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.
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'?
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.
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
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
olcott wrote:
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.
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
On 10/25/2021 10:00 AM, Peter wrote:
olcott wrote:
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.
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.
"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
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