Re: Vacuously TRUE vs Vacuously FALSE? [ natural preexisting order of the body of knowledge ]

[olcott]

On 10/24/2021 10:46 AM, André G. Isaak wrote:
> On 2021-10-23 21:21, olcott wrote:
>> On 10/23/2021 9:37 PM, André G. Isaak wrote:
>
>> When the goal is to define the mathematical basis of infallible
>> reasoning that references natural language semantics logical implication
>
> Logic doesn't have that goal.
>

Logic is supposed to at least be a system of correct reasoning.

>> seems to be at least unnecessary and at most quite harmful.
>>
>> Although the common base meaning of A implies B is maintained the
>> overloaded meaning totally screws this up.
>
> How do you determine which of the various meanings of a natural language
> term is the 'base meaning'?

When we define the unique set of all semantic meanings and
(a) Disallow every trace of redundancy
(b) Disallow overloading the same term with more than one unique
semantic meaning
(c) Assign each unique semantic meaning to a GUID

Then the natural preexisting order of the body of all knowledge is
specified.

> And if you think overloading 'screws things
> up', then you should be objecting to natural language, not logic, though
> this objection would be utterly pointless since natural language always
> has and always will allow multiple meanings for the same word. Maybe you
> should learn how natural language works.
>
>> 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
>
> Many natural language expressions *are* interpreted as material
> implication. For example "If you under eighteen then you cannot purchase
> alcohol".
>
> The meaning of the logical connective → unambiguously refers to this one
> specific meaning of if...then. I fail to see why you see this as a problem.
>

It is better to replace
X ⇒ Y
with
X ⊨ Y (requiring a semantic connection between X and Y)

This prevents nonsense from being contrued as logically correct.

> Why is this more problematic than the fact that natural language 'or'
> can be either exclusive or inclusive whereas logical or is unambiguously
> inclusive?
>
> Or the fact that logical and is unambiguously truth-functional whereas
> natural language uses it in other ways? (e.g. "a zebra has black and
> white stripes".)
>
> André
>


--
Copyright 2021 Pete Olcott

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

[Peter]

If you look up "modus ponens" and "deduction theorem" you will see that
X ⇒ Y and X ⊨ Y go hand-in-hand. So an (imagined) problem with one is
an (imagined) problem with the other.

>
>> Why is this more problematic than the fact that natural language 'or'
>> can be either exclusive or inclusive whereas logical or is
>> unambiguously inclusive?
>>
>> Or the fact that logical and is unambiguously truth-functional whereas
>> natural language uses it in other ways? (e.g. "a zebra has black and
>> white stripes".)
>>
>> André
>>
>
>


--

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

[olcott]

"This sentence is not true", is simply not a truth bearer. When an
expression of language is not a truth bearer then it is not an
expression of logic, thus eliminating any need for three-valued logic.

>>
>>> Why is this more problematic than the fact that natural language 'or'
>>> can be either exclusive or inclusive whereas logical or is
>>> unambiguously inclusive?
>>>
>>> Or the fact that logical and is unambiguously truth-functional
>>> whereas natural language uses it in other ways? (e.g. "a zebra has
>>> black and white stripes".)
>>>
>>> André
>>>
>>
>>
>
>


--

[Peter]

It's also irrelevant to the matter being discussed. I wonder how you
get on in real life. In my mind's eye I see you making a cup of coffee
and half way though changing to making a cup of tea simply because you
cannot concentrate on one thing for any length of time.

> . When an
> expression of language is not a truth bearer then it is not an
> expression of logic, thus eliminating any need for three-valued logic.
>
>>>
>>>> Why is this more problematic than the fact that natural language
>>>> 'or' can be either exclusive or inclusive whereas logical or is
>>>> unambiguously inclusive?
>>>>
>>>> Or the fact that logical and is unambiguously truth-functional
>>>> whereas natural language uses it in other ways? (e.g. "a zebra has
>>>> black and white stripes".)
>>>>
>>>> André
>>>>
>>>
>>>
>>
>>
>
>


--