The soul is what animates [anima] and all living things have a soul, though only human persons have an immortal soul.
The way the philosophers of the Church put it, the soul is the vital principle of living organisms. This applies to man, animal, plants and bacteria (many of which are either/or/both plant and/or animal).
Mithrandylan is correct. Animals have material souls that perish when their bodies do. So Patches and Fido won't be greeting us in the World to Come...
The fact that this troubles so many people (many in my own familiy, in fact) is evidence that we as a culture have taken our affection for our pets much, much too far.
When an animal or plant dies, its material soul returns to the potency of matter.
This teaching is troubling to many moderns because we live in an age of great confusion, and many people don't know what to believe. Add on top of that the fidelity, constancy and companionship that animals offer as pets, and it is understandable on an EMOTIONAL level how people today may be unwilling to let go of their expectation to have their favorite pets with them in paradise.
I have known otherwise solid Catholics who have said, "If heaven means not having my pet Fifi with me forever, I don't think I want to go."
When there has been no human being who has given them the "good feelings" they get from their pets, AND they base their faith on emotionalism, the consequence is this error. But the ROOT error is basing our faith on emotionalism. That is essentially Modernism, to say that religion is a 'feeling' -- or, in the most distilled version, "God is immanent." That is Modernism in its strictest essence.
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