Of misuse of syllogisms!
Personally, I like syllogisms because they are a very elegant argument and easy to use... however, these suckers are also quite easy to use to argue false points...
Here is a syllogism that is used correctly. I will use it to demonstrate the flaws in the arguments:
All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.
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P1. The experience of free will is no more than an appearance.
P2. If the experience of free will is no more than an appearance, then people don't really have free will.
C1. So, people don't really have free will.
What proof do you have that free will is no more than an appearance? In my example syllogism, we have proof that men are mortal, and that Socrates is a man, but in your syllogism, we have no proof that free will is no more than an appearance. Nice attempt but... NEXT:
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P1. If a choice is free, then it is not caused.
P2. If a choice is not caused, then it is a random occurrence.
P3. But, if a choice is free, then it is not a random occurrence.
C1. So, if a choice is free, then it is both a random occurrence and not a random occurrence, which is impossible.
C2. So, no choice can be free.
In all 36 definitions of the word "free" on the online dictionary, I saw no definition that stated that something "free" is not caused. That may possible be a scientific or mathematical definition somewhere, but scientific or mathematical definitions usually don't work in philosophy. Thus, the rest of your argument does not follow, and is in fact, somewhat ridiculous. Here is my definition of free will:
free: the power to determine action without restraint.
will: the faculty of conscious and especially of deliberate action; the power of control the mind has over its own actions:
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P1. Whatever future events will happen, it is now true that these future events will happen as they do. (E.g., if I will in fact sing tomorrow, then it is true, and it is true now, that I will sing tomorrow.)
P2. If it is now true that these future events will happen as they do, then it is now not possible for anyone to bring it about that any of these future events will not happen. (E.g., if it is now true that I will sing tomorrow, then it is now not possible for me to bring it about that I will not sing tomorrow.)
P3. If it is now not possible for anyone to bring it about that any of these future events will not happen, then people are not free with respect to any future events.
C1. So, people are not free with respect to any future events.
Unless you are either god or a fortune teller, you can have no way of knowing what is going to happen tomorrow. I personally doubt the existence of both. So, your argument does not follow. I can SAY "I will sing tomorrow", but if this evening I'm in a car crash and end up being unconscious tomorrow, it's pretty certain I won't be singing. Your first statement is flawed, and thus the other statements fall apart under it.
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P1. Computers can perform every task that people can perform.
P2. Computers do not have free will.
C1. So, no task that people can perform requires that people have free will.
P3. If no human activity requires free will, then we have no reason to believe that people have free will.
P4. If we have no reason to believe that people have free will, then we should not believe that people have free will.
C2. So, we should not believe that people have free will.
First of all, let's pretend that this is 1000 years from now and computers can, in fact, do everything that people can.
The main problem with your argument is P3. We call this a slippery slope. If no human activity REQUIRES, free will, you argue, then there is no free will.
However, your conclusion does not automatically follow. What if we have free will anyway? Computers and humans are completely different constructs. Computers make a choice based on programming, and humans make their choices based on.... what? Some may say there's a god, but others may say that god has given us free will. There is no proof for or against. Unless you're willing to attempt to prove that people are computers, your argument, again, has a shaky foundation.
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P1. Things made only of matter can only have actions that are caused.
P2. Things that can only have actions that are caused do not have free will.
C1. So, things made only of matter do not have free will.
C2. So, if people are made only of matter, then people do not have free will.
Again, you're using science (Isn't science fun??!!) to argue about human actions. True, in science, there is only potential or kinetic energy, and objects with energy transfer it to others, giving objects kinetic (active) energy. Humans are matter, this is true, and our MATTER may not have a lot of free will... however, who decides what our matter does? We do! We have the ability to decide what our bodies do. If you were to actually believe your above argument, there would be no need to get up in the morning. We'd just sit around and wait for stuff to happen to us. I sure hope it rains, 'cause I'm thirsty.
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P1. The entire human body (including the brain) is made up of cells each of which has no freedom of choice.
P2. If the entire human body (including the brain) is made up of cells each of which has no freedom of choice, then a human being cannot have freedom of choice.
C1. So, a human being cannot have freedom of choice.
I'm sure that there's a name for the fallacy you made here, but I can't remember. You're right, in the sense, that cells probably don't really have conscious thought, and probably don't actively choose what they do. However, the brain is BUILT of cells, it isn't just a bunch of cells... and when those cells are put together they create something (the brain) that DOES have free will. The qualities of the parts do not reflect the qualities of the WHOLE.