True Sentences

None of which has anything to do with what I said. If sentences are neither true nor false, and the meanings of words are unstable, how is truth transmitted by words?

I don't see how the fact (if it is one) that sentences are neither true nor false implies, or even suggests, that the meanings of words are unstable

I replied to a post in which you pointed out that words have no stability.

I don't even know what it means to say that, so I doubt I said that. If you want to point me at where you believe I said that, I'll try to remind you of what I actually did say.

The Barber Paradox and the Russell Paradox, share a common formulation.

EyAx(x is shaved by y <-> ~(x is shaved by x)) and
EyAx(x is a member of y <-> ~(x is a member of x)),
are both instances of the proposition:
EyAx(xRy <-> ~(xRx)).

There is a y such that: Ax(xRy <-> ~(xRx)), is a contradiction.

Proof:

Ax(xRy <-> ~(xRx)) -> ((yRy) <-> ~(yRy)), ...when x=y.
But, (yRy) <-> ~(yRy), is of the form (p <-> ~p) which is a contradiction for all p.

That is, Ax(xRy <-> ~(xRx)) implies a contradiction, therefore, Ax(xRy <-> ~(xRx)), is false for all y.
That is to say, ~EyAx(xRy <-> ~(xRx)) is a theorem, for all R.

Therefore, neither the Barber nor the Russell class exist.

Does the Barber shave himself? No, it cannot 'do' anything because it does not exist.
Is the Russell Class a member of itself? No, it cannot be a member of any set, because it does not exist.

Note: There are instantiations of the predicate ~(x is a member of x) but there is no such class as {x's:~(x is a member of x)}.

For example, the class of cars is not a member of itself, ie. it satisfies the predicate ~(x is a member of x), but....the class of cars is not a member of the class of those classes which are not members of themselves.

It is false to say: if a predicate is instantiated by some individual then that individual is a member of the class determined by that predicate, for all predicates.

It is fallacious to think that the meaning a word has now is the meaning it originally had, since meanings change through time. Still, it is seldom that the etymology of a word cannot shed light on its meaning. The etymology of the word "paradox" is from the ancient Greek words "doxa" and "para", which meant "common opinion" and "contrary to" respectively. So, a paradox would be something that was "contrary to common opinion" or, against what we ordinarily believe is true. So, for instance, of of Zeno's paradoxes is that if Achilles and a tortoise engaged in a race, Achilles could not win against the tortoise. That is, of course, contrary to what we ordinarily believe is true. We believe that Achilles would win such a race, hands down. In the present instance, the paradox is known as the Barbershop paradox. It begins by supposing a barber who shaves all, and only, those who do not shave themselves. And it asks the innocent seeming question, does that barber shave himself or not. And quickly (I hope) we see that supposition implies a contradiction, for if the barber were to shave himself that would be contrary to the supposition, and it the barber were not to shave himself, then that would be contrary to the supposition. It would then follow that such a barber (supposing, of course, there were one) would have both to shave himself and (also) not shave himself. But that, of course is a contradiction. Literally, no one can perform a contradictory action (not even God). So, in the light of all this, what is the answer to the question, supposing there were such a barber, would he shave himself or not? The only answer there can be is that the supposition is, itself, false. That it is impossible that there should be such a barber, because the supposition of such a barber implies a contradiction, and therefore, the supposition is, itself, a contradiction, since what implies a contradiction is itself a contradiction. So, the paradox is that it would be ordinarily believed (doxa) that there could be such a barber, but it turns out, upon analysis, that there could not be such a barber, and so, paradoxa, a paradox!

There are several lessons to be drawn from this example. Two of them are: 1. That reason can show that something does not exist. That is something that inspired the epistemology of Rationalism which is the view that thought (what Kant called, "pure reason") that demonstrate that something does not exist, and therefore, it is reasonable to believe that is can demonstrate that something must exist. (But this argument is fallacious). 2. Closer to home, is that we see that a person can hold a self-contradictory belief without realizing that he does. That should make us all more modest.

Mrs. Anderson (the wife) asked handicaped little Annie if cats meow, and little Annie responds, "dogs bark." Mr. Anderson (the husband) shakes his head and says, "well, at least it's a true sentence."

A philosopher standing nearby thinks to himself, "not really." He thinks: The proposition expressed by the sentence is true, but the sentence itself isn't true, for it's not sentences (but rather propositions) that are true.

The philosopher later tells me what he thinks, and I wonder, should I believe him?

I don't know what sound deductive arguments can be made to show that sentences that express true propositions are therefore true sentences, but such an interpretation doesn't seem unreasonable to me. Is there a good inductive argument we can use?

If not, I think we should reexamine why it is okay to say that beliefs are true or false.

It is fallacious to think that the meaning a word has now is the meaning it originally had, since meanings change through time.

This is wrong, because "meaning" don ` t change over time.

Then how come the word, "lunatic" used to mean a person who was influenced by the Moon, but it no longer means that?

Then how come the word, "lunatic" used to mean a person who was influenced by the Moon, but it no longer means that?

This is wrong, because "meaning" don ` t change over time.

Read and learn about the etymological fallacy.

You are both right...They change and they are very stable..

You're using the word "true" differently than I am. I believe that women should be true to their husbands, so I believe that women should be true, and if I believe that, then let us hope that I also believe that being true is something women can do, but when I say, "I believe that women should be true to their husbands," I am not (in any way) using the word "true" as I would be if I said, "the proposition, 'the cat is on the mat' is true."

See, the word "true" is ambiguous, and that just means that the word has more than one meaning, but don't go away thinking that propositions cannot be true just because propositions can't be true in the same way women can be true to their husbands.

What "both"? As another example take the word, "gay". The ordinary use of that term (say) fifty years ago to mean carefree or light-hearted is very different from it use now to mean, homosexual. The very same term meant one thing fifty years ago, and means something quite different now.

Why, do you suppose, people prefer confusion to clarity? I suppose that some of them just think that in order to philosophize you have to be confused, and that when matters become clear they are rather let down.