Greg Egan's Axiomatic.

This is his first collection of short stories. Half of them are fictional explorations of what it would really be like, for the mind to be literally a physical process of the brain, usually with some near-future technology thrown in to sharpen the issues. The title story is about choosing your own utility function, "Learning To Be Me" is Philosophy of Uploading 101, "A Kidnapping" is about stealing a copy of someone's upload, and the others look at other aspects. "Seeing" uses no future science, only present-day knowledge, but is still squarely a science fiction story -- the science just happens to be already here.

Another strong theme is ethics, and especially the ethical issues that arise from our greater physical understanding of what people are: "Blood Sisters", "The Cutie", "Appropriate Love", "The Moat", "The Moral Virologist", and again "Axiomatic".

"The Hundred Light-Year Diary" is about predestination and free will, a theme that appears in several of the other stories. "Whatever the unchangeable future holds, I'm sure of one thing: who I am is still a part of what always has, and always will, decide it." (A theme of Eliezer's on occasion.)

One story is about the many-worlds theory, and another is about the exponential probability distribution.

After which you can read his second short story collection.