[FOM] Disjunction: in or ex?

abaker1@swarthmore.edu abaker1 at swarthmore.edu
Fri Jan 12 09:23:06 EST 2007

On Thu, January 11, 2007 17:03, Martin Davis wrote:

> Legal: In contracts in the US, I have seen "and/or" used to indicate
inclusive disjunction.

The use of "and/or" to disambiguate in favor of inclusive disjunction is
indeed quite common -- both in legal and everyday contexts. However, it
turns out that this move will not help someone who is unsure across the
board about whether any 'plain' disjunction is inclusive or exclusive.

Note first that "and/or" has a component symbol, "/", which is intended to
represent a disjunction. Unpacking this, we get

A and/or B   =  (A and B) or (A or B).

What truth-function this designates depends on the interpretation of the
two constituent 'or's. Three of the four possibilities yield inclusive
disjunction, but if the first 'or' is read exclusively and the second 'or'
is read inclusively then we have

(A and B) xor (A or B).

It is straightforward to see that when both A and B are true, this
expression is false (since both disjuncts are true), so it designates
exclusive disjunction.

Of course in practice pragmatic factors make "and/or" unambiguous, since
its use is recognized as designating inclusive disjunction. Nonetheless,
someone who was familiar with its component expressions, "and", "/", "or",
but had never come across "and/or", could not be sure that this compound
expression is actually inclusive.

Alan Baker
Department of Philosophy
Swarthmore College
Swarthmore PA 19081

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