Propositional Calculus III:
Reductio ad Absurdum
Selmer Bringsjord
Rensselaer AI & Reasoning (RAIR) Lab
Department of Cognitive Science
Department of Computer Science
Lally School of Management & Technology
Rensselaer Polytechnic Institute (RPI)
Troy, New York 12180 USA
Intro to Logic
2/16/2017
Logistics (incl. HyperGrader)…
HyperGrader work has been launched. Only
students signed up, & signed up correctly, will
be able to record successes & points (and
compete).
For some reason, we are still missing signups,
which means a number of students are not
able to make progress toward passing, let
along acing, the course!
Signup sheet will circulate yet again; pls
include your email address. (Some addresses
in sis aren’t RPI addresses, and this sheet will
be “ground truth.”)
Once again, your code:
Once again, your code:
And again, the SLA:
And again, the SLA:
And again, the SLA:
Mac OS
And again, the SLA:
Mac OS
Windows
HyperGrader …
http://www.logicamodernapproach.com/allProblems
[email protected]
HyperGrader …
http://www.logicamodernapproach.com/allProblems
[email protected]
Reductio …
“Reductio ad absurdum, which Euclid loved so
much, is one of a mathematician's finest weapons.
It is a far finer gambit than any chess gambit: a
chess player may offer the sacrifice of a pawn or
even a piece, but a mathematician offers the game.”
–G. H. Hardy
A Greek-shocking Example …
Going in this vicinity for informal proofs
on Test 1, but we need to first reach
equilibrium w.r.t. Slate & Hypergrader.
Explosion
GIVEN. φ ∧ ¬φ
{GIVEN} Assume ✓
PC ⊢ ✓
GOAL. ψ
{GIVEN}
Explosion: Partial Proof Plan
GreenCheeseMoon1
GIVEN. ¬(P → (Q → P))
{GIVEN} Assume ✓
PC ⊢ ✓
GOAL. G
{GIVEN}
GreenCheeseMoon1: Partial Proof Plan
Sub-Proof Here