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computers / comp.ai.philosophy / Re: Vacuously TRUE vs Vacuously FALSE? [ properties of elements of the empty set ]

Re: Vacuously TRUE vs Vacuously FALSE? [ properties of elements of the empty set ]

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Subject: Re: Vacuously TRUE vs Vacuously FALSE? [ properties of elements of
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From: NoO...@NoWhere.com (olcott)
Date: Mon, 25 Oct 2021 09:24:16 -0500
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by: olcott - Mon, 25 Oct 2021 14:24 UTC

On 10/24/2021 9:59 AM, Dan Christensen wrote:
> On Sunday, October 24, 2021 at 1:17:12 AM UTC-4, olcott wrote:
>> On 10/24/2021 12:06 AM, Dan Christensen wrote:
>>> On Saturday, October 23, 2021 at 11:21:12 PM UTC-4, olcott wrote:
>>>
>>>>
>>>> If natural language conditionals were understood in the same way, that
>>>> would mean that the sentence "If the Nazis won World War Two, everybody
>>>> would be happy" is true.
>>>> https://en.wikipedia.org/wiki/Paradoxes_of_material_implication
>>>>
>>>
>>> An educated person might point out that such a statement is pure speculation. And that it is an opinion, and not a verifiable fact. As such it is not a logical analysis of the current state of the world.
>>>
>>> Dan
>>>
>>> Download my DC Proof 2.0 freeware at http://www.dcproof.com
>>> Visit my Math Blog at http://www.dcproof.wordpress.com
>>>
>> Logical implication
>> p q p ⇒ q
>> T T T
>> T F F
>> F T T
>> F F T
>> When we apply semantics to the variables material implication asserts
>> that the is a relationship between unrelated things. This is an error.
>> The last two rows of the truth table are mistaken.
>
> You really need to be able to formally prove that A & B => B & A. Your system is DOA otherwise.

A = dogs are animals
B = dogs are not animals
A & B => not one damn thing

A = it is raining outside
B = you go outside unprotected from the rain
C = you get wet
A & B ⊨ C

>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com
>

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Re: Vacuously TRUE vs Vacuously FALSE? [ properties of elements of the empty set ]

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From: peterxpe...@hotmail.com (Peter)
Newsgroups: sci.logic,comp.ai.philosophy
Subject: Re: Vacuously TRUE vs Vacuously FALSE? [ properties of elements of
the empty set ]
Date: Mon, 25 Oct 2021 15:51:32 +0100
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by: Peter - Mon, 25 Oct 2021 14:51 UTC

olcott wrote:
> On 10/24/2021 9:59 AM, Dan Christensen wrote:
>> On Sunday, October 24, 2021 at 1:17:12 AM UTC-4, olcott wrote:
>>> On 10/24/2021 12:06 AM, Dan Christensen wrote:
>>>> On Saturday, October 23, 2021 at 11:21:12 PM UTC-4, olcott wrote:
>>>>
>>>>>
>>>>> If natural language conditionals were understood in the same way, that
>>>>> would mean that the sentence "If the Nazis won World War Two,
>>>>> everybody
>>>>> would be happy" is true.
>>>>> https://en.wikipedia.org/wiki/Paradoxes_of_material_implication
>>>>>
>>>>
>>>> An educated person might point out that such a statement is pure
>>>> speculation. And that it is an opinion, and not a verifiable fact.
>>>> As such it is not a logical analysis of the current state of the world.
>>>>
>>>> Dan
>>>>
>>>> Download my DC Proof 2.0 freeware at http://www.dcproof.com
>>>> Visit my Math Blog at http://www.dcproof.wordpress.com
>>>>
>>> Logical implication
>>> p q p ⇒ q
>>> T T T
>>> T F F
>>> F T T
>>> F F T
>>> When we apply semantics to the variables material implication asserts
>>> that the is a relationship between unrelated things. This is an error.
>>> The last two rows of the truth table are mistaken.
>>
>> You really need to be able to formally prove that A & B => B & A. Your
>> system is DOA otherwise.
>
> A = dogs are animals
> B = dogs are not animals
> A & B => not one damn thing
>
> A = it is raining outside
> B = you go outside unprotected from the rain
> C = you get wet
> A & B ⊨ C

Not only do you know no formal logic, you know informal logic either.
One cannot prove a generality (here that A & B => B & A) by appealing to
individual cases (also, your use of the individual case above is silly).
If Dan asks you to prove that A & B => B & A, just say that you can't.
(The reference to "Your system" is so much noise. You have no system.)
>
>>
>> Dan
>>
>> Download my DC Proof 2.0 freeware at http://www.dcproof.com
>> Visit my Math Blog at http://www.dcproof.wordpress.com
>>
>
>

--
The world will little note, nor long remember what we say here
Abraham Lincoln at Gettysburg

Subject	Author
Re: Vacuously TRUE vs Vacuously FALSE? [ properties of elements of	olcott
Re: Vacuously TRUE vs Vacuously FALSE? [ properties of elements of	Peter