Is free will binary or a spectrum?

the want to deny a piece of cake could just be another urge that you do not have control over

Was gonna say this Furthermore, the fact that you didn't consider the infinite "possible" paths of action is another proof of the limit of our freedom. Why is it more likely for you to follow a basic schedule, performing normal activities everyday, rather than randomly screaming, catching fire to yourself, walking 2 steps to the left, running 20 steps to the right, kissing the closest object, blinking repeatedly, etc?
Everything you do is just a result of the most powerful desire at the moment. Not eating the cake is a rational desire; you know that not eating it produces a physical benefit. So, the desire not to eat the cake was simply stronger than the desire to eat it.

>Not eating the cake is a rational desire; you know that not eating it produces a physical benefit.
You think people always make decisions based on what rationality determines is beneficial to them? Also you're being pedantic with regard to the infinite number of choices. I was making the point that free will is the ability to choose any action you want regardless of stimuli. You could choose to walk away, there are many choices while a person without free will is railroaded along a path where they have no choice but to follow base urges.

I can choose to perform any action I want at any time. I don't need any rational explanation, in fact I could do something incredibly detrimental to my wellbeing like smashing my hand with a hammer. That's how I know I have free will. The ability to choose any action available to me at any time, not just being corralled into specific choices based on programming.

I don't understand why you seem to believe being insane implies freedom?

>if I do have free will then I can simply choose not to eat it
Refraining from eating a cake isn't a magical behavior exempt from causality. You can neither eat a cake nor refrain from eating a cake without there being physical causes for your behavior. The fact there are multiple competing processes in your brain isn't an indication of "free will," it's an indication that the brain is more complicated than a single yes/no circuit, which shouldn't be surprising because plenty of other phenomena in the world are more complicated than a single yes/no circuit. Does the weather have "free will" because more than one competing process determines its behavior?

So? Free will isn't incompatible with the physical processes of the brain. You're spouting middle school brainlet tier misunderstandings.

It seems you think stimuli can only be external. Why can two people react differently in the same environment? Internal stimuli. Is it possible that external stimuli produce internal stimula, which you realize consciously, but didn't produce, leading you to think you did produce your thoughts? What makes you think walking away isn't the result of a biological desire? I want to know why you think it's impossible that you don't have free will. Consider these questions:
Do animals have free will? Does A.I, such as a chess engine, have free will?
Can you control, plan, and pause your thoughts? Can you change something you love into something you hate, and vice versa? If your brain is made of chemicals, and chemicals follow the laws of physics, is your brain not determined? If you have a soul, and it has substance, is it not also determined? Could you have more free will than you do now? Does God have more than you? If your will is free, what is it free from?

I don't understand why you think sane implies freedom?

>Is it possible that external stimuli produce internal stimula, which you realize consciously, but didn't produce, leading you to think you did produce your thoughts
No. Back to smoking weed and thinking "deep thoughts" with you.

our brain reacts to external stimuli and produces a result.