There are various senses in which we might imagine something can be 'reduced' to 'behaviour'.
(This is an old chestnut, so I want to explain why I'm turning it over:
The 'technology' of language - the squiggles and noises, the semaphore, anything which can be reproduced by a machine process - is a kind of 'behaviour'. At some level it is tempting to think 'but this is all there really is. What else can there be?' Except that that question itself cannot be reduced to the characters used to present it here ... not even to those characters in a 'wider context' which is assumed also to be of the same nature - squiggles, noises, the machinery of representation ...)
So. Behaviour. Three cases:
We might literally have a behavioural definition: certain semaphore signals can be translated into alphabetic characters because we have a complete set of rules for how to do this. (We must assume, of course, that we are translating semaphore, but I will pass over this because I want to use the case as an example without letting too much depend upon it.)
The second case is where we imagine there is some such set of rules, but that we do not know, or do not know entirely, what they are. We imagine that with enough time and computational capacity we could encode and enact them and that only 'human limitations' prevent this. We imagine we are dealing with something that is in principle like semaphore, that it is the chess to semaphore's noughts and crosses.
The third case is where we know that even in principle there is no way to write down all the behavioural rules, and we know that natural language is like this because the rules must be written down in some part of it, and so will remain, to some extent, systematically ambiguous because of the 'open question' problem.
In this third case, we might imagine, however, that some 'semaphore' or 'in principle semaphore' metaphor can be appealed to, even though we know that the metaphor can never be fully 'unpacked'. This, of course, is a profound and misleading mistake.
(It can be hard to accept this, because we might still find ourselves asking 'but what else is there?' - and this just demonstrates the power of the metaphor. It's like believing that some step forward is taken when we 'recognise that everything is just atoms' - or some other materialistic substrate. Before we can make statements like these, we have to know what 'all interaction is behaviour' or 'everything is just atoms' means, and this question cannot be answered in terms of behaviour or atoms ...)
There are two dimensions to this mistake - one is the OQ issue, which I've discussed at length.
The other is to do with the explanatory power of metaphor.
A metaphor may suggest a way to speak, but it cannot command, or even support, semantic conformity. We can see, for instance, the ways in which electricity 'flow' is somewhat like fluid flow, and this might help us to understand some aspects of an electrical circuit (although it makes others more obscure ...).
But if someone tried to explain basic arithmetic, or the principle of non-contradiction, by way of a metaphor we would wonder whether they properly understood the subject. Equally, we cannot regard arithmetic or logic as simply a 'game' with 'rules' since they are anchors of the intelligibility of our explanations, and so of the intelligibility of our shared world. (And we have to include, here, explanations of what we do when we appeal to metaphors ...)
The 'rules' we should be interested in are only those without which we cannot explicate rules. And these rules are rules about how to speak that turn out to be, through that, rules about the way the world must be.
