Talk:Truth table
The comments about "finite mathematics" are silly. "Finite mathematics" is not a field within mathematics, but rather a collection of diverse topics in elementary mathematics that the curriculum brings togetther in a single undergraduate course for business students. Truth tables are not different in "finite mathematics" than in other disciplines. -- Mike Hardy
The "arrow" connective, it is to be understood as a truth-functional operator, should bot be described as "implication." This involves confusing the use-mention distinction that Quine first noticed and spent his whole career trying to enforce (Perhaps hopelessly: quantified modal logic is deeply infected with use-mention confusions.) See his Mathematical Logic, Section 5.
In any case, "if...then" is not the same as "implies." "Implies" is a relation between sentences: a two-place predicate that takes sentences as the values of its variables and produces a sentence from them: it is a function from names of sentences--terms--to a sentence.
By constrast "if then" is a not a predicate but a connective; it is a funtion from sentences to a sentence. It does not take anything as values because it does not contain variables.
"Implies" talks about--mentions--two sentences, and can only be used in a meta-language. "If...then" uses two sentences; it mentions whatever the sentences mention, and is itself a term within the object language. Shortly:
If A then B. If the light goes out then the monsters will come.
but
"A" implies "B". "The light goes out" implies "The monsters will come".
Sorry for the rant. If anyone sees this mistake elsewhere, please correct it.