(Varieties of) 'Implication'

 

[under development]

 

'Implication'

 

Implication is a relation between 'statements' (in the sense of 'truth-evaluable entities'), and it relates statements by virtue of their truth-values. That one statement 'implies' another means that if the former is true then so is the latter (i.e., if the latter is false, then so is the former). For example, that "John is a bachelor" 'implies' "John is male" means that if "John is a bachelor" is true, then so is "John is male" (i.e., if "John is male" is false, then so is "John is a bachelor").

 

Philosophers usually fail to see, or ignore, or neglect that there is a variety of different relations called "implication", or worth calling "implication". Furthermore, there is a tendency among them (philosophers) to appeal to "material implication" when what is at issue, and what they actually mean, is really something else. Thus, for example, material implication is often used for definitions of intensions, even though the relation expressed by material implication does not concern the intensions of the statements in question. [EXAMPLE The mistake becomes particularly obvious in Bach & Harnish 1979, 'convention', where an extra clause must be inserted only to mend the inability of material implication.]

 

[... @Russell, xxx.]

 

 

 

Material implication

Material implication is a relation which takes place between statements (just) by virtue of their truth values (rather than, for example, by virtue of their meanings).

 

That ... 'materially implies' __ means that either the term replacing "..." is false, or the term replacing "__" is true (or both). Thus, that 'Albert is a schemer' materially implies '2+2=4' means that either 'Albert is a schemer' is false, or '2+2=4' is true (or both).

 

Assuming that ... 'materially implies' __, we can deduce that if the term replacing "..." is true then so is the term replacing "__" (i.e., that if the term replacing "__" is false then so is the term replacing "...").

 

Necessary implication

That ... 'necessarily implies' __ means that by necessity, if the term replacing "..." is true then so is the term replacing "__" (i.e., that if the term replacing "__" is false then so is the term replacing "...").

[Notice that there are various kinds of necessity. For some details click here.]

 

Logical implication 

That ... 'logically implies' __ means that as a matter of logic, if the term replacing "..." is true then so is the term replacing "__" (i.e., that if the term replacing "__" is false then so is the term replacing "..."). Another fitting name for this would be 'a priori implication'.

[For more details about the term 'a priori' click here.]

 

Semantical implication 

That ... 'semantically implies' __ means that, given the meanings of the terms replacing "..." and "__", if the term replacing "..." is true then so is the term replacing "__" (i.e., that if the term replacing "__" is false then so is the term replacing "...").

 

[?] Analytical implication [=> "analytic truth"]

That ... 'analytically implies' __ means that, given the meaning of the term replacing "...", if the term replacing "..." is true then so is the term replacing "__" (i.e., that if the term replacing "__" is false then so is the term replacing "...").