"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)

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

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.

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.

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

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.

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.

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

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

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
>

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

On Thursday, December 14, 2023 at 7:56:56 PM UTC-8, 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.
>
> 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
>
> --
> To email remove 'invalid' & replace 'gm' with well known Google mail
> service.

What you do is enumerate the permutations and read it out,
making sure that it's not ambiguous the order, or that in at
least one order it's unambiguous.

So, there's no "combinatorial explosion: unbounded",
because it's hedged with "combinatorial enumeration: grounded".

Of course, then argument by contradiction must be entirely
self-contained with the very initial premise at the beginning
and only its single contradiction at the end, ..., and
that everything up to the end is exactly one premise.

On Thursday, December 14, 2023 at 9:34:03 PM UTC-8, Ross Finlayson wrote:
> On Thursday, December 14, 2023 at 7:56:56 PM UTC-8, 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.
> >
> > 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
> >
> > --
> > To email remove 'invalid' & replace 'gm' with well known Google mail
> > service.
> What you do is enumerate the permutations and read it out,
> making sure that it's not ambiguous the order, or that in at
> least one order it's unambiguous.
>
> So, there's no "combinatorial explosion: unbounded",
> because it's hedged with "combinatorial enumeration: grounded".
>
> Of course, then argument by contradiction must be entirely
> self-contained with the very initial premise at the beginning
> and only its single contradiction at the end, ..., and
> that everything up to the end is exactly one premise.

What, you've never seen a proof by contradiction end before?

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

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.

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

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.

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

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.

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

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.

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.

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

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.

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

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).

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,

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.
>

"So what do we need to change?"

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

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

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.

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

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

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.

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

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

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

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.

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)

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