Re: How a True(X) predicate can be defined for the set of analytic knowledge

On 3/25/25 10:15 PM, olcott wrote:

On 3/25/2025 8:08 PM, Richard Damon wrote:

On 3/25/25 10:56 AM, olcott wrote:

On 3/25/2025 5:19 AM, Mikko wrote:

On 2025-03-22 17:53:28 +0000, olcott said:
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On 3/22/2025 11:43 AM, Mikko wrote:

On 2025-03-21 12:49:06 +0000, olcott said:
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On 3/21/2025 3:57 AM, Mikko wrote:

On 2025-03-20 15:02:42 +0000, olcott said:
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On 3/20/2025 8:09 AM, Mikko wrote:

On 2025-03-20 02:42:53 +0000, olcott said:
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It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.

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A simple example is the first order group theory.
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When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.

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There is no computable predicate that tells whether a sentence
of the first order group theory can be proven.
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Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.

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However, it is possible that someone finds a proof of the conjecture
or its negation. Then the predicate True is no longer complete.
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The set of all human general knowledge that can
be expressed using language gets updated.
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When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.

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However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
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When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.

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The set of human knowledge that can be expressed using language
is not a tautology.
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tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.

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And human knowledge is not.
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What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
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How do you DEFINE what is actually knowledge?
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 *This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.

SO that means that "Cats are Dogs" is part of Knowldedge?

 

How do we know what we think to be True is actually True?
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 Stimulated relations between finite strings are necessarily
true. "cats" <are> "animals"

Only if "cats" and "animals" have the appropriate definitions.
The trator down the street that is a "cat" isn't an animal, but sometimes the person that operates it can be a bit of one.

 

In FORMAL systems we can rigorously define what is true in that system, as we start with a defined set of given facts (which is why you can't change the definitions and stay in the system, as those definitions are what made the system).

 Almost the same idea as basic facts.

Yes, but more than basic facts. Note,

 

When you talk about "Human Knowledge" for the "Real World" you run into the problem that we don't have a listing of the fundamental facts that define the system, but are trying to discover our best explainations by observation.
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 Basic facts that cannot be derived from anything else.

So what makes them true? Note, EVERYTHING we know about the real world starts with observations, and observations are always only approximate.

 

Thus we hit the problem that Philosophers debate about how can we know what we know?
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 Epistemology is my favorite subject.

Then why are you so ignorant of it?

 

This is, as I just explained, only a problem in the "real world", as in a Formal System, Truth has a precise definition, as does Knowledge.
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 There is no real world problem with the actual set of knowledge
that can be expressed using language.

So, you admit that you system won't be able to rebute the climate deniers, as that problem can't be expressed?

 

Your problem is your "True" predicate detects the later, not actually Truth, and thus calling it True is just a lie.

 It is stipulated that the system is the actual set of knowledge
that can be expressed in language. For this set the True(X)
predicate is infallible.
 

And is itself just a lie, as it is really a knowledge predicate, and not even a good one as it is knowledge at a given point in time predicate.
Your problem is you like to stipulate yourself out of the problem domain that people are interested in.
All you system seems to be able to do is say, "We already knew that one".