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Dec 14, 2023, 10:58:34 AM12/14/23

to

"from a contradiction, any proposition (including its negation)

can be inferred from it; this is known as deductive explosion."

https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full

semantics of the contradiction as defined sets.

(a) All Cats are dogs

(b) Some Cats are not dogs // AKA Not(All Cats are dogs)

(c) therefore NULL (the empty set)

--

Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius

hits a target no one else can see." Arthur Schopenhauer

can be inferred from it; this is known as deductive explosion."

https://en.wikipedia.org/wiki/Principle_of_explosion

Here is a contradiction as a syllogism that integrates the full

semantics of the contradiction as defined sets.

(a) All Cats are dogs

(b) Some Cats are not dogs // AKA Not(All Cats are dogs)

(c) therefore NULL (the empty set)

--

Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius

hits a target no one else can see." Arthur Schopenhauer

Dec 14, 2023, 6:36:24 PM12/14/23

to

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

> "from a contradiction, any proposition (including its negation)

> can be inferred from it; this is known as deductive explosion."

> https://en.wikipedia.org/wiki/Principle_of_explosion

>

> Here is a contradiction as a syllogism that integrates the full

> semantics of the contradiction as defined sets.

> (a) All Cats are dogs

> (b) Some Cats are not dogs // AKA Not(All Cats are dogs)

> (c) therefore NULL (the empty set)

>

Nope, it establishes that some Dogs are not Dogs. That is a FULL
> "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)

>

"semantic" reasoning from the premises.

This comes because the cats that are the "Some Cats" in (b), MUST BE, by

(a) Dogs, so we can conclude that Those Dogs are Not Dogs.

In other words, it proves the system is inconsistant.

Dec 14, 2023, 7:14:43 PM12/14/23

to

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)
> "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)

>

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.

Dec 14, 2023, 7:27:12 PM12/14/23

to

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

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

>> "from a contradiction, any proposition (including its negation)

>> can be inferred from it; this is known as deductive explosion."

>> https://en.wikipedia.org/wiki/Principle_of_explosion

>>

>> Here is a contradiction as a syllogism that integrates the full

>> semantics of the contradiction as defined sets.

>> (a) All Cats are dogs

>> (b) Some Cats are not dogs // AKA Not(All Cats are dogs)

>> (c) therefore NULL (the empty set)

>>

>

> The principle of explosion would says that (a) and (b)

> proves that the Moon is made from green cheese.

>

> Whereas the intersection of the sets specified by

> (a) and (b) is the empty set, thus derives no conclusion.

>

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

>

sense, the Union.

Or, are you saying that it implies that it is describing a world with no

cats or dogs?

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

implies existance.

Dec 14, 2023, 10:56:55 PM12/14/23

to

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
> 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.

principle of explosion says that for any statement X, "A & ¬A therefore

X" is a *valid* argument.

To *prove* a statement, the statement needs to appear as the conclusion

to a *sound* argument (being valid is necessary but not sufficient), and

the principle of explosion does *not* claim that your hypothetical

argument is sound.

André

--

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

service.

Dec 14, 2023, 11:20:57 PM12/14/23

to

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*
> 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.

>

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

>

--

Dec 15, 2023, 7:49:33 AM12/15/23

to

On 12/14/23 11:20 PM, 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.

Which it is, according to the rules of the logic system. You are just
> 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.

showing your lack of understanding.

Any system which claims to be non-contradictory in logc form, that has a

pair of statements that are contradictory, is just broken. The Principle

of Explosion just makes the breakage total,

>

> This eliminates the Principle of Explosion before it

> even gets started.

Truth is established by having a set (possibly infinite) of valid steps

from the initial truthmakers of the system to the statement.

A Proof is just a finite listing of one possible set of those links,

thus anything that can be proven, must be true.

Yes, if you limit the forms of links that can be used as steps, you can

make some things not provable, but this MIGHT also reduce what is

actually true in the system.

Dec 15, 2023, 2:27:53 PM12/15/23

to

Dec 15, 2023, 8:05:37 PM12/15/23

to

On 12/14/23 11:20 PM, 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.

And they are.
> 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.

Note, ANY system that starts with a contradiction in it is just "broken"

and "necessary consequence" isn't really defined.

Your problem is you don't understand the nature of the proof of the

principle of explosion.

It isn't removed by use of "meaning", as a system that allows the

contradiction in the first place has already broken the definition of

"meaning", but is removed by weaking the logic system to restrict how

broad of a circle the break can infest.

>

> This eliminates the Principle of Explosion before it

> even gets started.

allowed the derivation of the contradiction were added to the system.

Dec 15, 2023, 8:05:39 PM12/15/23

to

On 12/14/23 11:20 PM, 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.

> 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.

And they are.

Note, ANY system that starts with a contradiction in it is just "broken"

and "necessary consequence" isn't really defined.

Your problem is you don't understand the nature of the proof of the

principle of explosion.

It isn't removed by use of "meaning", as a system that allows the

contradiction in the first place has already broken the definition of

"meaning", but is removed by weaking the logic system to restrict how

broad of a circle the break can infest.

>

Note, ANY system that starts with a contradiction in it is just "broken"

and "necessary consequence" isn't really defined.

Your problem is you don't understand the nature of the proof of the

principle of explosion.

It isn't removed by use of "meaning", as a system that allows the

contradiction in the first place has already broken the definition of

"meaning", but is removed by weaking the logic system to restrict how

broad of a circle the break can infest.

>

> This eliminates the Principle of Explosion before it

> even gets started.

> even gets started.

Nope, the logic system was broken as soon as the truthmakers that

allowed the derivation of the contradiction were added to the system.

>

allowed the derivation of the contradiction were added to the system.

>

Dec 17, 2023, 3:17:43 AM12/17/23

to

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?

Dec 17, 2023, 12:11:44 PM12/17/23

to

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.

Dec 17, 2023, 12:29:45 PM12/17/23

to

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.

Dec 18, 2023, 12:37:51 PM12/18/23

to

Dec 18, 2023, 10:02:20 PM12/18/23

to

analytical body of knowledge.

Dec 19, 2023, 8:34:41 AM12/19/23

to

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
> 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.

>

philosophy, not computer science or mathematical logic.

Dec 19, 2023, 10:22:47 AM12/19/23

to

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.

Dec 19, 2023, 10:55:48 AM12/19/23

to

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 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.

>

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...

Dec 19, 2023, 12:05:21 PM12/19/23

to

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

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

>> A deductive argument is said to be valid if and only if it takes a form

>> that makes it impossible for the premises to be true and the conclusion

>> nevertheless to be false. https://iep.utm.edu/val-snd/

>>

>> On that basis we can conclude that this sentence is valid:

>> "Kittens are 15 story office buildings therefore water is H2O."

>>

>> When we redefine value to be a conclusion must be a necessary

>> consequence of all of its premises then the above nonsense

>> sentence is not valid.

>>

> What is a necessary consequence?

>

◊ means possibly
> On 12/19/23 16:22, olcott wrote:

>> A deductive argument is said to be valid if and only if it takes a form

>> that makes it impossible for the premises to be true and the conclusion

>> nevertheless to be false. https://iep.utm.edu/val-snd/

>>

>> On that basis we can conclude that this sentence is valid:

>> "Kittens are 15 story office buildings therefore water is H2O."

>>

>> When we redefine value to be a conclusion must be a necessary

>> consequence of all of its premises then the above nonsense

>> sentence is not valid.

>>

> What is a necessary consequence?

>

◻ means 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...

Dec 19, 2023, 12:26:54 PM12/19/23

to

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

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.

Dec 19, 2023, 2:45:37 PM12/19/23

to

On 12/19/23 10:22 AM, olcott wrote:

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

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

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

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

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

>>>>>>

>>>>>> "The moon is made from green cheese" is a necessary consequence of

>>>>>> "all cats are dogs" and "some cats are not dogs". Or can you

>>>>>> imagine a world where all cats are dogs and some cats are not

>>>>>> dogs, but the moon isn't made from green cheese?

>>>>>

>>>>> It is not true that anything is semantically entailed by any

>>>>> contradiction. When the Principle of explosion says that everything is

>>>>> syntactically entailed by a contradiction the POE is a liar that

>>>>> denies

>>>>> the law of non-contradiction. For analytical truth coherence is the

>>>>> measure.

>>>>>

>>>>

>>>> Can you imagine a world where all cats are dogs and some cats are

>>>> not dogs, but the moon isn't made from green cheese?

>>>

>>> That would be incoherent: The coherence theory of truth applies to

>>> the analytical body of knowledge.

>>>

>> I've never heard of these two, and they seem to be fully immersed in

>> philosophy, not computer science or mathematical logic.

>

> Without Philosophy logic has no basis. The basis that logic does have is

> incoherent because they got the philosophy wrong.

Nope, Without logic, Philosophy has no basis.
> 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."

Is there a case where we have Kittens as 15 story office buildings and

NOT have water as H2O?

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

really understand philosophy.

>

> When we redefine value to be a conclusion must be a necessary

> consequence of all of its premises then the above nonsense

> sentence is not valid.

>

false statement not to be not true.

Dec 19, 2023, 2:51:57 PM12/19/23

to

On 12/19/23 12:05 PM, olcott wrote:

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

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

>>> A deductive argument is said to be valid if and only if it takes a form

>>> that makes it impossible for the premises to be true and the conclusion

>>> nevertheless to be false. https://iep.utm.edu/val-snd/

>>>

>>> On that basis we can conclude that this sentence is valid:

>>> "Kittens are 15 story office buildings therefore water is H2O."

>>>

>>> When we redefine value to be a conclusion must be a necessary

>>> consequence of all of its premises then the above nonsense

>>> sentence is not valid.

>>>

>> What is a necessary consequence?

>>

>

> ◊ means possibly

> ◻ means necessarily

> ¬ means not

> ◊P means ¬◻¬P

> ◻P means ¬◊¬P

>

> A---B---A ◻ B

> t---t-----t

> t---f-----f

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

>

>

In other words, your system of logic can not assign a validity to an
> On 12/19/2023 9:55 AM, immibis wrote:

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

>>> A deductive argument is said to be valid if and only if it takes a form

>>> that makes it impossible for the premises to be true and the conclusion

>>> nevertheless to be false. https://iep.utm.edu/val-snd/

>>>

>>> On that basis we can conclude that this sentence is valid:

>>> "Kittens are 15 story office buildings therefore water is H2O."

>>>

>>> When we redefine value to be a conclusion must be a necessary

>>> consequence of all of its premises then the above nonsense

>>> sentence is not valid.

>>>

>> What is a necessary consequence?

>>

>

> ◊ means possibly

> ◻ means necessarily

> ¬ means not

> ◊P means ¬◻¬P

> ◻P means ¬◊¬P

>

> A---B---A ◻ B

> t---t-----t

> t---f-----f

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

>

>

implication.

Note, your "conclusion" actually comes out of the normal definition of

implication, since A->B is true for A being false and B being either

True or False, then we know nothing about B.

Note, for YOUR "truth Table" if we know that A -> B is a true sttement,

then we can not determine that A is false from knowing that B is false.

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

Dec 19, 2023, 2:58:40 PM12/19/23

to

actual statement about getting wet) is just a false implication an not

valid.

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

So, a implication like

If (a) I go outside, and (b) I eat a popsicle, then (c) I get wet is

just a false implication, as there are cases where (a) and (b) are true

but (c) isn't.

Somehow you don't seem to understand that not all implications that can

be stated are true.

Note, just because ONE time I went outside and ate a popsicle I got wet,

does NOT prove that implication, as to prove it you need to be able to

look at ALL POSSIBLE cases.

But, I guess since you think proof by example is valid, I guess that

shows your problem with implication,

Dec 20, 2023, 2:24:46 AM12/20/23

to

On 12/19/23 18:26, olcott wrote:

> *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.

>

>

Alright so the moon being blue is a necessary consequence of me being
> *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.

>

>

wet and not wet. If I'm wet and not wet, this proves the moon is blue,

we can tell that, so it's a necessary consequence.

Message has been deleted

Message has been deleted

Dec 24, 2023, 2:41:18 PM12/24/23

to

On 12/24/2023 1:11 PM, Nicki makethings wrote:

> Without facts there is no proof, but, everything in philosophy is down to semantics.

Good job, I think that you got it!

Good job, I think that you got it!

Dec 25, 2023, 11:03:30 PM12/25/23

to

On 12/24/2023 1:11 PM, Nicki makethings wrote:

> On Tuesday, December 19, 2023 at 3:22:47 PM UTC, olcott wrote:

> On Tuesday, December 19, 2023 at 3:22:47 PM UTC, olcott wrote:

> Without facts there is no proof, but, everything in philosophy is down to semantics.

All of analytic truth has two forms
(1) Expressions stipulated to be true (AKA Facts)

(2) Expressions derived from (1)

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