Cont: Deeper than primes - Continuation 2

[doronshadmi]

That's the second time you agree that ~A is not the negation of A. Again, thank you.
Can we now drop this?

A = object that has two optional properties (this is the considered premise).

~A = object that does not have two optional properties (this is the negation of the considered premise).

A OR ~A --> T since the premise and its negation are not simultaneously taken.

A AND ~A --> ~T since the premise and its negation are simultaneously taken.

As about http://www.internationalskeptics.com/forums/showpost.php?p=11359072&postcount=1898, in order to follow after it please take A and ~A in terms the claims about the optional properties.

 

[jsfisher]

Before you go off on to your void and complement tangent, you'd need to formally define how braces are part of set theory.

contradiction and tautology are...

This is all great, of course, but it has nothing to do with formally defining how braces are a part of set theory.

It's kind of ironic, too, Doronshadmi, that you chastise me and others for being limited to objects in our thinking, though untrue that may be, and here you are not just limited by but actually obsessed with a pair of objects, braces.

The outer braces represent tautology, where tautology is neither object nor option....

What outer braces? You have not yet formally defined how braces are a part of set theory.

Be that as it may, your response is unrelated to the text you quoted.

 

[jsfisher]

... are simultaneously taken ...

You continue to animate your math.

 

[doronshadmi]

You continue to animate your math.

You continue to ignore the difference between A AND ~A and A OR ~A.

Moreover, you continue the exclude mathematicians as factors of Mathematics, and by doing this you demonstrate your ignorance of how Mathematics is actually discovered OR invented.

 

[doronshadmi]

This is all great, of course, but it has nothing to do with formally defining how braces are a part of set theory.

By defining the void between the outer braces as contradiction and the outer braces as tautology, one formally defining the void and the outer braces as parts of set theory, where being a member of a given set is ~contradiction AND ~tautology.

http://www.internationalskeptics.com/forums/showpost.php?p=11359138&postcount=1900 goes through your current reasoning, but it seems that your current reasoning is too gross in order to interact with it.

 

[doronshadmi]

What outer braces? You have not yet formally defined how braces are a part of set theory.

They are tautology exactly as very simply defined in http://www.internationalskeptics.com/forums/showpost.php?p=11359138&postcount=1900, but your current used reasoning can't interact with this simplicity.

Be that as it may, your response is unrelated to the text you quoted.

Your current used reasoning can't interact with this simplicity, so actually it can't be used in order to conclude anything about this simplecity inducing a phrase like "your response is unrelated to the text you quoted".

 

[jsfisher]

You continue to ignore the difference between A AND ~A and A OR ~A.

Yet another thing you have simply made up to support your fantasy.

By defining the void between the outer braces...

You are still jumping the gun on this. Braces are not part of set theory. If you'd like them added, you need to describe how that addition works. Only after that can you tell us about what exciting characteristics these braces then must have.

 

[doronshadmi]

Braces are not part of set theory.

With such an axiomatic approach, there is no wonder that http://www.internationalskeptics.com/forums/showpost.php?p=11359138&postcount=1900 goes through your mind without interacting with it.

If you'd like them added, you need to describe how that addition works. Only after that can you tell us about what exciting characteristics these braces then must have.

Already done in http://www.internationalskeptics.com/forums/showpost.php?p=11359138&postcount=1900 and the related links, but as you have said "Projection can be so transparent" since there is nothing on your mind that interacts with it.

 

[jsfisher]

Already done

You use this phrase so frequently, and I don't recall a single occasion where it were true.

Your approach continues to be without Mathematics. Let me know if you ever change that.

 

[doronshadmi]

Yet another thing you have simply made up to support your fantasy.

You simply do not understand that A OR ~A is a tautology exactly because A|~A is not simultaneously taken.

You simply do not understand that A AND ~A is a contradiction exactly because A|~A is simultaneously taken.

 

[doronshadmi]

You use this phrase so frequently, and I don't recall a single occasion where it were true.

Your approach continues to be without Mathematics. Let me know if you ever change that.

It is not going to happen as long as "Braces are not part of set theory" is your trivial axiomatic notion, that ignores outer braces as representation of tautology as a part of set theory.

I am still waiting for your effective criticism, so please try being deeper about http://www.internationalskeptics.com/forums/showpost.php?p=11359138&postcount=1900 and its related links.

 

[jsfisher]

It is not going to happen as long as "Braces are not part of set theory" is your trivial axiomatic notion

It is a point of fact. Formal set theory consists of a handful of axioms (and axiom schemas) expressed in first-order predicate calculus and two primitive concepts defined implicitly by those axioms.

No braces.

If you feel compelled to add braces to set theory, then do so, but until you do, all the posting you've done (and will no doubt continue to do) about what you imagine them to represent is meaningless.

 

[doronshadmi]

jsfisher, please reply to http://www.internationalskeptics.com/forums/showpost.php?p=11359813&postcount=1910.

 

[doronshadmi]

It is a point of fact. Formal set theory consists of a handful of axioms (and axiom schemas) expressed in first-order predicate calculus and two primitive concepts defined implicitly by those axioms.

No braces.

http://www.internationalskeptics.com/forums/showpost.php?p=11341196&postcount=1782 clearly demonstrates that you have no case, by your own reply.

As about the set concept, I logically define the outer braces as tautology, where the void between the the outer braces is logically defined as contradiction.

Contradiction and tautology are the logical bounds of Mathematics, where set theory is a formal mathematical framework exactly because its it based on these bounds.

The members of set theory are logically defined as ~contradiction AND ~tautology.

The usefulness of defining set theory by logical foundations is seen in http://www.internationalskeptics.com/forums/showpost.php?p=11359138&postcount=1900 and the related links.

Yet by using http://www.internationalskeptics.com/forums/showpost.php?p=11341196&postcount=1782, you are inconsistent by avoiding any detailed criticism about http://www.internationalskeptics.com/forums./showpost.php?p=11359138&postcount=1900.

 

[MetalPig]

Could you stop contradicyting yourself?

Yesterday:

So the truth table of A AND ~A is:

 A AND ~A
---------
~T     ~T --> ~T
~T      T -->  ~T
 T     ~T -->  ~T
[HILITE] T      T -->  T[/HILITE]

And today:

A AND ~A --> ~T since the premise and its negation are simultaneously taken.

Your logic is bad and you should feel bad.

 

[doronshadmi]

Your logic is bad and you should feel bad.

In http://www.internationalskeptics.co...forums/showpost.php?p=11359072&postcount=1898 ~A is defined by the claims about the defined options.

It is T to claim that the two possible options are simultaneously taken (written as T(for one option) AND T(for the other option) --> T(for simultaneously be taken), and since they are simultaneously taken indeed A AND ~A ---> ~T (contradiction) since A,~A are simultaneously taken, exactly as claimed.

 

[doronshadmi]

Some refinement and corrections of my previews post:

In http://www.internationalskeptics.com/forums/showpost.php?p=11359187&postcount=1901 ~A is defined such that no options are defined.

In that case A AND ~A ---> ~T (contradiction) since A,~A are simultaneously taken.

In http://www.internationalskeptics.com/forums/showpost.php?p=11359072&postcount=1898 ~A is defined by the claims about the defined options.

It is T to claim that the two defined options are simultaneously taken (written as T(for one option) AND T(for the other option) --> T(for simultaneously be taken)) and since they are simultaneously taken, indeed A AND ~A ---> ~T (contradiction) exactly as claimed about the defined options by T AND T --> T.

Also let's correct what was written about the claims about the defined options in case of A AND ~A truth table:

By using AND logical connective between the defined options, the truth table is as follows:

It is ~T to claim that no one of the defined options is possible (written as ~T AND ~T --> ~T)

It is ~T to claim that only one of the defined options is possible (written as T AND ~T --> ~T, ~T AND T --> ~T)

It is T to claim that the two defined options are simultaneously taken (written as T AND T --> T)

So the truth table of A AND ~A is:

 A AND ~A
---------
~T     ~T --> ~T
~T      T -->  ~T
 T     ~T -->  ~T
 T      T -->  T

AND logical connective guarantees that the two defined options are simultaneously taken, so the contradiction is not avoided (A AND ~A --> ~T).

 

[doronshadmi]

Here is a correction of the second link in the last part of post http://www.internationalskeptics.com/forums/showpost.php?p=11360720&postcount=1914.

Yet by using http://www.internationalskeptics.com/forums/showpost.php?p=11341196&postcount=1782, you are inconsistent by avoiding any detailed criticism about http://www.internationalskeptics.com/forums/showpost.php?p=11359138&postcount=1900.

 

[jsfisher]

jsfisher, please reply to http://www.internationalskeptics.com/forums/showpost.php?p=11359813&postcount=1910.

It is not math. It warrants no other reply.

 

[jsfisher]

http://www.internationalskeptics.com/forums/showpost.php?p=11341196&postcount=1782 clearly demonstrates that you have no case, by your own reply.

The starting point of this little arc was that there is a notation useful in the discussions of sets. That has never been denied. The notation is a convenience, nothing more. It is not a formal part of set theory.

Braces are not part of set theory. Attempting to give those typographic squiggles some deep set theoretic meaning is neither mathematics nor completely rational.