Cont: Deeper than primes - Continuation 2

[doronshadmi]

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

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

Since being a successor is an optional (non-essential) property of {X}, being a successor is defined exactly by the following wff:

({X} IsSuccessorOf X) OR ({X} ~IsSuccessorOf X).

Since being complete is an optional (non-essential) property of X, being complete is defined exactly by the following wff:

(X is incomplete, in case that {X} IsSuccessorOf X) OR (X is complete, in case that {X} ~IsSuccessorOf X).

Since by your reasoning a useful wff must be of the form X <=> Y, your reasoning can't distinguish between optional (non-essential) and non-optional (essential) properties of mathematical objects.

We actually enable to combine the different optional (non-essential) properties of the primitives {X} and X into a one fruitful mathematical framework, as can be found in the links starting in post http://www.internationalskeptics.com/forums/showpost.php?p=11292718&postcount=1565.

 

[jsfisher]

Since being a successor is an optional (non-essential) property of {X}....

Yeah, you keep saying this, but (1) successor is a relationship between two entities, not one. You may only be interested in the successor-relationship between {A} and A, but that is just a special case of the successor-relationship between B and A. (2) Though it may be a "non-essential" property (whatever that means), you have provided no way determine if something has it.

How, then, for any specific set A can we determine if {A} has this optional (non-essential) property of being a successor of A?

How, then, for any specific pair of sets A and B can we determine if B has this optional (non-essential) property of being a successor of A?

 

[doronshadmi]

Yeah, you keep saying this, but (1) successor is a relationship between two entities, not one. You may only be interested in the successor-relationship between {A} and A, but that is just a special case of the successor-relationship between B and A.

{A} may be OR may not be a successor of A, without loss of generality.

(2) Though it may be a "non-essential" property (whatever that means)

It simply means that {X} or X are primitives that are independent of the nature of their relations with each other (as explained ,for example, in http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485).

How, then, for any specific set A can we determine if {A} has this optional (non-essential) property of being a successor of A?

Since being a successor is optional (non-essential), {X} may be (can be notated as {X} IsSuccessorOf X) OR may not be (can be notated as {X} ~IsSuccessorOf X) a successor of X.

Nothing has to be determined in advanced about optional (non-essential) properties.

How, then, for any specific pair of sets A and B can we determine if B has this optional (non-essential) property of being a successor of A?

Again, nothing has to be determined in advanced about optional (non-essential) properties.

Also the notations "A" or "B" are actually {X} or X without loss of generality.

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

jsfisher, you continue to use reasoning that can't handle with http://www.internationalskeptics.com/forums/showpost.php?p=11284073&postcount=1525.

 

[jsfisher]

{A} may be OR may not be a successor of A, without loss of generality.

And there is absolutely no way to tell which it is.

 

[doronshadmi]

And there is absolutely no way to tell which it is.

There is no absolute determination about optional (non-essential) properties, and this is exactly what provides the fruitfulness of a framework that enables non-optional (essential) and optional (non-essential) properties "under a one roof".

 

[doronshadmi]

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?

Hi TheGnome welcome.

Thank you for being also positive and not just skeptic ad absurdum.

Schroedinger's alive/~alive cat has no influence on the notion that in both options, we deal with a primitive called "cat".

By using this primitive it may be alive (or successor, of you will) OR ~alive (or ~successor, of you will).

 

[Nonpareil]

Since being a successor is an optional (non-essential) property of {X}, being a successor is defined exactly by the following wff:

({X} IsSuccessorOf X) OR ({X} ~IsSuccessorOf X).

No, it isn't.

That is not a definition and never will be, no matter how many times you try to assert that it is.

{A} may be OR may not be a successor of A, without loss of generality.

That is also not a definition. A definition would be an explanation of how you determine whether or not {A} is the successor of A.

It simply means that {X} or X are primitives that are independent of the nature of their relations with each other (as explained ,for example, in http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485).

Even primitive notions can be defined, doronshadmi. Axiomatic set theory treats the definition of "set" as a primitive notion, and still manages to say "it's a grouping of elements treated as a single unit". You can't even do that.

You can't even muster up the coherence necessary to create a primitive.

Again, nothing has to be determined in advanced about optional (non-essential) properties.

Essentially, "it's a successor if I want it to be and not if I don't".

 

[jsfisher]

There is no absolute determination about optional (non-essential) properties

And yet you told us categorically that the set, I, guaranteed by the Axiom of Infinity was incomplete, which in turn would require {I} be a successor of I. So, successor relations can be determined when you find it convenient?

Of course, you have told us many things in this thread and later contradicted them. This is simply yet another example; there is no really surprise.

...and this is exactly what provides the fruitfulness of a framework that enables non-optional (essential) and optional (non-essential) properties "under a one roof".

You misspelled 'uselessness'.

 

[doronshadmi]

And yet you told us categorically that the set, I, guaranteed by the Axiom of Infinity was incomplete, which in turn would require {I} be a successor of I. So, successor relations can be determined when you find it convenient?

The primitive concept known as set can be complete OR incomplete.

If the primiteve {y} is used as a successor of primiteve y, as used in

, then y is incomplete.

 

[doronshadmi]

Even primitive notions can be defined, doronshadmi. Axiomatic set theory treats the definition of "set" as a primitive notion, and still manages to say "it's a grouping of elements treated as a single unit". You can't even do that.

And that single unit (where "single unit" is another name of being primitive) may be complete OR incomplete, since completeness is its optional (non-essential) property.

You and jsfisher simply can't handle with the fruitfulness of a framework that enables non-optional (essential) and optional (non-essential) properties "under a one roof".

For example, http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485 is gibberish for you.

By the combined framework of the essential with the non-essential, if a collection is considered, then infinite AND complete is a contradiction, and so is finite AND incomplete.

The reason is very simple, the primitive known as set may be finite OR infinite, complete OR incomplete, where those with the OR logical connective are optional (non-essential) properties of the primitive.

 

[Nonpareil]

The primitive concept known as set can be complete OR incomplete.

If the primiteve {y} is used as a successor of primiteve y, as used in [qimg]https://c2.staticflickr.com/8/7197/26818050985_2764b1dc92.jpg[/qimg], then y is incomplete.

Oh, good. Doronshadmi has found another term that he doesn't understand, and is determined to run it into the ground.

Again, doron, primitive notions are defined. If they weren't, they would be worthless. The definition may not be mathematically formulated, but it can still be expressed. Sets are primitive; sets are defined.

You claim that "successor" is primitive, but thus far, it is undefined.

And that single unit (where "single unit" is another name of being primitive) may be complete OR incomplete, since completeness is its optional (non-essential) property.

You and jsfisher simply can't handle with the fruitfulness of a framework that enables non-optional (essential) and optional (non-essential) properties "under a one roof".

Well, no. The existence of properties that a given entity may or may not have is hardly a difficult one.

The issue is that you have not yet defined these properties, let alone explained how they may be determined to apply or not apply.

For example, http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485 is gibberish for you.

That's because you're very, very bad at this.

By the combined framework of the essential with the non-essential, if a collection is considered, then infinite AND complete is a contradiction, and so is finite AND incomplete.

Define "complete".

 

[jsfisher]

If ... then ... incomplete.

And if not, then complete.

Not a very useful construct if you can never tell which it is.

 

[doronshadmi]

And if not, then complete.

Not a very useful construct if you can never tell which it is.

Again, doron, primitive notions are defined. If they weren't, they would be worthless. The definition may not be mathematically formulated, but it can still be expressed.

Any reasonable person that reads, for example, http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485 easily understands that "an inexhaustible energy source" or "a car" are the defined primitives, where a primitive is independent of its relations with other primitives.

For example:

"an inexhaustible energy source" is defined independently of its optional relations with "a car".

"a car" is defined independently of its optional relations with "an inexhaustible energy source".

If both primiteves AND there optional relations with each other are considered, then http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485 is some example of what we get.

Even a simpler case like http://www.internationalskeptics.com/forums/showpost.php?p=11295089&postcount=1586, can't be handled by jsfisher and Nonpareil reasoning.

 

[Nonpareil]

Any reasonable person that reads, for example, http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485 easily understands that "an inexhaustible energy source" or "a car" are the defined primitives, where a primitive is independent of its relations with other primitives.

And neither is related to a definition of "successor".

 

[doronshadmi]

And neither is related to a definition of "successor".

Even a simpler case like http://www.internationalskeptics.com/forums/showpost.php?p=11295089&postcount=1586, can't be handled by jsfisher and Nonpareil reasoning.

So, the following is definitely not handled by your reasoning:

"an inexhaustible energy source" is defined independently of its optional relations with "a car".

"a car" is defined independently of its optional relations with "an inexhaustible energy source".

If both primiteves AND there optional relations with each other are considered, then http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485 is some example of what we get.

 

[jsfisher]

The set of the first four positive integers, complete or not complete? Which one, and how do you know?

 

[doronshadmi]

The set of the first four positive integers, complete or not complete? Which one, and how do you know?

Any finite set is complete.

Any infinite set is incomplete.

Finite, complete, infinite, incomplete are optional properties of a primitive called set.

It is easily understood, for example, by http://www.internationalskeptics.com/forums/showpost.php?p=11279727&postcount=1485 and http://www.internationalskeptics.com/forums/showpost.php?p=11297273&postcount=1593 further explanation.

Once again, jsfisher, your reasoning simply can't handle with the fruitfulness of a framework that enables non-optional (essential) and optional (non-essential) properties "under a one roof".

 

[Nonpareil]

Any finite set is complete.

Any infinite set is incomplete.

Finite, complete, infinite, incomplete are optional properties of a primitive called set.

Wonderful. Now define those properties.

Or define "successor". Whichever you choose.

 

[jsfisher]

Once again, jsfisher, your reasoning simply can't handle with the fruitfulness of a framework that enables non-optional (essential) and optional (non-essential) properties "under a one roof".

There is nothing fruitful (or truthful) about any of this, doron. As with all of Doronetics, you just make stuff up. You have manufactured a few meaningless terms, meaningless because you are completely unable to define them, and applied them in arbitrary ways.

You have constructed just one large circle. Infinite sets have this peculiar property you've named 'incomplete'. You can't say what means or why it is significant, but you you know those sets are incomplete because they are infinite.

Mathematics continues unblemished by your confusion. Doronetics fails yet again.

Enjoy your contrivance.

 

[doronshadmi]

There is nothing fruitful (or truthful) about any of this, doron. As with all of Doronetics, you just make stuff up. You have manufactured a few meaningless terms, meaningless because you are completely unable to define them, and applied them in arbitrary ways.

You have constructed just one large circle. Infinite sets have this peculiar property you've named 'incomplete'. You can't say what means or why it is significant, but you you know those sets are incomplete because they are infinite.

Mathematics continues unblemished by your confusion. Doronetics fails yet again.

Enjoy your contrivance.

There is no much to say to a person who uses a reasoning that can't distinguish between "{} = {}" and "({X} IsSuccessorOf X) OR ({X} ~IsSuccessorOf X)".

More details are found in http://www.internationalskeptics.com/forums/showpost.php?p=11294638&postcount=1581 (and its links).

Also http://www.internationalskeptics.com/forums/showpost.php?p=11271084&postcount=1374 is straightforward about the issue at hand.