Talk:Corresponding conditional

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New article explaining meaning and use of corresponding conditionals in Logic Philogo 02:10, 6 February 2007 (UTC)Reply

Refs:- corresponding conditional

Trimmed--Philogo 23:30, 21 July 2008 (UTC)

Note ref which explains all more succintly but more tehcnically:

> Every derivation, A1, A2,...An therefore B, can be re-expressed as a conditional statement, (A1 o A2 o ...o An) =>B, called the corresponding conditional of the argument.

Corresponding conditional from the Free On-line Dictionary of Computing

This article aims to be less technical.

Lead A In logic a corresponding conditional is a statement whose principal connective is the material implication symbol, and whose antecedent is the conjunction of the premises or an argument and whose consequent is the conclusion of that argument.

B In logic, a corresponding conditional is a proposition that corresponds to an argument. Every argument in first order logic may be represented as a corresponding conditional.

A is better than B, becuase B uses the vague "corresponds to" and "may be represented" which tell you very little, if anything. It uses the term "proposition" which is controversial. A defines quite clearly what a cooresponding conditional is. Thefore I shall revert to A but substitute "sentence" for "statement" being even less controversial.--Philogo 23:35, 22 July 2008 (UTC)

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The follwing is now redundant so I will del: Given an argument, the corresponding conditional is a material conditional statement whose antecedent is the conjunction of the argument's premises and whose consequent is the argument's conclusion.--Philogo 23:35, 22 July 2008 (UTC)

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C An argument is valid if and only of its corresponding conditional is a necessary truth.

D An argument is valid if and only if its corresponding conditional is necessarily true.

I see litle point in wikilinking "if and only if", the words being used in the normal way. I think "necessary truth" is a tad more specific. Therefore I will rev to C but substitute "just in case" for "if an only if".--Philogo 23:35, 22 July 2008 (UTC)

Example E

If an argument A were of the form

Either P or Q

Not P

Therefore Q

Then its corresponding conditional C would be:

((P${\displaystyle \lor }$Q) ${\displaystyle \wedge }$ ${\displaystyle \neg }$P)${\displaystyle \to }$ Q

F

1. Plato is either alive (A) or dead (D).
2. Plato is not alive (not A).
3. Therefore, Plato is dead (D).

F is a very strange and confusing way to set out an argument. Are the As and Ds part of the argument or in line refs.? What do they stand for? E is clearer and more conventional therefore I will reinstate it.--Philogo 23:51, 22 July 2008 (UTC) ---

Th following is redundant and introduduces other issues not germane to the article therefore I will del:-

${\displaystyle (A\oplus D)\land \lnot A\to D}$

This statement is necessarily true if and only if the original argument is valid. The statement may be rewritten as follows since exclusive or implies logical or,

${\displaystyle (A\lor D)\land \lnot A\to D}$

Although logical or does not imply exclusive or, these two statements can be shown to be logically equivalent, so the latter is also a corresponding conditional since it satisfies the if-and-only-if criterion

Your points are well taken, so I will reply to them individually. First, I based the "Plato" argument on precedent of using Plato in logical argument seen elsewhere on Wikipedia: namely First_order_logic#Why_is_first-order_logic_needed.3F and statement (logic). Perhaps "Socrates" would be more appropriate. Also, since this article is about connecting arguments to propositions, I thought it fitting that we present the same statements in two contexts, as phrases (e.g., "Plato is alive") and as symbols (e.g., A), since this similar to how this concept may be encountered in logic and mathematics.

Second, I don't think proposition is "controversial". The article should use the words proposition and statement, since these are well defined in Wikipedia.

Third, I agree that the section about exclusive or and logical or is not relevant. --Beefyt (talk) 02:12, 23 July 2008 (UTC)Reply

I am sorry but I think your propsed new exasmple is very poor and confusing to a reader for the reasons previously given. I cannot understand why you think it is an improvement.

Quine and others attacked the concept of a "proposition". The alternative "statement" was promoted by Strawson in 1957 but this has also been critised for various reasons. The term "sentence" tends to be used by modern text books for referring to certain wffs. In talking about natural languages the term sentence as used by logicians as more or less shorthand for meaningful declarative sentence but that itself is open to dispute (makes use of term menaingful - Is "The King of France is Bald" meaningful but false, meaningless, or failing to make a statement). Its a minefield, but the term sentence is the most neutral and thefore to be preferred. I suggest some books you could read on this intersting issue, I am afraid you certainly should not rely on Wikipedia on this issue! The following definition is correct but we want to write an article that's more user frinedly. You will see there is nothing in the definition that restricts it to first order logic:

> Every derivation, A1, A2,...An therefore B, can be re-expressed as a conditional statement, (A1 o A2 o ...o An) =>B, called the corresponding conditional of the argument.

Corresponding conditional from the Free On-line Dictionary of Computing

If its all the same, the current version does not use "sentence", "proposition", or "statement", but only "argument" and "logical implication." Does this suffice to get the point across?

Not really, beacause a correpsonding condition is a sentence whereas a logical impliction is a relation see logical implication. In Logic, sentences (which are declarative sentences, also variously called propositions or statements) are those strings of words or symbols which are either true or false. See Atomic sentence

Am I mistaken in thinking that a corresponding conditional is a logical implication? I may not be an expert, but how is a statement such as ((P${\displaystyle \lor }$Q) ${\displaystyle \wedge }$ ${\displaystyle \neg }$P)${\displaystyle \to }$ Q not a logical implication? Or, is the issue the fact that saying a corresponding conditional is a logical implication is not precise enough? Please shed some light on the subject, because although you are interested in making this article as precise as possible for students of logic, I am interested in making it understandable for non-experts. I hope we can find a middle ground. --Beefyt (talk) 02:05, 26 July 2008 (UTC)Reply

The purpose of the example is give illustrate how a real argument in sentences, as you put it, corresponds to a symbolic statement. I believe your original example did not satisfy this, since the argument put forward contained only symbols to begin with. I merely substituted these symbols for plain English statement such as "Socrates is dead"=D and "Socrates is alive"=A. How is this confusing? Can you explain how a reader might not understand this? --Beefyt (talk) 14:43, 24 July 2008

(UTC)

Now I see. You fancy an argument in natural language. Translate this into symbols, then construct the corresponding conditional. I'll tell you what I'll do. I'll leave your example as is for now, but put back my original (as well) preceeded by the argument in natural language. Don't just revert things make comments and we can work together: more satisfying and productive. I am not sure how much logic you have studied but the article is intended for people who are or ae studying it at elementary level and may come across this term. My origianl example assume familiarity with sentencial logic not first order so it would be accessible to somebody doing an introductory course in Logic.--Philogo 12:55, 25 July 2008 (UTC)

The reason I originally changed your example to mine is because I believed the two were equivalent. Is this not the case? Is there some subtle point of logic here I am just missing? --Beefyt (talk) 02:05, 26 July 2008 (UTC)Reply

BTW the negation of a tautology IS a contradition, not just a sentence that "leads" to a contradition. So the corresposnding conditional of a valid argument (or derivation) IS a tuatolgy (you know all trues in its truth table) and its negation IS a contradiction (all false in its truth table).--Philogo 13:22, 25 July 2008 (UTC)

I think the language you are referencing was originally added by you, as seen in this revision before I began editing this article. I have no complaints with these changes, but I do think "denial" reads more clearly than "negation", although it does not seem as precise, and "necessarily true" reads more clearly than "tautology", which I think of as a violation of WP:JARGON. --Beefyt (talk) 02:12, 26 July 2008 (UTC)Reply

I think this definition is correct: In logic a corresponding conditional is a sentence whose principal connective is the material implication symbol, and whose antecedent is the conjunction of the premises or an argument (or a derivation) and whose consequent is the conclusion of that argument. An argument is valid if and only of its corresponding conditional is a necessary truth.

The corresponding conditional may be a tautology but not necessarily so. A tautology is one type of necessary truth. I appluad making articles understandable for non-experts (without loss of precision) and be very happy to work with you on this. One problem is that often terms have a technical meaning not the same as the common meaning. (Argument, tautolgy, statement, proposition and valid are e.g.s in logic; force, momentum, intertia ar e.g.s in physics.) A solution is to footnote or wikilink any techinical terms to a definition. --Philogo 11:21, 26 July 2008 (UTC)

This article elucidates the definition of "corresponding conditional" as described in "argument". Also, it is substantiated by the Free Online Dictionary of Computing. Considering these points, I do not believe this article should be classified as "junk," as it obviously is a valid and useful concept, so I am removing the deletion proposal. --Beefyt (talk) 04:38, 7 August 2008 (UTC)Reply

Please give any reasons here for diverting to strict conditional before doing so again. Thanks--Philogo 12:43, 13 October 2008 (UTC)

Very well. Philogo: please give some thought to Glemtpm's suggestion that corresponding conditional and strict conditional be combined into a larger article about conditions in general. Gemtpm: can you give a better reason for merging the articles? --Beefyt (talk) 15:58, 13 October 2008 (UTC)Reply

I have reverted this article to the state it was in before merging with strict conditional. Philogo: if you have any changes in mind please consider first establishing consensus, i.e., do not make 10 edits in a row and revert sections to previous versions. That kind of consensus should be established on this page first. I recommend making small changes and waiting to see if any editors disagree with the change. Silence implies consent. --Beefyt (talk) 16:11, 13 October 2008 (UTC)Reply

Where is "Glemtpm's suggestion that corresponding conditional and strict conditional be combined into a larger article about conditions in general." to be read? There do not appear to be any other editors who wish to help improve this article with whom to form a consensus. Check the history. I'll carry on improving it to my best ability but if anybody thinks I have got it wrong or could make it even better pleae comment here. OK? Thanks --Philogo 22:09, 13 October 2008 (UTC)

The article is now more or less in the state it was when it was last comprehensible. Subequen edits havd caused deteriroration to such an extent that deletion was suggested. I have added a new paragraph this PM explaining in more detial how a cc can be used practically to test an argument for validity. To my best knowledge the only reason that you would want to know about ccs is because it give you a useful technique for testing an argument for validity. In other words its usefullness in pedagogical. I a;ways used it when I helped teach logoc to undergradutea for about three years and it proved both useful and easy to understnad. It also serves to bridge the gap beween Arguments, which is what people are interested in when they take up logic, and formal text books whihc hardly mention then after caheter 1! When I originally wrote the article back in February 2007 I had an example derivation but I dumped that because I thought it would be too complicated for people who might be reading this article, which is pitched at readers who have embarked on a course in elementary logic at undergrad level . If I ever got the time I might do one on truth trees as well. Any suggestions just holler here! But please no more divert or wholesale deletions of material without giving some reasons first! If we don't agree I am sure I can get another member of the Logic ask force to drop by and comment. --Philogo 22:35, 13 October 2008 (UTC)

Since 2007 this article has had 156 edits by 17 editors and to date has no sources or references. External links that qualify as references should be used as such. An external link has a specific purpose and Wikipedia content is governed by core policies that also includes no original research and neutral point of view. Ideally I would hope that someone would take a look at this and see if there are references and "if" any of the listed external links can be used as such. Otr500 (talk) 23:20, 22 December 2011 (UTC)Reply