A word for words that are both the same and opposite

Question

I just had a conversation where the sentence 'The system is broken because it's fixed!' was correctly spoken under the pretense where fixed means that it's rigged. Assuming that context of rigged matches as a weak synonym for broken, the question came up - what's the word for a pair of words that are simultaneously synonyms and antonyms?

I am not asking about autoantonyms. I am not even looking for a single word. I am trying to find a term to describe the relationship of two different words, where one is an autoantonym and where one of its definitions is synonymous with the second word, causing the two words to be synonyms and antonyms at the same time.

In my example:

• fixed = rigged: fixed and rigged are synonyms
• fixed = repaired: fixed and rigged are antonyms

What is the label given to the relationship between fixed and rigged?

Answer 1

You seem to describe an auto-antonym, "a word with a homograph (another word of the same spelling) which is also an antonym."

Fixed can be construed as an auto-antonym since it means both "working properly" and "not working properly—because rigged."

Any auto-antonym can be paired with one of its synonyms to create a pair of different words that are both synonyms and antonyms. For example, the pair fixed/broken. It seems doubtful that there is a special name for such pairs.

Here is the complete passage from Wikipedia which gives many alternative names for the phenomenon:

An auto-antonym (sometimes spelled autantonym), or contronym (also spelled contranym), is a word with a homograph (another word of the same spelling) which is also an antonym (a word with the opposite meaning). An auto-antonym is alternatively called an antagonym, Janus word (after the Roman god), enantiodrome, self-antonym, antilogy, or addad (Arabic, singular didd). It is a word with multiple meanings, one of which is defined as the reverse of one of its other meanings. This phenomenon is called enantiosemy, enantionymy or antilogy.