Skwim
Veteran Member
While sometimes called "mathematical logic," in the logic books I have it's called "symbolic" or "formal" logic. So the designation "mathematical logic," is merely a name, and doesn't signify anything different than symbolic or formal logic. It's an irrelevant distinction you're attempting to establish.Are you not certain that the symbolization you are using is MATH? Will you deny what you are using is MATH and not LOGIC?
You are using MATHEMATICAL LOGIC specifically (specifically called mathematical logic) and not pure deduction. It is NOT the SAME THING.
There are distinctions among the following types of deductive logic: classical logic (aka Aristotelian logic), Medevial logic (aka some called it Material Logic), Symbolic logic (aka Modern logic), Mathematical logic, modal logic (partly deductive and partly not deductive), etc.
In any case; from ratiocinator's post 119
E - Events
D - Events that result from deterministic processes
R - Events that result from randomness
C - Conscious choices
F - Conscious choices that are entirely the result of free will
P1: All E are (D or R)
P2: All C are E
IC1: All C are (D or R) [syllogism - Middle: E, Subject: C, Predicate: (D or R)]
P2.1: All F are C
IC2: All F are (D or R) [syllogism]
P3: F not R
C: F are D [disjunctive syllogism]
____________________________________________________
Recast in bare standard syllogistic form (Barbara: name of the valid syllogistic form. Disjunctive: type of argument form)
ORIGINAL FORM .........................BARE FORM
P1: All E are (D or R).....................All E are (D or R)
P2: All C are E...............................All C are E
__________________.........................._____________........Barbara
IC1: All C are (D or R)...................All C are (D or R)
IC1: All C are (D or R)................. All C are (D or R)
P2.1: All F are C...........................All F are C
__________________........................______________.......Barbara
IC2: All F are (D or R)..................All F are (D or R)
IC2: All F are (D or R)..................All F are (D or R)
P3: F not R...................................No F are R
__________________.......................______________......Disjunctive
C: F are D....................................∴..All F are D
P1: All E are (D or R).....................All E are (D or R)
P2: All C are E...............................All C are E
__________________.........................._____________........Barbara
IC1: All C are (D or R)...................All C are (D or R)
IC1: All C are (D or R)................. All C are (D or R)
P2.1: All F are C...........................All F are C
__________________........................______________.......Barbara
IC2: All F are (D or R)..................All F are (D or R)
IC2: All F are (D or R)..................All F are (D or R)
P3: F not R...................................No F are R
__________________.......................______________......Disjunctive
C: F are D....................................∴..All F are D
Which is a completely valid progression of syllogisms and conclusion. Not sound mind you (C and F are not true), but valid.
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