The Binary Logical Connectives

The Binary Logical Connectives

There are sixteen binary logical connectives, a sufficiently small number to encourage obsessive compulsive behavior (cf. our genetics page).

In English as far as I am aware, we use the following: and, or, nor implies, if, unless, and tantamount (in the form "is tantamount to") and we get two more using not as binary connective, and two more, on certain occasions, via "the former" and "the latter". In addition, not saying anything can possibly be construed as one more. On the other hand, the identically false connective does not seem to be easily expressible. The phrase "yes and no" comes to mind, however.

On a relatively generous assessment we achieve twelve of the sixteen. We seem to be missing the negations of implications and equivalence, and the ability to manufacture a completely false expression efficiently.

The question has arisen as to whether all possible connectives are expressed succinctly in at least one natural language. See Manin, pp. 40-41, for some obscure remarks on the topic (djvu format, viewer required), and see the last link for some less obscure references.


© G. Cherlin 2005