reconstructive theories (e.g., syntax) are an attempt to develop
*criteria* -- to discover these criteria.  This is a stipulation,
from the pov of the theory constructor; but also a discovery, from
the pov of that theory correctly describing reality.  The 'laws'
discovered are a kind of criteria -- so criteria need not be viewed 
simply and always as 'nominalistic' stipulations.

Note: that there is a distinction to be made between (a) explaining 
why X counts as Y, by appeal to criteria which we have in hand, and 
(b) explaining what it is to count as Y, by reconstructing (discovering)
the criteria, not heretofore had.

So it might look like what *I've* been calling constitutive explanations
are just of type (a), and so take all the (b) examples off the table
for my purposes.  But my idea of constitutive explanation is still 
useful for properly understanding (b) cases -- because we see, from my
account of constitutive explanations, how (and why) such (b) theories are 
'non-literal'.  (B) theories state what it is to count as Y, not what
causes or brings about Y's.  This is why transformational grammar is not
to be read as a 'process theory' (i.e., as an account of the psychological
processes that led up to an utterance of the sentence); it is instead
to be read as an account of what it is to qualify as a grammatical sentence
of (say) English.    

Also: lay out what 'explaining what it is to count as Y' amounts to.  
Grammatical theory sets out criteria for grammaticality.  What are
these criteria, and what precisely do they state?  Basically, such a 
'criterial theory' specifies an *extension* that agrees with the acceptance/
rejection judgments and intuitions.