I don’t know if infinitesimal logic is the best idea I’ve ever had, but it’s definitely the best name.
So here’s the idea: a multivalued logic in which there are truth values that are not nearly as true as ‘standard’ truth, and others that are not nearly as false as ‘standard’ falsity.
An example should help. Suppose you go to the travel agent and ask if if you can get a flight (1) to Ottawa and (2) in an aisle seat. If the agent says “yes” (meaning true in the standard sense), you’re done. However, if the agent says “no” (meaning false in the standard sense) you don’t know where you stand – maybe there is no flight to Ottawa, or maybe you just can’t get an aisle seat. You can always ask another question, but it would have been more helpful if the agent had given you some indication of the difficulty of flying to Ottawa in an aisle seat.
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