People often send us papers and data via Twitter that they believe rule out a radical, non-representational theory of cognition. Because I have yet to agree about any of these studies, these people then often ask in exasperated tones 'well, what would you accept as evidence?'.
My current best answer is "about 20 years of hard work".
First, no single study will ever refute radical embodied cognition, for the same reason single studies should never be trusted. Replicate or get out.
Second, no argument from theory will ever manage it. Theory is important, but without data an elegant theory is just that; elegant. We need accurate theories, and that means data.
Third, most studies are motivated by and interpreted within a more traditional cognitive science framework. This means that even a series of studies replicating an effect REC hasn't investigated and interpreting it as requiring representations, etc is not enough. Just because everyone is asking the wrong question doesn't make it the right question.
There's really only one way to refute REC, and that's to engage in a systematic series of studies around a carefully selected topic, and to have these studies carefully pit predictions of REC and your non-radical theory against one another. You will need to be fair to all sides, and not stack the deck by willfully misrepresenting what a given theory would predict. After accumulating evidence for a period of many years and many studies, then you would have reason to say you've ruled it out (if that's what the data suggest).
(A little update to be more specific, thanks to Christian Hummeluhr for quizzing me on Twitter about this;
What about the data would let you rule out REC? The key to our radical embodiment is information. If there is information present that can support the behaviour and people can detect it, then they should use it and not a representation. If this research programme did the right task analysis, identified the set of candidate information variables, ran the perturbation studies but then found that none of them impacted behaviour, then REC would be in trouble.)
This seems so unreasonable, though. Why should it take this much work? Well, first, get a grip, science is hard and doing it right takes time and effort. Second, proponents of various forms of embodied cognition, ecological psychology and dynamical systems approaches have been engaged in exactly this process for a long time now, and it's their successes we point to when asked why we think embodied cognition is the way to go. The best example remains Smith and Thelen taking on the A-not-B error (Thelen et al, 2001) but there are others; Geoff Bingham regularly sets up explicit comparisons between the ecological and information-processing accounts in his work and then demonstrates how only the former can explain the data (e.g. information vs. function learning in throwing; Zhu & Bingham, 2010, or information vs. cue combination with the example of height-in-the-visual-field; Mon-Williams & Bingham, 2008).
Even scientists not explicitly in the 'radical' camp have been doing this kind of work. Research on collective action (swarming, flocking, pack hunting, etc) has spent many years pitting simple dynamical systems explanations against complex cognitive ones for years and finding over and over again that complex coordinated activity emerges from the activity of individual animals engaged in simple behaviours in groups (e.g. see this recent post by Ed Yong on work with baboons). The success of people like Iain Couzins comes from their hard work in showing not only that their simple models work, but that they out-perform other, more complicated theories in both prediction success and in the scope of behaviours they successfully explain.
Science is hard, and it takes time and effort. The radical embodied approaches have a head start on this kind of 'head-to-head' work because just to get going, they had to show they could out-explain other theories. They've done this by making successful predictions no other theory would have (e.g. that the A-not-B error would exist without an object present, something an object concept theory would never even think to suggest; Smith et al, 1999) and they've done it over a series of studies (see Thelen et al, 2001 for a comprehensive review).
The mainstream simply hasn't been pitting its ideas directly against the predictions of the radical analysis of their task (if one exists) and so your data, while interesting, does not yet pack the punch you think it does. If you want to rule REC out, get cracking with the science and we'll see you in 20 years (unless anyone's up for a hostile collaboration? :)
Mon-Williams, M. & Bingham, G.P. (2008). Ontological issues in distance perception: Cue use under full cue conditions cannot be inferred from use under controlled conditions. Perception & Psychophysics, 70(3), 551-561. Download
Smith, L. B., Thelen, E., Titzer, R., and McLin, D. (1999). Knowing in the context of action: the task dynamics of the A-not-B error. Psychological Review, 106, 235–260. Download
Thelen, E., Schöner, G., Scheier, C., and Smith, L. B. (2001). The dynamics of embodiment: a field theory of infant perseverative reaching. Behavioural and Brain Sciences, 24, 1–86. Download
Zhu, Q. & Bingham, G.P. (2010). Learning To Perceive the Affordance for Long-Distance Throwing: Smart Mechanism or Function Learning? Journal of Experimental Psychology: Human Perception and Performance, 36(4), 862-875. Download