English-Finnish translations for material implication

Definition of material implication

• An implication as defined in classical propositional logic, leading to the truth of such as $Q\; \backslash vdash\; P\; \backslash to\; Q$, to be read as "any proposition whatsoever is a sufficient condition for a true proposition

Synonyms

• material conditional

Examples

• In the truth table in Figure 1, the first row corresponds to modus ponens, the last row corresponds to modus tollens, the second row could be taken to represent an invalid argument (where P→Q is the argument and P is a premise or conjunction of premises), and the third row helps ensure that an argument of the form $P\; \backslash rightarrow\; Q,\; \backslash neg\; P\; \backslash vdash\; \backslash neg\; Q$ is invalid.
•     The following paradox (and also axiom) of material implication: $P\; \backslash rightarrow\; (Q\; \backslash rightarrow\; P)$ could be taken to mean the monotonicity of entailment, that is, if P is true then no other or new fact Q should be able to arise which would imply the nullification of Ps truth, i.e., it could not be the case, for any Q, that Q → ¬P.

Related words

• entailment