Formal Proof About Classical Free Will

MichaelDonovan

United States1453 Posts

May 28 2014 20:21 GMT

Sup doods. I've been playing around with some logic lately. Kind of a fun little proof. Let me know what you think. I don't normally put formal logic stuff like this up here, but I figured I'd just see how it goes. Maybe you guys will appreciate this more than my prose type stuff. I dunno.

Some background information...

Classical free will is defined as "the ability to do otherwise." That is, if we have classical free will, then it means that when we do an action, it was possible that we could have made a different choice. For example, we could always just hold our breath and die instead of doing the action.

The classical free will thesis is just the thesis that says we have classical free will.

Hokay. So here it is:

Proof: The classical free will thesis is false.

If the classical free will thesis is correct, that is, if we have classical free will, then the following proposition is true:

Proposition (The classical definition of free will): If an agent did some action A, then it was possible for the agent to have done some contrary action B.

Definition: Two actions are contrary actions if an agent cannot perform both of them.

Contrapositive of the proposition: If it was not possible for the agent to have done B, then the agent did not do A.

We will attempt to disprove the proposition by showing that its logically equivalent contrapositive leads to a contradiction.

So we assume (for reductio) that it was not possible for the agent to have done B. If the proposition is true, then it should follow that the agent did not do A. We will show that this is not the case.

Let B* be the proposition that the agent performs action B, and let A* be the proposition that the agent performs action A.

Note that B is defined as an action contrary to A.

So by definition of B, we get the bi-conditional:

(1) B* <-> ~A*

This can be broken into the following:

(2) B* -> ~A*
(3) ~A* -> B*

Recall that we have assumed that B is not possible. Since B is not possible, we deduce:
(4) ~B*.
Thus,
(5) ~B* -> ~~A* by (3) Contraposition
(6) ~B* -> A* by (4) Double Negative Elimination
Therefore,
(7) A* by (4)(6) Modus Ponens

Thus we have shown that if B was not possible, then the agent must have done A.

Therefore, it follows from our proposition:

(8) "If it was not possible for the agent to have done B, then the agent did not do A."

that it was possible for the agent to have done B. (By (7)(8) Modus Tollens)

Therefore we have the following contradiction:
(P) It was not possible for the agent to have done B (assumed for reductio)
(Q) It was possible for the agent to have done B (deduced from (P))

Since our proposition defending classical free will leads to a contradiction, the proposition must be false. Because the proposition is false, the classical free will thesis is thus false by Modus Tollens.

SamuelGreen

Sweden292 Posts

May 28 2014 21:05 GMT

Indeed. Id even say free will as a concept can only be True if all human are equal (in all possible ways) and are not in need of essentials like food. As long as anyone has more power than me my will is not free. It may appear as though I have a free will. But since the goal for all is to live, I have very limited choice.

Just sayin.

MichaelDonovan

United States1453 Posts

May 28 2014 21:16 GMT

On May 29 2014 06:05 SamuelGreen wrote:
Indeed. Id even say free will as a concept can only be True if all human are equal (in all possible ways) and are not in need of essentials like food. As long as anyone has more power than me my will is not free. It may appear as though I have a free will. But since the goal for all is to live, I have very limited choice.

Just sayin.

Ok so a few things:

The goal for all is not necessarily to live. Suicide is a thing. Self Sacrifice for greater causes is a thing.

The question of free will is not a question of power or obedience. One with more power than you might be able to force you to do an action, and impose his will upon you such that you are a means to his end. However, nobody can ever force you to will that his end become your own. Coercion is against the will. The will itself remains unmoved.

What we're really talking about here is more like,

"If God knows everything that I will ever do, how can I ever do anything other than that?"

Or,

"If everything in the world since the big bang is governed by natural laws (like the laws of physics and whatnot), then are all my choices not just the product of a chain of cause and effect? In which case, is it possible for me to freely make a choice at all? Or is it the case that I was always going to do what I did and I never could have made any other choice?"

That kind of thing.

spinesheath

Germany8679 Posts

May 28 2014 21:17 GMT

So you have a contradiction if you assume that there is some B that was not possible.

Then obviously everything is possible.

urboss

Austria1223 Posts

May 28 2014 21:20 GMT

On May 29 2014 05:21 MichaelDonovan wrote:
...
Note that B is defined as an action contrary to A.

So by definition of B, we get the bi-conditional:

(1) B* <-> ~A*

...

I'm confused here.
How can you make the statement that B is defined as contrary to A?

MichaelDonovan

United States1453 Posts

May 28 2014 21:23 GMT

On May 29 2014 06:20 urboss wrote:

Show nested quote +

I'm confused here.
How can you make the statement that B is defined as contrary to A?

That's just what we defined B to be in the original proposition. B is some action contrary to A.

MichaelDonovan

United States1453 Posts

May 28 2014 21:24 GMT

On May 29 2014 06:17 spinesheath wrote:
So you have a contradiction if you assume that there is some B that was not possible.

Then obviously everything is possible.

I don't think I understand what you're getting at.

L3gendary

Canada1470 Posts

May 28 2014 21:36 GMT

Even though I don't believe in free will this isn't a very good argument. Basically you said that A and B=NOT A need to be both possible for free will to exist. And then (with some added unnecessary operations) concluded that it's impossible because A and NOT A can't simultaneously be true (something can't be both true and false).

So this is just the old argument that any proposition (even those about the future) must be either true or false right now. In other words you've concluded that free will doesn't exist by assuming that logical determinism is true.

urboss

Austria1223 Posts

May 28 2014 21:42 GMT

On May 29 2014 06:23 MichaelDonovan wrote:

Show nested quote +

That's just what we defined B to be in the original proposition. B is some action contrary to A.

The way you are doing it, you are already negating free will in the premise itself.

The original proposition is A* -> B*.
Saying B is contrary to A already contradicts this statement.
That means, you can say B* IS NOT A*.
But you cannot say, IF B* THEN NOT A*.

ninazerg

United States7291 Posts

May 28 2014 21:43 GMT

#10

One time, I ate a potato and also didn't eat the potato at the same time. The really weird part of this is that I was eating a raw potato.

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pebble444

Italy2497 Posts

May 28 2014 21:53 GMT

#11

On May 29 2014 06:24 MichaelDonovan wrote:

Show nested quote +

I don't think I understand what you're getting at.

If hes thinking the same thing i am, then this: You are offering 2 possibilities and for the sake of your "proof" and then you are beforehand excluding the B. It think your proof is wrong: first of all, you are not limited to 2 choices. The choices are virtually infinite, and the only boundary to them is exactly how they say your imagination. If you can imagine it, then it is possible, if it respects the laws of physics. In a situation where you are presented with 2 different choices, you have more than 2. Its just you are not able to imagine having more than 2. Therefore the rest of the theory is wrong

In my opinion Free will exists and it is simply not applied most of the time. What generally people think is free will is defiled by peoples thoughts, their dreams, there desire to appear a certain way. Many a time do people do act of of free will.

Also sorry to say your example of breathing is wrong. The act of breathing is carried out most of the time and while you sleep by the sub-counscious mind. While you and me and any human being do excerise an amount of control over it, like holding your breath underwater, i dare you to find me 1 example of someone who stopped breathing volontairly, WITHOUT external influeces like say a bag for suffocation or a moment of extreme shock.

MichaelDonovan

United States1453 Posts

May 28 2014 22:02 GMT

#12

On May 29 2014 06:42 urboss wrote:

Show nested quote +

The way you are doing it, you are already negating free will in the premise itself.
I think you are mixing up the meaning of contrary.

The original proposition is A* -> B*.
And B is contrary to A.
That means, you can say B* IS NOT A*.
But you cannot say, IF B* THEN NOT A*.

The original proposition is:

If an agent did some action A, then it was possible for him to have done some contrary action B.

So there it is. B is an action contrary to A. That's just what it's defined as.

nunez

Norway4003 Posts

May 28 2014 22:02 GMT

#13

it was already proven in 1993 that willy is indeed free, by modus jackson (rest in peace).

airen

Sweden82 Posts

May 28 2014 22:08 GMT

#14

I also think that the assumption that "if I don't do A, then I must have done B" seems like the weak point. Otherwise the deductions seems to hold. You know that there is a branch of modal logic that deals with possibilities and necessities right? Using them you could formalize the entire thing much more.

I do believe in free will, in the compatibilist sense, however it does nothing against your argumentation.
Logic is about whether things can be deduced from assumptions or not, but it doesn't care about if we like the the assumptions or the conclusion. If the reasoning is sound, it is sound.
Check out Gödel's ontological proof for crazy assumptions.

2Pacalypse-

Croatia9505 Posts

May 28 2014 22:09 GMT

#15

A good video on free will by Sam Harris that made it painfully obvious (to me) that free will is an illusion:

MichaelDonovan

United States1453 Posts

May 28 2014 22:12 GMT

#16

On May 29 2014 06:53 pebble444 wrote:

Show nested quote +

B is not any particular action. B can just be anything contrary to A. So A is one action, and B is everything else.

Whether or not there are infiinite options or just two is not relevant to the question. In fact it's probably easier and better to just imagine for the sake of argument that there are only two options to keep it simple. Let's say you ONLY have two options. If you have classical free will, and you choose to do the first option, then it must be true that the second option was possible (and that you weren't fated to do the first option). This whole business about "infinite possibilities" is beside the point.

We are excluding the B before hand merely as a logical consequence of contraposition. Basically what it's saying is that if there was no contrary action possible in a world with classical free will, then the only possible explanation for this is that there was no original action A for it to be contrary to.

That's kind of a hazy way to talk about it, so let's just stick to the logic:

(1) If P then Q.
The contrapositive of (1) is:
(2) If not Q then not P.

Statements (1) and two (2) are logically equivalent, so disproving the statement in either form works just the same. I put the original proposition in its contrapositive form so that it's easier to work with logically.

The breathing example was just a hasty one. Basically all I mean by that is that if classical free will exists, then it's always possible that you could have not done what you did. Even if it seems like your options are really narrow, it's always possible to just remain inactive and not do the action, at least, if there are no other options. Like, it might seem like the only choice I have is to walk the plank, since the pirate is pointing his sword at me, but I always have the option of making him stab me or push me off the plank instead of jumping myself. I dunno these examples are all non-formal ones so it's easy to poke holes in them, but they are kind of beside the point since they are just illustrative.

MichaelDonovan

United States1453 Posts

May 28 2014 22:14 GMT

#17

On May 29 2014 07:09 2Pacalypse- wrote:
A good video on free will by Sam Harris that made it painfully obvious (to me) that free will is an illusion:

http://www.youtube.com/watch?v=hzj1helboAE

I would be wary of believing anything that seems to be "painfully obvious." If something like this were painfully obvious, we wouldn't be arguing about it for hundreds of years.

urboss

Austria1223 Posts

May 28 2014 22:18 GMT

#18

On May 29 2014 07:02 MichaelDonovan wrote:

Show nested quote +

Who has come up with this definition of free will?
Is this how logic defines free will?

It says that A* -> B* and A* -> ~B*.
This is in itself already a contradiction.
There is no need to further prove or disprove it.
The proposition itself returns already a false statement!

MichaelDonovan

United States1453 Posts

May 28 2014 22:19 GMT

#19

On May 29 2014 07:08 airen wrote:
I also think that the assumption that "if I don't do A, then I must have done B" seems like the weak point. Otherwise the deductions seems to hold. You know that there is a branch of modal logic that deals with possibilities and necessities right? Using them you could formalize the entire thing much more.

I do believe in free will, in the compatibilist sense, however it does nothing against your argumentation.
Logic is about whether things can be deduced from assumptions or not, but it doesn't care about if we like the the assumptions or the conclusion. If the reasoning is sound, it is sound.
Check out Gödel's ontological proof for crazy assumptions.

Well since B is by definition any action contrary to A, then the action of not doing A (perhaps even the choice of remaining inactive and not doing anything) is contained in B by definition. Does that make sense?

Regarding the modal bit, I actually wrote this proof in such away as to do away with modality. I wrote it so that it doesn't need modal logic in order to be valid. The only part where I use modal logic is where I say:

"Since we assume B is not possible (or ~PB or something like that), we conclude ~B*."

That is, since we assume B isn't possible, it follows that the agent could not have done B.

After that, modal logic isn't necessary.

MichaelDonovan

United States1453 Posts

May 28 2014 22:24 GMT

#20

On May 29 2014 07:18 urboss wrote:

Show nested quote +

Who has come up with this definition of free will?
Is this how logic defines free will?

It says that A* -> B* and A* -> ~B*.
This is in itself already a contradiction.
There is no need to further proof or disprove it.
The proposition itself returns already a false statement!

Classical free will is the old definition of free will that philosophers had been using for a very long time. It just defines free will as the ability to do otherwise. Meaning, if you did something, then looking back you could have chosen to do something else. Basically meaning that you aren't pidgeon holed into one choice by fatalism.

There are no a few other definitions of free will that compete with the classical version. I'm just tackling the logical inconsistency of the classical view here. I'm not showing that free will doesn't exist. I'm just showing that the classical free will thesis is incoherent.

Also, I think you might be misunderstanding the logic a bit.

What we have is the biconditional: B* -> ~A* and ~A* -> B*.

This is just from that definition of contrary action which says that you can't do both of them. Like you can't both slap your girlfriend on the ass and also not slap her on the ass. You either slap her on the ass, or you do something else.

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