Classically a statement is either true or false, there's no in between. The idea that something can be nearly, somewhat or a little true, like the truth even if false is something that seems obvious. Saying just what it is for a statement to be "like the truth" is, though, a bit of a bugger.
Its a problem though that I thought I'd have a crack at and have written a first draft of some thoughts on the issue. I would be very grateful for any comments. As the draft includes diagrams, changes in formatting etc. I've put it in a PDF and uploaded it to Google Documents.
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