Jon, List,
The kind of implication that is linguistically expressed with "a implies b" and "if a then b" is classification, isnt it? I think there are two more kinds of logical implication, which are equally fundamental, though have to be expressed with more words. I think, the three kinds of implication or hierarchy are: Composition, power, and classification:
Composition: "a contains b" or "b is a part of a", "if we have a, then we have b too".
Power: "a can have an effect on b", "if a changes, then b is not safe of remaining unchanged either".
Classification: "b is a kind of a" or "a implies b", "if a then b".
Though composition and power take more words to express them linguistically, they are of the same fundamentality as classification, I think, and cannot justifiedly be reduced to, or symbolically replaced, or metaphorized by, classification. It can, however, to some extent: Classification matters may be symbolized with compositional symbols, such as sets in set theory. But this abstraction is not satisfying, I think. It is reverse than with composition: Classification: (mammals (mouses)): If you have a mouse, then you have a mammal: The subset implies the superset. But composition: (Mouse skeleton (mouse skull)): If you have a mouse skeleton, then you have a mouse skull too: the superset implies the subset.
So I think, that there are three different kinds of logical implication, and may be assigned to the three Peircean categories: Composition (1), power (2), classification (3). You may read more on www.signs-in-time.de . I didnt write "logical implication" there, but "systems hierarchies". Same? Why classification is regarded most fundamental, and to be the one thing every logic might be reduced to, is just because of the word "is" in indoeuropean languages (e, est, es, ist, hai...), which still counts, besides identity, in its shortness for classification only, even if left away, like in "if a then b".
Best,
Helmut
Peircers,
It being a rainy day I am saved from having to work in the yard,
so let me go ahead and copy out the first part of this article
on Logical Implication, as I find I am still pleased with all
I was able to say in such a short space.
<quote>
Logical Implication
===================
http://intersci.ss.uci.edu/wiki/index.php/Logical_implication
https://en.wikiversity.org/wiki/Logical_implication
The concept of logical implication encompasses a specific logical function,
a specific logical relation, and the various symbols that are used to denote
this function and this relation. In order to define the specific function,
relation, and symbols in question it is first necessary to establish a few
ideas about the connections among them.
Close approximations to the concept of logical implication are expressed
in ordinary language by means of linguistic forms like the following:
“p implies q.”
“if p then q.”
Here p and q are propositional variables that stand for any propositions
in a given language. In a statement of the form “if p then q”, the first
term, p, is called the antecedent and the second term, q, is called the
consequent, while the statement as a whole is called either the conditional
or the consequence. Assuming that the conditional statement is true, then
the truth of the antecedent is a sufficient condition for the truth of the
consequent, while the truth of the consequent is a necessary condition for
the truth of the antecedent.
Note. Many writers draw a technical distinction between the form “p implies q”
and the form “if p then q”. In this usage, writing “p implies q” asserts the
existence of a certain relation between the logical value of p and the logical
value of q, whereas writing “if p then q” merely forms a compound statement
whose logical value is a function of the logical values of p and q. This
will be discussed in detail below.
</quote>
To be continued ...
--
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academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
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It being a rainy day I am saved from having to work in the yard,
so let me go ahead and copy out the first part of this article
on Logical Implication, as I find I am still pleased with all
I was able to say in such a short space.
<quote>
Logical Implication
===================
http://intersci.ss.uci.edu/wiki/index.php/Logical_implication
https://en.wikiversity.org/wiki/Logical_implication
The concept of logical implication encompasses a specific logical function,
a specific logical relation, and the various symbols that are used to denote
this function and this relation. In order to define the specific function,
relation, and symbols in question it is first necessary to establish a few
ideas about the connections among them.
Close approximations to the concept of logical implication are expressed
in ordinary language by means of linguistic forms like the following:
“p implies q.”
“if p then q.”
Here p and q are propositional variables that stand for any propositions
in a given language. In a statement of the form “if p then q”, the first
term, p, is called the antecedent and the second term, q, is called the
consequent, while the statement as a whole is called either the conditional
or the consequence. Assuming that the conditional statement is true, then
the truth of the antecedent is a sufficient condition for the truth of the
consequent, while the truth of the consequent is a necessary condition for
the truth of the antecedent.
Note. Many writers draw a technical distinction between the form “p implies q”
and the form “if p then q”. In this usage, writing “p implies q” asserts the
existence of a certain relation between the logical value of p and the logical
value of q, whereas writing “if p then q” merely forms a compound statement
whose logical value is a function of the logical values of p and q. This
will be discussed in detail below.
</quote>
To be continued ...
--
inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
facebook page: https://www.facebook.com/JonnyCache
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
