An indexical is a pointing word, one used to refer directly to something. (To remember this, think of your index finger, the one you use to point with.) Examples include ‘I’, ‘you’, ‘he’, ‘she’, ‘it’, ‘we’, ‘they’, ‘this’, ‘that’, ‘here’, and ‘now’. Clearly, indexicals are an important part of our speech. In fact, nearly every statement we make contains an indexical (sometimes implicitly).
A proposition, as I understand it, is an assertible unit of meaning. It is an abstract representation of a state of affairs that, when asserted, posits that state of affairs as a fact. Statements (i.e., declarative sentences) express propositions, that is, they express something assertible.
A typical statement contains one or more indexicals and expresses a proposition. But what is the relation between indexicals and propositions? In particular, can there be anything in a proposition itself that functions indexically? Can an abstract representation contain a pointer to something? If so, can that something lie in the representation itself, can it lie outside it, or both? If not, then our use of indexicals would seem to reflect something external to the proposition, the operation on a proposition of something fundamentally non-propositional.
Consider the following argument:
- Propositions can contain elements that function indexically (by pointing to something) .
- tAny representation of the meaning of The meaning of all indexical terms is either reducible to or contains as a constituent a representation of the self or I (a first-person representation).
- The self or I cannot be represented as such (i.e., a representation of a self cannot be a self but must be something other, something non-self.)
- Propositions are representations.
- Therefore, no proposition can contain an irreducible representation of a self or I. (2,3)
- Therefore, no proposition can contain an irreducible representation of an indexical. (1,4)
With regard to (1), let’s consider a few indexical terms:
- ‘here’ = where I am
- ‘now’ = when I am speaking/acting/etc.
- ‘you’ = the person I am speaking to
- ‘he/she/it’ = the person/thing I am speaking about/referring to
Given that examples like this could be multiplied, (1) looks fairly plausible.
Premise (2) seems beyond doubt. The self or I, as such, is a subject (an essentially first-person type of entity). A representation is an object (an essentially third-person type of entity), and that only in relation to some actual or possible subject. In other words, the I is a necessary condition for the possibility of representation, for it is that to which a representation is presented. How, then, can that which is essentially subject be represented as subject? That would requirely it to be both an essentially first-person entity and an essentially third-person entity at the same time, which is contradictory.
Premise (3) I take to be true by definition of proposition.
(4) follows from (2) and (3) because if no representation of the selft can be a self, then it must be reductible to something non-self.
any representation of the self