The phrase "impossibility of a complete" is grammatically correct and can be used in written English.
It is typically used to refer to a situation or concept that is unable to be fully achieved or accomplished. Example sentence: The impossibility of a complete cure for cancer continues to plague medical researchers.
As Merleau-Ponty (1962:xiv) famously wrote: "The most important lesson which the reduction teaches us is the impossibility of a complete reduction".
Then, of course, the unexpected happened when Gödel proved the impossibility of a complete formalization of elementary arithmetic, and, as it was soon interpreted, the impossibility of proving the consistency of arithmetic by finitary means, the only ones judged "absolutely reliable" by Hilbert.
Carol Karp remarks (1964, 166), "At the International Congress of Logic, Methodology and the Philosophy of Science at Stanford University in 1960, Dana Scott circulated an outline of a proof of the impossibility of a complete definable formal system for languages with a single two-place predicate symbol in addition to the equality symbol".
Besides muscle contracture and joint retraction, another possible cause of muscle hypertonia is the impossibility of achieving a complete muscle relaxation.
Embedded in it is the melancholic acknowledgment of the impossibility of ever having a complete view.
After surgical resection of the primitive liposarcoma, factors determining the probability of recurrence and survival are: histological type, the impossibility to perform a complete resection, the removal of adjoining organs and the advanced age [ 4].
The anatomical complexity of dental root canals represents a major limitation for a successful endodontic treatment, due to the impossibility of complete instrumentation.
Others recognized the impossibility of complete objectivity.
13 patients (20%) had initial endoscopic treatment of the disease; nonsurgical oncological therapy had been indicated due to the impossibility of complete resection of the tumor or because patients rejected radicalization procedures.
Every patient should, previous to operation, be clearly and frankly as possible told of the impossibility of restoration of complete normal joint function, and that the most he can hope for is improvement after a long and tedious treatment".
Now we can see the point of Kripke's analogy between the impossibility of a private language and the impossibility of central planning.
