Wednesday, September 08, 2004

Three Senses of 'Or'

‘Or’ is a troublesome particle in dire need of regimentation. Besides its two disjunctive meanings, the inclusive and the exclusive, there is also what I call the ‘or’ of identity. The inclusive meaning, corresponding to the Latin vel, is illustrated by ‘He is either morally obtuse or intellectually obtuse.’ This allows that the person in question may be both. The exclusive meaning, corresponding to the Latin aut, is exemplified by the standard menu inscription, ‘soup or salad,’ which means one or the other, but not both. Logicians view the inclusive ‘or’ as a basic propositional connective. Thus our first example would be symbolized by p v q, where p is the proposition expressed by ‘He is morally obtuse’; q the proposition expressed by ‘He is intellectually obtuse’; with ‘v’ – in honor of vel – standing for inclusive disjunction. Exclusive ‘or’ can now be defined as follows: p aut q =df p v q & ~(p & q), where the tilde and the ampersand, both propositional connectives, represent negation and conjunction respectively.

How is ‘or’ functioning in this sentence: ‘Philosophers of a realist bent posit facts or states of affairs as truth-makers.’ Clearly, no disjunction is being conveyed. The idea is that facts just are states of affairs, or that ‘fact’ and ‘state of affairs’ are being used interchangeably. Indeed, the preceding sentence exemplifies a use of ‘or’ that does not express a disjunction. Hence, ‘or’ of identity. Such uses of ‘or’ can be replaced by ‘i.e.,’ id est.

Why is this important? Well, it is important if your aim to is write and think with precision and self-awareness. If that is not your aim, then it ought to be.