Compatibilist views on free will: some apparent inconsistencies in approach

[subsymbolic]

[quote=""ruby sparks""]

Sorry added a bit in a cross edit:

Oh I'm not saying that there's no such thing as deduction. I just tend to think it's all ultimately predicated on experience, if you dig down far enough, to the foundations. And I tend to think of experience as only providing inductive justification. As you say, we leave a ladder behind.

I think we left the ladder behind us when the Principia Mathematica was published it just helped us to discover maths but led us astray beyond that. There's been a fair bit done since then and maths has it's own unique world. Either way, you are the mathematician and I most certainly am not. So have a think about whether there are any things that can be done by following the laws of maths but not by following the laws of physics. Because if there are then as I said, we have a choice of axioms...

Now I really must get going.

Well, you can multiply the ('imaginary') square root of minus 1 by the square root of minus 1 and (according to some rules) get 1. Though not in real numbers as I understand it. Which is only partially. I'm not even sure it's allowed/valid in imaginary numbers or complex numbers. The analogy with this in the real world would be a bit like saying that you can get a possible from combining two impossibles. Quite a feat. But, as I see it (and I'm not really really a mathematician, I just tutor it up to A level and even at that I'm not fully up to speed on A2 yet) the internal rules are ultimately arbitrary.[/QUOTE]

Arbitrary as a whole perhaps, but once you are playing the tautological(?) game called maths, the rules are pretty damn fixed. Although you do get a choice of axioms as I keep hinting.

So if I were being stalked by Laplace and he were predicting my every move using physics, would I be able to evade him if I were to decide to go left if I could make an impossible out of a possible and right if I couldn't? There are better examples, but this will do.

It's a minimal case, but it does demonstrate some of the teeth of stances and anomalous monism in a way that should be more palatable. Imagine if you had a case like this but involving an absolutely false theory that allowed you to predict your own behaviour and act on the prediction. Not as tidy as Banach Tarski, but it's still objects that don't and can't exist in a physical realm!

[ruby sparks]

[quote=""subsymbolic""]

Deductive logic all on its ownsome?

I thought all axioms were arrived at inductively?

depending on definitions, not at all. We are free to create models using any axioms we wish. Some have more utility than others.

As for what I meant about stuff not necessarily translating to the real world...take numbers for example, or regular geometry. They're essentially 'platonic'.

Also, some (for example numbers) aren't even translatable within maths. In real numbers there is no such thing as the square root of minus 1. It's called an imaginary number. But it can be used in complex number maths (at which I am not proficient) nonetheless.

Can you give me a non-inductive axiom?

No, he can't. But you might want to think if this is what you mean when you use the word induction:

https://en.wikipedia.org/wiki/Mathematical_induction

Or if you might be conflating an a priori process with an a posteriori process that has an unfortunately similar name?[/QUOTE]

Hm. I tend to think that there's nothing actually a priori.

I wouldn't bet my life on it, but...so I might be putting my head on the block in saying it.

[ruby sparks]

[quote=""subsymbolic""]

Oh I'm not saying that there's no such thing as deduction. I just tend to think it's all ultimately predicated on experience, if you dig down far enough, to the foundations. And I tend to think of experience as only providing inductive justification. As you say, we leave a ladder behind.

I think we left the ladder behind us when the Principia Mathematica was published it just helped us to discover maths but led us astray beyond that. There's been a fair bit done since then and maths has it's own unique world. Either way, you are the mathematician and I most certainly am not. So have a think about whether there are any things that can be done by following the laws of maths but not by following the laws of physics. Because if there are then as I said, we have a choice of axioms...

Now I really must get going.

Well, you can multiply the ('imaginary') square root of minus 1 by the square root of minus 1 and (according to some rules) get 1. Though not in real numbers as I understand it. Which is only partially. I'm not even sure it's allowed/valid in imaginary numbers or complex numbers. The analogy with this in the real world would be a bit like saying that you can get a possible from combining two impossibles. Quite a feat. But, as I see it (and I'm not really really a mathematician, I just tutor it up to A level and even at that I'm not fully up to speed on A2 yet) the internal rules are ultimately arbitrary.

Arbitrary as a whole perhaps, but once you are playing the tautological(?) game called maths, the rules are pretty damn fixed. Although you do get a choice of axioms as I keep hinting.

So if I were being stalked by Laplace and he were predicting my every move using physics, would I be able to evade him if I were to decide to go left if I could make an impossible out of a possible and right if I couldn't? There are better examples, but this will do.

It's a minimal case, but it does demonstrate some of the teeth of stances and anomalous monism in a way that should be more palatable.[/QUOTE]

Ok so Laplace's demon is a bit hypothetical. As far as I am aware, some things can't be calculated. I'm talking about incalculable numbers.

Also, I tend to include for the possibility of genuine random.

But, assuming Laplace's demon, I would say no, you couldn't evade him.

[subsymbolic]

Ok so Laplace's demon is a bit hypothetical.

No he's not, he's just a metaphor for the physical determinist world.

As far as I am aware, some things can't be calculated. I'm talking about incalculable numbers.

And I'm thinking about the axiom of choice and the class of 'axiom of choice' problems like the Banach Tarski 'paradox'.

Also, I tend to include for the possibility of genuine random.

Sure, Bell's inequality, but that is completely irrelevant here.

But, assuming Laplace's demon, I would say no, you couldn't evade him.

I could: two balls I go left, one ball I go right. He'd go right. I'd go left. Although as I cross posted:

It's a minimal case, but it does demonstrate some of the teeth of stances and anomalous monism in a way that should be more palatable. Imagine if you had a case like this but involving an absolutely false theory that allowed you to predict your own behaviour and act on the prediction. Not as tidy as Banach Tarski, but it's still objects that don't and can't exist in a physical realm!

[ruby sparks]

[quote=""subsymbolic""]

Ok so Laplace's demon is a bit hypothetical.

No he's not, he's just a metaphor for the physical determinist world. [/quote]

Maybe I meant metaphor. What I meant was that it may be an impossibility, to be such a demon. As I understand it, he's more than just a metaphor for a determinist world, he's something that can predict it, which is different. Some things may be incalculable and unpredictable, but still determined. Or they can be determined and/or random (my holy caveat).

[quote=""subsymbolic""]And I'm thinking about the axiom of choice and the class of 'axiom of choice' problems like the Banach Tarski 'paradox'. [/quote]

As I understand it, again only vaguely, the axiom of choice is a mathematical problem, and controversial even in maths. If maths is not necessarily of the real world, and/or is based on ultimately arbitrary or abstract rules, then it's not clear that you can map stuff like the A of C onto the state of affairs which is what we call the universe. This is why something 'not impossible' in maths may be impossible in reality. Simple, clumsy example, arbitrary rule 'only blue is valid' makes red impossible.

The big question seems to be 'is the impossible possible in the real world?' and the answer, obviously, would appear to be that that would be a contradiction.


[quote=""subsymbolic""]Sure, Bell's inequality, but that is completely irrelevant here. [/quote]

I'm not even sure I'm necessarily relying on Bell's inequality. I just include for the possibility of random, in principle (philosophically) because bare determinism may not be the actual state of affairs.

[quote=""subsymbolic""]

I could: two balls I go left, one ball I go right. He'd go right. I'd go left. Although as I cross posted:[/quote]

But surely if L's Demon existed, he'd know what you would do? I'm saying he can't exist.

[quote=""subsymbolic""]It's a minimal case, but it does demonstrate some of the teeth of stances and anomalous monism in a way that should be more palatable. Imagine if you had a case like this but involving an absolutely false theory that allowed you to predict your own behaviour and act on the prediction. Not as tidy as Banach Tarski, but it's still objects that don't and can't exist in a physical realm!
[/quote]

I'm fine with prediction. The capacities we have are pretty good for that, a lot of the time. Often, the process seems to be heuristic, even when it's conscious.

[plebian]

[quote=""ruby sparks""]

Deductive logic all on its ownsome?

I thought all axioms were arrived at inductively?

depending on definitions, not at all. We are free to create models using any axioms we wish. Some have more utility than others.

As for what I meant about stuff not necessarily translating to the real world...take numbers for example, or regular geometry. They're essentially 'platonic'.

Also, some (for example numbers) aren't even translatable within maths. In real numbers there is no such thing as the square root of minus 1. It's called an imaginary number. But it can be used in complex number maths (at which I am not proficient) nonetheless.

Can you give me a non-inductive axiom?[/QUOTE]

The axiom of infinity and the, er, axiom of, um, choice? There are probably dozens at this point though that we actually use. However, that wasn't my point. We can choose any set of axioms we wish, all an axiom is is a rule. We could choose any rule we want. Logic just requires we follow the rules we choose. Lots of rules are inductively generated, typically the most useful ones, but that doesn't mean they need to be. It's just a matter of convenience.

[plebian]

[quote=""subsymbolic""]

The self is free to act within the map of the external world, which allows the body to be free to act within the external world.

How does it get that first freedom? That's largely what this whole thread has been about.

Are you accidentally equivocating between freewill in the first case and freedom in the second?

It's not an equivocation if the freewill belongs to the first case and freedom the second.

Perhaps, but that renders the word 'act' problematic...[/QUOTE]
Or forces the user to keep their levels of analysis straight.

[ruby sparks]

[quote=""plebian""]The axiom of infinity.......[/quote]

I'm not sure that's not inductive.

In fact, I'd say it is inductive.

[quote=""plebian""]We can choose any set of axioms we wish, all an axiom is is a rule. We could choose any rule we want. Logic just requires we follow the rules we choose. Lots of rules are inductively generated, typically the most useful ones, but that doesn't mean they need to be. It's just a matter of convenience.[/quote]

I'm not mainly doing utility. As I said before, utility is fine, but it's utility.

That the sun goes around the earth is an idea that has great utility, for example.

[subsymbolic]

Oh determinism is false alright and yes Laplace's demon is impossible. However, that's not the point. Just focus on the Banach Tarski paradox

https://en.wikipedia.org/wiki/Banach%E2 ... ki_paradox

Logic/maths and the laws of physics are not equivalent. Therefore there are processes in your brain that, while supervenient upon the physical world and entirely physical, do not follow the same rules and thus can have outcomes that are not predictable from any physical stance. As Wittgenstein pointed out, any self consistent logical world may have this property.

I'm just using this example because you are a mathematician and anomalous monism didn't go down well last time.

[subsymbolic]

[quote=""plebian""]

How does it get that first freedom? That's largely what this whole thread has been about.

Are you accidentally equivocating between freewill in the first case and freedom in the second?

It's not an equivocation if the freewill belongs to the first case and freedom the second.

Perhaps, but that renders the word 'act' problematic...

Or forces the user to keep their levels of analysis straight.[/QUOTE]

if the former was an act then the latter would be an event, if the latter was an act then the former would be an epiphenomena. Yeah, I'm being pedantic, but hey, that's what they pay me for.

[plebian]

[quote=""ruby sparks""]

The axiom of infinity.......

I'm not sure that's not inductive.

In fact, I'd say it is inductive.

[quote=""plebian""]We can choose any set of axioms we wish, all an axiom is is a rule. We could choose any rule we want. Logic just requires we follow the rules we choose. Lots of rules are inductively generated, typically the most useful ones, but that doesn't mean they need to be. It's just a matter of convenience.[/quote]

I'm not mainly doing utility. As I said before, utility is fine, but it's utility.

That the sun goes around the earth is an idea that has great utility, for example.[/QUOTE]

Ah. I see. Are you using induction to mean a generalization from examples or as in a mathematical proof? Because, if it's the second, that isn't helpful for a physical determinism model. I really don't think the axiom of infinity has any inductive justification at all. It's a pure maths sort of thing that works as a kludge to some extent. It's a rule that shores up some rules. Maybe a mathematician could help.

Eta: I see subsymbolic already brought this up.

[plebian]

[quote=""subsymbolic""]

It's not an equivocation if the freewill belongs to the first case and freedom the second.

Perhaps, but that renders the word 'act' problematic...

Or forces the user to keep their levels of analysis straight.

if the former was an act then the latter would be an event, if the latter was an act then the former would be an epiphenomena. Yeah, I'm being pedantic, but hey, that's what they pay me for.[/QUOTE]
It's totally fair and gets at the issue of keeping your levels straight. The word 'act' is already problematic but seems to me to simply mean movement that is purpose driven when purpose is a quality of the system. A heart pumps. A kidney filters, a brain regulates and thinks, the systems together as a larger system have a different purpose.

[subsymbolic]

But before we start saying anything is or isn't true, it might be worth pausing for a moment to think how we generate a truth value, because this sort of problem can become contagious and leads fools (like Dennett) to prefere utility over truth.

Don't forget, Dennett is absolutely clear that the justification for using the intentional stance is that it works and all there is to being an intentional system is being, as he put it, 'reliably and voluminously predictable from the intentional stance'.

Stop looking smug Plebian.

Now I'm off to bed with almost no papers marked.

Cheers.

[ruby sparks]

[quote=""subsymbolic""]Oh determinism is false alright and yes Laplace's demon is impossible. However, that's not the point. Just focus on the Banach Tarski paradox

https://en.wikipedia.org/wiki/Banach%E2 ... ki_paradox

Logic/maths and the laws of physics are not equivalent. Therefore there are processes in your brain that, while supervenient upon the physical world and entirely physical, do not follow the same rules and thus can have outcomes that are not predictable from any physical stance. As Wittgenstein pointed out, any self consistent logical world may have this property.[/quote]

That's quite a claim, that the rules of mathematics play out in the real world. As I understand it, that maths paradox starts by assuming stuff like volume, stops using it in the middle, and then uses it again at the end. Rabbit out of a hat. We can make an infinite number of spheres from just one. But it seems we have changed the arbitrary rules during the game.

Even self-consistency will only be internally consistent.


In a nutshell, I'm not sure that any world we create will be the real one.

[subsymbolic]

[quote=""plebian""]

Perhaps, but that renders the word 'act' problematic...

Or forces the user to keep their levels of analysis straight.

if the former was an act then the latter would be an event, if the latter was an act then the former would be an epiphenomena. Yeah, I'm being pedantic, but hey, that's what they pay me for.

It's totally fair and gets at the issue of keeping your levels straight. The word 'act' is already problematic but seems to me to simply mean movement that is purpose driven when purpose is a quality of the system. A heart pumps. A kidney filters, a brain regulates and thinks, the systems together as a larger system have a different purpose.[/QUOTE]

Sure but then we are locating purposivity in two places. If that was a deliberate abuse of language for explanatory effect it's a win, but I don't think it was.

[plebian]

[quote=""subsymbolic""]

Or forces the user to keep their levels of analysis straight.

if the former was an act then the latter would be an event, if the latter was an act then the former would be an epiphenomena. Yeah, I'm being pedantic, but hey, that's what they pay me for.

It's totally fair and gets at the issue of keeping your levels straight. The word 'act' is already problematic but seems to me to simply mean movement that is purpose driven when purpose is a quality of the system. A heart pumps. A kidney filters, a brain regulates and thinks, the systems together as a larger system have a different purpose.

Sure but then we are locating purposivity in two places. If that was a deliberate abuse of language for explanatory effect it's a win, but I don't think it was.[/QUOTE]

It definitely was. That's exactly the point of the intentional stance as far as I can see. Each level of organization has its own recursive set of systemic qualities. What is purpose but a linearization of attractor basins as outputs?

[ruby sparks]

[quote=""plebian""]Ah. I see. Are you using induction to mean a generalization from examples or as in a mathematical proof? Because, if it's the second, that isn't helpful for a physical determinism model. I really don't think the axiom of infinity has any inductive justification at all. It's a pure maths sort of thing that works as a kludge to some extent. It's a rule that shores up some rules. Maybe a mathematician could help.

Eta: I see subsymbolic already brought this up. [/quote]

The axiom of infinity assumes there are numbers. That's arrived at inductively, at bottom.

Helpful? As I keep saying, if you want utility and helpful, utilitarian explanations are mostly pretty.....useful. That's why the idea that the sun goes around the earth was (and still is, to a lesser extent) so useful.

[plebian]

[quote=""ruby sparks""]

Oh determinism is false alright and yes Laplace's demon is impossible. However, that's not the point. Just focus on the Banach Tarski paradox

https://en.wikipedia.org/wiki/Banach%E2 ... ki_paradox

Logic/maths and the laws of physics are not equivalent. Therefore there are processes in your brain that, while supervenient upon the physical world and entirely physical, do not follow the same rules and thus can have outcomes that are not predictable from any physical stance. As Wittgenstein pointed out, any self consistent logical world may have this property.

That's quite a claim, that the rules of mathematics play out in the real world. As I understand it, that maths paradox starts by assuming stuff like volume, stops using it in the middle, and then uses it again at the end. Rabbit out of a hat. We can make an infinite number of spheres from just one. But it seems we have changed the arbitrary rules during the game.

Even self-consistency will only be internally consistent.


In a nutshell, I'm not sure that any world we create will be the real one.[/QUOTE]
You can't make an infinite number of spheres out of one in that example.

[subsymbolic]

[quote=""ruby sparks""]

Oh determinism is false alright and yes Laplace's demon is impossible. However, that's not the point. Just focus on the Banach Tarski paradox

https://en.wikipedia.org/wiki/Banach%E2 ... ki_paradox

Logic/maths and the laws of physics are not equivalent. Therefore there are processes in your brain that, while supervenient upon the physical world and entirely physical, do not follow the same rules and thus can have outcomes that are not predictable from any physical stance. As Wittgenstein pointed out, any self consistent logical world may have this property.

That's quite a claim, that the rules of mathematics play out in the real world. As I understand it, that maths paradox starts by assuming stuff like volume, stops using it in the middle, and then uses it again at the end. Rabbit out of a hat. We can make an infinite number of spheres from just one. But it seems we have changed the arbitrary rules during the game.

Even self-consistency will only be internally consistent.


In a nutshell, I'm not sure that any world we create will be the real one.[/QUOTE]

Who cares if it means I definitely get to go left while Laplace goes right?

And he would. Because I'd have two balls and he'd be Hitler. Stances, powerful things...

[plebian]

[quote=""ruby sparks""]

Ah. I see. Are you using induction to mean a generalization from examples or as in a mathematical proof? Because, if it's the second, that isn't helpful for a physical determinism model. I really don't think the axiom of infinity has any inductive justification at all. It's a pure maths sort of thing that works as a kludge to some extent. It's a rule that shores up some rules. Maybe a mathematician could help.

Eta: I see subsymbolic already brought this up.

The axiom of infinity assumes there are numbers. That's arrived at inductively, at bottom.

Helpful? As I keep saying, if you want utility and helpful, utilitarian explanations are mostly pretty.....useful. That's why the idea that the sun goes around the earth was (and still is, to a lesser extent) so useful.[/QUOTE]

Hmm. We are using some different references.

[ruby sparks]

[quote=""subsymbolic""]Who cares if it means I definitely get to go left while Laplace goes right? [/quote]

Sorry, I thought Laplace's demon was only predicting what YOU would do, not making its own choice.

If you don't mean 'goes right' but opts 'right' as its prediction for you, then, that wouldn't happen, if L's Demon could exist (AND the world is fully determined).

[ruby sparks]

[quote=""plebian""]You can't make an infinite number of spheres out of one in that example.[/quote]

Mathematically, you can, apparently.

[plebian]

[quote=""ruby sparks""]

You can't make an infinite number of spheres out of one in that example.

Mathematically, you can, apparently.[/QUOTE]

Sort of. It's a different thing though.

[ruby sparks]

[quote=""plebian""]

You can't make an infinite number of spheres out of one in that example.

Mathematically, you can, apparently.

Sort of. It's a different thing though.[/QUOTE]

It uses the Banach–Tarski paradox, apparently. Either way, if you could make an infinite number of identical copies out of one object in the real world, you might be onto something big, and not just as regards free will. We'd have to reappraise the NT story about feeding the five thousand for starters and consider it a mere trifle.

This seems to be part of the problem with mapping maths onto the real world.

[subsymbolic]

[quote=""ruby sparks""]

Who cares if it means I definitely get to go left while Laplace goes right?

Sorry, I thought Laplace's demon was only predicting what YOU would do, not making its own choice.

If you don't mean 'goes right' but opts 'right' as its prediction for you, then, that wouldn't happen, if L's Demon could exist (AND the world is fully determined).[/QUOTE]

Sure, it goes right, because it opts right as its prediction for you. Maths, just like certain stances, isn't just emergent, once you take that stance, there are aspects that follow with their own necessity, which isn't physical but logical necessity. A necessity which is only apparent from a paricular stance. Laplace's demon isn't taking that stance, it's only tracking physical stuff following physical laws. As such it will be blind to any consequences of taking that stance.

Of course, following the laws of logic is no more free or mysterious than being knocked off course by a random event. However, it's another way that the demon is blinded and, I thought, it would be a clear and unambiguous example for a mathematician. I rather hoped that this insight could then be brought across to following the logic of a different stance, an intentional one, that opens the door to following the laws of logic in a more self controlling way...