On 2021-10-18 09:56, olcott wrote:
I abolished Russell's paradox a using a knowledge ontology.
You did this? All by yourself?
Russell's paradox is only a problem for *naive* set theory. It hasn't
been a problem for set theory since 1908. Neither Russell's own set
theory based on the theory of types nor ZF(C) suffer from Russell's
paradox.
So how is your proposal different from theirs or in any way original?
Since no thing (physical or conceptual) can totally contain itself
such that its outer physical or conceptual boundary is contained
within this same physical or conceptual boundary then we can know that
no set can be a member of itself.
You can't make inferences about how sets behave based on how physical
objects behave since sets are not physical objects. Both Russell's
theory of types and ZFC avoid Russell's paradox, but they do so without making silly arguments like the above.
This becomes more clear when we try to draw a Venn diagram of a set
that contains itself that it not a Venn diagram of an identical set.
Venn diagrams are not set theory. They are simply a tool useful for
solving very *simple* problems in logic and set theory.
André
On 2021-10-18 10:44, olcott wrote:
On 10/18/2021 11:14 AM, André G. Isaak wrote:
On 2021-10-18 09:56, olcott wrote:
I abolished Russell's paradox a using a knowledge ontology.
You did this? All by yourself?
Russell's paradox is only a problem for *naive* set theory. It hasn't
been a problem for set theory since 1908. Neither Russell's own set
theory based on the theory of types nor ZF(C) suffer from Russell's
paradox.
So how is your proposal different from theirs or in any way original?
Since no thing (physical or conceptual) can totally contain itself
such that its outer physical or conceptual boundary is contained
within this same physical or conceptual boundary then we can know
that no set can be a member of itself.
You can't make inferences about how sets behave based on how physical
objects behave since sets are not physical objects. Both Russell's
theory of types and ZFC avoid Russell's paradox, but they do so
without making silly arguments like the above.
The base class of the definition of physical and conceptual total
containment from which physical and conceptual total containment
inherits its base semantic meaning is essentially an axiom that
stipulates that no physical or conceptual thing can totally contain
itself. This axiom prohibits a set from totally containing itself thus
prohibits a set from being a member of itself.
Classes and sets are two different things. And neither corresponds to
the notion of C++ classes which is what you seem to be talking about above.
Russell's paradox is about *sets*.
If you want to talk about either classes or C++, it isn't relevant.
André
I abolished Russell's paradox a using a knowledge ontology.
Since no thing (physical or conceptual) can totally contain itself such
that its outer physical or conceptual boundary is contained within this
same physical or conceptual boundary then we can know that no set can be
a member of itself.
This becomes more clear when we try to draw a Venn diagram of a set that contains itself that it not a Venn diagram of an identical set.
olcott wrote:
I abolished Russell's paradox a using a knowledge ontology.
Since no thing (physical or conceptual) can totally contain itself
such that its outer physical or conceptual boundary is contained
within this same physical or conceptual boundary then we can know that
no set can be a member of itself.
This becomes more clear when we try to draw a Venn diagram of a set
that contains itself that it not a Venn diagram of an identical set.
Venn diagrams are not a useful method for determining the truth or
falsity of statements about sets.
On 10/19/2021 12:48 PM, Peter wrote:
olcott wrote:
I abolished Russell's paradox a using a knowledge ontology.
Since no thing (physical or conceptual) can totally contain itself
such that its outer physical or conceptual boundary is contained
within this same physical or conceptual boundary then we can know
that no set can be a member of itself.
This becomes more clear when we try to draw a Venn diagram of a set
that contains itself that it not a Venn diagram of an identical set.
Venn diagrams are not a useful method for determining the truth or
falsity of statements about sets.
Venn diagrams conclusively prove that a set that is a member of itself
cannot be distinguished from a pair of identical sets in both cases we
only have a single circle. This shows that a set being a member of
itself is incoherent.
On 10/19/2021 12:48 PM, Peter wrote:
olcott wrote:
I abolished Russell's paradox a using a knowledge ontology.
Since no thing (physical or conceptual) can totally contain itself
such that its outer physical or conceptual boundary is contained
within this same physical or conceptual boundary then we can know
that no set can be a member of itself.
This becomes more clear when we try to draw a Venn diagram of a set
that contains itself that it not a Venn diagram of an identical set.
Venn diagrams are not a useful method for determining the truth or
falsity of statements about sets.
Venn diagrams conclusively prove
that a set that is a member of itself
cannot be distinguished from a pair of identical sets in both cases we
only have a single circle. This shows that a set being a member of
itself is incoherent.
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