On 12/14/23 10:58 AM, olcott wrote:

"from a contradiction, any proposition (including its negation)
 can be inferred from it; this is known as deductive explosion." https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

Nope, it establishes that some Dogs are not Dogs. That is a FULL
"semantic" reasoning from the premises.

This comes because the cats that are the "Some Cats" in (b), MUST BE, by
(a) Dogs, so we can conclude that Those Dogs are Not Dogs.

In other words, it proves the system is inconsistant.

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On 12/14/23 7:14 PM, olcott wrote:

On 12/14/2023 9:58 AM, olcott wrote:

"from a contradiction, any proposition (including its negation)
  can be inferred from it; this is known as deductive explosion."
https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

The principle of explosion would says that (a) and (b)
proves that the Moon is made from green cheese.

Whereas the intersection of the sets specified by
(a) and (b) is the empty set, thus derives no conclusion.

But logic doesn't take the intersetion of the premises, but, in one
sense, the Union.

Or, are you saying that it implies that it is describing a world with no
cats or dogs?

But that would violate the clear meaning of the word "Some", which
implies existance.

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On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation)
can be inferred from it; this is known as deductive explosion." https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule
of syllogistic logic.

Mikko

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On 12/15/23 10:35 AM, olcott wrote:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation)
  can be inferred from it; this is known as deductive explosion."
https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule
of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the empty set.

Which "Sets"

The first statement has its set being that of ALL Cats, and states that
they are dogs

The second statement has its set being those cats that are not dogs,
with the quallifier that this is not the empty set(Some implies
existance), but since these cats are members of "All Cats" when we take
the intersection, we get the set of "Cats that are Dogs that are also
Not Dogs" with the qualification that it is NOT the empty set.

So, you are just stating that in your logic system, the empty set has
members and isn't empty.

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On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation)
  can be inferred from it; this is known as deductive explosion."
https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule
of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the empty set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping
maps false to the empty set. The principle of explosion maps
to the principle that the empty set is a subset of every set.

The rules of set theory mimic the rules of ordinary logic, not
of syllgistic logic. Terefore they don't show what is or is not
provable with syllogistic logic.

Mikko

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On 12/16/23 10:46 AM, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation)
  can be inferred from it; this is known as deductive explosion."
https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule
of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the empty set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping
maps false to the empty set. The principle of explosion maps
to the principle that the empty set is a subset of every set.

The rules of set theory mimic the rules of ordinary logic, not
of syllgistic logic. Terefore they don't show what is or is not
provable with syllogistic logic.

Mikko

Syllogisms are build from categorical propositions that define sets that
can be diagrammed using Venn diagrams. A pair of contradictory Venn
diagrams has no intersection.

(a) All cats are animals
(b) All Animals are living things
(c) The intersection of Cats/Animals/Living Things exists.

Since you can't actually draw your (a) and (b) from your contradiction
set farther above in a single Venn diagram, they can't exist together,
so you logic breaks.

The shape for "Cats" must both fully exist with the shape for Dogs
(since all Cats are Dogs) but also must have space with an element
outside of Dogs (since some Cats are not Dogs), which is IMPOSSIBLE, so
your system is just broken.

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On 12/16/23 3:06 PM, olcott wrote:

On 12/16/2023 9:46 AM, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation)
  can be inferred from it; this is known as deductive explosion." >>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule
of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the empty set. >>>

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping
maps false to the empty set. The principle of explosion maps
to the principle that the empty set is a subset of every set.

The rules of set theory mimic the rules of ordinary logic, not
of syllgistic logic. Terefore they don't show what is or is not
provable with syllogistic logic.

Mikko

Syllogisms are build from categorical propositions that define sets
that can be diagrammed using Venn diagrams. A pair of contradictory
Venn diagrams has no intersection.

(a) All cats are animals
(b) All Animals are living things
(c) The intersection of Cats/Animals/Living Things exists.

The intersection of the sets defined by contradictory categorical propositions <is> the empty set thus proving that the Principle of
Explosion is nonsense.

I think that every syllogism can be construed as the intersection
of the sets specified in its categorical propositions, thus when
this intersection is the empty set then nothing can be concluded.

So what do we need to change?

Is it no longer true that the intersection of a set (like All Cats) with
a subset of that set (The Some Cats that are not Dogs) results in that
sub set?

or, does the existance clause, "Some Cats" allow for it to be
established by an Empty Set (and thus we can truthfully say that Some
Donald Trumps won the 2020 election)

or, does the Empty Set possible contain members (like the some cats from
above)

or does you logic system just allow throwing out Truth makers that we
don't want?

or, is your logic system just not built on needing to be logical?

(It seems that last is your actual assertion, since you have never been
able to actually make a proper argument for anything meaningful).

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On 12/16/23 3:36 PM, olcott wrote:

On 12/16/2023 2:06 PM, olcott wrote:

On 12/16/2023 9:46 AM, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation)
  can be inferred from it; this is known as deductive explosion." >>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule
of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the empty
set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping
maps false to the empty set. The principle of explosion maps
to the principle that the empty set is a subset of every set.

The rules of set theory mimic the rules of ordinary logic, not
of syllgistic logic. Terefore they don't show what is or is not
provable with syllogistic logic.

Mikko

Syllogisms are build from categorical propositions that define sets
that can be diagrammed using Venn diagrams. A pair of contradictory
Venn diagrams has no intersection.

(a) All cats are animals
(b) All Animals are living things
(c) The intersection of Cats/Animals/Living Things exists.

The intersection of the sets defined by contradictory categorical
propositions <is> the empty set thus proving that the Principle of
Explosion is nonsense.

I think that every syllogism can be construed as the intersection
of the sets specified in its categorical propositions, thus when
this intersection is the empty set then nothing can be concluded.

The intersection of (All S <are> P) and (No S <are> P) is the empty set.
This can be directly see on the Venn diagrams of these two sets.

So for THAT logic, the conclusion is that S is the empty set, correct.

But NO S are P and some S are not P are difffent statements.

Some S are not P asserts that some S do exist.

You don't seem to understand basic logic,

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On 12/16/23 4:53 PM, olcott wrote:

"So what do we need to change?"

Understand that the Principle of Explosion has always been ridiculous nonsense.

Ok, so you admit the last case, you logic just isn't built on logic.

Thank you for you clarification, you admit that logic is just
ridiculous nonsense.

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On 2023-12-16 08:46, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation)
  can be inferred from it; this is known as deductive explosion."
https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule
of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the empty set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping
maps false to the empty set. The principle of explosion maps
to the principle that the empty set is a subset of every set.

Apologies for piggybacking.

Mikko is correct. Neither (a) nor (b) are sets. They are statements
which mention a variety of different sets. (a) mentions the set of cats
and the set of dogs. (b) mentions a set of cats which are not dogs which
itself makes reference to the set complement of the set of dogs. So to
talk about the intersection of (a) and (b) is meaningless. You need to
clearly state *which* set you are talking about (and why their
intersection should be relevant).

I'm going to assume (and I might be wrong) that what you intend are (A)
the set of cats and (B) the set of cats which are not dogs [note that
I'm using capital letters to refer to these sets while I use lowercase
letters to refer to the statements (not sets) which you provide in your premises].

Since the set of cats which are not dogs is obviously a subset of the
set of cats, the intersection of A and B is clearly simply going to be B.

But how exactly is it that you conclude that B is the empty set?
According to your premise (a), B is empty, but according to your premise
(b), B is non-empty. So why does (a) take priority over (b)? Both of
your premises contradict one another on whether B is empty or non-empty,
which means that you can argue either that it is empty or non-empty
depending on which premise you focus on. [and that, btw, is what we call
an explosion].

If confronted with such an argument in real life, the reasonable person
would conclude from the contradiction that one of the premises must be
wrong. But why do you conclude that it must be (b) that is wrong rather
than (a)? (especially since in the real world it is premise (a) that is
wrong, not premise (b)).

Additionally, since you claim that all the world's problems can be
solved by restricting oneself to syllogistic logic, you have still not identified exactly which principles of syllogistic logic you are using
to derive 'the empty set' as a conclusion [conclusions are normally
statements, not sets], nor for that matter which principle of
syllogistic logic tells you to take the intersection of sets A and B.

It seems like you're just making stuff up according to what your
personal intuitions tell you should be the case, and then claiming that syllogistic logic somehow supports your intuitions. But logic doesn't
work that way. You need to actually explicitly state which
principles/rules of inference of syllogistic logic are leading you to
your conclusion. Or at least you need to to do this if you want to claim
that you are using syllogistic logic.

The rules of set theory mimic the rules of ordinary logic, not
of syllgistic logic. Terefore they don't show what is or is not
provable with syllogistic logic.

Mikko

Syllogisms are build from categorical propositions that define sets that
can be diagrammed using Venn diagrams. A pair of contradictory Venn
diagrams has no intersection.

(a) All cats are animals
(b) All Animals are living things
(c) The intersection of Cats/Animals/Living Things exists.

Note that your conclusion above is a statement, as it should be, not a
set. If we followed the structure of your original argument, the above
would read:

(a) All cats are animals
(b) All animals are living things

therefore

(c) the intersection of cats/animals/living things.

Which, of course, makes no sense. Maybe try rephrasing your original
argument such that the conclusion is actually a statement.

The most obvious way would be to state it as:

(c) the intersection of cats and cats which are not dogs is the empty set.

This, of course, is a conclusion (though not one which follows from the premises for the reasons given above). But in your original formulation
you seemed to be using NULL to mean 'therefore it is not possible to
conclude anything from this'. So how can you draw this conclusion?

You're suffering from a terrible case of muddled thinking.

André

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On 12/16/23 9:34 PM, olcott wrote:

On 12/16/2023 6:23 PM, André G. Isaak wrote:

On 2023-12-16 08:46, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation)
  can be inferred from it; this is known as deductive explosion." >>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule
of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the empty
set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping
maps false to the empty set. The principle of explosion maps
to the principle that the empty set is a subset of every set.

Apologies for piggybacking.

Mikko is correct. Neither (a) nor (b) are sets.

(a) Has the Venn diagram of two totally overlapping circles where
one is labeled cats and the other is labeled dogs.

(b) Has the Venn diagram of two partially overlapping circles where
one is labeled cats and the other is labeled dogs.

Since (a) and (b) have been diagrammed with Venn diagrams this seems to
prove that they are sets.

And there is no Venn diagram that expresses both at the same time, as is
needed by both (a) and (b) being true at the same time.

Thus, your system is broken, and you are a LIAR.

The system is inconsistant and thus IMPOSSIBLE, and your claiming it
implies ANYTHING (other than the system being broken) just proves your
concept of logic is broken.

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On 2023-12-16 19:34, olcott wrote:

On 12/16/2023 6:23 PM, André G. Isaak wrote:

On 2023-12-16 08:46, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation)
  can be inferred from it; this is known as deductive explosion." >>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule
of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the empty
set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping
maps false to the empty set. The principle of explosion maps
to the principle that the empty set is a subset of every set.

Apologies for piggybacking.

Mikko is correct. Neither (a) nor (b) are sets.

(a) Has the Venn diagram of two totally overlapping circles where
one is labeled cats and the other is labeled dogs.

That's a relationship between two sets. A relationship between two sets
is not a set, it's a relationship.

(b) Has the Venn diagram of two partially overlapping circles where
one is labeled cats and the other is labeled dogs.

Again, that's a relationship between two sets. A relationship between
two sets is not a set; it's a relationship.

Since (a) and (b) have been diagrammed with Venn diagrams this seems to
prove that they are sets.

At the risk of being repetitive, Venn diagrams are used to express relationships between sets. They are not themselves sets. They are
graphical representations of relationships between sets.

André

--
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service.

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On 2023-12-16 20:05, olcott wrote:

On 12/16/2023 8:50 PM, André G. Isaak wrote:

On 2023-12-16 19:34, olcott wrote:

On 12/16/2023 6:23 PM, André G. Isaak wrote:

On 2023-12-16 08:46, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation) >>>>>>>>>   can be inferred from it; this is known as deductive explosion." >>>>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full >>>>>>>>> semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule >>>>>>>> of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the
empty set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping
maps false to the empty set. The principle of explosion maps
to the principle that the empty set is a subset of every set.

Apologies for piggybacking.

Mikko is correct. Neither (a) nor (b) are sets.

(a) Has the Venn diagram of two totally overlapping circles where
one is labeled cats and the other is labeled dogs.

That's a relationship between two sets. A relationship between two
sets is not a set, it's a relationship.

(b) Has the Venn diagram of two partially overlapping circles where
one is labeled cats and the other is labeled dogs.

Again, that's a relationship between two sets. A relationship between
two sets is not a set; it's a relationship.

Since (a) and (b) have been diagrammed with Venn diagrams this seems to
prove that they are sets.

At the risk of being repetitive, Venn diagrams are used to express
relationships between sets. They are not themselves sets. They are
graphical representations of relationships between sets.

André

Thus the <intersection> relationship between two sets
is not itself a set. Wrongo !!! https://en.wikipedia.org/wiki/Intersection_(set_theory)

You seem to be missing my point. As an example take your premise (a)
which expresses a relationship between two sets: the set of cats and the
set of dogs. It states that the former is a subset of the latter.

So exactly which set does your (a) REFER to? Does it refer to the set of
cats or the set of dogs? Answer: It refers to neither of these; rather,
it expresses that a particular relationship exists between these two sets.

If you really want to claim that (a) refers to a set, then you should be
able to replace it with either:

(a) the set of cats

or

(b) the set of dogs.

So your argument ultimately should end up looking something like this:

premise a: the set of cats
premise b: the set of cats which are not dogs
conclusion: the empty set

Do you seriously believe that the above is coherent?

André


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On 2023-12-16 20:05, olcott wrote:

Thus the <intersection> relationship between two sets
is not itself a set. Wrongo !!! https://en.wikipedia.org/wiki/Intersection_(set_theory)

Addendum to my previous post: 'intersection' is an operation, not a relationship. Your initial premise talked about subsets, which is a relationship, not an operation.

André

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On 2023-12-16 20:56, olcott wrote:

On 12/16/2023 9:19 PM, André G. Isaak wrote:

On 2023-12-16 20:05, olcott wrote:

Thus the <intersection> relationship between two sets
is not itself a set. Wrongo !!!
https://en.wikipedia.org/wiki/Intersection_(set_theory)

Addendum to my previous post: 'intersection' is an operation, not a
relationship. Your initial premise talked about subsets, which is a
relationship, not an operation.

André

Categorical propositions do define sets in terms of Venn diagrams. https://en.wikipedia.org/wiki/File:Square_of_opposition,_set_diagrams.svg

Which has dick all to do with the point I made.

André

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On 2023-12-16 20:51, olcott wrote:

On 12/16/2023 9:13 PM, André G. Isaak wrote:

On 2023-12-16 20:05, olcott wrote:

On 12/16/2023 8:50 PM, André G. Isaak wrote:

On 2023-12-16 19:34, olcott wrote:

On 12/16/2023 6:23 PM, André G. Isaak wrote:

On 2023-12-16 08:46, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation) >>>>>>>>>>>   can be inferred from it; this is known as deductive
explosion."
https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full >>>>>>>>>>> semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs) >>>>>>>>>>> (c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule >>>>>>>>>> of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the >>>>>>>>> empty set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping >>>>>>>> maps false to the empty set. The principle of explosion maps
to the principle that the empty set is a subset of every set.

Apologies for piggybacking.

Mikko is correct. Neither (a) nor (b) are sets.

(a) Has the Venn diagram of two totally overlapping circles where
one is labeled cats and the other is labeled dogs.

That's a relationship between two sets. A relationship between two
sets is not a set, it's a relationship.

(b) Has the Venn diagram of two partially overlapping circles where
one is labeled cats and the other is labeled dogs.

Again, that's a relationship between two sets. A relationship
between two sets is not a set; it's a relationship.

Since (a) and (b) have been diagrammed with Venn diagrams this
seems to
prove that they are sets.

At the risk of being repetitive, Venn diagrams are used to express
relationships between sets. They are not themselves sets. They are
graphical representations of relationships between sets.

André

Thus the <intersection> relationship between two sets
is not itself a set. Wrongo !!!
https://en.wikipedia.org/wiki/Intersection_(set_theory)

You seem to be missing my point. As an example take your premise (a)
which expresses a relationship between two sets: the set of cats and
the set of dogs. It states that the former is a subset of the latter.

Factually incorrect. It states that they are identical sets.

Not in any set theory which I am aware of. 'All cats are dogs' states
that cats are a subset of dogs. It most certainly does not claim that
they are identical sets.

Set operations and categorical propositions define sets in
terms of other sets.

(b) entails that the set of cats and dogs are not the identical set.

The only actual semantic conclusion is NULL.

NULL isn't a conclusion at all since it isn't a statement. What
statement do you think this represents?

If your son tells you that they are going to the movies at 7:00 PM
and instead he robs a liquor store at 7:00 PM we do not conclude
that this entails that the Moon is made from green cheese as the
principle of explosion requires instead we conclude that he lied.

Yes. When confronted with a contradiction we normally assume that one of
the two contradictory statements is actually false.

What you are failing to grasp is that when talking about arguments,
premises are statements which are assumed to be *true*. When confronted
with contradictory premises you cannot justify rejecting one of them any
more than you can justify rejecting the other.

There is never any case where anything besides NULL is the
result of a contradiction. When we anchor these things in
semantic meanings then the dictatorial fiat of the POE
is proved to be nonsense.

Non sequitur.

André

So exactly which set does your (a) REFER to? Does it refer to the set
of cats or the set of dogs? Answer: It refers to neither of these;
rather, it expresses that a particular relationship exists between
these two sets.

If you really want to claim that (a) refers to a set, then you should
be able to replace it with either:

(a) the set of cats

or

(b) the set of dogs.

So your argument ultimately should end up looking something like this:

premise a: the set of cats
premise b: the set of cats which are not dogs
conclusion: the empty set

Do you seriously believe that the above is coherent?

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/16/23 10:51 PM, olcott wrote:

On 12/16/2023 9:13 PM, André G. Isaak wrote:

On 2023-12-16 20:05, olcott wrote:

On 12/16/2023 8:50 PM, André G. Isaak wrote:

On 2023-12-16 19:34, olcott wrote:

On 12/16/2023 6:23 PM, André G. Isaak wrote:

On 2023-12-16 08:46, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its negation) >>>>>>>>>>>   can be inferred from it; this is known as deductive
explosion."
https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full >>>>>>>>>>> semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs) >>>>>>>>>>> (c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule >>>>>>>>>> of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the >>>>>>>>> empty set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping >>>>>>>> maps false to the empty set. The principle of explosion maps
to the principle that the empty set is a subset of every set.

Apologies for piggybacking.

Mikko is correct. Neither (a) nor (b) are sets.

(a) Has the Venn diagram of two totally overlapping circles where
one is labeled cats and the other is labeled dogs.

That's a relationship between two sets. A relationship between two
sets is not a set, it's a relationship.

(b) Has the Venn diagram of two partially overlapping circles where
one is labeled cats and the other is labeled dogs.

Again, that's a relationship between two sets. A relationship
between two sets is not a set; it's a relationship.

Since (a) and (b) have been diagrammed with Venn diagrams this
seems to
prove that they are sets.

At the risk of being repetitive, Venn diagrams are used to express
relationships between sets. They are not themselves sets. They are
graphical representations of relationships between sets.

André

Thus the <intersection> relationship between two sets
is not itself a set. Wrongo !!!
https://en.wikipedia.org/wiki/Intersection_(set_theory)

You seem to be missing my point. As an example take your premise (a)
which expresses a relationship between two sets: the set of cats and
the set of dogs. It states that the former is a subset of the latter.

Factually incorrect. It states that they are identical sets.

Set operations and categorical propositions define sets in
terms of other sets.

(b) entails that the set of cats and dogs are not the identical set.

The only actual semantic conclusion is NULL.

Which means your data is INVALID.

The fact that your "logic" accepts it and give a result you claim is
sensible, says your logic is nonsensical.

If your son tells you that they are going to the movies at 7:00 PM
and instead he robs a liquor store at 7:00 PM we do not conclude
that this entails that the Moon is made from green cheese as the
principle of explosion requires instead we conclude that he lied.

There is never any case where anything besides NULL is the
result of a contradiction. When we anchor these things in
semantic meanings then the dictatorial fiat of the POE
is proved to be nonsense.

No, the result of the contradiction is the repudiation of the full
system that data was in.

Unless that is what you mean by the answr is NULL, you are just wrong.

And that doesn't negate the Principle of Explosion, but just certifies it.

A system that has contradictory information (in a logic system that
claims to not be contradictory) is just WRONG and the discovery of that
data has just blown the system up.

Your failure to understand that just shows you are totally ignorant.

So exactly which set does your (a) REFER to? Does it refer to the set
of cats or the set of dogs? Answer: It refers to neither of these;
rather, it expresses that a particular relationship exists between
these two sets.

If you really want to claim that (a) refers to a set, then you should
be able to replace it with either:

(a) the set of cats

or

(b) the set of dogs.

So your argument ultimately should end up looking something like this:

premise a: the set of cats
premise b: the set of cats which are not dogs
conclusion: the empty set

Do you seriously believe that the above is coherent?

André

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/17/23 12:11 PM, olcott wrote:

On 12/17/2023 2:17 AM, immibis wrote:

On 12/15/23 05:20, olcott wrote:

On 12/14/2023 9:56 PM, André G. Isaak wrote:

On 2023-12-14 17:14, olcott wrote:

On 12/14/2023 9:58 AM, olcott wrote:

"from a contradiction, any proposition (including its negation)
  can be inferred from it; this is known as deductive explosion." >>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)

The principle of explosion would says that (a) and (b)
proves that the Moon is made from green cheese.

No. It doesn't say that. Given a contradiction (I'll use A & ¬A),
the principle of explosion says that for any statement X, "A & ¬A
therefore X" is a *valid* argument.

*Which is itself conventionally defined incorrectly*
The correct way that valid should be defined is that the
conclusion is a necessary consequence of all of its premises.

This eliminates the Principle of Explosion before it
even gets started.

To *prove* a statement, the statement needs to appear as the
conclusion to a *sound* argument (being valid is necessary but not
sufficient), and the principle of explosion does *not* claim that
your hypothetical argument is sound.

André

"The moon is made from green cheese" is a necessary consequence of
"all cats are dogs" and "some cats are not dogs". Or can you imagine a
world where all cats are dogs and some cats are not dogs, but the moon
isn't made from green cheese?

It is not true that anything is semantically entailed by any
contradiction. When the Principle of explosion says that everything is syntactically entailed by a contradiction the POE is a liar that denies
the law of non-contradiction. For analytical truth coherence is the
measure.

Just shows you don't understand how semantic logic actually works.

The Principle of Explosion says that, for a logic system with certain
logical operations, that are normally included in logic, once you have a contradiction provable in the system, you can prove any statement from it.

Yes, there are systems with weakened logic system that this does not
apply to, but such system can not prove as many true statements themselves.

It is also a fact, that ANY logic system, which claims to have logic
that is non-contradictory, that can prove a contradiction, is no longer
a sound logic system, as at least one of its truth makers must not be
actually true.

So, in one sense you are right, give the statements shown to be true in
a system that (a) All Cats are Dogs, and (b) Some Cats are not Dog, yes,
we can conclude that the FULL logic system shows the NULL set, as
nothing in the set can be believed.

If that is your goal, to assert that it is impossible to know if
anything is actually true, and thus it is just as valid to claim any
stateement we want as true, you have succeeded with your logic system.

That seems to be just the opposite of what you have claimed to be trying
to do, so you are just at total failure.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/17/23 12:22 PM, olcott wrote:

On 12/17/2023 2:31 AM, Ross Finlayson wrote:

On Saturday, December 16, 2023 at 8:13:50 PM UTC-8, Richard Damon wrote: >>> On 12/16/23 10:51 PM, olcott wrote:

On 12/16/2023 9:13 PM, André G. Isaak wrote:

On 2023-12-16 20:05, olcott wrote:

On 12/16/2023 8:50 PM, André G. Isaak wrote:

On 2023-12-16 19:34, olcott wrote:

On 12/16/2023 6:23 PM, André G. Isaak wrote:

On 2023-12-16 08:46, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its >>>>>>>>>>>>>> negation)
   can be inferred from it; this is known as deductive >>>>>>>>>>>>>> explosion."
https://en.wikipedia.org/wiki/Principle_of_explosion >>>>>>>>>>>>>>
Here is a contradiction as a syllogism that integrates the >>>>>>>>>>>>>> full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs) >>>>>>>>>>>>>> (c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference >>>>>>>>>>>>> rule
of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the >>>>>>>>>>>> empty set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping >>>>>>>>>>> maps false to the empty set. The principle of explosion maps >>>>>>>>>>> to the principle that the empty set is a subset of every set. >>>>>>>>>

Apologies for piggybacking.

Mikko is correct. Neither (a) nor (b) are sets.

(a) Has the Venn diagram of two totally overlapping circles where >>>>>>>> one is labeled cats and the other is labeled dogs.

That's a relationship between two sets. A relationship between two >>>>>>> sets is not a set, it's a relationship.

(b) Has the Venn diagram of two partially overlapping circles where >>>>>>>> one is labeled cats and the other is labeled dogs.

Again, that's a relationship between two sets. A relationship
between two sets is not a set; it's a relationship.

Since (a) and (b) have been diagrammed with Venn diagrams this >>>>>>>> seems to
prove that they are sets.

At the risk of being repetitive, Venn diagrams are used to express >>>>>>> relationships between sets. They are not themselves sets. They are >>>>>>> graphical representations of relationships between sets.

André

Thus the <intersection> relationship between two sets
is not itself a set. Wrongo !!!
https://en.wikipedia.org/wiki/Intersection_(set_theory)

You seem to be missing my point. As an example take your premise (a) >>>>> which expresses a relationship between two sets: the set of cats and >>>>> the set of dogs. It states that the former is a subset of the latter. >>>>

Factually incorrect. It states that they are identical sets.

Set operations and categorical propositions define sets in
terms of other sets.

(b) entails that the set of cats and dogs are not the identical set.

The only actual semantic conclusion is NULL.

Which means your data is INVALID.

The fact that your "logic" accepts it and give a result you claim is
sensible, says your logic is nonsensical.

If your son tells you that they are going to the movies at 7:00 PM
and instead he robs a liquor store at 7:00 PM we do not conclude
that this entails that the Moon is made from green cheese as the
principle of explosion requires instead we conclude that he lied.

There is never any case where anything besides NULL is the
result of a contradiction. When we anchor these things in
semantic meanings then the dictatorial fiat of the POE
is proved to be nonsense.

No, the result of the contradiction is the repudiation of the full
system that data was in.

Unless that is what you mean by the answr is NULL, you are just wrong.

And that doesn't negate the Principle of Explosion, but just
certifies it.

A system that has contradictory information (in a logic system that
claims to not be contradictory) is just WRONG and the discovery of that
data has just blown the system up.

Your failure to understand that just shows you are totally ignorant.

So exactly which set does your (a) REFER to? Does it refer to the set >>>>> of cats or the set of dogs? Answer: It refers to neither of these;
rather, it expresses that a particular relationship exists between
these two sets.

If you really want to claim that (a) refers to a set, then you should >>>>> be able to replace it with either:

(a) the set of cats

or

(b) the set of dogs.

So your argument ultimately should end up looking something like this: >>>>>
premise a: the set of cats
premise b: the set of cats which are not dogs
conclusion: the empty set

Do you seriously believe that the above is coherent?

André

Of course nobody "needs" material implication, there's also a model
with direct implication that suffices.  Similarly combinatorial
enumeration
fills out components for syollogism, and the tact of a proof by
contradiction
reduces it to an atomic sort of term as so connected to what supports it.




So, it's not like such, "features", of "classical", ahem, logic, have
models
in other theories with models of the logical inferences generally
considered:
"true".


Other relevant logics suitably general purpose don't model those at all.
(Except as example of fallacies following their own contradictions.)




As long as it's impossible for one to naively derive fallacies from the
"paradoxes of material implication", nor that evaluation ordering of
the components of syllogism affects their result, nor that contradiction
ever affects more than the negation of stipulation introduced, then
it should be OK.

The way it is though, common readings of "classical", ahem, logic,
make that naive readers would wreck that right up, if'n they didn't
know already, already weren't naive, the corresponding surrounds.

Constructivism has a lot to say about it like "we don't use proof by
contradiction", it's really monotonic the entailment, there's only
direct implication.


I.e., given that one makes blind the terms, and randomizes them,
then that the evaluator only naively runs through inference,
and out the terms it gives, unless there's not the ambiguities as above,
those depending on those might get results they would think false.






Of course nobody "needs" material implication, there's also a model
with direct implication that suffices.  Similarly combinatorial
enumeration
fills out components for syollogism, and the tact of a proof by
contradiction
reduces it to an atomic sort of term as so connected to what supports it.

p q p ⇒ q
T T   T
T F   F
F T   T
F F   T

The correct way to do this is to replace the use of the
material implication operator ⇒ with the modal logic
operator necessarily operator: □

The above truth table is replaced by

p q p □ q // q is a necessary consequence of p
T T   T
T F   F
F T   ?
F F   ?

This forces symbolic logic to conform to correct reasoning.

So, what is the truth value of ?

It seems you logic system now needs to be tri-valued, and thus you need
a 9 element table, as each of p and q could be a statement about
"necessarily" operator.

Hint, this has been done, many different ways, which one are you using.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/17/23 12:41 PM, olcott wrote:

On 12/16/2023 10:10 PM, André G. Isaak wrote:

On 2023-12-16 20:51, olcott wrote:

On 12/16/2023 9:13 PM, André G. Isaak wrote:

On 2023-12-16 20:05, olcott wrote:

On 12/16/2023 8:50 PM, André G. Isaak wrote:

On 2023-12-16 19:34, olcott wrote:

On 12/16/2023 6:23 PM, André G. Isaak wrote:

On 2023-12-16 08:46, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its >>>>>>>>>>>>> negation)
  can be inferred from it; this is known as deductive >>>>>>>>>>>>> explosion."
https://en.wikipedia.org/wiki/Principle_of_explosion >>>>>>>>>>>>>
Here is a contradiction as a syllogism that integrates the >>>>>>>>>>>>> full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs) >>>>>>>>>>>>> (c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference rule >>>>>>>>>>>> of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the >>>>>>>>>>> empty set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That mapping >>>>>>>>>> maps false to the empty set. The principle of explosion maps >>>>>>>>>> to the principle that the empty set is a subset of every set. >>>>>>>>

Apologies for piggybacking.

Mikko is correct. Neither (a) nor (b) are sets.

(a) Has the Venn diagram of two totally overlapping circles where >>>>>>> one is labeled cats and the other is labeled dogs.

That's a relationship between two sets. A relationship between two >>>>>> sets is not a set, it's a relationship.

(b) Has the Venn diagram of two partially overlapping circles where >>>>>>> one is labeled cats and the other is labeled dogs.

Again, that's a relationship between two sets. A relationship
between two sets is not a set; it's a relationship.

Since (a) and (b) have been diagrammed with Venn diagrams this
seems to
prove that they are sets.

At the risk of being repetitive, Venn diagrams are used to express >>>>>> relationships between sets. They are not themselves sets. They are >>>>>> graphical representations of relationships between sets.

André

Thus the <intersection> relationship between two sets
is not itself a set. Wrongo !!!
https://en.wikipedia.org/wiki/Intersection_(set_theory)

You seem to be missing my point. As an example take your premise (a)
which expresses a relationship between two sets: the set of cats and
the set of dogs. It states that the former is a subset of the latter.

Factually incorrect. It states that they are identical sets.

Not in any set theory which I am aware of. 'All cats are dogs' states
that cats are a subset of dogs. It most certainly does not claim that
they are identical sets.

I got that one incorrectly.
The intersection of (All S are P) and (No S are P)
is the empty set.

And All S are P and No S are P is not a contradiciton if S is allowed to
be the empty set, at least as long as you are working in a system where universal qualification does not imply existance.

Set operations and categorical propositions define sets in
terms of other sets.

(b) entails that the set of cats and dogs are not the identical set.

The only actual semantic conclusion is NULL.

NULL isn't a conclusion at all since it isn't a statement. What
statement do you think this represents?

The intersection of (All S are P) and (No S are P)
is the empty set.

NULL is one way to encode the empty set.

If your son tells you that they are going to the movies at 7:00 PM
and instead he robs a liquor store at 7:00 PM we do not conclude
that this entails that the Moon is made from green cheese as the
principle of explosion requires instead we conclude that he lied.

Yes. When confronted with a contradiction we normally assume that one
of the two contradictory statements is actually false.

Yet the principle of explosion has the psychotic break from
reality and assumes that it proves everything.

Nope, the system with the contradiction in it had the psychotic break
from reality. The Principle of Explosion just shows how bad that break
can be.

What you are failing to grasp is that when talking about arguments,
premises are statements which are assumed to be *true*. When
confronted with contradictory premises you cannot justify rejecting
one of them any more than you can justify rejecting the other.

We toss out the whole argument as unsound.
Alternatively when you son robs a liquor store
we could take this as proof that he is the king of the universe.

No, you need to toss the SYSTEM as unsound (unless it is defined in a
way that allows contradictions, in which case it needs some other rules
in it that break the requirement of the Principle of Explosion or the
system really does assert that anything can be true once it asserts one cotradiction.

There is never any case where anything besides NULL is the
result of a contradiction. When we anchor these things in
semantic meanings then the dictatorial fiat of the POE
is proved to be nonsense.

Non sequitur.

The POE <is> a non-sequitur that is much more obvious
when we plug semantic meanings into the terms and require
semantic entailment.

In other words, LOGIC is a non-sequitur to you, and you think we should
be able to just claim anything we want.

You are just showing your total ignorance.

André

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12/17/23 1:26 PM, olcott wrote:

On 12/17/2023 11:56 AM, Ross Finlayson wrote:

On Sunday, December 17, 2023 at 9:41:46 AM UTC-8, olcott wrote:

On 12/16/2023 10:10 PM, André G. Isaak wrote:

On 2023-12-16 20:51, olcott wrote:

On 12/16/2023 9:13 PM, André G. Isaak wrote:

On 2023-12-16 20:05, olcott wrote:

On 12/16/2023 8:50 PM, André G. Isaak wrote:

On 2023-12-16 19:34, olcott wrote:

On 12/16/2023 6:23 PM, André G. Isaak wrote:

On 2023-12-16 08:46, olcott wrote:

On 12/16/2023 2:27 AM, Mikko wrote:

On 2023-12-15 15:35:25 +0000, olcott said:

On 12/15/2023 5:43 AM, Mikko wrote:

On 2023-12-14 15:58:30 +0000, olcott said:

"from a contradiction, any proposition (including its >>>>>>>>>>>>>>> negation)
   can be inferred from it; this is known as deductive >>>>>>>>>>>>>>> explosion."
https://en.wikipedia.org/wiki/Principle_of_explosion >>>>>>>>>>>>>>>
Here is a contradiction as a syllogism that integrates >>>>>>>>>>>>>>> the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs) >>>>>>>>>>>>>>> (c) therefore NULL (the empty set)

That (c) does not follow from (a) and (b) by any inference >>>>>>>>>>>>>> rule
of syllogistic logic.

Mikko

The intersection of the sets defined by (a) and (b) <is> the >>>>>>>>>>>>> empty set.

(a) and (b) are not sets.
If logic is mapped to set theory, they map to sets. That >>>>>>>>>>>> mapping
maps false to the empty set. The principle of explosion maps >>>>>>>>>>>> to the principle that the empty set is a subset of every set. >>>>>>>>>>

Apologies for piggybacking.

Mikko is correct. Neither (a) nor (b) are sets.

(a) Has the Venn diagram of two totally overlapping circles where >>>>>>>>> one is labeled cats and the other is labeled dogs.

That's a relationship between two sets. A relationship between two >>>>>>>> sets is not a set, it's a relationship.

(b) Has the Venn diagram of two partially overlapping circles >>>>>>>>> where
one is labeled cats and the other is labeled dogs.

Again, that's a relationship between two sets. A relationship
between two sets is not a set; it's a relationship.

Since (a) and (b) have been diagrammed with Venn diagrams this >>>>>>>>> seems to
prove that they are sets.

At the risk of being repetitive, Venn diagrams are used to express >>>>>>>> relationships between sets. They are not themselves sets. They are >>>>>>>> graphical representations of relationships between sets.

André

Thus the <intersection> relationship between two sets
is not itself a set. Wrongo !!!
https://en.wikipedia.org/wiki/Intersection_(set_theory)

You seem to be missing my point. As an example take your premise (a) >>>>>> which expresses a relationship between two sets: the set of cats and >>>>>> the set of dogs. It states that the former is a subset of the latter. >>>>>

Factually incorrect. It states that they are identical sets.

Not in any set theory which I am aware of. 'All cats are dogs' states
that cats are a subset of dogs. It most certainly does not claim that
they are identical sets.

I got that one incorrectly.
The intersection of (All S are P) and (No S are P)
is the empty set.

Set operations and categorical propositions define sets in
terms of other sets.

(b) entails that the set of cats and dogs are not the identical set. >>>>>
The only actual semantic conclusion is NULL.

NULL isn't a conclusion at all since it isn't a statement. What
statement do you think this represents?

The intersection of (All S are P) and (No S are P)
is the empty set.
NULL is one way to encode the empty set.

If your son tells you that they are going to the movies at 7:00 PM
and instead he robs a liquor store at 7:00 PM we do not conclude
that this entails that the Moon is made from green cheese as the
principle of explosion requires instead we conclude that he lied.

Yes. When confronted with a contradiction we normally assume that
one of
the two contradictory statements is actually false.

Yet the principle of explosion has the psychotic break from
reality and assumes that it proves everything.

What you are failing to grasp is that when talking about arguments,
premises are statements which are assumed to be *true*. When confronted >>>> with contradictory premises you cannot justify rejecting one of them
any
more than you can justify rejecting the other.

We toss out the whole argument as unsound.
Alternatively when you son robs a liquor store
we could take this as proof that he is the king of the universe.

There is never any case where anything besides NULL is the
result of a contradiction. When we anchor these things in
semantic meanings then the dictatorial fiat of the POE
is proved to be nonsense.

Non sequitur.

The POE <is> a non-sequitur that is much more obvious
when we plug semantic meanings into the terms and require
semantic entailment.

André

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

void null empty true false don't-know don't-care known-unfaithful

There are many quasi-modal logics, or their calculi,
that are totally sensitive what they're given,
but given correct input will align with other logics,
here that "classical logic" is a milieu for some simple things, fast,
and it's always forever more, "classical quasi-modal logic".

... where "the logic" is modal and temporal.



'Struth.


... where "truth-value" is a model of knowledge, ....

Although there may be many logics there is only one defined process
of correct reasoning such that any divergence is necessarily incorrect.

But, sinse you can't figure out how to actually DEFINE this mystical
thing, it doesn't help you.

All you have done so far is show that by you trying to apply correct
reasoning you get many incorrect answers.

--- SoupGate-Win32 v1.05
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On 12/19/23 12:05 PM, olcott wrote:

On 12/19/2023 9:55 AM, immibis wrote:

On 12/19/23 16:22, olcott wrote:

A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion
nevertheless to be false. https://iep.utm.edu/val-snd/

On that basis we can conclude that this sentence is valid:
"Kittens are 15 story office buildings therefore water is H2O."

When we redefine value to be a conclusion must be a necessary
consequence of all of its premises then the above nonsense
sentence is not valid.

What is a necessary consequence?

◊ means possibly
◻ means necessarily
¬ means not
◊P means ¬◻¬P
◻P means ¬◊¬P

A---B---A ◻ B
t---t-----t
t---f-----f
f---?-----? When A is false then we know nothing about B

In other words, your system of logic can not assign a validity to an implication.

Note, your "conclusion" actually comes out of the normal definition of implication, since A->B is true for A being false and B being either
True or False, then we know nothing about B.

Note, for YOUR "truth Table" if we know that A -> B is a true sttement,
then we can not determine that A is false from knowing that B is false.

You have lost the relationship that A -> B alse means that ~B -> ~A

A consequence is said to be necessary if and only if it takes a form
that makes it impossible for the antecedents to be true and the
consequence nevertheless to be false...

--- SoupGate-Win32 v1.05
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On 12/19/23 12:26 PM, olcott wrote:

On 12/19/2023 9:55 AM, immibis wrote:

On 12/19/23 16:22, olcott wrote:

A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion
nevertheless to be false. https://iep.utm.edu/val-snd/

On that basis we can conclude that this sentence is valid:
"Kittens are 15 story office buildings therefore water is H2O."

When we redefine value to be a conclusion must be a necessary
consequence of all of its premises then the above nonsense
sentence is not valid.

What is a necessary consequence?

A consequence is said to be necessary if and only if it takes a form
that makes it impossible for the antecedents to be true and the
consequence nevertheless to be false...

*This may be a more exactly precise way to say what I mean*
My correction to the notion of a valid argument means that the
truth of the conclusion depends on the truth all of the premises.

If any premise is false or irrelevant then the conclusion is not proved.
(a) I go outside
(b) I am unprotected from the rain
(c) then I get wet.

(a) I go outside
(b) I eat a popsicle
(c) Do I get wet? impossible to tell.

Which means, for standard logic, your second set (where (c) makes an
actual statement about getting wet) is just a false implication an not
valid.

A & B -> C is true ONLY if any time A and B are True then C is also True.

So, a implication like

If (a) I go outside, and (b) I eat a popsicle, then (c) I get wet is
just a false implication, as there are cases where (a) and (b) are true
but (c) isn't.

Somehow you don't seem to understand that not all implications that can
be stated are true.

Note, just because ONE time I went outside and ate a popsicle I got wet,
does NOT prove that implication, as to prove it you need to be able to
look at ALL POSSIBLE cases.

But, I guess since you think proof by example is valid, I guess that
shows your problem with implication,

--- SoupGate-Win32 v1.05
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On 12/19/23 10:22 AM, olcott wrote:

On 12/19/2023 7:34 AM, immibis wrote:

On 12/19/23 04:02, olcott wrote:

On 12/18/2023 11:37 AM, immibis wrote:

On 12/17/23 18:11, olcott wrote:

On 12/17/2023 2:17 AM, immibis wrote:

"The moon is made from green cheese" is a necessary consequence of >>>>>> "all cats are dogs" and "some cats are not dogs". Or can you
imagine a world where all cats are dogs and some cats are not
dogs, but the moon isn't made from green cheese?

It is not true that anything is semantically entailed by any
contradiction. When the Principle of explosion says that everything is >>>>> syntactically entailed by a contradiction the POE is a liar that
denies
the law of non-contradiction. For analytical truth coherence is the
measure.

Can you imagine a world where all cats are dogs and some cats are
not dogs, but the moon isn't made from green cheese?

That would be incoherent: The coherence theory of truth applies to
the analytical body of knowledge.

I've never heard of these two, and they seem to be fully immersed in
philosophy, not computer science or mathematical logic.

Without Philosophy logic has no basis. The basis that logic does have is incoherent because they got the philosophy wrong.

Nope, Without logic, Philosophy has no basis.

A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion nevertheless to be false. https://iep.utm.edu/val-snd/

On that basis we can conclude that this sentence is valid:
"Kittens are 15 story office buildings therefore water is H2O."

Yes. Can you show it to NOT be valid?

Is there a case where we have Kittens as 15 story office buildings and
NOT have water as H2O?

Your problem is you don't understand how logic works, and thus you don't
really understand philosophy.

When we redefine value to be a conclusion must be a necessary
consequence of all of its premises then the above nonsense
sentence is not valid.

--- SoupGate-Win32 v1.05
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