Is there a diff. between the propositions 'P' and 'P is true'?
Is there a diff. between the propositions 'P' and 'P is true'? | |
•derrick.farnell
Initiate Usergroup: Members Joined: Oct 21, 2009 Location: Edinburgh Total Topics: 7 Total Posts: 24 |
Posted Mar 26, 2012 - 3:45 AM:
Subject: Is there a diff. between the propositions 'P' and 'P is true'? Hello
and
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•fdrake
Hoak, Hogan. Usergroup: Members Joined: Aug 13, 2010 Location: Bonnie Scotland Total Topics: 24 Total Posts: 1187 |
Posted Mar 26, 2012 - 4:01 AM:
Propositions in the same language which entail eachother are logically equivalent. One thing to watch is that P and " "P" is true " aren't necessarily propositions in the same language, as P's being true isn't P. Even if P, then "P is true" is true, and if "P is true" then P, the entailments might be different. As in "P => "P is true"", as far as I'm aware, isn't a well-formed-formula of propositional logic, so the entailment we use there isn't the material conditional. P => P is true says more than P=>P. |
•derrick.farnell
Initiate Usergroup: Members Joined: Oct 21, 2009 Location: Edinburgh Total Topics: 7 Total Posts: 24 |
Posted Mar 26, 2012 - 6:16 AM:
Thanks very much for your reply fdrake.
Therefore,
As I said, given that 'P is true' is a proposition about the proposition P, it seems to me that they can't be the same proposition. |
•derrick.farnell
Initiate Usergroup: Members Joined: Oct 21, 2009 Location: Edinburgh Total Topics: 7 Total Posts: 24 |
Posted Mar 26, 2012 - 6:21 AM:
Sorry, upon re-reading your post, I see that you seem to indeed be agreeing that they're distinct propositions: 'P => P is true says more than P=>P' |
•Willemien
Blond Dutch Mensa meisje Usergroup: Sponsors Joined: Apr 05, 2011 Location: London (UK) Total Topics: 74 Total Posts: 996 ♀ |
Posted Mar 26, 2012 - 7:10 AM:
derrick.farnell wrote: Hello Please could you help me with the above question. For example, is there a difference between the propositions: Edinburgh is the capital of Scotland. and The proposition 'Edinburgh is the capital of Scotland' is true. ? Given that the second proposition is a proposition about the first proposition, it seems to me that they can't be the same proposition. Instead, each merely directly implies the other. That is, if Edinburgh is the capital of Scotland, then the proposition ‘Edinburgh is the capital of Scotland’ is true - and vice versa. Is there a term for a pair of propositions that directly imply each other? Derrick There are books written about this. And all those writers disagee with eachother. some opinions: - Tarski : "is true" is not a predicate so "X is true" is not a logical statement. - ? : they have the same logical content - ? : the X is true is a stronger statement than X |
•derrick.farnell
Initiate Usergroup: Members Joined: Oct 21, 2009 Location: Edinburgh Total Topics: 7 Total Posts: 24 |
Posted Mar 26, 2012 - 7:52 AM:
Thanks Willemien. Re your selection of other's opinions, I think that my opinion is not just different from the first two, but also from the third - that is, it's not that I think that 'P is true' is 'stronger' than P, but that it's just different, because it's a proposition about P, and so can't be the same proposition as P. |
•ughaibu
Unmoderated Member Usergroup: Unmoderated Member Joined: May 01, 2006 Total Topics: 25 Total Posts: 359 |
Posted Mar 26, 2012 - 8:07 AM:
On the face of it, it seems to be obvious that they're not the same. Let P be the proposition X is false. X is false is not the same as X is false is true. |
•Owen
Resident Usergroup: Members Joined: Oct 17, 2004 Total Topics: 25 Total Posts: 277 |
Posted Mar 26, 2012 - 1:23 PM:
ughaibu wrote: On the face of it, it seems to be obvious that they're not the same. Let P be the proposition X is false. X is false is not the same as X is false is true. I don't agree. p =df (p is true). ~p =df (p is false) (p is false) is true <-> (~p) is true <-> ~p. (p is false) is false <-> (~p) is false <-> ~(~p) <-> p. Edited by Owen on Mar 26, 2012 - 1:38 PM |
•Pneumenon
What're you all about? Usergroup: Sponsors Joined: Jan 03, 2012 Total Topics: 30 Total Posts: 430 ♂ |
Posted Mar 26, 2012 - 5:45 PM:
Is the sentence, "Everything John says is true," equivalent to "Everything John says"? |
•Owen
Resident Usergroup: Members Joined: Oct 17, 2004 Total Topics: 25 Total Posts: 277 |
Posted Mar 26, 2012 - 6:52 PM:
Pneumenon wrote: Is the sentence, "Everything John says is true," equivalent to "Everything John says"? Of course..If all propositions that John says include p1, p2, p3, etc. then what John asserts is that p1, p2, p3, etc., are true. That is to say, (p1, p2, p3, ..) <-> (p1, p2, p3, ..) is true. 'Is true' is a redundent predicate of propositions. (((p is true) is true) is true) <-> p. |
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