I should hope. Sadly, I don't have high hopes for most of the "mainstream" logic articles. Nortexoid 00:57, 7 November 2007 (UTC)
I think there's always a question of audience--even for an encyclopedia. It's not obvious who the audience is here--but I do think that the approach you appear to advocate has a place here, but perhaps in a linked article entitled something like 'Validity (mathematical logic)'.--jbessie 02:59, 7 November 2007 (UTC)

This can't be right:

For the purposes of this article, an argument is a set of statements, one of which is the conclusion and the rest of which are premises. The premises are reasons intended to show that the conclusion is, or is probably, true.

What about arguments that seek to show a conclusion is false; or those that are hypothetical, where nothing is being asserted?

And what have "reasons" got to do with anything? I suspect the author of this article has confused logic with informal logic.

Rosa Lichtenstein 01:29, 7 October 2007 (UTC)

Re. 'This can't be right':
The definition is fairly standard; use of 'reasons' instead of another word (or none at all, e.g., 'the premisese are intended to show...') is because validity is not confined to the context of formal logic. 'Reason' suggests an ordinary context of argumentation, is a familiar word, etc. It wouldn't bother me if the word 'reason' were left out, though.
Regarding arguments that seek to show a conclusion false: what form would such arguments take? An argument is not presented to show that its own conclusion is false. Perhaps what is meant is that arguments are presented to show that some statement is false, in the sense that a conclusion is put in the form 'not-p', e.g., 'it is false that cows live on the moon'. However, the statement, 'it is false that cows live on the moon' is itself argued to be true--this is the conclusion of the argument. --jbessie 16:44, 8 October 2007 (UTC)

I am sorry but this is confused.

"Standard"? I think not.

If the author of this article had meant to include informal notions of validity then this should have been made clear.

As to the second point, are you kidding me? Hypothetical argumentation depends on not knowing whether the conclusions are true or false, and in certain circumstances, someone might know/suspect a conclusion is false and seek to show it is. This happens in science all the time.

And, of course, RAA depends on this property of validity.

Finally, I suspect you are confusing negation with falsehood.

http://www.earlham.edu/~peters/courses/log/tru-val.htm

Rosa Lichtenstein 02:57, 3 November 2007 (UTC)

'Standard' is meant in the sense of 'it's pretty typical of introductory logic texts,' both formal and informal. If what is wanted is an article on formal validity, that of course can be presented--but see my comments on nortexoid, above. That was a fairly straighforward treatment of validity in mathematical logic. Even use of the word 'formal' in 'formal logic' is somewhat open to nuance.
Regarding your rejoinder to the second point, 'hypothetical argumentation'--not exactly sure what you have in mind. Let us suppose that it is not known whether or not p. You suggest there are contexts in which one might attempt to 'show it is [false]'. An explicit rendition of the argument might then be something like, " A1, A2,...,An, therefore, 'p' is false." Note that what is argued for in this is: 'p' is false. But this last, the whole statement, viz., " 'p' is false " is itself the conclusion of the argument. It is a statement, and if the argument successfuly shows that 'p' is false, then the argument has shown that " 'p' is false " is a true statement. Again, all this is pretty standard stuff.
Finally, no, I'm not making a confusion between a syntactic notion and a semantic one.
I haven't said anything that would be surprising or odd to professional logicians (having been one myself...)--jbessie 01:12, 5 November 2007 (UTC)
Well, OK, I take it back: what I said will be odd to mathematical logicians who prefer the context of discussion in the presentation of validity be entirely formal (recent exchange, above, w/ Nortexoid). Then the characterization of validity would be more like,"A statement s is a consequence of a set of statements G just in case there is no model under which all elements of G are true but s false," i.e., the inference of s from G is valid just in case... etc. However, at least for me, part of what's at issue is identifying what it is that such formulations are (or were) intended to capture. One way of looking at it is that the question of validity (viz., cast as the impossibility of true premises but false conclusion) now becomes a quesetion of mathematical existence: there exists no model in which the premises are all true but the conclusion false, which, presumably, involves more tractable mathematical concepts and constructs than than the difficult notions of possibility and impossibility. However, at least at the introductory level, it's useful to begin with the more naive characterization (which is not entirely unintuitive nor does it lack applicability--and it is arguable that it aptly captures what we mean by 's really does logically follow from G' in some intuitive sense) before drawing the inquiring mind into deeper and more formal attempts to cash out the meaning and give something that can be used, e.g., in solving a decision problem, etc.
The characterization of argument presented here is apt for discussion of (deductive--some would say the only kind of) validity. In the context of scientific reasoning, some other sense of 'argument' could of course be presented, especially if it acommodates discussion of inductive strength, statistical reasoning, etc--jbessie 13:57, 7 November 2007 (UTC)

[edit] Fresheneesz edit undone

I have reverted Fresheneesz's edit of this article not because I disagree with the general aim of condensing the treatment nor of attempting to make the thing read more easily and be clearer, but because I believe the changed content is incorrect and/or misleading. Fresheneesz's edit speaks, e.g., of valid arguments as well as statements--and this is fine (although I'm a little bit hesitant to speak of statements as 'valid', preferring instead locutions like 'logically true', 'tautologous', 'analytic', 'necessary truth', etc., which are philosophical/logical expressions typically applied specifically to statements and not to arguments; many texts do define valid statements or sentences). But the content then goes on to characterize both valid statements and arguments as "always true." Generally speaking, the concept of truth isn't considered a property of arguments--since an argument is a set of statements with an implied structural relationship. I do note a precedent for Fresheneesz's approach to the subject in some composition texts (as opposed to philosophy or logic texts). Academic expertise in the subject itself, however, is usually accepted as residing in philosophy and mathematics, and so I favor this article being informed by approaches to the subject stemming from those disciplines.

OK, I'm finally going to try to let go of this article and will now take it off my watch list...--jbessie 16:29, 8 November 2007 (UTC)


[edit] Not-Just-Yeti edit undone

OK, I'm back for a moment. Not-Just-Yeti had edited the definition of 'argument' to read as follows:

"For the purposes of this article, an argument is a sequence of statements, starting with premises (assumptions), followed by deductions (each of which follows from previous statements); the final statement is the conclusion."

I undid this edit for a couple of reasons: (a) an argument need not be a sequence of statements, nor (b) even if it is, it need not be the case that the initial statements be followed by deductions, where each statement in the lenghthening sequence follows from previous statements until the final statement is reached. In the former case (a), an argument is usually just a set of statements (typical logic text/math-logic text definition), and in the case of (b) the rewordinig suggests a definition of (formal) proof, not argument. Moreover, even though the concept of validity is in a deductive context, the definition of argument itself need not be confined to deductive reasoning (another reason to avoid referring specifically to a sequence of deductions). A key context-setter is the preface, "for the purposes of this article." If a more discourse-oriented exposition is wanted, more of the article would need to change.--jbessie 21:41, 14 November 2007 (UTC)

[edit] Importance?

Is this article really worthy of 'top' importance status? It's a bit confusing whether importance is for the whole project or just the work group (logic, and I believe it is the latter), but even just for logic I wouldn't think validity would be more than high importance. Richard001 (talk) 07:35, 27 January 2008 (UTC)