On May 29 2014 05:21 MichaelDonovan wrote: 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.
My issue is with the red above.
I don't think the statement actually says what you intend for it to say. Let me try rewording it:
Proposition: If an agent did some action (A), then there exists at least one contrary action that the agent could have done instead. Contrapositive: If no contrary action to action (A) exists, then an agent could not have taken action (A).
This of course assumes that every action has an alternative, which may or may not be too strong of a definition for free will. Even if this assumption is disproved, you haven't really accomplished much since free will, in general, can still exist. Regardless, I find the way I phrased the proposition less confusing and error-prone. Frankly, I'm not sure if I can follow your analysis beyond there without reading up on philosophical logic, but usually in these types of situations the phrasing of the initial statements is the most important part of avoiding weird or invalid conclusions.... or confusion from your readers.
I like this rewording much better as well, nice.
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?
You could start by investigating the definition of action, which might expand into considerations of quite a bit more than you at first assume. As usual it comes back to unpacking what the language is holding, which generally leads to messes and tears and bloodshed.
If you say "If you did A, then it was possible to do ~A [anything other than A]" and take the contrapositive "If ~A was precluded, then you did not do A", the only takeaway is that nothing is possible -- a silly state of affairs -- which I think is what that earlier poster was getting at.
Ok so two things:
First, what I am actually trying to show is that classical free will is in fact a silly state of affairs. So the fact that it seems to be a silly state of affairs is only a consequence of its silliness to begin with.
Second, the way I interpret the contrapositve (since it's not really intuitive to think about when you first look at it) is just that if there is no contrary action B possible, then there was no action A to begin with for it to be contrary to. It's not to say that nothing is possible, but just that nothing happened.
Does that make sense? Maybe still a little hairy..
On May 29 2014 08:22 Paljas wrote: people in this thread need to realise that the proof is correct. the only way to attack it is to dismiss the proposition.
however, id agree with the OP that the classic definition is problematic
No its not: the equivalence in (i) does not follow from the definition of B being contrary to A.
On May 29 2014 08:15 NewEyes wrote: You do know that your assumption already contains what you were trying to proof right?
So far you havent said anything but 'I'll assume the concepts of + and - and i'll assume that 1+1=3, therefore 3-1=1.'
I'm not sure I understand what you're trying to say.
Your assumption is 'B is not possbile' which is equal to A. And then you use this to contradict the statement of 'either A or B is possible'. So basically you just said 'always A' -> 'always A'. While this isnt mathmatically wrong you also havent proven anything because your assumption and your conclusion are both the same. You just phrased them a little differently.
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.
I happily accept that B can represent every possible action that A was not.
This thread was definitely a fun exercise, and the deduction is very interesting. I did some logic a couple of years ago, but never tried to actually apply it to any actual philosophy.
And now I'm kind of bumping my head into the fundamentals of it: you assumed that "it was not possible for the agent to have done B", then you deduce a contradiction from that. But doesn't this just say that the assumption is impossible given the proposition? How does this extend to that "it WAS possible for the agent to have done B" will result in a contradiction along with the proposition? I honestly believe that I'm the one missing something here.
On May 29 2014 08:15 NewEyes wrote: You do know that your assumption already contains what you were trying to proof right?
So far you havent said anything but 'I'll assume the concepts of + and - and i'll assume that 1+1=3, therefore 3-1=1.'
I'm not sure I understand what you're trying to say.
Your assumption is 'B is not possbile' which is equal to A. And then you use this to contradict the statement of 'either A or B is possible'. So basically you just said 'always A' -> 'always A'. While this isnt mathmatically wrong you also havent proven anything because your assumption and your conclusion are both the same. You just phrased them a little differently.
"either A or B is possible" isn't exactly what I'm saying. My assumption isn't that "B is not possible", it's that "if B is not possible, then the agent did not do A". There's more to this proposition than you're including.
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?
On May 29 2014 08:35 airen wrote: I happily accept that B can represent every possible action that A was not.
This thread was definitely a fun exercise, and the deduction is very interesting. I did some logic a couple of years ago, but never tried to actually apply it to any actual philosophy.
And now I'm kind of bumping my head into the fundamentals of it: you assumed that "it was not possible for the agent to have done B", then you deduce a contradiction from that. But doesn't this just say that the assumption is impossible given the proposition? How does this extend to that "it WAS possible for the agent to have done B" will result in a contradiction along with the proposition? I honestly believe that I'm the one missing something here.
Well basically, we assume that B isn't possible. Then logic tells that as a result of B not being possible, that B is possible. This is a logical inconsistency. If you deduce from a statement its opposite, then you have a contradiction and the statement can't be true.
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.
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.
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?
On May 29 2014 08:22 Paljas wrote: people in this thread need to realise that the proof is correct. the only way to attack it is to dismiss the proposition.
however, id agree with the OP that the classic definition is problematic
No its not: the equivalence in (i) does not follow from the definition of B being contrary to A.
If it is the case that you cannot both do A and B (definition of contrary action), and B is any action contrary to A, then the following statements must be true:
If you did B, then you could not have done A. If you did not do A, then you did an action contrary to A, which is contained in B by the proposition. So you did some B.
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?
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.
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.
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.
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.
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.
EPT
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