Rules and Intentionality

Various people (Crispin Wright, Ruth Millikan & others) have drawn attention to a potential role for intentionality in resolving Kripke's paradox, since intentional states seem to have the scope and reliability we would wish to attribute to competent rule-following.

I think it would be a mistake to take this (as Millikan and Wright do) as a cue for producing a better account of intentionality, if by 'account' we mean 'reductive account'. For reasons that I've probably laboured elsewhere in this blog (more open questions ...), I think any reductive account is almost certain to generate a version of Kripke's paradox.

An account of intentionality in terms of physical behaviour (e.g. of a machine) is obviously ruled out by this kind of objection, since questions about the reliability of the machine would always make sense - and these questions would be questions about whether the machine appropriately fulfilled its function; whether it appropriately 'modelled' the intentional state it was meant to underpin.

It is difficult to think of how a reductive account could be given that could avoid this machine model objection.

In concert with accounts of truth and meaning (to which intentionality is obviously related), a recursive account can, however, be given. Since we have to be able to attribute intentional states in order to be able to speak, and since we can speak, we can start with the intentional states we must be able to attribute in order to be able to have this conversation (we don't need a complete list - just an articulable selection).

Following from this, we can give an account of rule following in terms of these intentional states, or from others that depend upon them. To follow a rule is to act in accordance with an intentional attribution.

Intentionality and rules

If I am in a certain intentional state - say believing something particular to be true (that today is Friday), then I will in general behave and speak in a ways that is consistent with this. The ways that might be consistent cannot be spelled out in advance, and not only because they are complex - also because unexpected situations will arise.

Who will adjudicate? I and my interlocutors, playing the shared language game within which the statement of my intentional state is held to be true. The intelligibility, the playability, of these adjudications will be one part of what makes the whole game possible; and if the become idiosyncratically unintelligible then so does the original statement of my intentional state - we will find that we did not know, after all, what we meant by attributing this state to me.

This process of adjudication and exploration is what the history of mathematics reveals to us about addition. Someone who has been quadding so far, but thinks they were adding, is not a competent participant in this conversation.