On 9/5/2018 2:57 AM, Francesco Bellucci wrote:
As I mentioned, I think we should recognize that Peirce uses "general"
in at least 3 senses: 1) symbols have a general object (vs indices,
which have an individual object), 2) legisigns are general in themselves
(as types that occur in replicas), 3) and universally quantified
sentences are also said to be "general" by Peirce ("distributively
general" his preferred term).
I agree. But I believe that it's important to use Peirce's own
tools for stating the criteria precisely: his versions of logic.
For each of those three senses, any definition in his algebraic
notation of 1885 would have a universal quantifier, and any
definition in existential graphs would have a line of identity
in a negative area.
That kind of explanation would have several advantages:
1. It would show the common feature that is present in all
uses of the word 'general'.
2. By the differences in the logical expressions, it would
show exactly how those three senses differ.
3. It would illustrate Peirce's claims about the utility
of his writings on formal logic.
4. It would enable anyone who knows logic, but has not yet
studied Peirce to get a better appreciation for Peirce's
work -- and perhaps begin to dig deeper into his writings.
John
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