# Logic terminology: does "conditional" etc refer to the operator or the WFF?

To be precise.... Do the terms we use to talk about the truth-functional operators (conditional, negation, conjunction, disjunction, biconditional) refer to the operator in isolation, or the WFF that is formed with the operator?

Ex. When I say "disjunction" am I supposed to be referring to "v" or "A v B"

I'm pretty sure I've heard the terms used flexibly, to refer to both.... Is that right, or is the proper use more precise?

• Both, the intended meaning is usually clear from context:"disjunction is a Boolean operation", "this is a disjunction of 5 terms". Compare to addition vs sum, or multiplication vs product. Sep 20 '19 at 0:18
• @Conifold - great! Thanks so much :D J
– Lily
Sep 20 '19 at 3:20

## 1 Answer

One should follow the use of these words as given in the source you are using.

For example, suppose Wikipedia is the source for the term logical disjunction. Here is how it is defined:

Logical disjunction is an operation on two logical values, typically the values of two propositions, that has a value of false if and only if both of its operands are false. More generally, a disjunction is a logical formula that can have one or more literals separated only by 'or's. A single literal is often considered to be a degenerate disjunction.

Here logical disjunction refers to a logical formula, not only the logical connective that separates the operands. Indeed, one can have a disjunction (a "degenerate disjunction") without any logical connective.

However, there is more to the definition:

The disjunctive identity is false, which is to say that the or of an expression with false has the same value as the original expression. In keeping with the concept of vacuous truth, when disjunction is defined as an operator or function of arbitrary arity, the empty disjunction (OR-ing over an empty set of operands) is generally defined as false.

This shows that in certain contexts disjunction can be defined as an operator or function having no operands. This also defines more terms: "disjunctive identity" and "empty disjunction".

One should follow the use of such terms in one's textbook paying attention to the context in which the term is used, how the term is defined, and what else is defined associated with the term. In this case there are contexts in which one can use the term either as a logical formula or an operator or function.

Wikipedia contributors. (2019, September 15). Logical disjunction. In Wikipedia, The Free Encyclopedia. Retrieved 12:23, September 20, 2019, from https://en.wikipedia.org/w/index.php?title=Logical_disjunction&oldid=915839057

• Thank you Frank Huberty!
– Lily
Sep 21 '19 at 14:56