One theory, .... "The", logic.

It's pretty simple as a universe of consistent objects, ..., to begin.

On 12/15/2023 1:51 PM, Ross Finlayson wrote:
> One theory, .... "The", logic.
>
> It's pretty simple as a universe of consistent objects, ..., to begin.

The foundations of logic from a logicians POV is whatever they learned
by rote. foundations of logic from a philosophers POV is every coherent
set of ideas that can possibly exist.

Gödel proved that expression G in PA cannot be proved in PA yet
can be proved in metamathematics. This assumes that different
orders of logic must be in different formal systems.

When we hypothesize a single formal system having ALL orders
of logic then instead of G cannot be proved in PA and can be
proved in metamathematics we have G cannot be proved in F[n]
and can be proved in F[n+1]. Thus incompleteness ceases to be
possible.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/15/23 4:12 PM, olcott wrote:
> On 12/15/2023 1:51 PM, Ross Finlayson wrote:
>> One theory, ....  "The", logic.
>>
>> It's pretty simple as a universe of consistent objects, ..., to begin.
>
> The foundations of logic from a logicians POV is whatever they learned
> by rote. foundations of logic from a philosophers POV is every coherent
> set of ideas that can possibly exist.
>
> Gödel proved that expression G in PA cannot be proved in PA yet
> can be proved in metamathematics. This assumes that different
> orders of logic must be in different formal systems.
>
> When we hypothesize a single formal system having ALL orders
> of logic then instead of G cannot be proved in PA and can be
> proved in metamathematics we have G cannot be proved in F[n]
> and can be proved in F[n+1]. Thus incompleteness ceases to be
> possible.
>

Which means you just don't understand what a "Formal System" actually
is, or what an "Order" is in Logic.

Note, "Orders of Logic" is a completely different thing then "Levels of
Meta-Logic", and thus your arguement is based on a Category Error.

On 12/15/2023 3:12 PM, olcott wrote:
> On 12/15/2023 1:51 PM, Ross Finlayson wrote:
>> One theory, ....  "The", logic.
>>
>> It's pretty simple as a universe of consistent objects, ..., to begin.
>
> The foundations of logic from a logicians POV is whatever they learned
> by rote. foundations of logic from a philosophers POV is every coherent
> set of ideas that can possibly exist.
>
> Gödel proved that expression G in PA cannot be proved in PA yet
> can be proved in metamathematics. This assumes that different
> orders of logic must be in different formal systems.
>
> When we hypothesize a single formal system having ALL orders
> of logic then instead of G cannot be proved in PA and can be
> proved in metamathematics we have G cannot be proved in F[n]
> and can be proved in F[n+1]. Thus incompleteness ceases to be
> possible.
>

As a concrete example:
This sentence is not true: "This sentence is not true" is true
because the inner sentence is not a truth bearer.
These two are one order of logic (level of indirect reference) apart.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2023-12-15 19:51:16 +0000, Ross Finlayson said:

> One theory, .... "The", logic.
>
> It's pretty simple as a universe of consistent objects, ..., to begin.

That is not a reliable foundation before you have enough
foundtaions that you can define "consistent".

Mikko

On 12/16/23 12:54 AM, olcott wrote:
> On 12/15/2023 3:12 PM, olcott wrote:
>> On 12/15/2023 1:51 PM, Ross Finlayson wrote:
>>> One theory, ....  "The", logic.
>>>
>>> It's pretty simple as a universe of consistent objects, ..., to begin.
>>
>> The foundations of logic from a logicians POV is whatever they learned
>> by rote. foundations of logic from a philosophers POV is every coherent
>> set of ideas that can possibly exist.
>>
>> Gödel proved that expression G in PA cannot be proved in PA yet
>> can be proved in metamathematics. This assumes that different
>> orders of logic must be in different formal systems.
>>
>> When we hypothesize a single formal system having ALL orders
>> of logic then instead of G cannot be proved in PA and can be
>> proved in metamathematics we have G cannot be proved in F[n]
>> and can be proved in F[n+1]. Thus incompleteness ceases to be
>> possible.
>>
>
> As a concrete example:
> This sentence is not true: "This sentence is not true" is true
> because the inner sentence is not a truth bearer.
> These two are one order of logic (level of indirect reference) apart.
> "Order of Logic" is NOT "Level of Indirection" but the category of what
Qualifiers span.

So, you are showing your ignorance of the theory,

It's a theory of truth.