- #1
cianfa72
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- TL;DR Summary
- logical implication makes sense only within specific context/models.
I'm still confused about the use of material implication (material conditional) vs logical implication .
From MSE the writing makes the meta-logical assertion/statement that the logical statement is logically implied by the logical statement .
First of all: saying for instance "logical statement ...." actually implicitly asserts that it is True, I guess.
Second: the meta-logical assertion as above should only make sense/apply within a specific context/model/interpretation. Consider for instance: This logical implication actually makes sense within the context/model/interpretation of mathematical theory of natural numbers, however it makes no sense in other contexts in which there is no notion of ordering (how should one interpreter the symbol in such a case ?).
Therefore from the above logical implication follows (from a meta-logical theorem) that the material implication/conditional : "If then "
is true (i.e. it is a tautology) only within the specific context in which the logical implication applies.
What do you think about? Thanks.
Ps. note that I tend to use the english term "implication" for the logical implication and the form "If...then" for the material implication/conditional .
From MSE the writing
First of all: saying for instance "logical statement
Second: the meta-logical assertion as above should only make sense/apply within a specific context/model/interpretation. Consider for instance:
Therefore from the above logical implication follows (from a meta-logical theorem) that the material implication/conditional
is true (i.e. it is a tautology) only within the specific context in which the logical implication applies.
What do you think about? Thanks.
Ps. note that I tend to use the english term "implication" for the logical implication
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