# Clarification of material conditional, logical necessity and causation

Are the following four statements always true -

1. If Proposition B is the Logical consequence of proposition A, then B is material conditionally connected with A.
2. If Proposition E is material conditionally connected with C, then it is NOT necessarily the case that E is a logical consequence of C.
3. 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.
4. 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.

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.

• It is not clear what "logical" or "material conditionally" means here, your source probably has some very specific definitions. In a formalized theory some consequences will be formal (if A then A), and some only material (if red then not green), i.e. specific to the matter of the theory. If "logical" means formal and "material conditionally" means generically valid then 1 and 2 are true. As for 3, 4, they will depend on what role causality plays in the theory, one can imagine theories with material postulates that do not involve causation, e.g. the red does not cause the non-green. May 31 '18 at 16:34
• These are the definitions of Logical necessity and material conditional. May 31 '18 at 16:41
• These are the definitions of Logical necessity and material conditional. 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. May 31 '18 at 16:48
• Logical Necessity : Proposition A is a logical consequence of proposition B, if the truth of proposition B (along with maybe other auxilary axioms), neccessitates the truth of Proposition A. Example The fact that an equilateral triangle has all three sides equal necessitates that all the three angle are each 60 degree May 31 '18 at 16:51
• Possible duplicate of What does the truth-value of a material implication represent? May 31 '18 at 17:39