- 17 Jan '07 07:32 / 6 edits

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.*Originally posted by Pawnokeyhole***Do you still maintain that all propositions are either true or false?**

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 true nor false. Or, if you'd like to spend your time more fruitfully instead of pursuing an idiot's project, do some research and learn the elementary and foundational concepts of logic and critical thinking. - 17 Jan '07 07:55 / 1 edit

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.*Originally posted by Nullifidian***"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." )

Goedel would laugh in your face if you tried to tell him you had constructed a proposition that had no truth value. - 17 Jan '07 08:57

I 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.*Originally posted by DoctorScribbles***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.

And the claim that the Liar Paradox and variants have no truth value is a defensible proposition put forth by some logicians, including Saul Kripke. Goedel would call, and indeed did call, such self-referential paradoxes "undecidable", that is to say neither refutable nor provable in a specific deductive system. Either way, it's impossible to call the Liar Paradox true or false without generating a contradiction. If the sentence "This sentence is not true" is true, then the sentence is not true, or if it is not true that "This sentence is not true" is true, then it is true. - 17 Jan '07 09:22 / 1 edit

How about Gödel's theorem on mathmatics:*Originally posted by DoctorScribbles***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.

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 have a theorem, G, which contradicts itself. A similar contradiction would occur if G could be proven false. So we are forced to conclude that G cannot be proven true or false.

If you think I've made it up google it and you'll find lots of searches under it. i repeat:

"we are forced to conclude that G cannot be proven true or false"

back to the drawing board doctor... rearrange your thinking and grow up - 17 Jan '07 09:55To 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.

Of course other people will have other understandings of the word but if so they should state their definition before making claims. - 17 Jan '07 10:11 / 1 edit

Agreed, the use of the word proposition in colloquial terms and in philosophical or mathematical terms differs.*Originally posted by twhitehead***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. - 17 Jan '07 15:40

Your generosity of spirit continues to impress.*Originally posted by DoctorScribbles***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.

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" - 17 Jan '07 15:41

I prefer to think he would be undecided about that.*Originally posted by DoctorScribbles***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. - 17 Jan '07 16:02 / 3 edits

You 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.*Originally posted by rooktakesqueen***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

Goedel never claims that G is a proposition with no truth value. The essense of his claim is that both it and its negation have no proof, which is something very different. - 17 Jan '07 16:13 / 7 edits

You 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.*Originally posted by Pawnokeyhole***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"

In order to comment on (1) and (2), I'd have to know that the Flying Spaghetti Monster exists in order to affirm that they are propositions at all, for if it doesn't, they each have a term with no referent, making them nonsense and thus void of propositional content.

Next, I'd have to know whether that monster, if he exists, does in fact have a noodly appendage in order to say which of the propositions is true.

Given the information available to me, I'd say it is likely that neither (1) nor (2) is a proposition at all. This holds unless you are of the school of thought that (1) is logically equivalent to "There exists an X such that X is a Flying Spaghetti Monster and for all Y not X, Y is not a Flying Spaghetti Monster, and X has a noodly appendage", [that is, the definite article serves as a unique existential qualifier] in which case both are propositions that I believe to be false.

Do you accept such a rendering of the propositional content of (1)? If not, please formulate all futher examples in symbolic logic so that there is no confusion, and so that you do not mistake linguistic nonsense having no propositional content for a proposition having no truth value. - 17 Jan '07 16:26 / 1 edit

Wrong. 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.*Originally posted by Nullifidian***Either way, it's impossible to call the Liar Paradox true or false without generating a contradiction.** - 17 Jan '07 16:29wikipedia again:

This statement is false. (A)

If we suppose that the statement is true, everything asserted in it must be true. However, because the statement asserts that it is itself false, it must be false. So the hypothesis that it is true leads to the contradiction that it is true and false. Yet we cannot conclude that the sentence is false for that hypothesis also leads to contradiction. If the statement is false, then what it says about itself is not true. It says that it is false, so that must not be true. Hence, it is true. Under either hypothesis, we end up concluding that the statement is both true and false. But it has to be either true or false (or so our common intuitions lead us to think), hence there seems to be a contradiction at the heart of our beliefs about truth and falsity.

However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is neither true nor false. This response to the paradox is, in effect, to reject a common beliefs about truth and falsity: the claim that every statement has to abide by the principle of bivalence, a concept related to the law of the excluded middle.