i know you have an issue with that, that was the point of my message. that Gettiers problem is not with the logical leap of faith required for the law of transitivity of identity but yours is. The statement, the winner will have ten coins in his pocket, is a true statement which qualifies for the third condition of knowledge. You want to ask that the statement isnt true because the winner described in the original statement is Yoeli. But without the background information that you have, if C would have just said out loud, that the winner will have ten coins in his pocket, without explaining how he came to that conclusion, wed have to check his pockets when he won and then confirm that the statement was true. the fact is that that statement is true and thats the important part of the problem. the question with that is that although all the conditions are met, we cannot suggest that Chaim knew that the winner had ten coins in his pocket as he didnt know what was in his own pocket.
As for your problem with transitive properties, consider:
A. elephants are grey
B. Steve is an elephant
The knowledge of A and B gives us the right to deduce c, that steve is grey. we can phrase this in a few different ways and still draw similar conclusions, we dont need to phrase it in every possible way. we dont need to say that steve the elephant is grey, just that steve is grey.
in the same way.
A Yoel will be the winner
B Yoel has ten coins in his pocket.
This allows us to deduce that the winner has ten coins in his pocket. at the time that this assumption is being made, we believe that Yoel will win and we are justified in beleiving so which validates the entire thought process. The conclusion to this line of thinking is that the winner has ten coins in his pocket.
was that any help?