Deeper than primes

[jsfisher]

To be fair, he was only using Constructivism as an example of where negation is handled differently.

Maybe, but with Doron there is only ONE Mathematics, and all the others are utter failures that don't work. It would be unfair of him to support a position of his using something he has already rejected as completely wrong.

Doron doesn't accept that Mathematics is open to many, many systems, all founded on their own basis. We have offered repeatedly to help him develop his own special version and given it an axiomatic basis, but he's been unwilling (well, unable is a more correct assessment) to work towards that goal.

He simply asserts he's correct, buries his argument in gibberish, continual relocation of goalposts, and blatant contradiction.

 

[Robin]

Definitions and direct proofs.

Definitions and direct proofs - but no theorems? What are the proofs proving?

And can you point to any actual proof in what you wrote?

 

[epix]

For example, MP.

If P, then Q.
P.
Therefore, Q.

There is also UI, for example:

"All ants are insects. Koko is an ant. Therefore Koko is an insect."

Please see http://en.wikipedia.org/wiki/Direct_proof .

Why do you direct folks to the Wikipedia, which doesn't take the proof all the way to the axiom?

If 'a' is an element of 'A' then 'a = A' describes the relationship (ant is insect). So the implication leans against the law of transitivity

If a = A and b = a, then b = A. (So Koko 'b' must be insect).

But transitivity is an axiom; it is the first Common Notion of Euclid that you have found redundant, coz A=A and that's all what matters, right? Now you use it as an example. LOL. Axioms are roots of the Tree of Mathematics and your next life will be commensurate to your present one: You shall be relegated and become a squirrel, coz it climbs trees being oblivious to the existence of the roots.

 

[doronshadmi]

So, earlier you claimed that MT was an indirect proof.

I said:

If "x implies y and not y implies not x" is equivalent to "p AND ~p" where ~p is the negation of p, then you are still using indirect proofs, which have no impact on direct proofs.

Let us clarify it.

If y is the negation of x ("x implies ~x and ~~x implies ~x"), then you are still using indirect proofs, which have no impact on direct proofs.

 

[doronshadmi]

it is the first Common Notion of Euclid that you have found redundant,

A = A even if A is uncertain (non-strict id = non-strict id).

We are not talking about the clarity of A, but we are talking about the relation of a thing to itself, whether it has strict id or not.

 

[doronshadmi]

Yes, I know.

So to you accept the fact that superposition is not a contradiction?

 

[Robin]

The current scientific method, which was developed since the 17th century, states that the researcher must be omitted form the research environment, in order to avoid results that are influenced by subjective tendencies of the researcher.

Actually this is not true - both Heisenberg and Bohr have written on this. Heisenberg has stated that part of the motivation for the Copenhagen Interpretation was to properly handle the influence of the scientist, which becomes inescapable in QM.

 

[Robin]

So to you accept the fact that superposition is not a contradiction?

I never said it was.

 

[doronshadmi]

Actually this is not true - both Heisenberg and Bohr have written on this. Heisenberg has stated that part of the motivation for the Copenhagen Interpretation was to properly handle the influence of the scientist, which becomes inescapable in QM.

And it is about time to do it also in the mathematical science, that currently is based on deduction.

 

[doronshadmi]

I never said it was.

In that case you can't use a framework, where p AND ~p is a contradiction, in order to understand a framework, where p AND ~p is a superposition.

 

[Robin]

I said:

Let us clarify it.

If "x implies y and not y implies not x" is equivalent to "p AND ~p" where ~p is the negation of p, then you are still using indirect proofs, which have no impact on direct proofs.

If y is the negation of x ("x implies ~x and ~~x implies ~x"), then you are still using indirect proofs, which have no impact on direct proofs.

But y isn't the negation of x. Why would you think that? I certainly didn't say so.

And this dichotomy between indirect and direct proofs - where did you get that?

RAA and MP are just different rules of inference. It is not somehow in a different class of rules of inference.

And what is your basis for saying that removing RAA has no effect on other rules of inference?

As I say, they are all related - you can't just arbitrarily decide one tautology is not a tautology after all and then blithely assume that it does not have an effect elsewhere.

You have to demonstrate this.

A good start would be to point out this proof that you claim to have presented.

 

[doronshadmi]

But y isn't the negation of x.

In that case (by your own words, which reject the possibility that y is the negation of x) you are at the kingdom of direct proofs.

And this dichotomy between indirect and direct proofs - where did you get that?

By your own words, which reject the possibility that y is the negation of x.

 

[jsfisher]

y is the negation of x

and

x implies ~x and ~~x implies ~x

are not equivalent statements. Why would you suggest they were?

 

[Robin]

In that case you can't use a framework, where p AND ~p is a contradiction, in order to understand a framework, where p AND ~p is a superposition.

Again - I never said you could.

I said you could not use a framework where "p and not p" is not a contradiction to do maths without rewriting your rules of inference.

 

[doronshadmi]

and


are not equivalent statements. Why would you suggest they were?

Robin wrote "x implies y and not y implies not x".

If y is the negation of x, then "x implies ~x and ~~x implies ~x".

 

[Robin]

In that case (by your own words, which reject the possibility that y is the negation of x) you are at the kingdom of direct proofs.

By your own words, which reject the possibility that y is the negation of x.

I didn't mean that there was no possiblity of y being the negation of x, I meant that y is not necessarily the negation of x.

Are you now saying that MT is an indirect proof if y happens to be the negation of x and a direct proof otherwise?

Can you define what you think it is that distinguishes an indirect proof from a direct one?

And again - show me this proof you claim to have presented.

 

[doronshadmi]

I didn't mean that there was no possiblity of y being the negation of x, I meant that y is not necessarily the negation of x.

Are you now saying that MT is an indirect proof if y happens to be the negation of x and a direct proof otherwise?

Can you define what you think it is that distinguishes an indirect proof from a direct one?

And again - show me this proof you claim to have presented.

It is 2:00 AM in Israel, let us continue after I take a good sleep.

 

[jsfisher]

If y is the negation of x, then "x implies ~x and ~~x implies ~x".

Repeating your incorrect statement doesn't make it more credible.

 

[Robin]

Robin wrote "x implies y and not y implies not x".

If y is the negation of x, then "x implies ~x and ~~x implies ~x".

So if MT is RAA when the first term is the negation of the second.

And MT is the contrapositive of MP.

Doesn't that indicate that they are all interrelated?

So why do you think you can decide one of these is not a tautology and the others will remain unaffected.

 

[Little 10 Toes]

If "x implies y and not y implies not x" is equivalent to "p AND ~p"

No it isn't.