Re: The philosophy of computation reformulates existing ideas on a new basis ---

On 11/3/2024 5:53 AM, Mikko wrote:

On 2024-11-02 11:43:02 +0000, olcott said:
 

On 11/2/2024 4:09 AM, Mikko wrote:

On 2024-11-01 12:19:03 +0000, olcott said:
>

On 11/1/2024 5:42 AM, Mikko wrote:

On 2024-10-30 12:46:25 +0000, olcott said:
>

ZFC only resolved Russell's Paradox because it tossed out
the incoherent foundation of https://en.wikipedia.org/wiki/ Naive_set_theory

>
Actually Zermelo did it. The F and C are simply minor improvements on
other aspects of the theory.

>
Thus establishing the precedent that replacing the foundational
basis of a problem is a valid way to resolve that problem.

>
No, that does not follow. In particular, Russell's paradox is not a
problem, just an element of the proof that the naive set theory is
inconsistent. The problem then is to construct a consistent set
theory. Zermelo proposed one set theory and ZF and ZFC are two other
proposals.

>
My view is that the same kind of self-reference issue that
showed naive set theory was inconsistent also shows that the
current notion of a formal system is inconsistent.

  From the proof of the exstence of Russell's set it is easy
to prove that 1 = 2. As long as no proof of 1 = 2 from a
self-reference in a formal system is shown there is no
reason to think that such system is inconsisten.

In other words you presume yourself to be all knowing about this.

And the
existence of insonstent formal systems does not mean that
the notion of a formal system is inconsistent.
 

The notion of formal systems is incoherent because they
rule that self-contradictory expressions prove that the
system is incomplete rather than the expression is incorrect.

When we handle this self-reference differently then this issue
is resolved.

 No proof ot that, either.
 

When a formal system is ONLY a sequence of truth preserving
operations applied to a consistent set of expressions that
have been stipulated to be true then expressions that would
otherwise show incompleteness are rejected because they have
no path to true or false.
>

You can't ignore this.
The above is the essence of my whole system
of thought.

The foundation of all these theories is classical logic.
>

>
The key error of classical logic is that it diverged from the
model of the syllogism where there is always a path to true or
false or the syllogism is ill-formed.

 Classical logic does not substantially diverge from the model of
syllogism.

When modern logic divides the formal system from the underlying
semantics there is no direct path to True(L,x) within the system,
thus no way to reject self-contradictory expressions on the basis
that they have no path to true or false.

It iextends it for situations that cannot be covered
with syllogistic logic. Presentational differences follow mainly
from the needs of the additional coverage.
 No error has been shown in classical logic.
 

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer