The theory of Stickiness

Concerning the problem of how a thought and its constituents bind together and how this binding imposes structure on the thought, Frege appears (according to King) to posit the following theory:  the senses of words in a sentence are the constituents of a thought.  These senses bind together to build a thought by means of an unsaturated sense being completed or saturated by other senses.  Finally, the way the words are structured in a sentence is mirrored by the structure of the senses in a thought.  For Frege, a thought must contain an unsaturated sense to hold the constituents (the other senses) together; it is the binding glue, so to speak.  An unsaturated sense must be completed by some other sense to have a thought.  Without going into detail how this works, I will turn to the criticism that King makes of this binding glue. 

King notes that while it appears we have been given an answer to the concerning problem, we have in fact been given very little to account for the binding of the constituents of a thought.  Attributing the binding power simply to the unsaturatedness of some constituent of a thought seems no better than claiming that the constituents of a thought hold together because some parts of a thought are “sticky”.  If this criticism holds than what is needed is a substantive theory of stickiness to provide a real account of binding, but we do not have this substantive theory, so Frege’s original theory seems at a loss of explaining.  We may construct the problem as follows,

1.  Either we do not have a real account of binding or we have a substantive theory of stickiness.

2.  If we do not have a real account of binding, then it is not the case that constituents of a thought bind together due to the unsaturatedness of some its parts.

3.  We do not have a substantive theory of stickiness.

4.  Therefore, we do not have a real account of binding. (1,2 DS)

5.  Therefore, it is not the case that constituents of a thought bind together due to the unsaturatedness of some its parts.(2,4 MP)

This argument seems to follow, and I agree with King that were we at a loss for some theory of stickiness beyond thinking that sticky parts hold a thought together, then we would lack a real account of what binds the constituents of a thought together.  However, it seems that we may resist granting truth to premise (3) by the following considerations.  To my untrained eye it seems that Frege still has some room to provide at least a proto-theory of stickiness which essentially derives its explanatory power from syntax rules pertaining to the language and sentences therein.  So, we can say for instance, that since concept words are predicative, then things that are predicative in a language constitute unsaturated concepts which contribute senses to our thought in question.   Also, just as is required by our syntax that a predicate alone does not make a sentence, then we require something else, either a subject, or another unsaturated concept, or a relation, etc to combine to make a sentence.  And each part contributes its part to the sentence which then expresses the thought. 

However this seems a little too obvious and so simple a referral to be a suitable consideration as a solution.  Perhaps I have not grasped the gravity or complexities of simply relying on syntax to determine how constituents of thoughts may be held together.  Furthermore, this would of course not solve much, since the problem of the arbitrariness by which we chose syntax rules arises and we have no absolute reason for why syntax rules should determine how things are ordered and held together.  Any suggestions?