Does Goodman's paradox show that there are restrictions on the kinds of predicates that can occur in acceptable generalizations? 

Yes!  The restrictions that Goodman's paradox highlights are the natural result of the interaction of our use of language with our innate abilities of pattern recognition.

Goodman's "new paradox of induction" presupposes Hume's older paradox of induction.  Hume argued that there is no way to fully justify ampliative induction.  Hume argued that inductive inference is simply a matter of a "habit of the mind".  We encounter patterns in our experiences, and assume as a matter of habit rather than as a matter of logic, that those patterns will continue into the future.  Hume argued that there is no justification in logic for the assumption of "futurity" -- that the future will be like the past.  Because Goodman's paradox must be understood in the context of a solution to Hume's paradox, it must be understood in a context that accepts as a valid aspect of inductive generalization the assumption of futurity.

Goodman's paradox is his claim that there seems to be no logical rational for the particular predicates to which we choose to apply the assumption of futurity.  His famous example was the predicate "grue" (applicable to "to all things examined before t just in case they are green, but to other things just in case they are blue").  We readily recognize that "grue" is somehow perverse.  But Goodman's paradox is the problem of explaining in a principled way just why it is that such predicates are perverse, while our normal predicates are not.

Goodman argued that it cannot be just that the perverse predicates contain a mention of some boundary ("t" in the case of "grue", but any boundary condition can be substituted).  To show this he proposed to match grue with "bleen" (applicable to "to all things examined before t just in case they are blue, but to other things just in case they are green).  Someone could think in terms of grue-ish (using the predicates of grue and bleen), and define green and blue in terms of grue and bleen and a change at t.  This would apparently transfer the boundary change to green and blue, making them, in the mind of someone thinking grue-ish, the perverse predicates.

But Goodman's argument ignores the consequences of grue-ish when applied to the patterns we observe around us.  We are an evolved species with a neural-net pattern recognition machine as a brain.  We have evolved the ability to identify useful patterns within our experiences.  If we notice a series of experiences and identify a pattern to those experiences, and want to talk or think about that pattern, we provide a name (say "q") to identify that pattern.  The assumption of futurity means that we assume that the pattern "q" will persist into the future without changing.  If it changes, then the pattern we have noticed no longer persists.  Now consider a different predicate (say "p"), that identifies a different pattern with which all of those experiences (and only those experiences) are fully consistent.  For "p" not to be a perverse predicate, it must be the case that the pattern it labels will persist into the future with no observable change.  Otherwise it is a perverse predicate.  The key is the noticed change to the experiences that occur across the boundary condition.

What this means for "grue" and "green" is that, regardless of how they are defined, if they are to persist into the future in a non-perverse way, there can be no detectable change as our experiences cross the boundary.  Otherwise, they are perverse predicates.  This means that for us, "grue" is a perverse predicate -- we will detect a change in the wave-length of light as our experiences cross the boundary condition.  Things which have shown the pattern of being green before the boundary, will suddenly exhibit the pattern of being blue.  The only way for it to come out non-perverse is if -- counter-factually -- we would not notice the change in colour across the boundary.  A mythical creature employing "grue" as a non-perverse predicate would have to be so constituted as to not be able to detect (personally or technologically) the change in light properties across the boundary condition.  The pattern of presently experienced grue things would have to remain unchanging across the boundary where ex hypothesi there will be a change in light properties.

An inductive generalization is just the identification of a pattern in our experiences.  It is the identification of a pattern for which we provide a name -- a predicate.  If the identified pattern we expect to persist into our future experiences without change, then the predicate is projectable and the generalization is acceptable.  If, instead, we add speculation to our experiences, and propose a pattern that goes beyond those experiences in a way that forecasts a change to our experiences across some boundary condition, then that is a non-projectable predicate.  And it is a non-acceptable generalization. 

We can take any observed pattern within our remembered experiences and draw a generalization.  For any such generalization, if we assume the pattern will persist into the future without change, it is an acceptable generalization.  The predicates we create to label these acceptable generalizations are all projectable.  We can also take the same observed pattern, based on those same remembered experiences, and create an infinite variety of other predicates that include some proposed change to the observed pattern as our future experiences cross some boundary condition.  Such predicates are non-projectable, and generalizations based on them are unacceptable. 

The futurity assumption that underlies all inductive reasoning is that the future will be like the past.  Assuming otherwise is not inductive reasoning.  A generalization that is based on change to the pattern behind the generalization rather than futurity is not an acceptable generalization.

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