fom
Posts:
1,099
Registered:
12/4/12
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Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Posted:
Feb 10, 2013 4:24 PM
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On 2/10/2013 2:38 AM, Graham Cooper wrote:
> On Feb 10, 5:47 pm, fom <fomJ...@nyms.net> wrote:
>> On 2/9/2013 6:19 PM, Charlie-Boo wrote:
>>
>>> On Feb 7, 1:51 am, fom <fomJ...@nyms.net> wrote:
>>
>>>> How do you see Logic and Set Theory as being the same?
>>
>>> Both are concerned with mappings to {true,false}. A propositional
>>> calculus proposition is 0-place. A set is 1-place. A relation is any
>>> number of places. (A relation is a set - of tuples.)
>>
>>> So you have the same rules of inference: Double Negative, DeMorgan
>>> etc. apply to propositions and sets.
>>
>>> To prove incompleteness, Godel had to generalize wffs as expressing
>>> propositions to expressing sets when the wff has a free variable.
>>
>> Hmm...
>>
>> This is naive set theory (which you have stated
>> as being fine with your views).
>>
>> I view set theory as being about the existence
>> of mathematical objects. Naive set theory failed,
>> in part, because of something in Aristotle--do not
>> negate "substance". Do not get me wrong. I am
>> not planning to run out and buy a number 2 while
>> I pick up my next Turing machine....
>>
>> The problem, however, is that the connection of
>> mathematics to any metaphysical truth (if such
>> a statement can be sensible) requires that the
>> objects represented in physics books (material
>> objects) correspond with some sort of mathematical
>> notion. So, while mathematics is abstract,
>> there must be some sort of interpretation that
>> accounts for its apparent ability to model
>> real-world situations.
>>
>> Either physics is a collection of mathematical
>> hallucinations or there is a better explanation
>> of set theory.
>>
>
> Right! the physical world cannot contravene the platonic, so a set of
> truths may exist and a set of lies not...
>
> ** in Plato land where (angle1+angle2+angle3=pi) **
>
> it's the 1 metaphysics principle I subscribe to!
>
> I think LOGIC is just applying MODUS PONENS.
>
> backwards to axioms
>
> a1
> \
> theorem ?
> /
> a2
>
> forwards to contradictions
>
> x
> /
> ~theorem
> \
> ~x
>
> Naive set theory should be able to cope with a SUBSET of WFF that have
> been sieved through various checks. if you can formulate what the
> real world contradiction is, it can be unstratified.
Herc,
What you say here is Kantian.
Kant called logic the negative criterion
of truth (forward to contradiction).
And he ascribed the discernment of natural
laws to presupposition analysis under the
presumption of causes (backwards to axioms).
For what this is worth, your arguments
against Cantor's diagonal have been based
on transversal designs.
The march to infinity is most likely taken
using finite projective planes described
by difference sets.
If you want to see why, do an internet
search on "perfect difference sets" and
"neighbor detection"
Identity requires infinity. Distinguishability
in the finitary context of automata is finite.
With respect to this, equivalence is defined
negatively. Hence, it presupposes infinity.
Now, identity and diversity are intertwined
by negation. Leibniz' principle of identity
of indiscernibles relates an object to all
of the objects of the system which are not
the given object. This is like a geometry
where every pair of points define a line.
Naming is quantization process that requires
fewer resources. It is Leibniz' principle
of indiscernibles restricted to "landmarks".
In network analysis they are using perfect
difference sets for this purpose.
Anyway, it may give you a different
perspective on some of your thoughts.
Glad you liked the remark.
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