Deeper than primes - Continuation

[realpaladin]

You are not in any position to determine my rights.

If you disagree with my argument as given in

Yes. Very much so.

Were you a bit agitated when you posted this? You forgot to post the link...

 

[realpaladin]

So, for the last time, please logically show that x is quantifier-free within (3).

I do not even *need* quantifier elimination for that.

- The fact that we write "x" implies that it is quantifier free because (Mind you the sign (+/-) has nothing to do with the number of occurrences.):

A) - In the case of *no* or zero (0) occurrences of "x" we would explicitly omit "x"
B) - In the case of 2 or more occurrences of "x" we would explicitly write n"x" where n is the number of occurrences.
C) - Only in the case of exactly one (1) occurrence do we write "x" without any quantifiers.

Therefore if we see any formula without a number, it *must* be quantifier free.

Q.E.D.

There you go Doron, logically shown that you do not need your 'there exists'.

Now, what were you saying?

@jsfisher I know, I know... *grin*

 

[realpaladin]

The cycle is familiar.

Also, I have *no* idea why we go on and on about this tautology stuff...

We all know that even if we do agree with him on that or even concede, we won't get far... at some point the argument will peter out, there will be a long silence and then he will start afresh.

There is no logic, rhyme or reason discernible as to where he wants to go with all of this.

 

[jsfisher]

My claim is logically supported in...

No, your claim is simply asserted in any of your various previous posts. Your claim, distilled down to the basics, is that ∃x is a well-formed formula. To be a well-formed formula, it must be constructable according to the rules for well-formed formulae.

To support your claim, to show that ∃x is a well-formed formula, you need show, let me say that again, this time with some emphasis, you need to show that ∃x can be constructed by the rules for well-formed formulae.

You can't, of course, because it isn't.

 

[doronshadmi]

No, your claim is simply asserted

<snip>

Another hand-waving of yours that do not deal in details with all of what is written in http://www.internationalskeptics.com/forums/showpost.php?p=10056698&postcount=4038 (including the link there).

 

[Little 10 Toes]

You haven't shown anything to support your claim.

 

[realpaladin]

Another hand-waving of yours that do not deal in details with all of what is written in http://www.internationalskeptics.com/forums/showpost.php?p=10056698&postcount=4038 (including the link there).

Yes, it does not have to deal with any of that. As it is cute, but it's wrong!

As long as Doron tries to do reductio ad absurdum, he can be scientifically discounted.

I guess this thread will now become a repetition of moves and then I will request the attention of a moderator to either move the whole thread to Abandon All Hope (since Doron does not make an effort to move forward), move only the repetitions to AAH or just lock the thread.

 

[doronshadmi]

EDIT:

You haven't shown anything to support your claim.

Please try to avoid the existence of variable x (representing objects of the universe of discourse) in following atomic formula:

3. ∃x Φ is a formula, when x is a variable and Φ is a formula.

For example, in the case of ZFC (which is some universe of discourse) the objects of the universe of discourse that must exist, are known as sets, and such an object exists even without any members.

Moreover, x is the object of the universe of discourse (3) according to (3), and without its existence in (3), (3) is not an atomic formula.

 

[jsfisher]

Please try to avoid the existence of variable x (representing objects of the universe of discourse)...

You are trying to move the goal posts. Let's just leave them right where they were.

Your claim: ∃x is a well-formed formula.

Your burden: Prove that ∃x can be constructed from the rules for well-formed formulae.

 

[doronshadmi]

You are trying to move the goal posts.

EDIT:

Not at all.

Again, here is some atomic formula (which is some universe of discourse):

3. ∃x Φ is a formula, when x is a variable and Φ is a formula.

x is the object of the universe of discourse (3) according to (3), and without its existence in (3), (3) is not an atomic formula.

More details are given in http://www.internationalskeptics.com/forums/showpost.php?p=10057848&postcount=4048.

You simply can't avoid "there exists" x, according to (3), in order to define (3) as an atomic formula.

In other words, ∃x is wff within (3) exactly as Φ is wff within (3).

Moreover, ∃ is unitary connective within (3) ("there exists" x or ∃x).

Furthermore, even if it is not explicitly written in (3), "there exists" Φ or ∃Φ within (3).

 

[realpaladin]

EDIT:

Not at all.

Again, here is some atomic formula (which is some universe of discourse):

3. ∃x Φ is a formula, when x is a variable and Φ is a formula.

x is the object of the universe of discourse (3) according to (3), and without its existence in (3), (3) is not an atomic formula.

More details are given in http://www.internationalskeptics.com/forums/showpost.php?p=10057848&postcount=4048.

You simply can't avoid "there exists" x, according to (3), in order to define (3) as an atomic formula.

In other words, ∃x is wff within (3) exactly as Φ is wff within (3).

Moreover, ∃ is unitary connective within (3) ("there exists" x or ∃x).

Furthermore, even if it is not explicitly written in (3), "there exists" Φ or ∃Φ within (3).

Strike 1.

 

[jsfisher]

Not at all.

So, you can show us your construction, then?

 

[doronshadmi]

So, you can show us your construction, then?

Another jsfisher's "Talk to the hand(-waving)" logical reaoning.

 

[realpaladin]

Another jsfisher's "Talk to the hand(-waving)" logical reaoning.

Strike 2.

Moving forward is not a variant of 'you don't get it' like the above.

Moving forward is either saying "My definition of wff is not conform the current mathematical definition." or saying "By using the current mathematical definition you can construct the formula in the following way: ..." (and no linguistic nonsense or reductio ad absurdum, those are variations of the 'you don't get it').

Doron, I urge you to stop pointing at people; it is a breach of the forum contract.

 

[doronshadmi]

Platonic existence is discovered.

Non-platonic existence is invented.

The existence of the invented depends ob the existence of the discovered, but not vice versa.

Again, here is some atomic formula (which is some universe of discourse):

3. ∃x Φ is a formula, when x is a variable and Φ is a formula.

x is the platonic object of the universe of discourse (3) according to (3), and without its existence within (3), (3) is not an atomic formula.

Moreover, Φ existence as wff within (3) (where this existence is non-platonic) depends on x existence within (3), because x existence within (3) is platonic ("First of all there exists x within (3), whether its properties are given by Φ, or not"), where Φ existence within (3) is non-platonic.

So, "∃x Φ is a formula" within (3) only if at least ∃x is a formula within (3).

The current agreement between mathematicians simply does not distinguish between platonic and non-platonic existence, and therefore misses the hierarchy of dependency between the platonic (the discovered) and the non-platonic (the invented).

As long as one asks to define things by the current agreement between mathematicians, one determines the indistinguishably between platonic existence and non-platonic existence, and in this case there is no way to communicate with this one about the difference between platonic and non-platonic existence, and the hierarchy of dependency between the platonic (the discovered) and the non-platonic (the invented).

Furthermore, the claim that I make up platonic existence, simply demonstrates that the one that uses this claim, uses only non-platonic view.

 

[Innocuous]

Would someone explain what "platonic existence" means? It seems important for the ongoing argument here, and my web searches have so far been uninformative. Thanks.

 

[doronshadmi]

Would someone explain what "platonic existence" means? It seems important for the ongoing argument here, and my web searches have so far been uninformative. Thanks.

Platonic existence is discovered, where discovered existence is independent on the moment of its discovery (it exists weather it is discovered, or not, or (by using logical terms) its existence is always true (a tautology)).

Non-platonic existence is invented, where invented existence dependents on the moment of its invention (it does not exist unless it is invented, or (by using logical terms) its existence is not always true (it is not a tautology)).

Moreover, non-tautological existence ("existence is not always true") depends on tautological existence ("existence is always true"), but not vice versa.

By following this reasoning, Φ existence depends on x existence within the following atomic formula:

3. ∃x Φ is a formula, when x is a variable and Φ is a formula.

So if Φ is a formula within (3), then ∃x must be a formula within (3).

For Plato’s Forms are not mental entities, nor even mind-dependent. They are independently existing entities whose existence and nature are graspable only by the mind, even though they do not depend on being so grasped in order to exist.

(http://faculty.washington.edu/smcohen/320/thforms.htm)

 

[Innocuous]

Platonic existence is discovered, where discovered existence is independent on the moment of its discovery

With this statement, are you defining two different types of existence (platonic existence and discovered existence)? Or are you saying that they are two names for the same type of existence?

 

[doronshadmi]

With this statement, are you defining two different types of existence (platonic existence and discovered existence)? Or are you saying that they are two names for the same type of existence?

Hi Innocuous.

Logically, platonic existence is independent on the moment of its discovery (platonic existence is always true), so the answer is:

Platonic existence is one and only one type of existence that is always true, whether it is discovered or not, so discovered existence is the same as platonic existence, because the moment of discovery has no impact on a type of existence that is always true (a tautology).

 

[jsfisher]

Again, here is some atomic formula....

It is not an atomic formula.

Be that as it may, though, since you have been unable to show that ∃x is a well-formed formula and since ∃x being such was a lynch pin to your maiming of the Axiom of Infinity, and the maiming was central to your claim the ZFC incorporated your latest concepts of how you'd like Mathematics to behave, I shall consider your claim abandoned.

ZFC was not founded on nor does it incorporate Shadmized concepts of discovered and invented existence.