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> Why should a human have a moral responsibility towards non-humans, while a cat doesn't have a moral responsibility towards non-cats, just because the human is capable of making moral judgements?

Because as a human you recognize patterns in other animals that are similar to ours - the deepest pattern being alive - so you can project your feelings over them. This is also called empathy, and some in our kind lack it completely, but I would dare to say that is globally one of the defining traits of the human species.

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You're answering a different question, which is "why do humans empathize with non-humans?" Humans can empathize with inanimate objects and with fictional people. The question of the origin of empathy really has nothing to do with what I asked.
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I think I do answered your question but maybe it was too implicit, so let me be more explicit. A human should have moral responsibility towards non-humans because of empathy and recognizing the fact that other animals are alive as well.
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Bacteria are alive too, and I'm going to guess you don't claim we have a moral responsibility to them. And as I said, humans can feel empathy for things that are not alive. The capacity to feel empathy rests entirely on the empathizer, and has nothing to do with any intrinsic properties of the empathizee. Is a psychopathic murderer morally in the right because he doesn't feel any empathy for his victims?
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It would be a great starting point if human felt moral responsibility towards other humans, before we take on the matter of ethics towards non-humans, simulated fireflies or LLMs. Yet here we are.
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