John Page

IMO that's exactly where you are wrong. Truth is a strongly held provisional belief, it is derved from comparison of transient information states....back to freshperson relativism.

Cheers, John

tronvillain

Clutch:

I would suggest an alternative exchange:

---- "In 1870, the rationally warranted view was that space and time are physically distinct."
-- "Right; that space and time are physically distinct appeared to be true in 1870."
-- "But nowadays space and time are not regarded as independent."
-- "Yes, nowadays it appears to be true that space and time are not independent."

In other words, given what we know, we have a better approximation of the nature of space and time than existed in 1870.

Clutch

tron, agreed. Absolutely. The important point is just keeping the provisional *appearance* of truth distinct from truth's actually being provisional.

If that sounds like a minor distinction... well, it isn't. (Pretty compelling argument, eh?)

Mr. Sammi

Miss Clutch,

We are back again, this time I hope you will not become Mrs. Clutch. I apologise for talking over your head. BUT, what is the paradox you speak of as a logician concerning knowability?

It is unrecognisable in its current format.

Again are you going to dispel doubts in my provisional truth concerning your status as people.

Sammi Na Boodie ()

Clutch

Sammi,

If you do not understand the Paradox, and would like me to explain its details to you, I am happy to do so. Provided you ask with a modicum of politeness.

[ July 05, 2002: Message edited by: Clutch ]</p>

tronvillain

Clutch:
Just as is importance is that truth will always appear provisional, since while the truth may not actually be provisional, there is no apparent way of achieving it.

Given what we currenly know, and what was known in 1870, it appears that we have a better approximation of the truth than they did back then. Do we actually have a better approximation of the truth than they did? We can only answer within the context of what we currently know.

Clutch

Tron, again, agreed. But the coherence of what you say, and what I agree with, hinges on the distinction between the approximations, and what they are approximations *to*.

Maybe we'll just asymptotically approach truth. My point, which would seem trivial were there not people keen to deny it, is that there is a crucial conceptual distinction between asymptote and axis.

Thanks.

Synaesthesia

I still don't understand in the least how this paradox follows, nor the precise premises from which it is supposed to follow.

Would anyone mind explicating it or pointing me in a direction where I might examine it in detail?

Clutch

Syn, for your viewing pleasure!

Ks = It is at some time known that s.

Knowability principle
"If p then it is possible for p to be known": p --&gt; Poss(Kp)
Necessitation: p is a theorem --&gt; Nec(p)
Weak interdefinability: Nec(not-p) --&gt; not-Poss(p)

1) Assume K(p & not-Kp)
2) Kp & K(not-Kp) [1, Distributivity of K]
3) K(not-Kp) [2, &-elimination]
4) not-Kp [3, Factivity of K]
5) Kp [2, &-elimination]
6) Kp & not-Kp [4, 5, &-introduction]
7) not-K(p & not-Kp) [1-6, RAA]

This much just establishes the absurdity of "It is sometime known both that p and that it will never be known that p"

8) Nec(not-K(p & not-Kp)) [1-7, Necessitation]
9) not-Poss(K(p & not-Kp)) [8, Weak interdefinability]
10) (p & not-Kp) --&gt; Poss(K(p & not-Kp)) [Instance of Knowability Principle]
11) not-(p & not-Kp) [9, 10, modus tollens]
12) p --&gt; not-not-Kp [11, equivalent]
13) p --&gt; Kp [12, Double negation elim]

There it is. From the Knowability Principle we can engineer a "modal collapse", making that possibility operator disappear to create a much less innocent-looking thesis. Even those who feel no powerful attraction to the Principle often find it surprising that it entails such a very strong formulation as (13).

[ July 05, 2002: Message edited by: Clutch ]</p>

tronvillain

Clutch, there is a crucial conceptual distinction between asymptote and axis, but the asymptote is all we have access to - we only infer the existence of the axis. We may actually reach truth, but the probablistic nature of knowledge means that we won't be completely sure that we have.