Saul Kripke contends that a natural language can in fact contain its own truth predicate without giving rise to contradiction. He showed how to construct one as follows:
Begin with a subset of sentences of a natural language that contains no occurrences of the expression "is true" (or "is false"). So The barn is big is included in the subset, but not " The barn is big is true", nor problematic sentences such as "This sentence is false".
Define truth just for the sentences in that subset.
Then extend the definition of truth to include sentences that predicate truth or falsity of one of the original subset of sentences. So "The barn is big is true" is now included, but not either "This sentence is false" nor "'The barn is big is true' is true".
Next, define truth for all sentences that predicate truth or falsity of a member of the second set. Imagine this process repeated infinitely, so that truth is defined for The barn is big; then for "The barn is big is true"; then for "'The barn is big is true' is true", and so on.
Notice that truth never gets defined for sentences like This sentence is false, since it was not in the original subset and does not predicate truth of any sentence in the original or any subsequent set. In Kripke's terms, these are "ungrounded." Since these sentences are never assigned either truth or falsehood even if the process is carried out infinitely, Kripke's theory implies that some sentences are neither true nor false. This contradicts the Principle of bivalence: every sentence must be either true or false. Since this principle is a key premise in deriving the Liar paradox, the paradox is dissolved.[63]
Perhaps it be better to ask... what, on your view, makes a proposition true? — creativesoul
Being true is not equivalent to being called "true". Exploring this difference(between being true and being called "true") can be interesting. — creativesoul
The Stanford site makes pretty clear that true as a general term does not have a single definition, but rather a constellation of differing and irreconcilable definitions. The details are extremely tedious - you're welcome to travel that path if you want to. More interesting to me is speculating on why. — tim wood
The Stanford site makes pretty clear that true as a general term does not have a single definition, but rather a constellation of differing and irreconcilable definitions. — tim wood
(For present purpose I'm defining true and truth as meaning the same thing, expressed as an adjective or a noun.)
By the way. What you've just quoted is a misrepresentation of the facts. It makes it seem as if I offered that answer to that quote. I didn't. I abhor insincerity. — creativesoul
Sure, that's the correspondence theory of truth. There are others - go back to the Stanford link; as noted, it's a place to start. In short, truth does not have a single definition.Statements are what's true/false. Correspondence to fact/reality is what makes them true. The lack thereof is what makes them false. — creativesoul
By the way. What you've just quoted is a misrepresentation of the facts. It makes it seem as if I offered that answer to that quote. I didn't. I abhor insincerity.
— creativesoul
Maybe you should read the post; it's just above. — tim wood
.My speculation is that truth is a comparison, a measure of equivalence or differentiation. This apple is red is a comparison of the apple's color to a predefined wavelength of light — AngleWyrm
A lot of slippery ground, here. In categorical reasoning - dialectic - "confidence" won't do. Not-T (or Not-F) won't do.The binary bifurcation of true/false can be enhanced to true/not-true/false, where not-true and false are not identical sets. That increase in resolution also demonstrates that further increases could result in a gradient, perhaps what we call confidence.
creativesoul does that mean then that some beliefs are inherent and are never questioned? — Myttenar
↪creativesoul "it" was in reference to your post about correspondence theory..
Thought and belief without propositional content.. to me resembles instinct.
I had assumed that propositional content was exactly the methodology used to develop beliefs.
Maybe I am unclear on the idea? — Myttenar
Now I'm really confused. I thought you were disagreeing with the article, as in, yes, truth does have a single definition, and my disagreement grounds my questions. Or is it, yes indeed, the article did say that, and the fact that it said it grounds my questions. But maybe this is a path we can quit together.When I wrote "Yes it does", 'it' referenced the article. — creativesoul
I'm also up for it if you would like to compare the different conceptions of "truth". Other than that, I would still like for you to answer the question I asked earlier. Twice. — creativesoul
Earlier you used the notion of what makes a true proposition true. I asked a question about that, but it has not been answered. — creativesoul
If that which makes a proposition true differs from true proposition to true proposition, then in what way does it differ? — creativesoul
Confidence in the mathematical sense used in probabilities and statistics. Roll a single six-sided die: Prior to the toss I am 5/6 confident (83%) that the result will not be a four. — AngleWyrm
How many ways are there to get a person to suspend their critical judgment in favour of acceptance? — tim wood
Sure, confidence, but you also have a categorical proposition about your chances that is true, if you've done the math right, and false, if you haven't. — tim wood
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