Well, this topic would be easier if we distinguished ourselves as either part metaphysical (soul, mind, etc.) or as purely physical. Since it seems we're on the basis of purely physical heres my few bits:
1. Our intelligence level, of course. This is in the sense of many things. We have the ability to comprehend logic and advanced problem solving methods. We are incredibly algorithmic. To the extent that we could never be recreated by a computer or anything else of the sort. This is especially apparent in our ability to create and comprehend mathematics.
2. Our innate prioritization. Our ability to comprehend and think for ourselves, somehow, in my opinion, allows us to prioritize our knowledge over much of our instinct. This is not always necessarily true, but this is especially apparent in ethics. Although there is the occassional dog that runs in to save a baby from a burning fire (I know you have your stories) we can do it consistently and with reason. Likewise, for example, if we were to be starving, we would know how and why to divide up our food at different times, instead of being overtaken by the compulsion to just eat. Our intelligence and experience is prioritized, in many circumstances, over innate instincts and feelings.
3. Pattern recognition and imaginative understanding. We have extremely complex pattern recognition abilities. You ever had that experience, where you think you look at the clock the same time everyday? Well you most likely weren't, you probably look at the clock different times everyday, but your mind is constantly hunting for patterns, and if you look at it twice in a row, or say, 4 times in one week, at the same time, it'll let you know. Imaginitive understanding again is important. We have the ability to mentally process things that we have no experience of. Language, ideally, should portray what we mean. Sadly, it does not (read Wittgenstein).
For example:
"My arm is in pain." Ideally, you should not be able to understand that sentence unless your arm has been in pain. Or, if it was a much more amazing language, it would actually create pain in your arm, or give you the immediate understanding of what's attempted to be portrayed.
However, instead we can imaginitively process. We know the definition of those words, and can apply them through our logic. Likewise, if I've had pain in my leg, I can imagine what pain in my arm might be like.
Pattern recognition and imaginitive understanding combined can be apparent in superstition, and religion (no offense). You find a coin tails up, and have a bad day. One week later, it repeats. You see the pattern, tails up coin picked up= bad day. Hence, superstition. You see a pattern and imagine what it means and why it is.
I'm sure there are many more, but I don't think people would keep reading
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Best wishes,
Theo