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

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

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.

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.

>
> 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
>
>

--
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 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

--
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 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

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

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.

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
>>
>>
>

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?

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.

On Sunday, December 17, 2023 at 12:31:26 AM UTC-8, 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.
>
>
>
>
> 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.)
>
> So, can you trust a naive interpreter that blindly randomizes your terms?
> Maybe so, but not if it's naively, ahem, "classical".
>
> I think "classical" logic needs a new name, "quasi-mode logic". It's quasi-modal.
>
>
> (Quasimodo was the hunchbacked, and sometimes deranged,
> bell-ringer of a cathedral, where he quite flew up and down.
> He's also the model for Frankenstein's assistant.)
>
>
> Hmm, "Comte-Boole-Russell 'classical' logic renamed to quasi-modal",
> I like the ring of it.

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.

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

On 12/17/2023 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.
>

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.

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.
>

On 12/16/2023 10:02 PM, André G. Isaak wrote:
> 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
>

Any claim that categorical propositions do not specify sets
that can be diagrammed by Venn diagrams is counter-factual.

--
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 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

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, ....

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
>

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.

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

On 12/17/23 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.
>

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?

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.

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

On 12/19/23 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.

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.

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.

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

On 12/19/23 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...