Are the following four statements always true -
- If Proposition B is the Logical consequence of proposition A, then B is material conditionally connected with A.
- If Proposition E is material conditionally connected with C, then it is NOT necessarily the case that E is a logical consequence of C.
- If proposition H corresponds to an observed fact H* which is supposed to be causally related to observed fact G* (say H* causes G*), then the proposition G corresponding to the observed fact G* is material conditionally connected with Proposition H.
- If proposition X is material conditionally connected with Proposition Y, then it is NOT necessarily the case that X and Y are causally related.
I am a student of Physics, researching on quantum logic. I am confused by the above statements which I hypothesized regarding classical logic. Any help would be much appreciated.
Definitions taken from the comments:
Material conditional: Proposition A is material conditionally connected with Proposition B, denoted as "If A then B" when the proposition "If A then B" has a truth value of false only if A is true and B false. For all other combinations of truth values assigned to A and B, "If A then B" is true.
Logical Necessity: Proposition A is a logical consequence of proposition B, if the truth of proposition B (along with maybe other auxiliary axioms), necessitates the truth of Proposition A. Example: The fact that an equilateral triangle has all three sides equal necessitates that all of the three angles are each 60 degrees.
Je, taarifa nne zifuatazo daima kweli - - Kama Proposition B ni matokeo ya mantiki ya Proposition A, basi B ni nyenzo conditionally kushikamana na A. Kama proposition H inalingana na ukweli H * ambayo inapaswa kuwa causal kuhusiana na ukweli G *, basi proposition G inayolingana na ukweli G * ni muhimu conditional kuhusiana na proposition H. Kama proposition X ni muhimu conditional kuhusiana na proposition Y, basi ni muhimu kuwa X na Y ni causal kuhusiana. Mimi ni mwanafunzi wa Fizikia, nikifanya utafiti juu ya mantiki ya quantum. Mimi nina kuchanganyikiwa na taarifa za juu ambayo mimi hypothesized kuhusu mantiki ya kawaida. Msaada wowote ungependelewa sana. "Kama ilivyoelezwa katika makala ya kwanza, ""Material conditional"" ni neno linalotumiwa kuelezea ""Material conditionally connected with proposition B"" (kama A na B ni kweli) na ""Material conditionally connected with proposition B"" (kama A na B ni uongo)." Kwa mchanganyiko mwingine wote wa maadili ya ukweli uliopewa A na B, "Ikiwa A basi B" ni kweli. "Uhitaji wa mantiki: ""A"" ni matokeo ya mantiki ya B, kama ukweli wa B (pamoja na labda axioms nyingine za msaidizi) inahitaji ukweli wa A." Kwa mfano, kwa sababu pembetatu ya equilateral ina pande zote tatu sawa, inahitajika kwamba pembe zote tatu ni digrii 60.