this would be what we might call, slightly adapting Lakatos' (1970, 1978) terminology, a 'degenerative' move, rather than a 'progressive' move.

Lakatos (1978: 1-7) distinguishes a progressive research programme and a degenerating research programme, as in (i).

(i) "... Thus, in a progressive research programme, theory leads to the discovery of hitherto unknown novel facts.
In degenerating programmes, however, theories are fabricated only in order to accommodate known facts."

Lakatos (1978, and earlier works, including his 1970 paper in Criticism and the Growth of Knowledge, edited by Lakatos and Musgrave, 1970, pp. 91-195) discusses these notions in relation to how a theory is saved from falsification. He mentions "a progressive research programme" when he talks about an auxiliary hypothesis not only saving the theory from falsification, but also making new predictions (that will later be confirmed). "A degenerating research programme" is mentioned when an auxiliary hypothesis is introduced only to save the theory from falsification. Popper (1974) calls the first type of 'saving hypothesis' an auxiliary hypothesis and the second type an ad hoc hypothesis.

In the context of generative grammar, we can certainly distinguish the two types of research attitude. Since we do not know what the facts are in generative grammar -- i.e., what linguistic judgments are directly due to properties of the Computational System, however, I would be inclined to say that we may in fact have (ii) and (iii), adopting the basic distinction between 'progressive' vs. 'degenerating' noted in (i) above.

(ii) a progressive way of establishing and dealing with generalizations
(iii) a degenerating way of dealing with generalizations

Suppose one comes up with a generalization G, either as something deduced from one's proposal or as a 'descriptive generalization'. The considerations in [28637] impose the following fundamental property on a generative generalization: a generalization must contain the 'specification' of (i) an Eg* (the schematic form of examples that are predicted to be unacceptable (with the specified interpretation) due to some property of the Computational System) and (ii) at least one Eg (the schematic form of examples that minimally differ from the Eg* with respect to the factor that is hypothesized to be responsible for the status of the Eg* examples).

Suppose someone shows the following.

(iv) The speaker judgments on some Eg* examples are not nearly as uniformly/systematically bad (at all) as claimed by G.

The researcher of the 'progressive attitude' would explore what is responsible for (iv), still at this point not giving up on the original generalization G or perhaps more accurately what G was intended to express. More specifically, s/he will try to identify a factor that must be controlled to obtain the judgments predicted under G. S/he may propose that a factor F is responsible for the 'unexpected' judgments on the Eg* examples. If F is grammatical in nature, there is a good chance that this would give rise to an independent negative prediction, on the basis of interaction between F and what is responsible for G, for example. Clearly, this would be a/the defining characteristic of a 'progressive research programme' of Lakatos, as it is 'applied to' the stage where one is trying to establish a 'generative generalization'. If F is not grammatical in nature, at least to the extent that we still cannot demonstrate that it is, we cannot make a negative prediction based on F. But the researcher with the 'progressive attitude' tries to see if F contributes to making some independent empirical discoveries, by serving as a non-grammatical factor that should and hopefully could be controlled in our syntactic experiments.

In summary, the 'progressive attitude' would be such that the researcher tries to establish new generalizations while making his/her attempt to save the original generalization G.

What about the 'degenerating attitude'? The researcher with this attitude would not be concerned with establishing new generalizations as part of his/her attempt to save the original generalization G. S/he would be content as long as G can be saved. Hence s/he would be content with coming up with some factor F that may be responsible for the unexpected judgments on the Eg*, and would not feel compelled to spell out what independent consequences F might have. S/he may refer to what appears to be the effects of F in other areas of the language under discussion or in other languages, and tries to make it plausible for us to accept F as the relevant factor in question, perhaps making reference to what is possible rather than what is impossible. S/he may also make remarks such as those in (v):

(v) a. As long as there is a contrast in judgment for some people, we can focus on that, at least for now, and proceed. Science progresses in the ocean of anomalies, anyway.
b. Judgments are always murky and we must focus on certain judgments in accordance with what the theory tells us in regard to what should be the most interesting and relevant set of judgments, among all the judgments we might get.

And at that point we wonder how the proposal can in principle be falsified once we have adopted the thesis that F is responsible for the unexpected judgments on the Eg* examples under discussion. This is of course independent from whether or not the advocates of the proposal would indeed abandon it in the face of the disconfirmation of the negative prediction; that would not be a logical matter, as acknowledged by Popper many years ago.

Lakatos 1978: "Science and Pseudoscience" by Imre Lakatos
is available at http://www.lse.ac.uk/collections/lakatos//Default.htm. The paper is published in Lakatos 1978, as "Introduction." Lakatos, Imre. 1978. The Methodology of Scientific Research Programmes: Philosophical Papers Volume 1, edited by John Worrall and Gregory Currie, Cambridge University Press.)

Popper 1974: Chapter 2, 'The Problem of Demarcation', sections 5-8 of "Replies to my Critics" in Part Three, 'The Philosopher Replies', of The Philosophy of Karl Popper, ed. by P.A. Schilpp, 1974, Vol. 2, pp. 961-1197.