Is/Ought problem

[Mak2]

Thanks fro the long explanation, ER, really appreciate it. One question, though:

If a there are mathematically true statements that can not be proven by this symbols shunting then the system is incomplete and if contradictory statements or mathematically false statements cand be formed then the system is inconsistent. But neither the terms inconsistent or incomplete have any meaning UNLESS the formal system has meaning attached to it. In other words it is only incomplete or inconsistent if we are trying to use it to model something else.

But doesn't the 2nd incompleteness theorem show that formal systems are incomplete even if they do not model something else? Seeing that they are shown not to be able to prove their own consistency.

This failure of mathematics to be modelled is really interesting. It hints to me that mathematics is something intrinsic about the universe. It is not purely a human mental construct as if it were just a model of reality then why can't it be modelled!!! There seems to be something intrinsicly mathematical about the universe and what Godel showed is that the human mind and human logic can not model it fully. Maths is more like physics or chemistry than logic. It is something we discover about the universe rather than invent.

I see better what you mean now, but I would tend to see it as a reality peculiar to human thought, rather than something completely outside it that can only be discovered.

OK what I meant to say is that we can use subset of physical reality to model other subsets. This is different to using pure abstarctions like formal systems.

I think the rigidity of formal systems models or mimics the rigidity of the laws of nature. When A happens, B will happen...

[evilreligion]

Thanks fro the long explanation, ER, really appreciate it. One question, though:

If a there are mathematically true statements that can not be proven by this symbols shunting then the system is incomplete and if contradictory statements or mathematically false statements cand be formed then the system is inconsistent. But neither the terms inconsistent or incomplete have any meaning UNLESS the formal system has meaning attached to it. In other words it is only incomplete or inconsistent if we are trying to use it to model something else.

But doesn't the 2nd incompleteness theorem show that formal systems are incomplete even if they do not model something else? Seeing that they are shown not to be able to prove their own consistency.

Formal systems can't prove anything on their own they are merely systems and rules for changing and moving symbols around.
They can only be said to be incomplete when we try to map the formal system to something i.e. attribute meaning to it.
Godels seond incompleteness theourm shows that IF a formal system is capable of modelling the arithemetic truths of natural numbers then one arithmentic truth that the system can not prove is the consistency of the system itself. So in order for the incompletness theorum to make sense we must atribute meaning to the formal systems in question i.e. that they map too and model the arithmetic of natural numbers. Without this mapping the formal system is just a set of rules for moving symbols around. The question of whether its complete, consistent or inconsistent is not a relevant question.

This failure of mathematics to be modelled is really interesting. It hints to me that mathematics is something intrinsic about the universe. It is not purely a human mental construct as if it were just a model of reality then why can't it be modelled!!! There seems to be something intrinsicly mathematical about the universe and what Godel showed is that the human mind and human logic can not model it fully. Maths is more like physics or chemistry than logic. It is something we discover about the universe rather than invent.

I see better what you mean now, but I would tend to see it as a reality peculiar to human thought, rather than something completely outside it that can only be discovered.

My hunch is that as human brains are phsyical objects then the thought that stems from them is grounded in the laws of mathematics. This is why our thought can model mathematics fairly well but not perfectly. Maths is both inside and outside us. It both shapes our thought and is to be modelled by our thought.

OK what I meant to say is that we can use subset of physical reality to model other subsets. This is different to using pure abstarctions like formal systems.

I think the rigidity of formal systems models or mimics the rigidity of the laws of nature. When A happens, B will happen...[/quote]
Yep they are good models to be sure..... but not perfect. The hardware that generates formal systems (the human brain) is very finite. The fact that it is made of the same stuff as the rest of the universe and its individual componets (atoms, electrons etc) obey the same rules means that the human brain can simulate and model a wider reality. But because the brain is a finite and limited object when comparred to the whole of the universe, these models will always be flawed. Human though may simply not be capable of understanding or modelling some aspects of reality. I think we can see this in quantum physics quite clearly. As Feynman said "Anyone who says they understand quantum theory does not understan quantum theory". The ability of the human brain to model relaity and understand it breaks down with things like quantum physics, we can't truely understand it. BUT mathematics, it seems, can allow us to make predictions and calculations at the quantum level. Even if we don't understand what it means for the a system to be in a supposition state we can calculate the effects of this state and what wil happen (or rather the probabilities of events). In this way we can see maths a bridging the gap into the unknown and unknowable.

[Mak2]

Formal systems can't prove anything on their own they are merely systems and rules for changing and moving symbols around.
They can only be said to be incomplete when we try to map the formal system to something i.e. attribute meaning to it.
Godels seond incompleteness theourm shows that IF a formal system is capable of modelling the arithemetic truths of natural numbers then one arithmentic truth that the system can not prove is the consistency of the system itself. So in order for the incompletness theorum to make sense we must atribute meaning to the formal systems in question i.e. that they map too and model the arithmetic of natural numbers. Without this mapping the formal system is just a set of rules for moving symbols around. The question of whether its complete, consistent or inconsistent is not a relevant question.

I see. But still (sorry to keep nagging about this, it does look like an intricate game of model/no-model and meaning/no-meaning) the problem seems to be, must be, in the formal system itself, because no matter what meaning is given to the symbols, Gödel's theorems apply. The problem must be formalization itself, not the use of a formal system as a model (even though, as you say, the problem won't surface before meaning is added).

My hunch is that as human brains are phsyical objects then the thought that stems from them is grounded in the laws of mathematics. This is why our thought can model mathematics fairly well but not perfectly. Maths is both inside and outside us. It both shapes our thought and is to be modelled by our thought.

O, but this sounds much better already, as it doesn't have the mind outside reality looking in.

The ability of the human brain to model relaity and understand it breaks down with things like quantum physics, we can't truely understand it. BUT mathematics, it seems, can allow us to make predictions and calculations at the quantum level. Even if we don't understand what it means for the a system to be in a supposition state we can calculate the effects of this state and what wil happen (or rather the probabilities of events). In this way we can see maths a bridging the gap into the unknown and unknowable.

Cool.

[evilreligion]

Formal systems can't prove anything on their own they are merely systems and rules for changing and moving symbols around.
They can only be said to be incomplete when we try to map the formal system to something i.e. attribute meaning to it.
Godels seond incompleteness theourm shows that IF a formal system is capable of modelling the arithemetic truths of natural numbers then one arithmentic truth that the system can not prove is the consistency of the system itself. So in order for the incompletness theorum to make sense we must atribute meaning to the formal systems in question i.e. that they map too and model the arithmetic of natural numbers. Without this mapping the formal system is just a set of rules for moving symbols around. The question of whether its complete, consistent or inconsistent is not a relevant question.

I see. But still (sorry to keep nagging about this, it does look like an intricate game of model/no-model and meaning/no-meaning) the problem seems to be, must be, in the formal system itself, because no matter what meaning is given to the symbols, Gödel's theorems apply.

Not really. Not all formal systems are inconsistent or incomplete. There are many formal systems that are both complete and consistent its just that any that is strong or big enough to map the rules of arithmetic will always be incomplete of inconsistent.

The problem must be formalization itself, not the use of a formal system as a model (even though, as you say, the problem won't surface before meaning is added).

I think Godel shows the limits of what formal systems can model fully. Above a certain level of complexity and they fail. Mathematics is above that cut off line. Whats really interesting is that formal logic is a formal system that describes logical thought. It is consistent and complete. The formal rules of logic never produce a "not A"and and "A" string (so it is consistent) and the rule of logic can be used to produce all valid strings (i.e. all arguments) so it is compete. Arithmetic can not be so logically described. Which is a somewhat surprising conclusion.

My hunch is that as human brains are phsyical objects then the thought that stems from them is grounded in the laws of mathematics. This is why our thought can model mathematics fairly well but not perfectly. Maths is both inside and outside us. It both shapes our thought and is to be modelled by our thought.

O, but this sounds much better already, as it doesn't have the mind outside reality looking in.

The ability of the human brain to model relaity and understand it breaks down with things like quantum physics, we can't truely understand it. BUT mathematics, it seems, can allow us to make predictions and calculations at the quantum level. Even if we don't understand what it means for the a system to be in a supposition state we can calculate the effects of this state and what wil happen (or rather the probabilities of events). In this way we can see maths a bridging the gap into the unknown and unknowable.

Cool.

Indeed.
The philosophy of maths course I did as part of my degree (15 years ago now) was one of the coolest course I did. When we went through the logical derivation of Godels theorums it was one of those light bulb momments. The proof was really elegant and incontravertable once you went through it and understood it you simply had to marvel at the mind that came up with. It was a little glimpse of into the mind of a genius. Sadly the intervening years have made me forget much of the derivation. But essentially what he does is assign each symbol in a formal system a number so that any derived string will have a unique godel number (that being the number of each symbol in sequence) . He then gets the formal system to talk about its own Godel number and essentially sets up the liar paradox statement "This statement is false" within the formal system.

The book Godel Escher Bach (An eternal golden braid by Douglas Hosftadder) is a good introduction to Godel and other things - a good (if hefty read). must re read myslef it as I really want to remember Godels proof.

[Mak2]

The book Godel Escher Bach (An eternal golden braid by Douglas Hosftadder) is a good introduction to Godel and other things - a good (if hefty read). must re read myslef it as I really want to remember Godels proof.

I tried that, but very big books and I don't get along very well; and I have a complete blind spot for all things Bach, so that didn't help much either.

But what you've made me do is buy a smaller book, about the man and his theorems, and about their implications. So basically what you did is rob me of € 16,50.

[Este]

How am I misinterpreting that? Rational is equivalent to long term well-being.

Yeah, I was using rational in the sense of prudent.

Prudent is exercising sound judgement, right?

Depends. If you define sound judgment as "reasoning consistent with whatever stated goal they have" then no. It's a "thicker" concept than that.

I don't think it's consistent with the usage of prudent to use it to describe someone who is taking risks for short-term gains.

Okay, but instead of this 'just so' manner, how about explaining why it's the case that someone who chooses to risk his life for an immensely enjoyable experience is therefore failing to exercise sound judgement. If you were just stating your opinion, that would be fine, but you're not, are you? You're saying it's an objective fact.

I don't think life is inherently valuable....

But if someone is putting themselves in a position that they get short-term euphoria, with the strong possibility that they will be harmed (say shooting up heroin with dirty needles) then they're disregarding their long-term wellbeing for a short-term gain. Which is what imprudence is. Otherwise, imprudence is meaningless - someone could put all their rent money into the lotto and be considered prudent. (Since their reasoning is "sound" insofar as they think it's worth the risk.)

For instance, how exactly is the free solo climber failing to exercise sound judgement? This method of climbing is attractive to some individuals because it presents intense mental challenges and adrenaline rushes. Many climbers have died. Just because it's high risk does not make it imprudent to get involved in the sport, IMO.

Sure it is. On the wiki page you quoted, there are relatively more prudent means of following the sport. They're more prudent (objectively) in that they further minimize risks.

What would be imprudent/reckless is to attempt to climb somewhere without first mentally mapping your route, or checking what the weather is likely to be like, etc.

That's more imprudent than not, yeah. Objectively so, since it minimizes risk further. Which is my point.

Taking risks for short-term gains can be consistent with the usage of prudent.

What if a free solo climber did what you just said was reckless because that aspect made it more thrilling?

They'd be more imprudent/reckless. Which is objectively true. And they'd be even more prudent to take more generalized safety measures. If the word "imprudent" means anything beyond "in my taste, that's not worth it."

A rapist is "irrational/unreasonable" insofar as prudence is part of what we consider 'rational' to mean in general.

Sorry but you're just reasserting that that is the case and offering no supporting argument. I would agree that a rapist who seizes a victim in a crowded place where he's immediately caught is behaving imprudently (unless he was wanting to be imprisoned for some reason – maybe he's institutionalised), but if he's careful, and is minimizing the risks as much as possible, then where's his lack of sound judgement exactly?

A rapist who "minimizes risk" might be more prudent than one that does it in public. But all rapists are more imprudent than someone who gets their pleasures without breaking the law. And since the risk can hardly be minimized to the point that someone can be reassured not to get caught, most people have motivation not to do it simply on that fact alone.

Back pedalling on that takes you all the way to page 2 and your 'Tommy is/ought' syllogisms where this whole business about long-term goals and rape stems from. You said- "It's true in the short term that it might make sense in the moment to rape someone, but that wouldn't be rational in the long-term. He'd end up either dead or in prison." If he's exercising sound judgement in minimizing the risk of being caught, why ought the rapist not rape?

Because he'd minimize the risks further by not raping. You've basically conceded that a rapist is "more prudent" if they lessen their chances of getting caught. Prudence comes in degrees. Not raping "minimizes the risk" of not getting caught even more then doing it with stealth. So it's more prudent.

The terms have to do with the sorts of motivations they are using.

Perhaps a life without rape is a relatively miserable life for the person who loves to dominate and overpower a person against their will compared to what his life is like with rape in it.

Sure. So they won't be motivated to be prudent... The way someone who is addicted to crack won't necessarily stop smoking crack just because they know it leads to various harms.

That doesn't change the fact that rape is imprudent (and unjust).

I would judge gay people who don't use protection for hook-ups where there is significant danger as straight-forwardly imprudent, though.

Yeah, I have to say I'm deeply sympathetic to that view because I'm pretty obsessive about safety myself. But then, what about 'bug chasers' whose enjoyment of sex goes up enormously precisely because of the risk factor of catching an STD?

They get off on imprudence.

If having sex with someone with a disease wasn't dangerous, it wouldn't give them the thrills it does. Same with free-solo.. The adrenaline rush comes from the risk. The risk is objective... So is the fact that they are doing something they'd describe as risky. Prudence simply doesn't mean the same as "being risky."

It's easy to say they're lacking prudence but what is such a judgement based on but our own subjective values?

It has nothing to do with our preferences. We can use hypotheticals to describe this sort of situation (like Homo Economicus). The risk is real and if prudence means not taking long term risks, then a hypothetical reasoner who minimized risks in terms of long-term happiness wouldn't do so. He'd go to therapy and figure out how to get his rocks off without being stupid. (No one is "doomed" to be a bug-chaser. And the idea that they can't experience the pleasures of sex without engaging in that behavior is extremely unlikely.)

It's a fascinating community to take a look into, and it cracks me up reading some of the ads- "Het cpl seeks bug chasers seeking Herpes and HPV". I mean, WTF?

Even the gods struggle in vain against stupidity.

Is it prudent to fear death? Epicurus argued that it wasn't, right? That's not to say he argued for living recklessly, but that we shouldn't let fear of death affect our judgement of the right way to live. People who cut out much of what's enjoyable in life because those things might shorten their life seem to be to focused on keeping death at arm's length at the expense of actually living life. A good life isn't measured in number of years lived, IMO.

Death isn't to be feared because there is no subject to experience death - and something we can't experience can't be a harm to us. I agree a good life isn't measured in years... It's measured in years happy versus years spent in pain. If your life-style is such that you are out trying to get herpes, you're setting yourself up for uncurable, recurring pains throughout life for a hour of bug-chasing fun?

That's imprudent. Better off changing your subjective desires so that you can enjoy yourself sexually without the risk.

Sure he's putting himself at risk (I put myself at risk when I climb ladders to do a roofing job) but if those risks produce beneficial results to the person, such as a compliant spouse for the rapist, how is he behaving without prudence?

Because his actions are risky - especially if he's in a context that has a reasonable justice system. The rapist's victim (if acting prudently) has every reason to kill the mother fucker. Incentivizing your death for someone who lives with you and who knows where you sleep isn't wise. It only takes the victim one fleeting thought of "I'm not putting up with this shit anymore" and a little poison to handle the problem.

If you value your long-term health more than being happy and content right now (assuming you can't be happy and content right now without a smoke), then sure, you're going against your better interest. Someone else, though, whose life motto is "scale back one's hopes to a brief future and drink one's wine" would disagree with you – and he could argue that it is you who's being imprudent for making yourself unhappy in the present moment for some future reward (good health later in life) that you may not even get to see.

He'd be wrong.

I don't need to smoke. I can be happy without it. So can most people. Our brains are plastic like that. If I think I can't be happy without a cig or someone thinks that they need to drink themselves to death to be happy, they're believing things that are just objectively not so. They might desire it now, but it's better to replace destructive and costly desires with cheap and healthy ones. Happiness isn't hard to get, and if that's what all our preferences break down to (I smoke a cig to get happy, etc) then it's objectively prudent to change our desires as much as possible to best get the thing we're really after.

The Cancer Society released some new information this week backed up by studies, saying that people should exercise 30mins daily, drink no more than one alcoholic beverage a day, eat healthily, lose weight, blah blah blah, to reduce their risk of developing cancer later on in life. Now, if someone values getting pissed, eating deliciously unhealthy food, being significantly overweight (which his chubby chasing boyfriend goes crazy for), and so on, is he living prudentially putting himself at risk of developing cancer?

Men should drink 1-2 (around) drinks a day. It's protective.

And no. If someone values getting pissed (etc) that means getting pissed (etc) makes them happy. And all those preferences lead to things the person almost certainly doesn't enjoy - like hangovers, joint pain, and the inability to perform for his chubby chasing boyfriend. He can still get the happiness without the pains (enjoying things that lead to other preferences being fulfilled is superior). He's better off learning moderation, losing a few pounds, trying new foods and so on. (And when he does indulge in an all-night binge of booze and pizza, it'll be all the more satisfying.) And if his chubby chasing boyfriend loves him, he's better off getting him to a safe weight and learning to like a healthier version of him. (Lots of desires are malleable. And people can learn to enjoy new things.)

Unless he's okay losing his boyfriend at a young age to heart disease in the name of sexual satisfaction... But that's also irrational. If he wants more happy days with his love, he can get them by learning to love his boyfriend's (healthier but not necessarily super-lean) ass. It'd be easier to moderate desires than dealing with grief. And most sexual desires are understandable in behaviorist terms... If he keeps having sex with his boyfriend, he'll relearn what sexy means gradually (especially if the bf is getting healthier gradually - it's not like the difference will be immediate)... CBT can help too.

This prudential business seems incredibly subjective in the arriving at one's judgements. And given these variables that exist in what people value, I fail to see how you could ever arrive at an objective standard of morality with sufficient detail to settle disputes about moral right and wrong.

It's not. Subjective preferences tend toward the same goal, psychologically. It's not the values themselves that matter, it's their end (enjoyment). And many preferences lead to things that we prefer not to occur. It's not impossible to change our desires, or at least to moderate them. And it's more prudent to do so, since the more our desires don't lead to pains, the happier we are in general. Which is the whole point IMO.

If healthy living is what does it for you, then more power to you. But if healthy living bores the life out of you, it's imprudent to live healthily just because you've bought this idea that a long life is what you should value.

IMO if healthy living bores the piss out of you, you're not trying hard enough to enjoy it. It's not like our preferences are set in stone. And I've bought the idea that I should value health because I am happier for it. Learn to like what's easy to get (and not dangerous) and you're happier without as many hangovers, constipation, etc. But to each their own.