As much as I would love the opportunity to be "cute and clever", the 2 dogs analogy was not MY take on anything, I was writing it by hand as the Judge was saying it, so you may need to send a little note to him instead!
I thought that the inference was pretty obvious, but apparently not, so here is some more clarification:
Judge Goodman was discussing Direct vs Circumstantial evidence.
Judge started by saying a dog owner puts food in a dish, watches the dog eat it, it is direct evidence. If same owner leaves the dog alone with full bowl, is out all day and returns and the food is gone it is circumstantial evidence, which is a legal term to describe indirect evidence.
He later returns to the dog analogy when discussing Proper Inference vs Inproper Inferences.
Proper Inferences can come from wisdom and life experience. They cant be speculation or conjecture.
The Judge then says now imagine the previous example with 2 dogs instead of one left with a full food bowl, and owners returns and it is empty. The owner will now not be able to properly infer about which dog ate the food, or if both dog ate some.
Judge then went on to say another example: Imagine my friend Richard thinks our neighbour won the lottery as he is over the moon happy and smiling. Yes this is consistent with winning the lottery. However, there are also countless reasons that have nothing to do with the lottery. It would be a wild guess/speculation and therefore an improper inference.
However, if I also heard that somebody in my small town had bought the winning ticket, the neighbour abruptly quit his job that he has always loved, and bought a brand new ferrari....
Judge speaking further on making inferences: Sometimes just because an inference is difficult to get to does not mean it is not valid. Also, sometimes there is more than one inference. Eg. If I left a hotel and there are puddles on the sidewalk I can infer that it rained. However, it could also be that the sprinkler system came on and soaked the sidewalk.