I redefined the foundation of formal logic that is just as expressive
and powerful as Higher Order Logic (HOL) and eliminates Gödel
Incompleteness and Tarski Undefinability.
We simply extend the notion of a syllogism and require that
*All conclusions must be a semantically necessary*
*consequence of all of their premises*
otherwise the argument is invalid. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
This is best accomplished by merging the notion of model theory directly
into higher order logic.
We get rid of Gödel Incompleteness in that every case where a conclusion cannot be proven from all of its premises determines that the logic
sentence is invalid.
We get rid of Tarski Undefinability in that True(L, x) is defined as
logic sentences where all the premises are known to be true.
We know that they are true because they are established facts such as
Haskell Curry’s elementary theorems. Expressions of language L within formal system T that are stipulated to have the semantic value of
Boolean True. https://www.liarparadox.org/Haskell_Curry_45.pdf
These facts could also be formalized natural language specifying facts
of the verbal model of the actual world. CycL seems to be the most
robust knowledge ontology language is anchored in Higher order logic. https://en.wikipedia.org/wiki/CycL
On 8/20/23 10:41 AM, olcott wrote:
I redefined the foundation of formal logic that is just as expressive
and powerful as Higher Order Logic (HOL) and eliminates Gödel
Incompleteness and Tarski Undefinability.
And what have you actually proved you can do with this?
Remember having changed the foundation, you need to TOTALLY rebuild the
logic
We simply extend the notion of a syllogism and require that
*All conclusions must be a semantically necessary*
*consequence of all of their premises*
otherwise the argument is invalid.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
And what exactly do you mean by that?
From everything you seem to have said, you have had to remove theNoticed I lost the rest of the thought:
ability to do "abstract" logic, and can only work with
This is best accomplished by merging the notion of model theory directly
into higher order logic.
We get rid of Gödel Incompleteness in that every case where a conclusion
cannot be proven from all of its premises determines that the logic
sentence is invalid.
And, as Godel has proven, this means that you logic system is either inconsistant or can not support the needed basic principles or the
natural numbers.
We get rid of Tarski Undefinability in that True(L, x) is defined as
logic sentences where all the premises are known to be true.
No, you haven't. You explainations just show that your logic system is limited to FINITE systems,
We know that they are true because they are established facts such as
Haskell Curry’s elementary theorems. Expressions of language L within
formal system T that are stipulated to have the semantic value of
Boolean True. https://www.liarparadox.org/Haskell_Curry_45.pdf
So, the only things that are True in your system are what you initially established as Truths?
Sounds like a VERY limited logic system.
These facts could also be formalized natural language specifying facts
of the verbal model of the actual world. CycL seems to be the most
robust knowledge ontology language is anchored in Higher order logic.
https://en.wikipedia.org/wiki/CycL
You seem to have a fundamental problem of distinguishing between
"Knowledge" and "Truth".
You have defined a logic system that can not do logic, since the only
"True" statements are those that were initially defined to be True.
Sounds like a very useful system (NOT!).
Sysop: | Keyop |
---|---|
Location: | Huddersfield, West Yorkshire, UK |
Users: | 366 |
Nodes: | 16 (2 / 14) |
Uptime: | 16:10:20 |
Calls: | 7,812 |
Files: | 12,927 |
Messages: | 5,766,137 |