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If we are purely deterministic, then no, there's no difference. Math only exists in our minds, so to me, if there's no consciousness, there's no math.

I didn't say we aren't conscious. I said that our consciousness is deterministic, i.e. we give the same outputs when we receive the same inputs. We are just a "physical structure and reaction."

I'd still like to know what you think about the Chinese room thought experiment. It seems very relevant to our discussion.

Why do you assume that we are deterministic? Don't you think it at least seems like we make choices?

We do make choices. I never said or even intentionally implied that we don't.

Determinism is simply the idea that everything in the universe has a causal relationship with everything else in the universe, and can only behave in one way. For example, let's say that I decide to eat a pizza for lunch instead of a salad. A determinist would say that all my past experiences, as well as the environment around me, and countless other things directly caused me to choose to eat the pizza.

Notice that from the deterministic perspective, I actually make a choice. I use all my memories to weigh both options and choose the one that benefits me the most.

Please, listen to the Radiolab clip I linked to. About five minutes in, they tell the story of a woman with transient global amnesia. It is an excellent example of human determinism.

I think most people (including me) would define "choice" in such a way that determinism contradicts it. If there was only ever one possible outcome, no choice was made, only the illusion of one.

I believe that humans are like computers; we have inputs and outputs. When we have the same inputs, we will have the same outputs.

But, we still make a choice. The woman in the clip decided to say the same things over and over, because her inputs were roughly the same.

Well, you're free to use the word that way, but I definitely assign a different meaning to the word, and I bet most people do too. To me, it sounds like the difference between perceiving a choice and actually making one.

Well then, how do you personally define the word "choice"?

Deciding between two potential outcomes. If there was only one potential outcome, it wasn't a choice, only the illusion of one. Real choice definitely implies free will and non-determinism.

But, in my example there were two potential outcomes, pizza or salad.

I'll try a new example: Alice has two options, she could have $1,000,000,000,000,000,000,000.00 deposited into her bank account, or she could have that much added to her debt. She weighs the two options, and decides to take the deposit because she perceives it to be in her best interest. She could have chosen the second option, but she didn't because she perceived it to not be in her best interest.

Alice's judgement is based on all her memories and past experiences, as well as her current environment, and many other small factors. In order for her choice to be non-deterministic, she would need to abandon all judgement and make her choice completely random.

So essentially, what you're saying is that in order to have freewill and have control over our fate, we need to make all our decisions completely random, without any consideration of how they effect us.

Not at all. You say: "She could have chosen the second option." But you also say there was never any chance she could have chosen the second option, because the series of events is deterministic. Do you really not see a conflict here?

Free will would allow Alice to choose between maximizing money, choosing at random, or simply pissing off Sheldor. In the first, picking the money is the rational choice. In the second, flipping a coin is a rational choice. In the third, not picking the money is the rational choice.

Memories and past experiences help judge what is the best action for each desired outcome, but don't restrict possible outcomes to a single one.

Yes, she could have picked the latter option. It was a potential outcome, as was the former. But, she did not. Why didn't she? Because she used her judgement and decided to pick the former.

Her knowledge and memories were the inputs to her judgement, and her decision was the output. Technically speaking, she did not have free will as her knowledge and memories were acquired from prior events. But, to have free will, she couldn't let prior events determine her decision, so she would have to abandon her judgement.

In conclusion, you can keep your free will,

I will choose a path that's clear
I will choose rational judgement.

Most people would choose the first, and again if repeated. But because there is an economic force acting against free will. Determinists find it fun, liberalists see it with horror.

It IS possible to destroy someones free will through force. Liberalists fight those situations so people can exert their free will without being opposed by externalities.

Another example, gravity. A determinist would brag no one can fly and there is no choice. A liberalist would build an airplane so people can choose to fly or not.