Some months having gone by since I first read it, I’ve been trying to get a feel for the significance of Travis’ ‘Reason’s Reach’. Equipped with a masterful summary drawn up by my colleague Gloria Ayob, I have more of a synoptic view of the article than I’ve had before. Without trespassing too much on her account (you’ll have to ask her), there are two kinds of argument at the heart of the article. But first some context.
Travis argues, first, that McDowell subscribes to a condition for experience to be able to exert a rational constraint on thought: ‘something non-conceptual… could not impinge rationally on what one is to think.’ [ibid: 180] Travis argues, however, that whilst McDowell attempts to accommodate the condition, it should be rejected because non-conceptual items can so impinge.
Second, we need the distinction, drawn from Frege, between extra conceptual and conceptual items on the left and right of a notional line. One point of contrast is that the former can be perceived but not the latter. So, eg., one might look at the rug to see that the meat is on the rug (pictured). But equally, one might look at Pia’s face. ‘That the sun has set (in Rostock) may be, in some sense, about a location. But it has none. The sun, perhaps, is in the sky. That it has set is not.’ 
Perceivable items can represent only under an interpretation but the fact that something is taken to represent is not itself perceivable. Furthermore and more importantly, conceptual items possess a kind of generality. Even the concept of being Frege could be instantiated in a number of ways even if only by Frege had he been taller or shorter or different in any number of non-essential ways.
Travis then advances two sorts of argument to support the claim that extra-conceptual items (to the left of Frege’s line) can rationally constrain judgement.
One sort runs (thanks to G for the next five sentences) as follows: If rational relations could only hold between two conceptual relata, this would mean that rational relations can only hold between generalities (since ‘the conceptual’ is defined as that which presupposes generalities). If rational relations held only between generalities, then things being as they are could not determine when one made an error in judging that an object instances being x (i.e. that the object fits a relevant range of cases), and when not. But things being as they are can determine whether or not one has made an error in judging that an object instances being x. So, rational relations do not hold only between generalities. Since the conceptual presupposes generality, this means that rational relations do not hold only between two conceptual relata (that is, the condition outlined at the start is mistaken).
This argument, it seems to me, is a powerful appeal to a pre-philosophical account. Travis reminds us of the fact that everyday objects – which instance generalities rather than being generalities – can rationally constrain judgement. Thus, any account that conflicts with this is, prima facie, falsified by our everyday understanding.
The other sort of argument concerns Travis’ philosophical signature dish: occasion sensitivity. Travis starts from the idea that the judgement that, for example, a packet of kidneys counts as meat depends on the occasion.
Handing you a packet from the butcher’s I say, ‘Here’s the meat I bought for dinner’. You open it and find the kidneys. ‘I don’t call that meat’, you say. ‘Meat, for me, is muscle’. ‘Well, I do’, I say helpfully. Again one of us may be demonstrably wrong. Lamb’s kidneys are no more meat than wool is, to one who knows what meat is. But perhaps not. In fact, there are various understandings one might have of being meat, consistent with what being meat is as such. In that sense, being meat admits of understandings. We sometimes distinguish (eg., in good markets) between meat and offal. Then if the kidneys wound up in the meat section they are in the wrong place.. On the other hand, one would not (usually) serve kidneys to a vegetarian with the remark, ‘I made sure there would be no meat at dinner’…. There are various ways being meat admits of being thought of. 
So with that reminder of occasion sensitivity in mind, Travis suggests that if seeing how things are is, as it seems, conceptually structured. But seeing things to be a particular way inherits the same occasion sensitivity as judgement and this sets up a contrast between seeing extra conceptual objects (pieces of meat) and the conceptualised correlates of judgements.
Travis suggests a scene in which there is meat on a rug.
Pia enters. What is there for her to see? For one thing, that [demonstrative] meat. That would be a right answer on any occasion for giving one. It is a relative fixed point across occasions for answering that question. I referred to the meat in speaking of it as meat... 
Suppose we decided to restrict [(with McDowell)] rational relations to the conceptual. Then, for one to see what bore on what he was to think, he would have to see things that belonged to the conceptual. So there would have to be such things to be seen; things which became visible to one, say, on entering the salon and looking at the rug. One would see these things on a different notion of seeing than the one on which one sees a piece of meat. One might, eg, see that the meat was on the rug. What one thus saw would not be literally in the surroundings. It could not have a location…
Suppose we ask the question just asked for seeing on the notion on which Pia saw the meat. What of the conceptual is visible in the scene in the salon? A prior question: what of it is present in things being as they (there) are? Here we lose the stability there was for what is present, and visible, of the non-conceptual. That that meat is present is relatively insensitive to occasions for saying so; that it…is visible roughly equally so. Not so with such things as that there is meat on the rug. For what is on the rug is liable to count as meat on some understandings of being meat but not on others (eg, if it is kidneys). 
Occasion sensitivity helps to strengthen an idea already in play: that concepts are general and apply to a range of cases whereas extra-conceptual objects instantiate such concepts and, themselves, lack generality. Occasion sensitivity plays up the idea that the range in play is flexible. And this puts pressure on the idea that, in experience, there might be something conceptual (a range of cases, a range which is sensitive to the occasion on which, eg., a question is asked). By making trouble for the idea that experience is conceptual – occasion sensitivity forces the question of which concepts? – Travis is able to push attention back to the claim that the extra-conceptual can constrain judgement, which he argues is innocent.
In his reply, McDowell argues that his picture of the conceptual as having no outer boundary was meant to undermine any worry that reason is shut off from embracing objects lying outside it. He accepts a condition even if not quite Travis’ condition: ‘reason’s reach extends no further than conceptual capacities can take it’ [ibid: 259] This places no objects outside it but does express a limit: nothing can impinge on a subject’s rationality except through their conceptual abilities. (It is this which underpins McDowell’s rejection of the Myth of the Given.) So left hand side extra conceptual items can impinge on rationality or reason but only via conceptual abilities.
There is nothing outside the conceptual. That is as much as to say: there is nothing beyond the reach of reason. In this context, to say reason’s reach coincides with the conceptual cannot be to draw a boundary around reason’s reach, leaving some things outside it. The image precisely rejects any boundary... Certainly pieces of meat, say, are not conceptual; they belong on the left-hand side of Frege’s line. But they are not outside the conceptual, in a sense that could possibly cohere with my image of unboundedness...
Certainly my condition sets a limit to reason’s reach. If it did not, there would be no point in affirming it. But a limit need not be a boundary, and this limit had better not be one. What my condition disallows is the idea that something, for instance a piece of meat, can impinge on a subject’s rationality without conceptual capacities, capacities that belong to reason, being drawn on in the subject’s being thus related to it. 
This is a strikingly relaxed response to the worry Travis presents. It seems at first as though Travis has both undermined the key claim of Mind and World – that to find intentionality unmysterious we need to acknowledge a transcendental role for experience which is itself only acceptable if experience is conceptually structured and also a form of direct openness – and that he has replaced it with a less philosophically loaded, more therapeutic picture. McDowell’s response claims that he is better placed to present that less loaded picture (in which pieces of meat can exert a rational constraint on our judgements).
So we need, I think, to assess both Travis’s argument against McDowell’s account of the content of experience and whether what Travis can say about experience is enough. Not that I will try that now. But, in reverse order, in ‘Reason’s reach’, this is what Travis says about the content of experience:
Pia seeing what she did as to how things were need not be seeing things to be such-and-such way. We may simply think of her experience as follows. Pia saw what she did of things being as they were, in the scene before her; thus saw what she did as to how they were (notably, though possibly not only, how the scene before her was). She was thus enabled to recognise the instancing of an indefinite variety of bits of the conceptual, within the limits of her grasp of what instancing them requires; and to treat the world accordingly within the limits of her appreciation of what difference it would then make that such-and-such generality was instanced. What she saw of how things were need no more (nor less) be that there was meat on the rug than that there were edible animal parts there – even though for things to be one way is not in general for them, ipso facto, to be the other. There need be no particular repertoire of conceptual items which, in the scene’s being as it was, just were those present and (all going right) visible – not even an infinite repertoire – nor any such repertoire which just were, as such, the ones Pia saw... 
Pia, like most of us, can adjust her way of saying what she saw to fit the occasion for saying it, so that, in the words she chooses, she will say the right thing. She may speak of meat as on a rug, when so doing would be saying the right thing. When it would not, then, seeing that, she can speak of something else – say, edible animal parts. What she saw is no more what she speaks of in some one such way than what she speaks of in another. Her experience is no more of any one such structuring of concepts than of any other. 
And McDowell charges that this isn’t enough, that it is an instance of the Myth of the Given.
[W]e stand in those cognitively significant relations to left-hand side items by having experiences in which conceptual capacities of ours are actualised. In Travis’ picture, by contrast, conceptual capacities are in play, in connection with experience, only in rational responses on our part to left-hand side items that experience anyway makes available to us for such responses: for instance in recognising something we see as a piece of meat... the presence to us of left-hand side items in experience... does not itself draw on capacities that belong to our reason. 
In Travis’s picture, as I said, the availability to us in experience of left-hand side items is not itself a matter of actualization of conceptual capacities. Actualization of conceptual capacities comes into play only in rational responses to things we anyway experience.This is a form of the Myth of the Given. 
This suggests a two-fold issue with Travis’ picture. First, is there a problem with the idea that extra-conceptual objects can hold sway over reason? Is McDowell’s basic intuition here (at the start of Mind and World) right? Second, is Travis’ very slimmed down account of experience right in its own right, aside from the broader strategic issues? Can we get away with saying so little?
What of Travis’ objection to McDowell’s account of experience? There is a distinct line of reasoning elsewhere (eg. ‘The silence of the senses’) but in this paper occasion sensitivity drives the idea that putting concepts into an account of experience invites the question ‘which concepts?’ and there is no stable answer to that. That worry seems to be the motivation for McDowell’s two-fold retreat from the Mind and World picture (experience is intuitionally rather than propositionally structured; and not just any concept can be directly involved in structuring experience although any can be the result of an act of recognition). Neither – neither Travis’ nor McDowell’s account – seems entirely attractive.
See this entry on ‘A sense of occasion’, this on ‘Reason’s reach’, this on ‘The twilight of empiricism’, and this on the discussion of rule following in Thought’s Footing.