Cont: Deeper than primes - Continuation 2

[doronshadmi]

Oh, that pesky math. So hard to understand, yet so easy to complain about.

A definition of a predicate is an equivalent expression using only previously defined predicates, functions, terms, etc.

For example,

IsSuccessorOf(X,Y) <=> X = {Y}​

would be an acceptable definition for the IsSuccessorOf predicate (shown here in function notation form) since an equivalent expression is provided using already known constructs.

As another example,

IsComplete(X) <=> IsSuccessorOf({X},X)​

would be an acceptable definition only after the meaning of IsSuccessorOf(,) is established.

The instantiation of a predicate is where all the free variables are bound to specific values.

EDIT:

What is written above does not establish the fact that {X} is not necessarily a successor of X, and once again: incompleteness OR completeness are possible properties of X.

In order to establish this fact consistently, OR logical connective is used between two true cases as follows:

({X} IsSuccessorOf X (in this case X property is incompleteness)) OR ({X} ~IsSuccessorOf X (in this case X property is completeness)).

An example of the mathematics that can be done by using these two true cases, is seen in http://www.internationalskeptics.com/forums/showpost.php?p=11274453&postcount=1427.

More details are found in http://www.internationalskeptics.com/forums/showpost.php?p=11272627&postcount=1405.

 

[jsfisher]

What is written above does not establish the fact that {X} is not necessarily a successor of X.

Since that was not the subject matter of the post, it would have been unreasonable for you to expect it to.

We are all still waiting for you, Doron, to define (provide an equivalent expression for) IsSuccessor(R,S). Given such a definition, we all would be able to determine for ourselves for all, some, or no instantiations of IsSuccessor({X},X) whether the expression is true.

 

[doronshadmi]

Since that was not the subject matter of the post, it would have been unreasonable for you to expect it to.

Since the subject matter is exactly the fact that {X} is not necessarily a successor of X, it would have been unreasonable for you to define {X} as if it is necessarily a successor of X.

EDIT:

So, by using the correct subject matter, please do not skip this time on the rest of http://www.internationalskeptics.com/forums/showpost.php?p=11275205&postcount=1441.

 

[jsfisher]

Since the subject matter is exactly the fact that {X} is not necessarily a successor of X, it would have been unreasonable for you to define {X} as if it is necessarily a successor of X.

Is that a fact? It is impossible for any of us to tell since you still haven't provided a definition.

 

[Little 10 Toes]

Is {A} a successor of A? yes.
Is {A, B} a successor of A? no, {{A, B}} is a successor of {A, B}.
Is A a successor of {}? only if A is {{}}.
Is {B} a successor of {A, B, C}? no, {{A, B, C}} is a successor of {A, B, C}.



{y} is a successor of y.

Once again, jsfisher, please handle with http://www.internationalskeptics.com/forums/showpost.php?p=11266696&postcount=1280 if you really wish to understand {y}$y.

Since the subject matter is exactly the fact that {X} is not necessarily a successor of X, it would have been unreasonable for you to define {X} as if it is necessarily a successor of X.

EDIT:

So, by using the correct subject matter, please do not skip this time on the rest of http://www.internationalskeptics.com/forums/showpost.php?p=11275205&postcount=1441.

So what is it? Is {y} a successor of y. Or is it not?

Will you ever define successor?

 

[doronshadmi]

Is that a fact?

Yes, this is exactly the relation between {X} and X, {X} is not necessarily a successor of X.

jsfisher, please use your mathematical skills in order to write wff that establishes the fact that {X} is not necessarily a successor of X.

 

[doronshadmi]

So what is it? Is {y} a successor of y. Or is it not?

Will you ever define successor?

You have missed http://www.internationalskeptics.com/forums/showpost.php?p=11268705&postcount=1323.

 

[Little 10 Toes]

You have missed http://www.internationalskeptics.com/forums/showpost.php?p=11268705&postcount=1323.

You have given examples, but have not defined it.

Edit: "It", meaning successor.

 

[jsfisher]

Yes, this is exactly the relation between {X} and X, {X} is not necessarily a successor of X.

jsfisher, please use your mathematical skills in order to write wff that establishes the fact that {X} is not necessarily a successor of X.

What it may (or may not) be is not at all helpful. That gets us that useless tautology thing you are so enamored by. A definition of what it is, though, would be great. Got one, Doron?

What is the definition for IsSuccessorOf(A,B). The world awaits.

 

[doronshadmi]

What it may (or may not) be is not at all helpful.

It is useful, helpful, etc., as clearly seen, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=11272627&postcount=1405, http://www.internationalskeptics.com/forums/showpost.php?p=11274453&postcount=1427, http://www.internationalskeptics.com/forums/showpost.php?p=11269502&postcount=1344 and http://www.internationalskeptics.com/forums/showpost.php?p=11271494&postcount=1388.

That gets us that useless tautology thing ...

It is not a useless tautology, you simply can't use your mathematical skills in order to define the relations between {X} and X, such that {X} is not necessarily a successor of X.

In other words, we simply insist to use unreasonable maneuvers in order to avoid http://www.internationalskeptics.com/forums/showpost.php?p=11275205&postcount=1441.

 

[jsfisher]

...snipped for lack of definition...

Still can't define it, can you?

IsSuccessorOf(A,B) <=> ...?​

 

[doronshadmi]

...snipped for lack of reason...

Still can't define the relation between {X} and X, such that {X} is not necessarily a successor of X, isn't it, jsfisher?

 

[Little 10 Toes]

Well, you say there is a relationship, but can't define that relationship.

 

[jsfisher]

...snipped for lack of reason...

Still can't define the relation between {X} and X, such that {X} is not necessarily a successor of X, isn't it, jsfisher?

I see you saw fit to deliberately misquote me without any indication of your changes to my post. Poor form, Doron. Not only have you again failed at providing any sort of competent definition for your invented terms, you have again demonstrated your willingness to lie.

 

[doronshadmi]

I see

You don't see.

Poor form, Doron.

Poor reasoning, Jsfisher.

Not only have you again failed at providing any sort of competent definition for your invented terms, you have again demonstrated your willingness to lie.

Not only have you again failed at providing any sort of definition for the relation between {X} and X, such that {X} is not necessarily a successor of X, you have again demonstrated your willingness to lie, exactly because ({X} IsSuccessorOf X) OR ({X} ~IsSuccessorOf X) and (X = Y) OR (X ~= Y) are equivalent wff, because both of them are based on http://www.internationalskeptics.com/forums/showpost.php?p=11269502&postcount=1344.

 

[Little 10 Toes]

Doronshadmi, are you ever going to define sucessor?

But then, what you define as a sucessor, may not truly be a sucessor.

 

[Nonpareil]

Not only have you again failed at providing any sort of definition for the relation between {X} and X, such that {X} is not necessarily a successor of X

It's your nonsense system, doron. It is your responsibility to define it.

 

[doronshadmi]

It is your responsibility to define it.

It is already wff, as seen in http://www.internationalskeptics.com/forums/showpost.php?p=11276574&postcount=1455.

 

[Nonpareil]

It is already wff, as seen in http://www.internationalskeptics.com/forums/showpost.php?p=11276574&postcount=1455.

Neither of the posts in that link contain a definition of "successor".

 

[doronshadmi]

Neither of the posts in that link contain a definition of "successor".

By, for example, the definition Y IsSuccessorOf Z <=> Y = {Z}, {Z} must be a successor of Z.

Since {Z} is not necessarily a successor of Z, Y IsSuccessorOf Z <=> Y = {Z} can't be the definition of {Z} as a successor Z.

On the contrary, by using the formation rules of wff, as shown in http://www.internationalskeptics.com/forums/showpost.php?p=11269502&postcount=1344, ({Z} IsSuccessorOf Z) OR ({Z} ~IsSuccessorOf Z) is a wff that defines {Z} such that it is not necessarily a successor of Z.

This definition and my non-standard notion of successor, are very simply explained in:

http://www.internationalskeptics.com/forums/showpost.php?p=11271494&postcount=1388

http://www.internationalskeptics.com/forums/showpost.php?p=11274453&postcount=1427

---------------

More useful details are found in http://www.internationalskeptics.com/forums/showpost.php?p=11272627&postcount=1405.

---------------

Again, by the standard definition of successor, Successor(Z) = Z u {Z}

By my non-standard definition of successor, Successor(Z) is {Z} only if {Z} is used as a successor of Z (which means that also {Z}~$Z holds).