TITLE: Are there examples of mathematical problems proven by abduction?
QUESTION [6 upvotes]: Proof by deduction is  simple. For example:

All humans are mortal, and Bill is a human; Therefore, Bill is mortal.

However, proof by abduction differs. A famous example: 

The lawn is wet. But if it rained last night, then it would be unsurprising that the lawn is wet. Therefore, by abductive
  reasoning, it rained last night.

There seems like a subtle difference, but it's actually huge  as abduction is uncertain rather than certain.

Question 1 
Are there examples of mathematical problems that have been proven by  only abduction, rather than by deduction
  or induction?
Question 2
If there are examples of this, are they limited to problems related to probability?

Thanks.

REPLY [3 votes]: While I am familiar with the phrase "abductive reasoning", the phrase "proof by abduction" seems like an oxymoron.  Consider your example:  While it is certainly true that if it rained last night it would be unsurprising that the lawn is wet, and it therefore is a reasonable inference that it probably rained last night, that is hardly the only possible explanation for why the lawn is wet.  Other possibilities include:

Dew
An in-ground sprinkler system that waters the lawn at night (which is actually a very practical idea)

Since the idea of mathematical proof is to achieve certitude, no, there are no proofs by abduction.