Inductive logic is not even remotely illogical - it's just a different type of logic.
For example, my first year Critical Thinking lecturer (a fantastic bloke named Ross Phillips) introduced the concept of physical possibility along these lines.
"Is it possible to drive from here to the city in an hour?" he asked the class. We answered the affirmative - from my uni to the city takes about half that time by car.
"Okay," he went on, "Is it possible to get to the city from here in thirty minutes?" Again, we replied in the affirmative. It might sometimes take longer, but good luck with lights and traffic would get you there within half an hour.
"How about twenty minutes?" he asked. We paused, and replied that it was possible, but you would have to speed and run red lights to do it.
"Ten minutes?" This time, we really thought hard and argued a bit amongst ourselves. We concluded that it would be possible if you were an excellent driver in a fast sportscar, and broke almost every road law in existence.
"Alright then... could you do it in five minutes?" he finally asked. We all agreed that five minutes was pretty much impossible, unless you had access to some kind of top secret military automotive technology - rocket-powered car, or something.
Now, there is no sharp line where the possible and impossible meet, in this instance, but most people would agree that you can't travel thirty kilometres by car through a city in five minutes, legally or otherwise. It's a fuzzy border, but that doesn't make it irrational or illogical.
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