In his front pocket was a picture of his buddy in the Pinocchio costume from just prior to going out to the bar, and on the back of the picture in sharpie was written “Don’t believe his lies!”

I think you’ve been arguing this whole time about something completely different from what the rest of us are talking about.

It means given the exact same inputs that you’d get the same output.

This is why the comment was first raised about amnesia — it’s as close as you can be to getting “the same inputs” — the same person, the same situation, and the same memory each time. Each time it’s a fresh occurrence  no recollection of the previous times, and the person asks the same quite-random question each time.

Of course even in this case it’s hardly “the exact same inputs.” There is certainly changing brain state and some imprinting going on even for a complete amnesiac, and the situation itself isn’t aways exactly the same (people in different positions, different nurses, etc). It would be impossible to actually create the exact same state down to the very last atom. But would certainly be interesting if, hypothetically, the closer you got to replicating the exact same input state in a human, the more their outputs were identical. If this were so, it would be suggestive that humans are deterministic.

http://huntersfiction.blogspot.co.uk/2010/05/reset.html

Some times it really feels like what is happening is that the environment is triggering a thought that is on the cusp of something else. The way you might run your tongue over the gap where a tooth was lost, over and over, never quite finding what should be there.

But then I think the idea and the sensation of free will are psychological phenomena. Probably necessary ones though.

All of your examples either change the state (two different people) or change the inputs (a different environment). They are non sequiters, completely unrelated to the question at hand.

I’m not entirely sure what you think your arguing against, but it isn’t deterministic behaviour.

Deterministic != Predetermined

So in Memento he could retain a memory long enough to tattoo it but if that memory was about a person he would need to write or tattoo it before they left and changed the context. 

As for the 50 First Dates reference, I always wondered how she handled the pregnancy/labor they skipped over to get to the last scene of the movie – that would be utterly terrifying.

You’ve argued that if the inputs change, or if we swap in a completely different black box, the outputs change, therefore the black box isn’t deterministic, which doesn’t make sense. Deterministic means that the inputs are a major factor in the output, and so is the internal state of the black box. It doesn’t mean that all black boxes have to be identical. Deterministic machines don’t have to be set in stone, merely non-random. If the black box is a mathematical one, taking an input number, and adds to the result the number of times input has been recieved, you get 7>8, 7>9, 7>10, 7>11. The pattern isn’t set in stone, but it’s still deterministic. With the memory loss added, it forgets how many times it’s done the operation and we start getting 7>11, 7>11, 7>11. If you swap in 29 or any other number, the output will be different because the input has changed.
If we really had something resembling free will, and had an internal mechanism allowing us to choose in a way that wasn’t solely based on our initial state plus the current inputs, people with retrograde amnesia wouldn’t loop so neatly. Sometimes they would ask a question, but other times that same person would be able to deduce that the detail isn’t worth mentioning. When given a room full of different inputs to comment on, they wouldn’t always pick the same one each time they forgot that they had made a comment about the room already.