16 Jan '07 21:44>
Do you still maintain that all propositions are either true or false?
Originally posted by PawnokeyholeLOL. Of course. That's part of the standard definition of the term. Having a single truth value is part and parcel of being a proposition.
Do you still maintain that all propositions are either true or false?
Originally posted by NullifidianIf you are going to assert that that thing is a proposition, then it is a false one. See the thread that sparked this call-out for an explanation.
"This sentence is not true."
Is this proposition true or not true? It can only be one or the other, after all.
("Paging Dr. Goedel. Paging Dr. Goedel. A poster in the Spirituality forum needs your attention, please." )
Originally posted by DoctorScribblesI have no idea what the thread was that sparked this call-out for an explanation, but I highly doubt from your response that it would be informative.
If you are going to assert that that thing is a proposition, then it is a false one. See the thread that sparked this call-out for an explanation.
Goedel would laugh in your face if you tried to tell him you had constructed a proposition that had no truth value.
Originally posted by DoctorScribblesHow about Gödel's theorem on mathmatics:
LOL. Of course. That's part of the standard definition of the term. Having a single truth value is part and parcel of being a proposition.
You can no sooner construct a proposition that is neither true nor false than you can construct a circle that has no radius.
If you think I'm wrong, then try to construct a proposition that is neither t research and learn the elementary and foundational concepts of logic and critical thinking.
Originally posted by twhiteheadAgreed, the use of the word proposition in colloquial terms and in philosophical or mathematical terms differs.
To have any real discussion a definition of the word 'proposition' must first be agreed upon.
In Wikipedia I found this: In common philosophical language, a proposition is the content of an assertion, that is, it is true-or-false and defined by the meaning of a particular piece of language. The proposition is independent of the medium of communication. ...[text shortened]... understandings of the word but if so they should state their definition before making claims.
Originally posted by DoctorScribblesYour generosity of spirit continues to impress.
LOL. Of course. That's part of the standard definition of the term. Having a single truth value is part and parcel of being a proposition.
You can no sooner construct a proposition that is neither true nor false than you can construct a circle that has no radius.
If you think I'm wrong, then try to construct a proposition that is neither t ...[text shortened]... research and learn the elementary and foundational concepts of logic and critical thinking.
Originally posted by DoctorScribblesI prefer to think he would be undecided about that.
If you are going to assert that that thing is a proposition, then it is a false one. See the thread that sparked this call-out for an explanation.
Goedel would laugh in your face if you tried to tell him you had constructed a proposition that had no truth value.
Originally posted by rooktakesqueenYou are confusing truth with proof and decidability. I know more mathematics than you could ever hope to grasp, although I'm forever at the drawing board.
How about Gödel's theorem on mathmatics:
Gödel's theorem appears as Proposition VI in his 1931 paper "On Formally Undecidable Propositions in Principia Mathematica and Related Systems I.
Roughly speaking, the Gödel statement, G, can be expressed: 'G cannot be proven true'. If G were proven true under the theory's axioms, then the theory would ha e or false"
back to the drawing board doctor... rearrange your thinking and grow up
Originally posted by PawnokeyholeYou are now confusing truth with knowledge. You are also mistkaing linguistic nonsense that has no propositional content for a proposition that has no truth value.
Your generosity of spirit continues to impress.
Okay, let's take this step by step. Could you remark upon the truth value of the following two propositions?
1: "The Flying Spaghetti Monster has a Noodly Appendage"
2: "The Flying Spaghetti Monster does not have a Noodly Appendage"
Originally posted by NullifidianWrong. You are confusing the linguistic rendering of the proposition with its propositional content. To the extent that it has propositional content at all, it is false because it asserts a contradiction; there is no paradox at all.
Either way, it's impossible to call the Liar Paradox true or false without generating a contradiction.