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Math is a product of your brain.

I disagree. The symbology is a product of human brains. "9" means what it does because humans have created that symbol and assigned a specific meaning to it. But regardless of the symbols used, 2x9=18 is a fact that is completely independent of whether humans ever existed. If 9 asteroids 5B years ago collided and split in two (each), you then have 18 asteroids...and 5B years ago there were no humans. Or back it up to 12B years ago and there almost certainly was no organic life anywhere. I believe it is a subject of much philosophical debate, but it appears that math (which is arguably the language of logic) is innate to the universe. It is independent of our brains, and is mostly discovered by us.

Not to put words into your mouth, but I think you assume your brain IS trustworthy unless proven otherwise

Sort of. I have to proceed in that way because there's really no practical alternative. But I know that may brain is unreliable. And so is yours. And Brian's. And benjd25's. They deceive and/or fail us routinely. I can be aware of that, and still proceed on the assumption that my brain is processing sensory input and reaching adequate conclusions to keep me from walking off a cliff.

Yes, I lead my life as if free will exists because there isn't a viable alternative. Further, I cannot know all the of the influences that have put me here, and you there, interacting in this forum, so that beyond the next few seconds I cannot predict where any of this will go in detail. So it appears I have free will (and you do) because I simply don't know what comes next. If I had perfect knowledge I could predict what will happen (outside of quantum effects, of course). But I don't, so it's all a "surprise", and my reaction to it is not anticipated until it happens. Looks like free will, but I don't think it is.

If I assert that I "feel" nauseous and you claim my feeling of nausea is false and I am delusional, who has the burden of proof?

I'm not asserting you don't. I'm saying I have no evidence, and the burden is on your to prove otherwise. This overlooks the magnitude of the claim. If you say you're nauseous, I'll be inclined to take your word for it. I know people get nauseous. I know what that is. And there is very little risk in my taking your word for it. It's a trivial claim, and I would be prone to accept it at face value. Same if you said you had a dog named Jim. People have dogs, people name dogs, and 'Jim' is a name one could give a dog. Fine. On the other hand, make an extraordinary claim such as "god loves you, and you have to obey these rules", I'm gonna require more than just your say-so. The more extraordinary the claim, the more extraordinary the evidence for that claim needs to be. The burden is definitely on the person making such claims.

Not clear to me that "no free will" makes fewer assumptions than free will.

Just to reiterate, my position is that I don't believe there is free will, NOT that I believe there is no free will. The claim that it's a property of matter would have to be demonstrated. Other than that, there is physics and a causal chain of events stretching back at least 13.8B years. If there is anything additional, it is not yet in evidence.
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