On 02 Dec 2012, at 13:11, Roger Clough wrote:
Hi Bruno Marchal
Semantic truth I think is 1p (personal, private) truth,
Truth is always semantical, and it can be 3p (it usually is).
Subjective truth, like with feeling, sensations, ... is 1p, but it is
only a personal relative view on something bigger. You might be
conflating God and the inner God, somehow.
Semantic is a sub-branch of mathematical logic, usually known as model
theory.
Note that logician use "model" in the sense of the painters. the model
is the reality, not the theory used to describe the reality. Logicians
studied explicitly the relation between theories and their models.
The 1p comes when *some* representable beliefs are true. A bit like
when you plunge a map in the territory described by the map: there
will be a fixed point which is the same in the territory and in
reality (the famous: "you are here" point).
which mnakes it contingent, while logical truth is necessary
Even logical truth can be said contingent on the logic chosen. There
are many logics. Now for a platonist, classical logic is single out,
but not as the most true one, but as the one which is the simpler to
make sense on ... the other logics.
as well as public or 3p truth. I think
comnputers have problems with 1p truth because
for one thing the coding is done by someone outside.
The 1p truth of the machine is not coded in the machine. Some actual
machines knows already that, and can justified that If there are
machine (and from outside we can know this to correct) then the 1p-
truth is not codable. The 1p truth are more related to the relation
between belief and reality (not necessarily physical reality, except
for observation and sensation).
Even the simple, and apparently formal Bp & p is NOT codable.
Most truth about machine, including some that they can know, are not
codable.
Many things true about us is not codable either.
Bruno
[Roger Clough], [[email protected]]
12/2/2012
"Forever is a long time, especially near the end." -Woody Allen
----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-12-02, 04:07:39
Subject: Re: Numbers in the Platonic Realm
On 30 Nov 2012, at 21:28, meekerdb wrote:
On 11/30/2012 10:02 AM, Roger Clough wrote:
And a transcendent truth could be arithmetic truth or
the truth of necessary logic.
True in logic and formal mathematics is just marker "T" that is
preserved by the rules of inference.
This makes no sense. You confuse the propositional constant T, with
the semantical notion of truth. The first is expressible/definable
formally (indeed by T, or by "0 = 0" in arithmetic), the second is
not (Tarski theorem). When we say that truth is preserved by the
rules of inference, we are concerned with the second notion.
In applications it is interpreted as if it were the correspondence
meaning of 'true'.
Like in arithmetic. Truth of "ExP(x)" means that it exists a n such
that P(n), at the "metalevel", which is the bare level in logic
(that explains many confusion).
But like all applications of mathematics, it may be only
approximate.
Yes, but for arithmetic it is pretty clear, as we share our
intuition on the so-called standard finite numbers.
Bruno
http://iridia.ulb.ac.be/~marchal/
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