"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)
On 12/14/2023 9:58 AM, olcott wrote:
"from a contradiction, any proposition (including its negation)
can be inferred from it; this is known as deductive explosion."
https://en.wikipedia.org/wiki/Principle_of_explosion
Here is a contradiction as a syllogism that integrates the full
semantics of the contradiction as defined sets.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
(c) therefore NULL (the empty set)
The principle of explosion would says that (a) and (b)
proves that the Moon is made from green cheese.
Whereas the intersection of the sets specified by
(a) and (b) is the empty set, thus derives no conclusion.
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.
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
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
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
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.
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.
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.
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.
On 12/19/2023 9:55 AM, immibis wrote:
On 12/19/23 16:22, olcott wrote:
A deductive argument is said to be valid if and only if it takes a formWhat is a necessary consequence?
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.
◊ means possibly
◻ means necessarily
¬ means not
◊P means ¬◻¬P
◻P means ¬◊¬P
A---B---A ◻ B
t---t-----t
t---f-----f
f---?-----? When A is false then we know nothing about B
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...
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:I've never heard of these two, and they seem to be fully immersed in
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.
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.
On 12/19/2023 9:55 AM, immibis wrote:
On 12/19/23 16:22, olcott wrote:
A deductive argument is said to be valid if and only if it takes a formWhat is a necessary consequence?
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.
A consequence is said to be necessary if and only if it takes a form
that makes it impossible for the antecedents to be true and the
consequence nevertheless to be false...
*This may be a more exactly precise way to say what I mean*
My correction to the notion of a valid argument means that the
truth of the conclusion depends on the truth all of the premises.
If any premise is false or irrelevant then the conclusion is not proved.
(a) I go outside
(b) I am unprotected from the rain
(c) then I get wet.
(a) I go outside
(b) I eat a popsicle
(c) Do I get wet? impossible to tell.
*This may be a more exactly precise way to say what I mean*
My correction to the notion of a valid argument means that the
truth of the conclusion depends on the truth all of the premises.
If any premise is false or irrelevant then the conclusion is not proved.
(a) I go outside
(b) I am unprotected from the rain
(c) then I get wet.
(a) I go outside
(b) I eat a popsicle
(c) Do I get wet? impossible to tell.
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