Cont: Deeper than primes - Continuation 2

[jsfisher]

Your "It would save some time and trouble if you'd just confirm it is still X IsSuccessorOf Y <=> X = {Y}" clearly shows what is the desired definition according to your reasoning.

That's one interpretation, I suppose. A better one would be that it was what you provided but that seemed to back away from. The request to confirm your definition was to eliminate the ambiguity you are so fond of.

Be that as it may, none of this matters. It is just another distraction you've injected to slink away from the real issue, the meaning of your term, successor. Your usage, so it is incumbent on you to provide the definition.

IsSuccessorOf(A,B) <=> ...?​

 

[doronshadmi]

That's one interpretation, I suppose. A better one ...

IsSuccessorOf(A,B) <=> ...?​

So it is very clear that:

1) By your reasoning a useful wff must be of the form X <=> Y.

2) You simply ignore the rest of http://www.internationalskeptics.com/forums/showpost.php?p=11291576&postcount=1559 since it does not fit to (1).

3) You refuse to answer to my question to you, which is found at the end of http://www.internationalskeptics.com/forums/showpost.php?p=11291576&postcount=1559.

 

[Little 10 Toes]

Speaking about refusing to answer my question to you, which is found at the end of many of my recent posts,

what is the definition of successor?

 

[jsfisher]

So it is very clear that:

1) By your reasoning a useful wff must be of the form X <=> Y.

Well, yeah. That is how definitions work, after all. X equivalent to Y can be presented as a definition of X as Y (as long as Y relies on already-defined terms).

 

[doronshadmi]

Well, yeah. That is how definitions work, after all. X equivalent to Y can be presented as a definition of X as Y (as long as Y relies on already-defined terms).

Since your reasoning is restricted to (1) (it simply can't deal with http://www.internationalskeptics.com/forums/showpost.php?p=11291576&postcount=1559) there is no use to continue the discussion with you on the issue at hand, which is not restricted to (1), as clearly seen in http://www.internationalskeptics.com/forums/showpost.php?p=11287835&postcount=1546, http://www.internationalskeptics.com/forums/showpost.php?p=11278652&postcount=1460 and by more links to my posts.

As for your refuse to reply to http://www.internationalskeptics.com/forums/showpost.php?p=11290882&postcount=1556, there is nothing to add about your evasion of it.

 

[jsfisher]

Since your reasoning is restricted to (1)...

Doron, I'm just looking for a definition. Got one?

 

[Nonpareil]

Doron, I'm just looking for a definition. Got one?

Why are we still asking this question when we all know the answer?

 

[doronshadmi]

Well, yeah. That is how definitions work, after all. X equivalent to Y can be presented as a definition of X as Y (as long as Y relies on already-defined terms).

Let's see:

A₁ equivalent to A₂ can be presented as a definition of A₁ as A₂ (as long as A₂ relies on already-defined A₃ terms, as long as A₃ relies on already-defined A₄ terms, as long as A₄ relies on already-defined A₅ terms, as long as ... ect. as infinitum, so incompleteness is not avoided also by your reasoning, yet you ignore it exactly because you are unable to distinguish between trivial tautology (for example: {} = {}) and nontrivial tautology (for example: (X IsSuccessorOf Y) OR (X ~IsSuccessorOf Y)).

http://www.internationalskeptics.com/forums/showpost.php?p=11287835&postcount=1546, http://www.internationalskeptics.com/forums/showpost.php?p=11278652&postcount=1460 and more links to my posts deal with nontrivial tautology, which is something that also related to your reasoning, but you simply unaware of it, since trivial tautology is all you get.

 

[Nonpareil]

Let's see:

A₁ equivalent to A₂ can be presented as a definition of A₁ as A₂ (as long as A₂ relies on already-defined A₃ terms, as long as A₃ relies on already-defined A₄ terms, as long as A₄ relies on already-defined A₅ terms, as long as ... ect. as infinitum, so incompleteness is not avoided also by your reasoning

So now doronshadmi is down to actively rejecting the concept of language.

This thread never ceases to astound me.

 

[jsfisher]

Oh, my! This is very exciting news. Very exciting!

Publishers' Clearinghouse has been trying reach you, doronshadmi. Remember, I said exciting news. Well, here it is:

You have won $10,000,000 OR you have not won $10,000,000.​

I said it was exciting, didn't I? We are all very happy for you. It's Publishers' Clearinghouse, after all, and you have won $10,000,000 OR you have not won $10,000,000.

Ten million dollars (US). That is a lot of money. Time to start making your plans.

Oh, one other thing. Your former girlfriend called, too. Something about exciting news related to a pregnancy test....

 

[TheGnome]

I don't really have anything to contribute to the discussion but I feel this thread is very much in need of a positive post.

I actually learned something about math here!

With resppect to the archimedean property, I just never thought of it in terms of one element being infinitesimal to another. I find this helps me a lot to understand its significance. Maybe the german literature I've read on this subject could be improved with this way of viewing it.

Oh and this long sought after definition, could this maybe be called Schroedinger's successor?

 

[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.
[snip]

Let's see:

A₁ equivalent to A₂ can be presented as a definition of A₁ as A₂ (as long as A₂ relies on already-defined A₃ terms, as long as A₃ relies on already-defined A₄ terms, as long as A₄ relies on already-defined A₅ terms, as long as ... ect. as infinitum, so incompleteness is not avoided also by your reasoning, yet you ignore it exactly because you are unable to distinguish between trivial tautology (for example: {} = {}) and nontrivial tautology (for example: (X IsSuccessorOf Y) OR (X ~IsSuccessorOf Y)).

http://www.internationalskeptics.com/forums/showpost.php?p=11287835&postcount=1546, http://www.internationalskeptics.com/forums/showpost.php?p=11278652&postcount=1460 and more links to my posts deal with nontrivial tautology, which is something that also related to your reasoning, but you simply unaware of it, since trivial tautology is all you get.

Lets's have a different look at your problem doron.

Once A₁ is defined you can then use it to define A₂, then you can use A₂ to define A₃, which can be used to define A₄, etc. You can't even define successor which in this case is A₁.

Or using your flawed analogy, successor is A_n where n is all the terms that you make up. Define A_n which is successor.

Define successor.

 

[doronshadmi]

Lets's have a different look at your problem doron.

Once A₁ is defined you can then use it to define A₂,

Not good, you get circular reasoning.

Also you are still missing http://www.internationalskeptics.com/forums/showpost.php?p=11268705&postcount=1323.

 

[doronshadmi]

You have won $10,000,000 OR you have not won $10,000,000.​

This is the one-track reasoning of trivial tautology, when all we care is that $10,000,000 = $10,000,000 AND $10,000,000 is ours.

(You have won $10,000,000) OR (you have not won $10,000,000) is not equivalent to (X IsSuccessorOf Y) OR (X ~IsSuccessorOf Y) since by each true option, a new word for discovery is open for research (in case of (X IsSuccessorOf Y) we research Y as an incomplete thing, where in case of (X ~IsSuccessorOf Y) we research Y as a complete thing, and we actually enable to combine the different properties of {X} and X into a one fruitful framework, as can be found in the links starting in post http://www.internationalskeptics.com/forums/showpost.php?p=11292718&postcount=1565).

 

[Nonpareil]

(You have won $10,000,000) OR (you have not won $10,000,000) is not equivalent to (X IsSuccessorOf Y) OR (X ~IsSuccessorOf Y) since by each true option

It is, in that neither is a definition of "successor".

 

[Little 10 Toes]

Not good, you get circular reasoning.

Also you are still missing http://www.internationalskeptics.com/forums/showpost.php?p=11268705&postcount=1323.

Nope. No circular reasoning. You start with a definition and then you use that definition to define other words or processes.

For example: Chemistry. You learn about the atom. Atoms make up elements. Elements make up molecules. If you don't understand how atoms work, you won't understand about elements.

Edit: If you don't understand the definitions of those words (atoms, elements, molecules).

More edit: Think about math, the subject that you have difficulty with. Think about the definitions of sine, cosine, tangent.

Even more edit: Computer science/programming use definitions on word, dword, interger, long, array and pointer. You base programs on types of data.

One last edit: English has specific definitions for parts of speech, like verb, adverb, participle, past perfect tense vs imperfect vs present subjunctive.

Also. I notice that you still haven't defined successor.

 

[doronshadmi]

Nope. No circular reasoning. You start with a definition and then you use that definition to define other words or processes.

You are missing this:

Well, yeah. That is how definitions work, after all. X equivalent to Y can be presented as a definition of X as Y (as long as Y relies on already-defined terms).

I have changed it to:

A₁ equivalent to A₂ can be presented as a definition of A₁ as A₂ (as long as A₂ relies on already-defined A₃ terms, A₃ relies on already-defined A₄ terms, A₄ relies on already-defined A₅ terms, ... etc. ad infinitum).

So it is not the case that A₂ is defined by A₁, exactly because A₁ is defined by the already-defined A₂ (or by jsfisher example: X is defined by the already-defined Y, where Y is not defined by X, otherwise we get a circular reasoning that according to it X is defined by Y AND Y is defined by X).

Once A₁ is defined you can then use it to define A₂

Again, this is a circular reasoning, since you use A₂ in order to define A₁ AND A₁ in order to define A₂.

 

[jsfisher]

A₁ equivalent to A₂ can be presented as a definition of A₁ as A₂ (as long as A₂ relies on already-defined A₃ terms, A₃ relies on already-defined A₄ terms, A₄ relies on already-defined A₅ terms, ... etc. ad infinitum).

It works the other way. There are those axiom things and primitive concepts (like set and membership) that provide the starting point. Those can be combined in various ways to define new things. Those new things along with the original axioms and concepts can be combined in various ways to define newer things. And so on, ad infinitum.

Time for you to add one. IsSuccessor(A,B) <=> ...?

 

[doronshadmi]

It works the other way. There are those axiom things and primitive concepts (like set and membership) that provide the starting point.

There are {X} and X as primitive concepts that provide the staring point that enables {X} and X optional (non-essential) properties, according to their relations with each other, as follows:

(If {X} IsSuccessorOf X, then X is incomplete) OR (If {X} ~IsSuccessorOf X, then X is complete).

The truth table of OR is:

 T OR ~T
~T    ~T --> ~T
~T     T -->  T
 T    ~T -->  T
 T     T -->  T

where the non-trivial tautology is based on T T --> T.

You try to force the truth table of XOR, which is:

 T XOR ~T
~T     ~T --> ~T
~T      T -->  T
 T     ~T -->  T
 T      T --> ~T

 

[jsfisher]

There are {X} and X ...

Great (OR not great)! Now, what is the definition of successor? ...of complete?

IsSuccessorOf(A,B) <=> ...?
IsComplete(A) <=> ...?​