Gary, list,
I am curious about this. It's a subject where I've tripped up before. It
apparently has to do with Peirce's removing the rule whereby 'there is
something blue or round' is equivalent to 'there is something blue or
there is something round'. That's also to remove the rule where by 'all
is blue and round' is equivalent to 'all is blue and all is round'.
Those are among the rules
http://en.wikipedia.org/wiki/Rules_of_passage_%28logic%29 now known in
logic as 'rules of passage' (so dubbed by Herbrand). To remove one of
them seems to be to remove all of them. My questions, for you or
Frederik or whomever, are:
(1) How is one to think of 'all is blue and round' as differing in
meaning from 'all is blue and all is round' ? Does one of them imply,
without being implied by, the other?
(2) Doesn't this change make the Beta graphs non-equivalent to
first-order logic? Or is this really a change for the purpose of Gamma
graphs? I'm no logician, so I may be confused here.
Best, Ben
On 1/14/2015 4:32 PM, Gary Richmond wrote:
Perhaps this is a good place to stop for now since at this point in
the chapter Frederik quotes the important long passage I mentioned in
my first post in this thread and analyzes it in terms of how Peirce
"relativized" material implication to go beyond it in revising parts
of his Beta and Gamma graphs. However, that is a somewhat technical
discussion and I'm am not sure that there is enough interest here in
EGs to continue it.
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