Cont: Deeper than primes - Continuation 2

[Nonpareil]

One can define X as complete OR incomplete

Which is not a definition of "successor".

{X}$Y OR {X}~$Y that is exactly the definition of how {X} is related to X as its successor.

No, that says "{X} could be the successor of Y, or it could not be".

That is not a definition of "successor".

No one cares about "complete" or "incomplete" right now. We can move on to those once you have defined "successor".

 

[jsfisher]

{X}$X OR {X}~$X is a wff that is syntactically a tautology (no semantics is involved).

No, semantics are what reveal it to be a tautology.

 

[Little 10 Toes]

You are wrong.

Nope.

One can define X as complete OR incomplete,

Don't care about X, complete, or incomplete at this time. Just want the definition of successor.

which is derived from {X}$Y OR {X}~$Y that is exactly the definition of how {X} is related to X as its successor.

Don't care about what is derived from what, or what is related to X at this time. Just want the definition of successor.

A tautology like {}={} can't be used in order to define X as complete OR incomplete.

A tautology like {X}$Y OR {X}~$Y can be used in order to define X as complete OR incomplete.

Don't care about defining complete or incomplete at this time. Just the definition of successor.

If you can't define it, just let us know..

 

[doronshadmi]

That is not a definition of "successor".[/i]

This is exactly how {X} is related to X, it can be its successor OR not its successor, so {X}$X OR {X}~$X is the exact definition of {X} w.r.t X as its successor.

Since by Y IsSuccessorOf X <=> Y = {X}, {X} must be a successor of X, this definition does not fully formalize all the possible relations between {X} and X, and as a result X completeness OR incompleteness can't be deduced.

 

[jsfisher]

This is exactly how {X} is related to X

That is not the question. We all know that Thing-1 may or may not be related to Thing-2 in some special way. No surprise there. Tautologies are like that. You belabor the obvious.

The non-obvious thing you have yet to tell us is the meaning of "successor" in your world.

 

[doronshadmi]

No, semantics are what reveal it to be a tautology.

Wrong, semantics is at least some model of correct formal syntax, where tautology does not need any model in order to be known.

This is exactly the reason of why you can't distinguish between, for example, the following tautologies: "{} = {}" or "{X}$X OR {X}~$X"

 

[doronshadmi]

That is not the question. We all know that Thing-1 may or may not be related to Thing-2 in some special way. No surprise there. Tautologies are like that. You belabor the obvious.

The non-obvious thing you have yet to tell us is the meaning of "successor" in your world.

The meaning (semantics) of {X} as a successor in my world, is inseparable of its possible relations with X, and "{X}$X OR {X}~$X" defines exactly this meaning, which in turn determines X properties as complete OR incomplete.

Any attempt to separately define {X} as a successor of X by ignoring the influence on X possible properties, is an essential mathematical failure of the issue at hand.

Those who essentially fail at the issue at hand, indeed get, for example, http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485 as gibberish.

 

[jsfisher]

The meaning (semantics) of {X} as a successor in my world is inseparable of its possible relations with X, and "{X}$X OR {X}~$X" defines exactly this meaning, which in turn determines X properties as complete OR incomplete.

You cannot define it, then.

Your perfect record remains unbroken.

 

[doronshadmi]

You cannot define it, then.

You can't define it in terms of your syntactic-only world.

Your perfect record of being conventional remains unbroken.

 

[doronshadmi]

In case that {y}$y, y is "externally" OR "internally" incomplete, as seen in http://www.internationalskeptics.com/forums/showpost.php?p=11266617&postcount=1277.

 

[Nonpareil]

This is exactly how {X} is related to X, it can be its successor OR not its successor

Yes, I said that.

The problem is that you can't tell us how to know if it actually is the successor.

 

[doronshadmi]

Yes, I said that.

The problem is that you can't tell us how to know if it actually is the successor.

{X} is the successor of X if it is related to it as such.

Also {X} is a set of its own that is not related to X as its successor.

Each case has a different impact on X property, exactly as explained, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485.

Also, as usual, your last reply is non-informative since you ignore the rest of http://www.internationalskeptics.com/forums/showpost.php?p=11282030&postcount=1504.

 

[jsfisher]

{X} is the successor of X if it is related to it as such.

This ball is red if it is colored as such.

 

[Nonpareil]

{X} is the successor of X if it is related to it as such.

"{X} is the successor of X if it is the successor of X."

Yes, thank you. That is very helpful.

Now, perhaps you could tell us what precise relationship makes it the successor.

 

[Little 10 Toes]

{X} is the successor of X if it is related to it as such.

Also {X} is a set of its own that is not related to X as its successor.

{X} is the garglblurgh of X if it is related to it as such.

Also {X} is a set of its own that is not related to X as its garglblurgh.

See, I can do it too.

How is that definition of successor coming along?

 

[doronshadmi]

This ball is red if it is colored as such.

There is a ball that its color is the result of how it is painted.

 

[doronshadmi]

{X} is the garglblurgh of X if it is related to it as such.

Also {X} is a set of its own that is not related to X as its garglblurgh.

See, I can do it too.

How is that definition of successor coming along?

And you ignore http://www.internationalskeptics.com/forums/showpost.php?p=11282274&postcount=1507.

 

[jsfisher]

There is a ball that its color is the result of how it is painted.

Not an arbitrary ball. I was referring to this ball, right here. It is red if it is colored as such.

Can you tell me the color of this ball?

 

[doronshadmi]

Being a successor is not essential for {X}, since it is determined according to its relations with X.

Being complete is not essential for X, since it is determined according to its relations with {X}.

More details are given, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485.

 

[Nonpareil]

Right, so. Doronshadmi has effectively admitted that he cannot define "successor".

Can we end the thread now?