What do you call a word that was invented or redefined by someone, but only used by that one person?
I think "neologism" is the general case, but I am not sure if there's a word for a neologism that's specifically used by only one person, or rarely used by anyone else. Is there any related word?
For example:
This philosopher uses a lot of _____, which makes him impossible to understand.
The term jargon refers to special words used by a group or a profession. It wouldn't make sense if your philosopher was talking to other philosophers, but otherwise it works well in your sample sentence.
Sniglet is too obscure and refers to deliberately constructed joke words (e.g. luposlipophobia, fear of being chased by wolves while wearing socks on a slippery floor).
If you say he coined a term or used a neologism, both imply he created a term that became generally used, which is not the case here.
To emphasize that these words are invented by and known only to the philosopher, I would call them nonsense words or non-words or just made-up words.
One term you could use is sniglet, but you should know that sniglet is a sniglet in its own right.
The term sniglet might go unrecognized by people who are not familiar with the pop-culture reference. Originally, most sniglets were designed to be more humorous than functional, but I’ve heard the word sniglet used on occasion. It was used in this 2011 blog post, for example, and was also apparently used in a New York Times crossword puzzle last year.
For the record, I think your suggestion of neologism would work better in a lot of contexts (particularly more formal ones). Nevertheless, sniglet is a viable informal term that could be used. (I almost didn’t even leave it as an answer, but opted to do so when I found the Wikipedia article about sniglets.)
These are sometimes called "nonce word". It comes from the (old, rare) expression "for the nonce" meaning "for now but not for later". It applies to words that seem to have been used only by a single author, and often only used once by that author.
Such words are also called "nonces". The term has been in use since before 1910. It was coined by the editor of the OED (who had to understand and define nonce words in old texts)
Note that "nonce" words are not "nonsense words" The meaning and etymology are different. A nonsense word may, or may not be a nonce.
