The problem with your argument is computers and animals are not cogitative, in any way similar to humans. There might be instances when animals come close, but that is no reason to imply all animals can. That means some come close.
Furthermore, I'd say that your over-focus on reasoning is misguided. There are many aspects of cognition and consciousness, and reasoning is just one of them. (And, as others have mentioned, there's plenty of evidence for various forms of abstract reasoning in studied animals.) Wikipedia's article on Animal Cognition has a convenient listing of different aspects that have been studied:
"The core difference between humans and animals is that humans can reason; we possess cogitative powers." (I have emphasized the point that was missed.)
A core difference between humans and animals is the cogitative powers of humans. Animals simply do not show the same cogitative powers. Animals do have cognition. I don't question that at all. I'm saying, in regards to cogitation (introspection), animals pale to humans.
For instance, your invocation of "introspection" is covered in the linked article by "theory of mind". And maybe in the second paragraph covering metacognition in "consciousness". I think this quote covers the ideas succinctly:
"Convergent evidence indicates that non-human animals have the neuroanatomical, neurochemical, and neurophysiological substrates of conscious states along with the capacity to exhibit intentional behaviors. Consequently, the weight of evidence indicates that humans are not unique in possessing the neurological substrates that generate consciousness. Non-human animals, including all mammals and birds, and many other creatures, including octopuses, also possess these neurological substrates." [0]
We've found evidence in some animal or another for pretty much everything we've ever thought was unique about human cognitive abilities. So far, the only unique thing about humans is how broad and powerful our cognition is. Which is maybe what you mean, and are having a hard time expressing.
[0] http://fcmconference.org/img/CambridgeDeclarationOnConscious...
Meanwhile, anyone who has a dog knows they have both dreams and nightmares, which is certainly some form of internal contemplation.
with us, unlike other animals, those limits are set by the linguistic expression of thought. If one has mastered the use of tenses and of temporal referring expressions, one can think of the past and the future. One can remember not only where – as exhibited in an animal’s seeking or homing behaviour – but also when. Non-human animals may prepare for the future – bury food for later consumption, build dams or dig burrows, but only man can plan for the future."
What particularly defines an "internally rich contemplative life" besides what is possible for humans, and not assigned to animals by humans?
Animals have an internal life. They are conscious. But by what means do we have to understand them as self-conscious? Can they distinguish between myself and my self? There is considerable debate about this. You end up in philosophy. You end up in conceptual analysis.
Eventually, it comes down to principles of sense and nonsense in language. What does it make sense to say of animals? Does it make sense to say a dog is planning for the next walk on August 30th? Or does it make more sense to say I think he is planning? The two say imply different things about the dog's capabilities.
Monkeys, crows, ravens, octopuses and other animals have been shown to be able to do stuff like this.
> but that is no reason to imply all animals can
I don't think anyone was making the claim that all animals can. (In case you're not a native english speaker, GP said "all sorts of animals", which means "many different kinds of animals" and not "all animals")
Obviously yes. There's nothing special to reason that requires a human.
Animals can solve puzzles. Solving puzzles, however, doesn't mean you can reason in the same way humans can. For instance, humans can ask why they are solving the puzzle. That's an expression of cogitative ability that animals don't have.
And we are fully capable of investigating that reason, that why, to find out whether it is reasonable or whether a better why can be provided. Animals cannot assign a reason, nor can we "investigate an animal's reason", because that's nonsense. Animals don't give why's.