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Sometimes my cat catches a bird or a rodent and doesn't finish it off. Should I take my cat to court?
Cat's aren't moral agents. You can't hold them responsible. You can, however, be responsible toward them; it's exactly like a human baby.
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I sometimes shoot my paint ball gun at rabbits to get them out of my garden, should this be a crime? They probably get a bruise.
You are attempting to minimize harm by doing so given all available options, so no. It's certainly worse to let your dogs on the garden rabbits and let them mangle them and leave them for dead then shooting them with a paintball gun. Using a dog to fetch a rabbit and then shooting it in the brain is less cruel. Using just the paintball gun is even less cruel. Using a loud noise that scared the **** out of them would probably be even less cruel. I'd honestly prefer that you go with a loud noise, but I'll take whatever I can get and just thank the stars that you aren't using dogs.
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What about my soda bottle wasp traps.
I don't have any idea, either about how those work, nor about the capacity for a wasp to suffer.
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I'm curious, what would be your minimum "cruelty" needed to go to criminal court?
Any cruelty at all... exactly as it is for humans.
Cruelty at the very least involves some sort of egregious harm, where it is not justified by any practical matter, or where there is a conscious attempt on your part to inflict pain rather than kill as painlessly as possible, or in cases of negligence where you should have known better, what the consequences of your actions would have been. Slapping your cat on the nose to discourage it from eating your chicken isn't cruel; holding its face to an electric range is.