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Formal Proof About Classical Free Will - Page 4

Blogs > MichaelDonovan
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MichaelDonovan
Profile Joined June 2011
United States1453 Posts
May 29 2014 00:22 GMT
#61
Too many paragraphs gettin thrown at me. I'm gonna be a little slow with my responses as a result. Hang on doods.
ninazerg
Profile Blog Joined October 2009
United States7291 Posts
May 29 2014 00:22 GMT
#62
On May 29 2014 08:38 MichaelDonovan wrote:
Show nested quote +
On May 29 2014 08:36 ninazerg wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
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:



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.


So the length of time by which we argue something determines how obvious it may or may not be?

Determines is a wrong word. Indicates is might be better. What I'm saying is that if the guy in this video actually came up with a solution so obvious that you couldn't argue with it, then I would have heard about it by now, and there would be nothing more to argue. But since people are still arguing, his solution can't be all that obvious.


Why is "determine" the wrong word? You're the one who said "If something like this were painfully obvious, we wouldn't be arguing about it for hundreds of years." which sounds fairly definitive. It also surprises me that you hadn't heard of Sam Harris. I think you should check out some of his debates or lectures, they're very entertaining at times.
"If two pregnant women get into a fist fight, it's like a mecha-battle between two unborn babies." - Fyodor Dostoevsky
MichaelDonovan
Profile Joined June 2011
United States1453 Posts
May 29 2014 00:24 GMT
#63
On May 29 2014 09:22 ninazerg wrote:
Show nested quote +
On May 29 2014 08:38 MichaelDonovan wrote:
On May 29 2014 08:36 ninazerg wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
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.


So the length of time by which we argue something determines how obvious it may or may not be?

Determines is a wrong word. Indicates is might be better. What I'm saying is that if the guy in this video actually came up with a solution so obvious that you couldn't argue with it, then I would have heard about it by now, and there would be nothing more to argue. But since people are still arguing, his solution can't be all that obvious.


Why is "determine" the wrong word? You're the one who said "If something like this were painfully obvious, we wouldn't be arguing about it for hundreds of years." which sounds fairly definitive. It also surprises me that you hadn't heard of Sam Harris. I think you should check out some of his debates or lectures, they're very entertaining at times.


Sam Harris mainly deals with the kind of philosophy that I'm not interested in, so his name doesn't really come up.
MichaelDonovan
Profile Joined June 2011
United States1453 Posts
May 29 2014 00:29 GMT
#64
On May 29 2014 08:39 Ghanburighan wrote:
Interesting stuff, but here are a few issues:

a) You're using classical propositional logic to discuss possibilities, you'd need modal logic for a better representation. "Recall that we have assumed that B is not possible. Since B is not possible, we deduce: (4) ~B*." You can't do this formally without modal logic. And if you use modal logic, make sure you pick a system in which ~Diamond B* entails ~B*.

b) If you do adopt a modal logic, the original thesis would be better described as "at some point (world, time, etc.) where Diamond A holds, Diamond B holds as well."

c) I'm assuming you're utilizing material implication for "->" which has many known puzzles and problems. I don't think we can say much about free will or other concepts in a system in which B makes true A->B, i.e., where sitting in your office, makes true the statement: if you were blown up by a bomb this morning, then you're sitting in your office.

d) To attain (5) you make use of contraposition, but this rule doesn't correspond to our view of rational reasoning with probabilities. Consider Grice's Yog and Zog puzzle:

Yog and Zog are playing chess with special rules. Yog gets white 9/10 times and there are no draws. They have already played around 100 games, and Yog emerged victorious in 80 out of 90 of the games in which Yog had white, but Zog won all the remaining games. Now, the following two sentences have different probabilities.

a. If Yog had white, Yog won.
b. If Yog lost, Yog had black.

The probability that the sentence (a) holds is 8/9 but it is only 1/2 for sentence (b). The problem with this situation is that (a) and (b) are equivalent if analyzed as material implication. This is because when you play chess, you use either the white or black pieces. So, playing with not white pieces is the same as playing with black pieces. And losing is the same as not winning when draws are taken out of the rules of chess. So if (a) is represented by p -> q then its contraposition ~q -> ~p is (b). But equivalent sentences should not have different probabilities, 8/9 and 1/2, respectively.


a) It is at this point in the proof where I am able to get rid of the need for any modal operators. I only need ~<>B* to show ~B*. And yes, I should have included that somewhere in my proof, but I am assuming that B being impossible entails that B* cannot be true.

b) Sure, I don't see any problem with saying it like that. Modal logic gets kind of messy though sometimes, so I wanted to try to do away with it.

c) This objection would be problematic if it were not for the fact that all of my statements in this arguments are based only on the logical structure of the proposition. That is, we don't really care if it makes sense empirically. What we're showing is that the classical free will thesis is logically incoherent. This doesn't say much about free will. It just says that the way the classical thesis is written leads to contradictions.

So, the fact that being blown up this morning makes it impossible for me to be sitting in my office isn't really important. If it were, we would include that statement in our argument, and the contradiction would be clear. I'm not sure if this a sufficient response to your objection though, so hammer it a bit more if you're dissatisfied.

d) That's a fun example. I'll have to think about that for a bit. But I don't think it's a problem for my argument because we either have free will or we don't. We either do action A or we do action not A. It's not like If you do action B, then you probably didn't do A. Or something like that. When you have mutually exclusive sets, the probability of their intersection is zero since their intersection is the empty set. I dunno if that addresses the problem completely, so again, hammer it some more if you're not satisfied.

Lixler
Profile Joined March 2010
United States265 Posts
Last Edited: 2014-05-29 00:44:27
May 29 2014 00:43 GMT
#65
On May 29 2014 08:39 Ghanburighan wrote:
Interesting stuff, but here are a few issues:

a) You're using classical propositional logic to discuss possibilities, you'd need modal logic for a better representation. "Recall that we have assumed that B is not possible. Since B is not possible, we deduce: (4) ~B*." You can't do this formally without modal logic. And if you use modal logic, make sure you pick a system in which ~Diamond B* entails ~B*.

b) If you do adopt a modal logic, the original thesis would be better described as "at some point (world, time, etc.) where Diamond A holds, Diamond B holds as well."

c) I'm assuming you're utilizing material implication for "->" which has many known puzzles and problems. I don't think we can say much about free will or other concepts in a system in which B makes true A->B, i.e., where sitting in your office, makes true the statement: if you were blown up by a bomb this morning, then you're sitting in your office.

d) To attain (5) you make use of contraposition, but this rule doesn't correspond to our view of rational reasoning with probabilities. Consider Grice's Yog and Zog puzzle:

Yog and Zog are playing chess with special rules. Yog gets white 9/10 times and there are no draws. They have already played around 100 games, and Yog emerged victorious in 80 out of 90 of the games in which Yog had white, but Zog won all the remaining games. Now, the following two sentences have different probabilities.

a. If Yog had white, Yog won.
b. If Yog lost, Yog had black.

The probability that the sentence (a) holds is 8/9 but it is only 1/2 for sentence (b). The problem with this situation is that (a) and (b) are equivalent if analyzed as material implication. This is because when you play chess, you use either the white or black pieces. So, playing with not white pieces is the same as playing with black pieces. And losing is the same as not winning when draws are taken out of the rules of chess. So if (a) is represented by p -> q then its contraposition ~q -> ~p is (b). But equivalent sentences should not have different probabilities, 8/9 and 1/2, respectively.

that example in d looks funny. so let's get everything straight. there are 80 games where Yog is white and Yog wins. there are 10 games where Yog is white and Yog loses. there are 10 games where Yog is black and Yog loses.

let's look at our conditionals and count up how many times they hold.

a. If Yog had white, Yog won.
so there are 80 times when Yog had white and won. but our conditional is also (vacuously) true whenever Yog had black, whether he won or not (we might want to think about possible worlds instead of chess games following each other in time, but whatever). so there are 10 more times where our conditional is true, viz. the 10 times Yog is black and loses. so there are 90/100 times where this conditional is true, or 9/10.

b. If Yog lost, Yog had black.
now there are 10 times where both of these are true. but the conditional is also (vacuously) true whenever the antecedent is false. and the antecendent is false exactly the number of times Yog wins - 80 times. so there are 90/100 times where this conditional is true, or 9/10.

our conditionals have equal possibility, so i don't see any contradiction. i'd have to read what grice actually wrote in order to deal with the problem more exactly, though. i anticipate that he either conflates material implication and probabilistic thinking or uses the distinction to deflate the problem.
MichaelDonovan
Profile Joined June 2011
United States1453 Posts
May 29 2014 00:45 GMT
#66
On May 29 2014 09:14 micronesia wrote:
Show nested quote +
On May 29 2014 09:07 MichaelDonovan wrote:
On May 29 2014 08:58 micronesia wrote:
On May 29 2014 08:33 MichaelDonovan wrote:
On May 29 2014 08:20 micronesia wrote:
It's unfortunate that I don't remember the mathematical rules of logic that well, but I don't see how you can use logic alone to prove the following:

It is not possible for every action to have at least one alternative, mutually exclusive action.

I don't think there are enough tools to work with. Putting technical lines of math aside, what is the reason why the above statement is true?


What you're getting at is the only non-formal assumption that I feel can be poked at in my proof.

My reasoning is as follows:

Recall that we are assuming for reductio that the classical free will thesis is true (we are then showing that a contradiction arises from this).

So since we are assuming classical free will exists, it would seem like no matter how pidgeon-holed into a line of action a person may seem to be, he always has the option of not doing that action, which is a contrary action in itself.

Here's why I say this:

Completing an action requires a break in inertia of sorts. That is, in order to execute an action, one must go from a state of inaction to a state of action and this requires some kind of effort, or at least a willing. If one does not will that the action be executed, they can choose not to act.

The way I think of it is like this: Imagine you are walking on a narrow path over an abyss. You cannot jump off the sides of the path because there is an invisible wall or something. And as you walk, the path behind you gets deleted such that you cannot go the other way. So it would seem as though you have only one choice, which is to continue walking forward. But it turns out that you still have the option of standing still.

I dunno. Maybe this is a weird example. But I think as long as we are assuming free will to exist (for reductio) we can assume that an action that you will should also have an alternative option if you were not to will it. It's easy to imagine a case were you are tide up with a sock in your mouth and you can't move, and say well, there seems to be no other option... But you have the option of willingly accepting your immobility or at least trying to escape (pointless as it may be). The action of accepting your captivity and the action of fighting it (regardless of the effectiveness of your struggle, which may be zero) are contrary actions.

Everything above seems to be an explanation supporting this classical free will thesis... following along using this plain-English approach, what is the contradiction?

The contradiction is probably something like this:

Taking a step forward is a sufficient condition for not having stood still.
Not having stood still is a necessary condition for having stepped forward.
Having stood still is a sufficient condition for not having stepped forward.
Not having stepped forward is a necessary condition for having stood still.

So if I chose to step forward, this makes it the case that I did not choose to stand still.
But not having chosen to stand still is the only way that it could have been possible to step forward. Thus, if you stepped forward, it must be the case that standing still was not possible.

Something like that.

Hm, when you put the 'contradiction' in plain English like this, it seems like your argument is teleological. As others have said, you are using your conclusion as evidence of your conclusion in a somewhat circular manner. Once again, I will not point to logical inaccuracies in your 'proof' as I do not have the necessarily knowledge to do so, but it seems a bit ridiculous to me to say:

"In order to choose an action, I had to not choose other actions, but it was necessary for me to not choose those other actions in order to choose the first action, so really I didn't have a choice," which is, in essence, what your contradiction is. It's almost a semantic argument rather than a logical one, when looked at in words rather than proofs.


Well... I'm not really satisfied with the way I worded it in plain English. It's kind of hard to say it properly because it's not all intuitive. Trying to explain why 1 + 1 = 2 in English without using formal logic to derive this truth from definitions leads to an explanation that won't really be satisfying and is probably full of holes. And I'm not sure I put the logic into words correctly there either...

Not having stepped forward is a necessary condition for having stood still. Was it possible for you to have stood still given that you stepped forward? No, because not having stepped forward is a necessary condition for having stood still. So given that you have stepped forward, it is impossible that you could have stood still.

I dunno.
MichaelDonovan
Profile Joined June 2011
United States1453 Posts
May 29 2014 00:53 GMT
#67
On May 29 2014 09:19 2Pacalypse- wrote:
Show nested quote +
On May 29 2014 07:54 MichaelDonovan wrote:
On May 29 2014 07:50 2Pacalypse- wrote:
On May 29 2014 07:35 MichaelDonovan wrote:
On May 29 2014 07:31 2Pacalypse- wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
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.

That's because philosophers love to argue. Until the real scientist comes along and puts the matter to rest with empiric evidence instead of pure thought .

Facetiousness aside, you should really watch the video. Sam makes a compelling argument on why the very concept of free will doesn't really make sense.


Empirical evidence is hard to rely on when our sense perception is so limited

There are really two versions of the world: The world as we perceive it to be and the world as it actually is outside of our experience of it. Truth can be found in the world as it actually is. What we perceive is only contingent on the accuracy and completeness of our sense perception. The only way to get at the way the world actually is, it would seem, through rational thought and deductive reasoning. A fairly lofty task though, to be sure.

Empirical evidence is hard to rely on? Is that why science doesn't make any progress?

The best method that we have to find out truth about the world, an objective truth, is scientific method. Rational thought and deductive reasoning go out the window once we're confronted with something that doesn't seem rational, eg. quantum mechanics.


Well the problem is that empirical evidence isn't foolproof. We can only gather evidence from what we can sense. How do we know we're not in the matrix world, for example? We don't really know that do we? No amount of empirical evidence can prove that we aren't dreaming or that we aren't just brains in vats being stimulated with the illusion of experience. This is because any empirical evidence we gather is contingent upon our trust for our ability to sense it.

Quantum mechanics is not irrational necessarily. It just defies some our previous assumptions about the world. It renders many statements false that were once though to be true. That doesn't mean it's logically incoherent. It just means we don't understand it based on our current assumptions.

We can't disprove that we're not living in the matrix world. We can't disprove an infinite number of things. That's why we don't pay attention to things unless there's some evidence for them (well, except religion). It wouldn't be very reasonable to start thinking about things that we have no shred of evidence for (like if there's a teapot orbiting around Jupiter). Sure, you can lock yourself up in a room and try to use deductive reasoning all you want, but until you actually go outside of the room and look at what the world is telling you, you won't make any progress and in fact, most of your deductions will be simply wrong.

Show nested quote +
On May 29 2014 08:38 MichaelDonovan wrote:
On May 29 2014 08:36 ninazerg wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
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.


So the length of time by which we argue something determines how obvious it may or may not be?

Determines is a wrong word. Indicates is might be better. What I'm saying is that if the guy in this video actually came up with a solution so obvious that you couldn't argue with it, then I would have heard about it by now, and there would be nothing more to argue. But since people are still arguing, his solution can't be all that obvious.

I did write it became obvious to *me*. This was not a formal scientific theory that Sam proposed, but rather a compelling argument that "makes sense" once you think about it. There are people who challenges his argument though, like philosopher Dan Dennett, but from what I've read it doesn't look like a very good challenge.

Also, people are still arguing about creation vs evolution so you can't possibly take the length of the arguing as an indicator to one's side validity. Perhaps just watch the video or read about Sam's arguments on free will.


I'm not saying that empirical endeavors are pointless. I'm just saying that you can't really value empirical evidence too highly and trust it too much.

And the only way of getting past the limits of our sense perception is probably to use logical deductions. You can't just go by empirical evidence for answers to your questions because your evidence is so very limited. That's not to say that logic alone can answer all your questions. Logic is merely a formal way of thinking. You have to fill the propositions with empirical assumptions on your own. And then any truth you derive is contingent upon those assumptions, which are contingent upon your sense perception.
2Pacalypse-
Profile Joined October 2006
Croatia9512 Posts
May 29 2014 00:59 GMT
#68
On May 29 2014 09:53 MichaelDonovan wrote:
Show nested quote +
On May 29 2014 09:19 2Pacalypse- wrote:
On May 29 2014 07:54 MichaelDonovan wrote:
On May 29 2014 07:50 2Pacalypse- wrote:
On May 29 2014 07:35 MichaelDonovan wrote:
On May 29 2014 07:31 2Pacalypse- wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
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.

That's because philosophers love to argue. Until the real scientist comes along and puts the matter to rest with empiric evidence instead of pure thought .

Facetiousness aside, you should really watch the video. Sam makes a compelling argument on why the very concept of free will doesn't really make sense.


Empirical evidence is hard to rely on when our sense perception is so limited

There are really two versions of the world: The world as we perceive it to be and the world as it actually is outside of our experience of it. Truth can be found in the world as it actually is. What we perceive is only contingent on the accuracy and completeness of our sense perception. The only way to get at the way the world actually is, it would seem, through rational thought and deductive reasoning. A fairly lofty task though, to be sure.

Empirical evidence is hard to rely on? Is that why science doesn't make any progress?

The best method that we have to find out truth about the world, an objective truth, is scientific method. Rational thought and deductive reasoning go out the window once we're confronted with something that doesn't seem rational, eg. quantum mechanics.


Well the problem is that empirical evidence isn't foolproof. We can only gather evidence from what we can sense. How do we know we're not in the matrix world, for example? We don't really know that do we? No amount of empirical evidence can prove that we aren't dreaming or that we aren't just brains in vats being stimulated with the illusion of experience. This is because any empirical evidence we gather is contingent upon our trust for our ability to sense it.

Quantum mechanics is not irrational necessarily. It just defies some our previous assumptions about the world. It renders many statements false that were once though to be true. That doesn't mean it's logically incoherent. It just means we don't understand it based on our current assumptions.

We can't disprove that we're not living in the matrix world. We can't disprove an infinite number of things. That's why we don't pay attention to things unless there's some evidence for them (well, except religion). It wouldn't be very reasonable to start thinking about things that we have no shred of evidence for (like if there's a teapot orbiting around Jupiter). Sure, you can lock yourself up in a room and try to use deductive reasoning all you want, but until you actually go outside of the room and look at what the world is telling you, you won't make any progress and in fact, most of your deductions will be simply wrong.

On May 29 2014 08:38 MichaelDonovan wrote:
On May 29 2014 08:36 ninazerg wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
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.


So the length of time by which we argue something determines how obvious it may or may not be?

Determines is a wrong word. Indicates is might be better. What I'm saying is that if the guy in this video actually came up with a solution so obvious that you couldn't argue with it, then I would have heard about it by now, and there would be nothing more to argue. But since people are still arguing, his solution can't be all that obvious.

I did write it became obvious to *me*. This was not a formal scientific theory that Sam proposed, but rather a compelling argument that "makes sense" once you think about it. There are people who challenges his argument though, like philosopher Dan Dennett, but from what I've read it doesn't look like a very good challenge.

Also, people are still arguing about creation vs evolution so you can't possibly take the length of the arguing as an indicator to one's side validity. Perhaps just watch the video or read about Sam's arguments on free will.


I'm not saying that empirical endeavors are pointless. I'm just saying that you can't really value empirical evidence too highly and trust it too much.

And the only way of getting past the limits of our sense perception is probably to use logical deductions. You can't just go by empirical evidence for answers to your questions because your evidence is so very limited. That's not to say that logic alone can answer all your questions. Logic is merely a formal way of thinking. You have to fill the propositions with empirical assumptions on your own. And then any truth you derive is contingent upon those assumptions, which are contingent upon your sense perception.

And that's what scientific method is: rational thinking applied to empiric evidence.
Moderator"We're a community of geniuses because we've found how to extract 95% of the feeling of doing something amazing without actually doing anything." - Chill
MichaelDonovan
Profile Joined June 2011
United States1453 Posts
Last Edited: 2014-05-29 01:19:52
May 29 2014 01:04 GMT
#69
On May 29 2014 09:59 2Pacalypse- wrote:
Show nested quote +
On May 29 2014 09:53 MichaelDonovan wrote:
On May 29 2014 09:19 2Pacalypse- wrote:
On May 29 2014 07:54 MichaelDonovan wrote:
On May 29 2014 07:50 2Pacalypse- wrote:
On May 29 2014 07:35 MichaelDonovan wrote:
On May 29 2014 07:31 2Pacalypse- wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
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.

That's because philosophers love to argue. Until the real scientist comes along and puts the matter to rest with empiric evidence instead of pure thought .

Facetiousness aside, you should really watch the video. Sam makes a compelling argument on why the very concept of free will doesn't really make sense.


Empirical evidence is hard to rely on when our sense perception is so limited

There are really two versions of the world: The world as we perceive it to be and the world as it actually is outside of our experience of it. Truth can be found in the world as it actually is. What we perceive is only contingent on the accuracy and completeness of our sense perception. The only way to get at the way the world actually is, it would seem, through rational thought and deductive reasoning. A fairly lofty task though, to be sure.

Empirical evidence is hard to rely on? Is that why science doesn't make any progress?

The best method that we have to find out truth about the world, an objective truth, is scientific method. Rational thought and deductive reasoning go out the window once we're confronted with something that doesn't seem rational, eg. quantum mechanics.


Well the problem is that empirical evidence isn't foolproof. We can only gather evidence from what we can sense. How do we know we're not in the matrix world, for example? We don't really know that do we? No amount of empirical evidence can prove that we aren't dreaming or that we aren't just brains in vats being stimulated with the illusion of experience. This is because any empirical evidence we gather is contingent upon our trust for our ability to sense it.

Quantum mechanics is not irrational necessarily. It just defies some our previous assumptions about the world. It renders many statements false that were once though to be true. That doesn't mean it's logically incoherent. It just means we don't understand it based on our current assumptions.

We can't disprove that we're not living in the matrix world. We can't disprove an infinite number of things. That's why we don't pay attention to things unless there's some evidence for them (well, except religion). It wouldn't be very reasonable to start thinking about things that we have no shred of evidence for (like if there's a teapot orbiting around Jupiter). Sure, you can lock yourself up in a room and try to use deductive reasoning all you want, but until you actually go outside of the room and look at what the world is telling you, you won't make any progress and in fact, most of your deductions will be simply wrong.

On May 29 2014 08:38 MichaelDonovan wrote:
On May 29 2014 08:36 ninazerg wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
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.


So the length of time by which we argue something determines how obvious it may or may not be?

Determines is a wrong word. Indicates is might be better. What I'm saying is that if the guy in this video actually came up with a solution so obvious that you couldn't argue with it, then I would have heard about it by now, and there would be nothing more to argue. But since people are still arguing, his solution can't be all that obvious.

I did write it became obvious to *me*. This was not a formal scientific theory that Sam proposed, but rather a compelling argument that "makes sense" once you think about it. There are people who challenges his argument though, like philosopher Dan Dennett, but from what I've read it doesn't look like a very good challenge.

Also, people are still arguing about creation vs evolution so you can't possibly take the length of the arguing as an indicator to one's side validity. Perhaps just watch the video or read about Sam's arguments on free will.


I'm not saying that empirical endeavors are pointless. I'm just saying that you can't really value empirical evidence too highly and trust it too much.

And the only way of getting past the limits of our sense perception is probably to use logical deductions. You can't just go by empirical evidence for answers to your questions because your evidence is so very limited. That's not to say that logic alone can answer all your questions. Logic is merely a formal way of thinking. You have to fill the propositions with empirical assumptions on your own. And then any truth you derive is contingent upon those assumptions, which are contingent upon your sense perception.

And that's what scientific method is: rational thinking applied to empiric evidence.

Right, but the difference is that if empirical evidence suggests something that logic denies, then we conclude that our sense perception misled us. But if logic implies something that empirical evidence seems to deny, then we again conclude that our sense perception is wrong.

What I'm saying is that sense perception and empirical evidence are always the first suspects for error. Logic is more trustworthy.
MichaelDonovan
Profile Joined June 2011
United States1453 Posts
May 29 2014 01:15 GMT
#70
On May 29 2014 09:09 Lixler wrote:
Show nested quote +
On May 29 2014 05:21 MichaelDonovan wrote:
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.


TL;DR of the following: for your reductio, you assume that the antecedent of the conditional is true. but the conditional can be true without the antecedent being true. if we assume, as we logically ought to, that our conditional as a whole is true, no contradiction follows. you have simply proven that the antecedent must be false (viz. that B could not be impossible)

let's fix your formalization somewhat: instead of using B, we'll just use ~A. we'll also introduce quantificational and modal symbols

so classical free will is:
a -> ◇~a
or more properly, since classical free will only says that some of our actions are freely willed:
Ǝa (a -> ◇~a)

the contrapositive (for our assumed a) is now
~◇~a -> ~a
or
□a -> ~a

we can conclude a few things from this, but first let's run through your logical proof with our new symbols.

our assumption, in attempt of the reductio, is that ~a was not possible, or rather that □a.

from □a -> ~a we conclude both (this is trivially true)
a
~a
and obviously this is a contradiction.

well, what went wrong? this: in attempt to prove that your conditional led to a contradiction, you assumed that the antecedent was true. but we don't assume the truth of our antecedent in order to prove that our conditional was false. we assume that our conditional was true! and there are three ways for our conditional to be true. they are, as follows
□a ^ ~a (which leads to a contradiction)
~□a ^ ~a
~□a ^ a

now our second set of truth values would lead to a contradiction, since we already assumed that a (we assumed there was some action such that we could have not done it). we are forced to conclude that ~□a ^ a. unfortunately for your proof, these two values do not lead to a contradiction.


I'm not really sure where to start with this. I feel like you've probably got me here, but this requires more thought.

I think what I want to point to is something like this:

We assume for reductio that ~<>B -> ~A*. (recall A* is the proposition that the agent performs A.)

~<>B -> ~B* (we'll just assume this).

so ~B* -> ~A*.

So we have assumed ~B* -> ~A*
But we come up with ~B* -> A*

This is a contradiction, so our assumed conditional (in its entirety) is false.

Does that make more sense? Or am I still screwing up?
teddyoojo
Profile Blog Joined June 2011
Germany22369 Posts
May 29 2014 01:21 GMT
#71
havent read all posts so im not sure if it has come up yet but i absolutely love this (a little paraphrased) quote by shopenhauer:

You can do what you want, but you cannot want what you want
Esports historian since 2000. Creator of 'The Universe' and 'The best scrambled Eggs 2013'. Host of 'Star Wars Marathon 2015'. Thinker of 'teddyoojo's Thoughts'. Earths and Moons leading CS:GO expert. Lord of the Rings.
2Pacalypse-
Profile Joined October 2006
Croatia9512 Posts
May 29 2014 01:22 GMT
#72
On May 29 2014 10:04 MichaelDonovan wrote:
Show nested quote +
On May 29 2014 09:59 2Pacalypse- wrote:
On May 29 2014 09:53 MichaelDonovan wrote:
On May 29 2014 09:19 2Pacalypse- wrote:
On May 29 2014 07:54 MichaelDonovan wrote:
On May 29 2014 07:50 2Pacalypse- wrote:
On May 29 2014 07:35 MichaelDonovan wrote:
On May 29 2014 07:31 2Pacalypse- wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
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.

That's because philosophers love to argue. Until the real scientist comes along and puts the matter to rest with empiric evidence instead of pure thought .

Facetiousness aside, you should really watch the video. Sam makes a compelling argument on why the very concept of free will doesn't really make sense.


Empirical evidence is hard to rely on when our sense perception is so limited

There are really two versions of the world: The world as we perceive it to be and the world as it actually is outside of our experience of it. Truth can be found in the world as it actually is. What we perceive is only contingent on the accuracy and completeness of our sense perception. The only way to get at the way the world actually is, it would seem, through rational thought and deductive reasoning. A fairly lofty task though, to be sure.

Empirical evidence is hard to rely on? Is that why science doesn't make any progress?

The best method that we have to find out truth about the world, an objective truth, is scientific method. Rational thought and deductive reasoning go out the window once we're confronted with something that doesn't seem rational, eg. quantum mechanics.


Well the problem is that empirical evidence isn't foolproof. We can only gather evidence from what we can sense. How do we know we're not in the matrix world, for example? We don't really know that do we? No amount of empirical evidence can prove that we aren't dreaming or that we aren't just brains in vats being stimulated with the illusion of experience. This is because any empirical evidence we gather is contingent upon our trust for our ability to sense it.

Quantum mechanics is not irrational necessarily. It just defies some our previous assumptions about the world. It renders many statements false that were once though to be true. That doesn't mean it's logically incoherent. It just means we don't understand it based on our current assumptions.

We can't disprove that we're not living in the matrix world. We can't disprove an infinite number of things. That's why we don't pay attention to things unless there's some evidence for them (well, except religion). It wouldn't be very reasonable to start thinking about things that we have no shred of evidence for (like if there's a teapot orbiting around Jupiter). Sure, you can lock yourself up in a room and try to use deductive reasoning all you want, but until you actually go outside of the room and look at what the world is telling you, you won't make any progress and in fact, most of your deductions will be simply wrong.

On May 29 2014 08:38 MichaelDonovan wrote:
On May 29 2014 08:36 ninazerg wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
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.


So the length of time by which we argue something determines how obvious it may or may not be?

Determines is a wrong word. Indicates is might be better. What I'm saying is that if the guy in this video actually came up with a solution so obvious that you couldn't argue with it, then I would have heard about it by now, and there would be nothing more to argue. But since people are still arguing, his solution can't be all that obvious.

I did write it became obvious to *me*. This was not a formal scientific theory that Sam proposed, but rather a compelling argument that "makes sense" once you think about it. There are people who challenges his argument though, like philosopher Dan Dennett, but from what I've read it doesn't look like a very good challenge.

Also, people are still arguing about creation vs evolution so you can't possibly take the length of the arguing as an indicator to one's side validity. Perhaps just watch the video or read about Sam's arguments on free will.


I'm not saying that empirical endeavors are pointless. I'm just saying that you can't really value empirical evidence too highly and trust it too much.

And the only way of getting past the limits of our sense perception is probably to use logical deductions. You can't just go by empirical evidence for answers to your questions because your evidence is so very limited. That's not to say that logic alone can answer all your questions. Logic is merely a formal way of thinking. You have to fill the propositions with empirical assumptions on your own. And then any truth you derive is contingent upon those assumptions, which are contingent upon your sense perception.

And that's what scientific method is: rational thinking applied to empiric evidence.

Right, but the difference is that if empirical evidence suggests something that logic denies, then we conclude that our sense perception misled us. But if logic implies something that empirical evidence seems to deny, then what do we again conclude that our sense perception is wrong.

What I'm saying is that sense perception and empirical evidence are always the first suspects for error. Logic is more trustworthy.

Uhm, no, it's the other way around.

When we demonstrated with empirical evidence that the electron can be at the two places at once, something that seems logically impossible, we didn't dismiss it due to our sense perception misleading us.

Sure, you can try to "update" logic to fit with the reality, but you can't update reality to fit with your logic.
Moderator"We're a community of geniuses because we've found how to extract 95% of the feeling of doing something amazing without actually doing anything." - Chill
MichaelDonovan
Profile Joined June 2011
United States1453 Posts
Last Edited: 2014-05-29 01:40:45
May 29 2014 01:26 GMT
#73
On May 29 2014 10:21 teddyoojo wrote:
havent read all posts so im not sure if it has come up yet but i absolutely love this (a little paraphrased) quote by shopenhauer:

Show nested quote +
You can do what you want, but you cannot want what you want

Haha yeah that's funny.

There is this idea out there called the "deep self view" which is applied to moral responsibility.

It's something like,

I want to do action A. But I don't want to want to do action A. So I'm not morally responsible for doing A.

But if I want to want to want to want to etc... do action A, then I'm morally responsible. Or something like that.

So like, Fred wants to smoke a cigarette really badly. But he doesn't want to want to smoke a cigarette since he's trying to quit smoking. So he's not morally responsible for smoking the cigarette because his desires didn't line up. I don't know if I'm doing this justice, though since I didn't really pay much attention to it when I read about it. It seems like a silly position to hold to me.
MichaelDonovan
Profile Joined June 2011
United States1453 Posts
Last Edited: 2014-05-29 01:39:34
May 29 2014 01:37 GMT
#74
On May 29 2014 10:22 2Pacalypse- wrote:
Show nested quote +
On May 29 2014 10:04 MichaelDonovan wrote:
On May 29 2014 09:59 2Pacalypse- wrote:
On May 29 2014 09:53 MichaelDonovan wrote:
On May 29 2014 09:19 2Pacalypse- wrote:
On May 29 2014 07:54 MichaelDonovan wrote:
On May 29 2014 07:50 2Pacalypse- wrote:
On May 29 2014 07:35 MichaelDonovan wrote:
On May 29 2014 07:31 2Pacalypse- wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
[quote]

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.

That's because philosophers love to argue. Until the real scientist comes along and puts the matter to rest with empiric evidence instead of pure thought .

Facetiousness aside, you should really watch the video. Sam makes a compelling argument on why the very concept of free will doesn't really make sense.


Empirical evidence is hard to rely on when our sense perception is so limited

There are really two versions of the world: The world as we perceive it to be and the world as it actually is outside of our experience of it. Truth can be found in the world as it actually is. What we perceive is only contingent on the accuracy and completeness of our sense perception. The only way to get at the way the world actually is, it would seem, through rational thought and deductive reasoning. A fairly lofty task though, to be sure.

Empirical evidence is hard to rely on? Is that why science doesn't make any progress?

The best method that we have to find out truth about the world, an objective truth, is scientific method. Rational thought and deductive reasoning go out the window once we're confronted with something that doesn't seem rational, eg. quantum mechanics.


Well the problem is that empirical evidence isn't foolproof. We can only gather evidence from what we can sense. How do we know we're not in the matrix world, for example? We don't really know that do we? No amount of empirical evidence can prove that we aren't dreaming or that we aren't just brains in vats being stimulated with the illusion of experience. This is because any empirical evidence we gather is contingent upon our trust for our ability to sense it.

Quantum mechanics is not irrational necessarily. It just defies some our previous assumptions about the world. It renders many statements false that were once though to be true. That doesn't mean it's logically incoherent. It just means we don't understand it based on our current assumptions.

We can't disprove that we're not living in the matrix world. We can't disprove an infinite number of things. That's why we don't pay attention to things unless there's some evidence for them (well, except religion). It wouldn't be very reasonable to start thinking about things that we have no shred of evidence for (like if there's a teapot orbiting around Jupiter). Sure, you can lock yourself up in a room and try to use deductive reasoning all you want, but until you actually go outside of the room and look at what the world is telling you, you won't make any progress and in fact, most of your deductions will be simply wrong.

On May 29 2014 08:38 MichaelDonovan wrote:
On May 29 2014 08:36 ninazerg wrote:
On May 29 2014 07:14 MichaelDonovan wrote:
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.


So the length of time by which we argue something determines how obvious it may or may not be?

Determines is a wrong word. Indicates is might be better. What I'm saying is that if the guy in this video actually came up with a solution so obvious that you couldn't argue with it, then I would have heard about it by now, and there would be nothing more to argue. But since people are still arguing, his solution can't be all that obvious.

I did write it became obvious to *me*. This was not a formal scientific theory that Sam proposed, but rather a compelling argument that "makes sense" once you think about it. There are people who challenges his argument though, like philosopher Dan Dennett, but from what I've read it doesn't look like a very good challenge.

Also, people are still arguing about creation vs evolution so you can't possibly take the length of the arguing as an indicator to one's side validity. Perhaps just watch the video or read about Sam's arguments on free will.


I'm not saying that empirical endeavors are pointless. I'm just saying that you can't really value empirical evidence too highly and trust it too much.

And the only way of getting past the limits of our sense perception is probably to use logical deductions. You can't just go by empirical evidence for answers to your questions because your evidence is so very limited. That's not to say that logic alone can answer all your questions. Logic is merely a formal way of thinking. You have to fill the propositions with empirical assumptions on your own. And then any truth you derive is contingent upon those assumptions, which are contingent upon your sense perception.

And that's what scientific method is: rational thinking applied to empiric evidence.

Right, but the difference is that if empirical evidence suggests something that logic denies, then we conclude that our sense perception misled us. But if logic implies something that empirical evidence seems to deny, then what do we again conclude that our sense perception is wrong.

What I'm saying is that sense perception and empirical evidence are always the first suspects for error. Logic is more trustworthy.

Uhm, no, it's the other way around.

When we demonstrated with empirical evidence that the electron can be at the two places at once, something that seems logically impossible, we didn't dismiss it due to our sense perception misleading us.

Sure, you can try to "update" logic to fit with the reality, but you can't update reality to fit with your logic.


Theres actually some debate about that electron business. I mean, all the Heisenberg uncertainty principle really says is:

At the instant of time when the position is determined, that is, at the instant when the photon is scattered by the electron, the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position. At the instant at which the position of the electron is known, its momentum therefore can be known only up to magnitudes which correspond to that discontinuous change; thus, the more precisely the position is determined, the less precisely the momentum is known, and conversely


This is just a statement about what we can know. In other words, it seems like a purely epistemological statement saying that we can't measure both values at the same time. It doesn't necessarily mean that the electron does not have both momentum and position values. It just says we can't measure them. So I dunno. It's not like everyone agrees on this stuff.

What I'm saying though is that absolute modality trumps natural modality.

Like, logic tells you that you can't both lick the back of your hand and not lick the back of your hand at the same time. Empirically, you will never ever ever be able to do this and give evidence against what was logically derived.

Ultimately it has been mathematical logic that has come up with the kind of theorems which cause us to throw out what we thought we already knew. edit: in history, i mean
Lixler
Profile Joined March 2010
United States265 Posts
May 29 2014 01:47 GMT
#75
On May 29 2014 10:15 MichaelDonovan wrote:
Show nested quote +
On May 29 2014 09:09 Lixler wrote:
On May 29 2014 05:21 MichaelDonovan wrote:
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.


TL;DR of the following: for your reductio, you assume that the antecedent of the conditional is true. but the conditional can be true without the antecedent being true. if we assume, as we logically ought to, that our conditional as a whole is true, no contradiction follows. you have simply proven that the antecedent must be false (viz. that B could not be impossible)

let's fix your formalization somewhat: instead of using B, we'll just use ~A. we'll also introduce quantificational and modal symbols

so classical free will is:
a -> ◇~a
or more properly, since classical free will only says that some of our actions are freely willed:
Ǝa (a -> ◇~a)

the contrapositive (for our assumed a) is now
~◇~a -> ~a
or
□a -> ~a

we can conclude a few things from this, but first let's run through your logical proof with our new symbols.

our assumption, in attempt of the reductio, is that ~a was not possible, or rather that □a.

from □a -> ~a we conclude both (this is trivially true)
a
~a
and obviously this is a contradiction.

well, what went wrong? this: in attempt to prove that your conditional led to a contradiction, you assumed that the antecedent was true. but we don't assume the truth of our antecedent in order to prove that our conditional was false. we assume that our conditional was true! and there are three ways for our conditional to be true. they are, as follows
□a ^ ~a (which leads to a contradiction)
~□a ^ ~a
~□a ^ a

now our second set of truth values would lead to a contradiction, since we already assumed that a (we assumed there was some action such that we could have not done it). we are forced to conclude that ~□a ^ a. unfortunately for your proof, these two values do not lead to a contradiction.


I'm not really sure where to start with this. I feel like you've probably got me here, but this requires more thought.

I think what I want to point to is something like this:

We assume for reductio that ~<>B -> ~A*. (recall A* is the proposition that the agent performs A.)

~<>B -> ~B* (we'll just assume this).

so ~B* -> ~A*.

So we have assumed ~B* -> ~A*
But we come up with ~B* -> A*

This is a contradiction, so our assumed conditional (in its entirety) is false.

Does that make more sense? Or am I still screwing up?

Let's again convert into my preferred symbolization.
We assume for reductio, again, ~◇~A -> ~A. Now, apparently, we're going to assume ~◇~A -> A (we don't need to assume it, since it's self-evident). From this, you conclude A -> ~A (you wrote it as ~B* -> ~A*). I don't know how you reach this conclusion. Anyway, let's move on. You produce the two conditionals A -> ~A and A -> A. I don't know where you produce these two conditionals, but note that they are not contradictory. They are both true when ~A. Now you might conclude that we have nonetheless concluded that ~A must be the case, but your logic was flawed in reaching this conclusion, so we aren't forced to conclude that.

Your step in
~<>B -> ~B* (we'll just assume this).

so ~B* -> ~A*.

I would write as
~◇~A -> A
moving to
A -> ~A
but I do not see how this follows.. Either □A ^ A, in which case the latter conditional is false, or ~□A ^ (A v ~A), in which case the latter conditional does not follow.

I don't know if you've understood my point better now, but here's a simple exercise. Take the truth values ~□A and A and see whether they produce a contradiction when we have ƎA (A -> ◇~A) and ~◇~A -> ~A (I'm not formalizing properly here but whatever). You produce a reductio by assuming □A (you write this as "assuming B is not possible"), but we need not assume □A in order for the premises that translate to the classical free will thesis to be true.

I think that if you 1) stick with proper formalization and 2) consider why your reductio won't work for the initial free will thesis (not its contrapositive) you'll see why your proof is not valid. Again, in assuming our contrapositive to be true, we do not need to assume that the antecedent is true. And it is obvious why a free will thesis-ist is not going to say the antecedent is true: it would directly follow from □A that ~◇~A, which is exactly the negation of the free will thesis.

I'll try to formalize this properly, just for my own edification.

We'll only quantify over actions, to simplify a little. P = "is performed by a human"
Free will thesis = Ǝx (Px ^ (Px -> ◇~Px)
We'll assume f is such an action. It follows that:
Pf ^ (Pf -> ◇~Pf)
And therefore
◇~Pf
Now it's also true that
~◇~Pf -> ~Pf
and
□Pf -> ~Pf
For your reductio, we assume that this statement is true. There are three ways for it to be true. We'll run through all possibilities to see if any are consistent.
1. □Pf ^ ~Pf
Clearly false. We already have Pf, so we cannot also have ~Pf.

2. ~□Pf ^ ~Pf
Same as 1.

3. ~□Pf ^ Pf
~□Pf -> ◇~Pf
◇~Pf
◇~Pf ^ Pf
I see no way to produce a contradiction from these truth values. Do you? Recall that our existing premises amount to:
Ǝx (Px ^ (Px -> ◇~Px)
Pf ^ (Pf -> ◇~Pf)
~◇~Pf -> ~Pf
Each of these statements seems to come out true when we assume ~□Pf ^ Pf.
MichaelDonovan
Profile Joined June 2011
United States1453 Posts
May 29 2014 01:57 GMT
#76
On May 29 2014 10:47 Lixler wrote:
Show nested quote +
On May 29 2014 10:15 MichaelDonovan wrote:
On May 29 2014 09:09 Lixler wrote:
On May 29 2014 05:21 MichaelDonovan wrote:
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.


TL;DR of the following: for your reductio, you assume that the antecedent of the conditional is true. but the conditional can be true without the antecedent being true. if we assume, as we logically ought to, that our conditional as a whole is true, no contradiction follows. you have simply proven that the antecedent must be false (viz. that B could not be impossible)

let's fix your formalization somewhat: instead of using B, we'll just use ~A. we'll also introduce quantificational and modal symbols

so classical free will is:
a -> ◇~a
or more properly, since classical free will only says that some of our actions are freely willed:
Ǝa (a -> ◇~a)

the contrapositive (for our assumed a) is now
~◇~a -> ~a
or
□a -> ~a

we can conclude a few things from this, but first let's run through your logical proof with our new symbols.

our assumption, in attempt of the reductio, is that ~a was not possible, or rather that □a.

from □a -> ~a we conclude both (this is trivially true)
a
~a
and obviously this is a contradiction.

well, what went wrong? this: in attempt to prove that your conditional led to a contradiction, you assumed that the antecedent was true. but we don't assume the truth of our antecedent in order to prove that our conditional was false. we assume that our conditional was true! and there are three ways for our conditional to be true. they are, as follows
□a ^ ~a (which leads to a contradiction)
~□a ^ ~a
~□a ^ a

now our second set of truth values would lead to a contradiction, since we already assumed that a (we assumed there was some action such that we could have not done it). we are forced to conclude that ~□a ^ a. unfortunately for your proof, these two values do not lead to a contradiction.


I'm not really sure where to start with this. I feel like you've probably got me here, but this requires more thought.

I think what I want to point to is something like this:

We assume for reductio that ~<>B -> ~A*. (recall A* is the proposition that the agent performs A.)

~<>B -> ~B* (we'll just assume this).

so ~B* -> ~A*.

So we have assumed ~B* -> ~A*
But we come up with ~B* -> A*

This is a contradiction, so our assumed conditional (in its entirety) is false.

Does that make more sense? Or am I still screwing up?

Let's again convert into my preferred symbolization.
We assume for reductio, again, ~◇~A -> ~A. Now, apparently, we're going to assume ~◇~A -> A (we don't need to assume it, since it's self-evident). From this, you conclude A -> ~A (you wrote it as ~B* -> ~A*). I don't know how you reach this conclusion. Anyway, let's move on. You produce the two conditionals A -> ~A and A -> A. I don't know where you produce these two conditionals, but note that they are not contradictory. They are both true when ~A. Now you might conclude that we have nonetheless concluded that ~A must be the case, but your logic was flawed in reaching this conclusion, so we aren't forced to conclude that.

Your step in
Show nested quote +
~<>B -> ~B* (we'll just assume this).

so ~B* -> ~A*.

I would write as
~◇~A -> A
moving to
A -> ~A
but I do not see how this follows.. Either □A ^ A, in which case the latter conditional is false, or ~□A ^ (A v ~A), in which case the latter conditional does not follow.

I don't know if you've understood my point better now, but here's a simple exercise. Take the truth values ~□A and A and see whether they produce a contradiction when we have ƎA (A -> ◇~A) and ~◇~A -> ~A (I'm not formalizing properly here but whatever). You produce a reductio by assuming □A (you write this as "assuming B is not possible"), but we need not assume □A in order for the premises that translate to the classical free will thesis to be true.

I think that if you 1) stick with proper formalization and 2) consider why your reductio won't work for the initial free will thesis (not its contrapositive) you'll see why your proof is not valid. Again, in assuming our contrapositive to be true, we do not need to assume that the antecedent is true. And it is obvious why a free will thesis-ist is not going to say the antecedent is true: it would directly follow from □A that ~◇~A, which is exactly the negation of the free will thesis.

I'll try to formalize this properly, just for my own edification.

We'll only quantify over actions, to simplify a little. P = "is performed by a human"
Free will thesis = Ǝx (Px ^ (Px -> ◇~Px)
We'll assume f is such an action. It follows that:
Pf ^ (Pf -> ◇~Pf)
And therefore
◇~Pf
Now it's also true that
~◇~Pf -> ~Pf
and
□Pf -> ~Pf
For your reductio, we assume that this statement is true. There are three ways for it to be true. We'll run through all possibilities to see if any are consistent.
1. □Pf ^ ~Pf
Clearly false. We already have Pf, so we cannot also have ~Pf.

2. ~□Pf ^ ~Pf
Same as 1.

3. ~□Pf ^ Pf
~□Pf -> ◇~Pf
◇~Pf
◇~Pf ^ Pf
I see no way to produce a contradiction from these truth values. Do you? Recall that our existing premises amount to:
Ǝx (Px ^ (Px -> ◇~Px)
Pf ^ (Pf -> ◇~Pf)
~◇~Pf -> ~Pf
Each of these statements seems to come out true when we assume ~□Pf ^ Pf.


Cool story bro.

Just kidding hahaha. No I think I see what you're getting at now. My brain is starting to get tired at this point so I think I'll just surrender. You've probably knocked my proof down pretty convincingly. If I think of a proper response I'll get back to you on it.
Nyxisto
Profile Joined August 2010
Germany6287 Posts
Last Edited: 2014-05-29 02:33:22
May 29 2014 02:32 GMT
#77
On May 29 2014 10:04 MichaelDonovan wrote:
Right, but the difference is that if empirical evidence suggests something that logic denies, then we conclude that our sense perception misled us. But if logic implies something that empirical evidence seems to deny, then we again conclude that our sense perception is wrong.

uhhmm.. no. There is no reason to believe that the world is logical. Logic is something we made up. Like English. It's a very specific kind of language with very precise rules. The reason logic helps us out a lot and would trick us into the idea that it is how the world works is because it is very abstract and shaped after very basic principles that occur in nature very often.

If we see something that does not work within our model we need to change our model, we can't change what we observe. At least no scientist does. That there is a external world independent from who observes it is the single most important premise that scientists need to believe, because if not, science doesn't make any sense.


So when it comes to free will, yeah logically it's a very strange concept because as many have pointed out before either stuff is determined, or it's random. But as I have to act as if I did have a free will, I think the question is kind of pointless anyway.
MichaelDonovan
Profile Joined June 2011
United States1453 Posts
May 29 2014 02:38 GMT
#78
On May 29 2014 11:32 Nyxisto wrote:
Show nested quote +
On May 29 2014 10:04 MichaelDonovan wrote:
Right, but the difference is that if empirical evidence suggests something that logic denies, then we conclude that our sense perception misled us. But if logic implies something that empirical evidence seems to deny, then we again conclude that our sense perception is wrong.

uhhmm.. no. There is no reason to believe that the world is logical. Logic is something we made up. Like English. It's a very specific kind of language with very precise rules. The reason logic helps us out a lot and would trick us into the idea that it is how the world works is because it is very abstract and shaped after very basic principles that occur in nature very often.

If we see something that does not work within our model we need to change our model, we can't change what we observe. At least no scientist does. That there is a external world independent from who observes it is the single most important premise that scientists need to believe, because if not, science doesn't make any sense.


So when it comes to free will, yeah logically it's a very strange concept because as many have pointed out before either stuff is determined, or it's random. But as I have to act as if I did have a free will, I think the question is kind of pointless anyway.

Well yeah that's why I say that all of our logical conclusions are contingent on logic being reliable.
MichaelDonovan
Profile Joined June 2011
United States1453 Posts
May 29 2014 02:39 GMT
#79
Hokay time to play counterstrike. I'll come back later and respond some more if need be. But I'm a little burnt out right now
Jerubaal
Profile Blog Joined June 2010
United States7684 Posts
May 29 2014 03:01 GMT
#80
I only watched about 10 minutes of that Sam Harris video, but it seems to me that he's putting forth a non-falsifiable argument. No matter what course of action a person takes, he's going to say it's a result of neurobiology and randomness. If you follow the crowd, you're a result of your environment. If you are an outlier, there must be some detail that caused you to deviate. Did he expect to find a "free will gland" in the brain? One of my favorite expressions is "when all you have is a hammer, everything looks like a nail". Although in this case maybe it should be amended to "you only see nails". A materialistic determinist like Harris is not going to find evidence of free will any more than a Marxist is going to make a non historicist account. It is the lens through which he sees things. The New Positivists seem bound by their shocking contempt for other disciplines, but, really, that's the cardinal sin of modernity, isn't it?

This thread is a real monument (sepulcher?) to analytic philosophy. What should be a useful field of philosophy is instead an abomination. It boasts of its own primacy, ensuring that to the casual onlooker philosophy appears like an abstruse and meaningless endeavor while outwardly arguing for the banishment of the whole discipline before the tide of the hard sciences, flanked by sociology and psychology of course.

@Nina- I will continue to taunt you, per your instructions.


I'm not stupid, a marauder just shot my brain.
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