Cf: Animated Logical Graphs • 40
http://inquiryintoinquiry.com/2020/09/26/animated-logical-graphs-40/
| Note: as always, follow the above link for better formatting,
| especially if the unicode math symbols fail to get through.
One way to see the difference between insight proofs and routine proofs
is to pick a single example of a theorem in propositional calculus and
prove it two ways, one more insightful and one more routine.
The praeclarum theorema, or splendid theorem, is a theorem
of propositional calculus noted and named by G.W. Leibniz,
who stated and proved it in the following manner.
<QUOTE>
If a is b and d is c, then ad will be bc.
This is a fine theorem, which is proved in this way:
a is b, therefore ad is bd (by what precedes),
d is c, therefore bd is bc (again by what precedes),
ad is bd, and bd is bc, therefore ad is bc. Q.E.D.
— Leibniz • Logical Papers, p. 41.
</QUOTE>
Expressed in contemporary logical notation,
the theorem may be written as follows.
Expressed in contemporary logical notation, the theorem may be written as
follows.
((a ⇒ b) ∧ (d ⇒ c)) ⇒ ((a ∧ d) ⇒ (b ∧ c))
Using teletype parentheses ( ... ) for the logical negation (p)
of a proposition p and simple concatenation pq for the logical
conjunction of propositions p, q permits the theorem to be
written in the following in-line and lispish ways.
Inline Syntax
=============
( (a (b)) (d (c)) ( (ad (bc)) ))
Lispish ("pretty-printed")
==========================
( (a (b)) (d (c))
( (ad (bc))
))
To be continued ...
Regards,
Jon
_ _ _ _ _ _ _ _ _ _
► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of
the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and
co-managed by him and Ben Udell.
