grammar - "causative of negative" vs "negative of causative"?

Wikipedia (Japanese Verb Conjugation):

Negatives [verb negative-conjugations] are not normally made into causatives. Instead, a negative ending is added to the causative of the verb. Thus, for example, Tabesasenai: "Do not let eat".

From the quote above, we can see that although negatives are not normally made into causatives, they can be made into causatives.

What is the difference between a causative-of-negative and a negative-of-causative? How do we decide when to use which?

For example, what is the difference in nuance between「これを食べさせない」and「これを食べなくさせる」?

Answer

Causative has two meanings: forcing and allowing. Let me first illustrate the semantic distinction considering only "forcing":

• Negation of causative of P = "not force doing P"


• Causative of negation of P = "force to not do P"

In general, there is a mismatch between the hierarchy in the syntactic structure (at the surface) and the hierarchy in the logical structure. For example, the English expression I cannot do P does not mean "It is possible ('can') for me to not do P" (potential of negation of P) but means "It is not the case that I can do P" (negation of potential of P). What the article is probably saying is that tabe-sase-nai syntactically looks like the hierarchy is "negation of causative of eat", but its meaning is "causative of negation of eat", or "forcing not to eat".

Now, there is the same semantic distinction for "allowing":

• Negation of causative of P = "not (particularly) allow doing P"


• Causative of negation of P = "allow not doing P"

Note that "forcing" and "allowing" are logically connected under the following formulae from modal logic (~ = negation, ◇ = possibility operator (i.e., "allowing" in this case), □ = necessity operator (i.e., "forcing" in this case)):

~◇P = □~P

~□P = ◇~P

From this, the expression tabe-sase-nai which means "forcing not to eat" can also be paraphrased as "not allowing to eat".