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Does the number π really exist? watch

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    (Original post by Smaug123)
    The is/ought distinction seems a bit contrived to me - it is possible that we will eventually create a way to read off everyone's brains and construct a moral system that seems objectively best to everyone. It's not inherently impossible, just practically difficult. It certainly isn't in a separate magisterium to "hard science".
    The "existence of a god" question is an interesting one from the perspective of cognitive bias and perhaps evolutionary psychology.


    You assert that "accepting the saving of six lives at the unwilling sacrifice of one" is an indicator of mental unsoundness. I'd be interested to know why you say that, other than personal aversion to the idea. I might not be able to sacrifice the healthy life to save the six (blasted idiot brain, causing me to murder six people instead of one), but it seems considerably better to me.
    Obviously when you look at blunt facts it would be stupid in fact not to kill one person to save six people if the purpose was to ensure mankinds survival but we have morals embedded in us that tell us this is unacceptable which is why the idea has never been discussed at any meaningful level. Something in us tells us it's wrong, not because we've been raised like this but it's just inside of us. Now rephrase your question a bit so it actually becomes a question worth debating and I'll be happy to weigh in.

    But you must ask yourself the reason that question has never been asked at any significant level is because it's just common sense. If your question were "How many people do you think is acceptable to kill to ensure the survival of mankind?" I think this is a much better question which is similar to your question but is one worth discussing.
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    Oh look, we've been moved away from the philosophy forum.. about time!
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    (Original post by majmuh24)
    Isn't mathematical logic a whole different thing from philosophical logic though :holmes:
    We use the same rules of inference so far as I know.
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    Even though the OP is clearly out of his depth here, I am gratified to see how many seriously coherent and intelligent responses he has received.

    Damn, you peepz on TSR iz smart yo.

    To wade into the philosophical/scientific debate a bit, I was always very interested in trying to determine the full philosophical implications of Godel's theorems. It seems like people on this thread may know some good starting material on this matter?
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    (Original post by KeepYourChinUp)
    Obviously when you look at blunt facts it would be stupid in fact not to kill one person to save six people if the purpose was to ensure mankinds survival but we have morals embedded in us that tell us this is unacceptable which is why the idea has never been discussed at any meaningful level. Something in us tells us it's wrong, not because we've been raised like this but it's just inside of us.
    But why is it unacceptable? People die because it's unacceptable. If the question became "Would you sacrifice all the nematode worms in existence, in a way that preserved the ecology, so that you would live", the answer is presumably unequivocably yes - now just move up the scale in intelligence and down the scale in numbers. How many dolphins would you have killed so that you would live? How many dolphins would you have killed so six people lived? How many people already on the verge of death would you have killed so that you would live? How many ill people would you have killed so that you would live? How many ill people would you have killed so that someone else would live? And we have hit the original problem.

    The trouble with your assertion that "we have morals embedded in us" is that we don't all have the same morals. If we did, then your definition would probably be fine, but it's clear that everyone has different morals (extreme example: mass murderers). In that case, you are back to asserting that your morals are the best.

    Also, you need to prove that morals are intrinsic. Morals certainly shift with time, and are presumably changed by upbringing (witness the existence of religious fundamentalists, and the fact that some convert to different religions or to atheism). Given that morals aren't even constant to a given person, why should you assert that "it is unequivocally wrong to <perform action that you admit is objectively better>"?

    But you must ask yourself the reason that question has never been asked at any significant level is because it's just common sense. If your question were "How many people do you think is acceptable to kill to ensure the survival of mankind?" I think this is a much better question which is similar to your question but is one worth discussing.
    "All but a breeding male and female", is surely the correct answer. Although it does become more interesting if there is a probability distribution of the number of people who survive if a given number is sacrificed - then you need to do some expectation algebra.
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    (Original post by ClickItBack)
    To wade into the philosophical/scientific debate a bit, I was always very interested in trying to determine the full philosophical implications of Godel's theorems. It seems like people on this thread may know some good starting material on this matter?
    Some people insist that Gödel's incompleteness theorems don't apply to humans. It depends on whether you insist that humans are simulatable by Turing machines (we have no good reason to believe not, that I'm aware of, but some people state that we have souls or something).
    If you go with what seems sensible to me (that we are exactly as powerful in computation as any other Turing machine) then Gödel's incompleteness theorem states that there are statements which are true but which we cannot prove to be true. (That's assuming there is a maximum level of meta we can attain, which seems sensible given that the speed of thought is finite and that the universe will have finite lifetime; I've assumed that we will not be able to prevent the death of the universe, and that we will not be able to enter a new universe; neither of these is certain.) As far as I know, it has no practical significance on human thought (we're far too imprecise and think too slowly about too few things for that), although it (and the related Löb's Theorem) has some very interesting consequences on artificial intelligence design. (http://intelligence.org/files/TilingAgents.pdf)
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    (Original post by majmuh24)
    Which one of his theorems are you talking about?

    I assume you are talking about the incompleteness theorem, one of which essentially says that no consistent system can be proven to be consistent using it's own rules, which means that the Peano arithmetic system that we use is defined as essentially incomplete
    Both his incompleteness theorems. And yes, I understand what the theorems say about axiomatic systems - that any consistent system that is capable of expressing elementary arithmetic must be incomplete and incapable of proving its own consistency. What I idly wondered on occasion though was the repercussions of this on other aspects of human knowledge.

    For example, if I was to create a formal axiomatic framework to tackle human morality, would this necessarily be incomplete? My understanding is that Godel's theorem only applies to systems that are 'capable of proving basic arithmetic truths'; my morality system wouldn't satisfy this.

    What about non-arithmetical but logical axioms? Is it possible to prove that a set of logical axioms is self-consistent?

    Furthermore, does it necessitate that our understanding of the universe (loose term since I allow for the possibility of multiverses or super-universes etc) is fundamentally limited outside mathematics?

    I'm sure I had these questions better phrased at some point in the past but I haven't thought about it for a while so I'm coming up with these on the fly
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    (Original post by Smaug123)
    Some people insist that Gödel's incompleteness theorems don't apply to humans. It depends on whether you insist that humans are simulatable by Turing machines (we have no good reason to believe not, that I'm aware of, but some people state that we have souls or something).
    If you go with what seems sensible to me (that we are exactly as powerful in computation as any other Turing machine) then Gödel's incompleteness theorem states that there are statements which are true but which we cannot prove to be true. (That's assuming there is a maximum level of meta we can attain, which seems sensible given that the speed of thought is finite and that the universe will have finite lifetime; I've assumed that we will not be able to prevent the death of the universe, and that we will not be able to enter a new universe; neither of these is certain.) As far as I know, it has no practical significance on human thought (we're far too imprecise and think too slowly about too few things for that), although it (and the related Löb's Theorem) has some very interesting consequences on artificial intelligence design. (http://intelligence.org/files/TilingAgents.pdf)
    When you say that there will be statements which are true but we cannot prove to be true, are you referring to non-arithmetical statements? Why does this follow from Godel's theorem and the assumption that humans are Turing machines?

    Lob's theorem is very cool indeed .
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    (Original post by Smaug123)
    ...
    I would say that anyone who deemed it acceptable to kill an innocent person to save 6 ill people belongs in a mental home. It isn't about what "I" think is correct. It's about what 99% of the world view as correct and sure there might be that 1% who think it's ok but when we have 99% of the population deeming it unacceptable... it's probably because it's morally wrong. Morals do change with time and this is because we learn things about the world. We don't all have the exact same morals but the 21st century world generally has similar shared morals although there are some countries which still behave like Ancient Egypt.

    If you were to ask me how many cats would I sacrifice to save 1 child? I would sacrifice as many as needed, but not so many that they would go extinct. We could sit here all day and ask thousands of pointless questions about different things but why not focus on questions which are worth debating and thinking about? We're never going to find ourselves in a situation where we are killing cats to save 1 person so the question isn't worth discussing at any meaningful length.

    This topic was initially about pi so I don't understand why it's being dragged into pure philosophy about a totally unrelated subject... Bottom line is I'm all for Philosophy and I'm a great supporter of it, I think it's been invaluable to mankind and it always will be but it's only useful when applied to meaningful questions.

    An example of a good question: - A 6 year old and a 45 year old are both on the donar list for a heart transplant. The 45 year old is first on the list and the child is second on the list. Does the doctor give the heart to the child or the 45 year old? Every fibre of your being would want to give the heart to the child but this is morally wrong as the 45 year old is before the child on the list.

    An example of a bad question: - How many Dolphins would you kill to save a baby? While this question can be discussed and opinions shared it's just a pointless question. If the baby is in a pool of Dolphins then obviously you're going to kill them all to save the baby if they're attacking the baby.

    Anyway this discussion has exhausted me so I think I'm going to pull out lol. Philosophy is great, but only when meaningful questions are asked.
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    (Original post by alow)
    What I have learned from this thread:

    Philosophers really shouldn't talk about maths.
    LOL. Offer for Maths and Philosophy at Oxford right here :L
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    (Original post by skunkboy)
    A constant? Why a constant? Is it really a constant? And if it's not a number, what exactly is it? I'm not close-minded.

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    I should copyright the question mark. That way, by the end of this thread, I will have made enough off of you to never have to work.
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    (Original post by alexmufc1995)
    LOL. Offer for Maths and Philosophy at Oxford right here :L
    I genuinely don't understand why people would take philosophy with any science subject. Why did you pick it over straight maths?
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    (Original post by alow)
    I genuinely don't understand why people would take philosophy with any science subject. Why did you pick it over straight maths?
    Philosophy at Oxford is the rigorous philosophy (logic etc.) so doing Maths & Phil is a pretty good combination. Not that I'd ever bother with Philosophy myself...
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    (Original post by Noble.)
    Philosophy at Oxford is the rigorous philosophy (logic etc.) so doing Maths & Phil is a pretty good combination. Not that I'd ever bother with Philosophy myself...
    It seems to me like you would be in a better position by just doing more maths :dontknow:
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    (Original post by alow)
    It seems to me like you would be in a better position by just doing more maths :dontknow:
    Better position to do what? If you're interested in the rigorous kind of philosophy there isn't really an opportunity to do it studying straight maths until third year, and even then there's not much (I think logic is the only option) - so if you are interested in doing philosophy then it doesn't make much sense doing straight maths at Oxford. Also, if you know you're not a fan of applied maths, you'd be better off not applying for straight maths.
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    (Original post by alow)
    I genuinely don't understand why people would take philosophy with any science subject. Why did you pick it over straight maths?
    Noble has summed up my reasoning pretty well. I've always enjoyed reading and writing essays, yet at the same time I find studying maths very interesting. I'd seen the combination a couple of years ago, during a 'Careers advice' meeting, and I've been working towards this ever since.

    Also, in terms of job prospects, doesn't the joint course show two different skills? Maybe it's just me, but I reckon that can lead to a greater number of areas where work is available?

    (Original post by Noble.)
    Philosophy at Oxford is the rigorous philosophy (logic etc.) so doing Maths & Phil is a pretty good combination. Not that I'd ever bother with Philosophy myself...
    Thanks I wouldn't really say that I dislike applied maths either, so it's a bit of a shame I have to miss out on that!
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    (Original post by alow)
    What I have learned from this thread:

    Philosophers really shouldn't talk about maths.
    hillarious, people on this forum are clearly clueless as to the field of study entitled 'the philosophy of mathematics' which well, David Hilbert, Godel, Poincare, Russell, Euclid and pretty much every mathematician worth noting have been concerned about, the question does there exist a number is actually much more difficult than you schmucks are making out
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    (Original post by alow)
    I genuinely don't understand why people would take philosophy with any science subject. Why did you pick it over straight maths?
    Um, maybe he wants to study both philosophy and mathematics? What's so surprising about that:confused:

    The fields are related to one another.
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    (Original post by John Stuart Mill)
    hillarious, people on this forum are clearly clueless as to the field of study entitled 'the philosophy of mathematics' which well, David Hilbert, Godel, Poincare, Russell, Euclid and pretty much every mathematician worth noting have been concerned about, the question does there exist a number is actually much more difficult than you schmucks are making out
    I completely agree, except from the last part.

    The OP is asking whether one particular number exits, while assuming that other numbers do (it makes no sense to ask whether a particular number exists as apposed to others if you question the existence of all of them), because you can't define the value of Pi using any quantity (probably the wrong word but oh well) other than Pi. Well, that's just retarded. I mean, using the op's argument, the number 2 does not exist, because you can't express the numeral value of 2 without referencing a value that equates to 2. It's just nonsense.
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    (Original post by Implication)
    I maintain that the existence of numbers is completely trivial once existence is defined. Numbers are abstract, so obviously they don't have physical existence as OP seems to want.

    Aside from the facets of ontology that have been supplanted by useful study such as science and mathematics, it seems to be little more than arguing over how to define things. I contend that most of the questions that empiricism cannot touch are either "dissolvable" (i.e. complete non-issues) or unanswerable in the first instance.
    Wow, touching upon a lot of huge philosophical points here. I don't want to get into a long discussion about all of them tbh

    You're correct that numbers have no physical existence, but them being abstracts doesn't prove they don't exist. Many mathematicians and philosophers would say that if all sentient beings died then the rules of mathematics and valid inference (which includes numbers), exist as a fundamental part of the universe. Others would argue that they're a purely human construct that happens describe the way the universe is, but are not an actual part of the way the universe is structured. Big philosophical issue there.

    Arguing over how to define things is far more important then you make out; logic, in practical terms, is useless without definitions that comply with reality.

    You're making an empiricist epistemological assumption; which is by no means a closed debate in philosophy.
 
 
 
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