>For instance , there is no one reason that I am able to recognize a dog as such. Any feature or combination of features I can think of can be had in another animal. Something deeper is happening when I am able to correctly identify dogs that is unexplainable, at least by me.

Well, your categorization judgement is probabilistic. Some features make "dogness" more likely, some less likely. However, there is in fact a specific causal structure which constitutes dogness (ie: organism grown via natural reproduction along the canid species-history, with the accompanying genotype and within normal phenotypical variation). Your brain tries to learn a causal model which approximates the correct causal structure, given the evidence available to your senses.

Better: the human brain also seems to perform second-order inference, reasoning about which models predict most precisely, what's relevant to what, and which latent parameters in the learned causal model are most relevant.

So when you see a dog-like tail versus a cat-like tail, you can identify which apparent features are making you say "dog" or "cat" most strongly, which ones are the strongest evidence.