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# Does the number π really exist? watch

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1. (Original post by ockhamsshotgun)
I do not mean to suggest that the symbols are important. I shall reformulate for clarity: Are the axioms of mathematics human or universal?

I ought to add that I believe they are universal, but the question itself is one of epistemological value.

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The axioms of mathematics are non-logical. They're just definitional: mathematics says "hey guys, if we assume these things then all this wonderful stuff pops out!". And we assume things in such a way as to create a system that is useful for describing the universe.

The axioms of mathematics are arbitrary in the sense that we were perfectly free to choose any axioms we wanted. We choose the ones we do because they give us a useful and sensible framework. If we'd chosen different axioms we might have got a different system, a useless system or no system at all: it's perfectly possible to choose axioms from which one can deduce absolutely nothing.

However, in some sense I think there is good reason (if such a concept can be applied here) to think that logical axioms (or rules of inference, more precisely) are completely objective and universal.

Can Q ever be false if P is true and P Q?
2. (Original post by St. Brynjar)
Pi is a ratio, and a number.
Actually, that ratio causes Pi. But Pi is a number? I'm not sure now.

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3. (Original post by KeepYourChinUp)
A doctor is just as less qualified as a lawyer to answer this question. Who in their right mind would deem it acceptable to kill a perfectly healthy human being in order to save 6 ill people? This just isn't how the world works and are philosophers seriously debating that question? If so then I'd strongly question the mental state of said philosophers. Now here is a meaningful question in my opinion and one that requires the input and thought of not just philosophers but mankind in general.

If you went into a burning building and saw a man unconcious but you hear the faint sound of a baby crying. Who do you go to rescue first? Do you take the time to find the source of the crying and rescue the baby or do you rescue the man before he dies from smoke inhalation? Instinct says to go find the baby although in my opinion this is the wrong choice. You rescue the first person you see unless that person is able to rescue themselves. The thing is there is no right answer to this type of question which is why it belongs in the philosophy section.

People have different opinions about different things and sometimes there is no right answer, only opinion which is why philosophy asks questions and science answers them, or some of them at least.
I think the question I posed is definitely a precarious one and often used against act utilitarianism. I used it because one could say that it is medical and demonstrating how even 'professionals' linked to this area could struggle and not even have any legitimacy in answering this sort of question.

Your proposition is one in which definitely poses difficulty and 'brings out' our intuitions vs logic. I agree definitely one for philosophy and definitely shows why someone, a fireman in this instance, may use philosophy to explore questions such as this.
4. (Original post by alow)
What I have learned from this thread:

Philosophers really shouldn't talk about maths.
Why not? Are we now living in North Korea or China? No more freedom?

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5. (Original post by Clip)
This is just turning into one of *those* late night conversations with some idiot who just wants to be annoying or contrary by questioning how you know you're not a hamster or trying (like a six year old) to answer every statement with "why?"
When someone is being contrary it is usually because they are involved in what is known as a debate. You, having contrary opinions may find this idiotic and annoying, but that is the nature of conversations and debates. It is important in debate to explore and exhaust all avenues of inquiry no matter how trivial or 'silly' in order to get a broad and informed picture of the subject.
6. (Original post by Noble.)
If you have to ask "What is the use of ?" one of the most fundamental constants in mathematics, you should probably go back to the drawing board and restart primary school level mathematics. It'd be quicker mentioning areas of mathematics where doesn't rear up.
It's about the existence of Pi and about its value , not talking about the use of it.

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7. The answer would be similar to the answer to the question: do perfect circles really exist?

Both exist in the mind of a mathematician.
8. (Original post by felamaslen)
Both exist in the mind of a mathematician.
and nothing exists in the mind of a philosopher it seems.
9. (Original post by majmuh24)
Keep your philosophy away from maths, it won't end well

Pi does exist, and it tends to pop up in a lot of areas of maths. It is formally defined as the ratio of a circle's circumference to it's diameter, but as it is a transcendental number (cannot be a root of any polynomial with rational coefficients), so it's exact value is never be calculated, although many series have been made that rapidly converge to an approximation and even some that can give you a specific digit of pi.
How do you know Pi does exist if its exact value never be calculated? Have you ever seen its exact value?

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10. (Original post by skunkboy)
Why not? Are we now living in North Korea or China? No more freedom?

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Nope, it just makes them look silly. Someone who doesn't understand rudimentary maths shouldn't be trying to pretend they can think deeply about maths.
11. (Original post by HJ M)
I think my last post bears in well on your point:
'Scientists generally specialize in their subjects whereas philosophers look at overall principles and how they work together, therefore not only examining all these different fields and questions but linking and combining them giving way to a sort of completeness of human understanding which is why philosophy is important and philosophical questions (where valid, unlike the questions you propose) are present in our everyday lives.'
I think a problem with this though is that in many cases specialist knowledge is required to understand philosophical implications. And this is evident when you consider how much quantum physics has been *******ised by pseudo-intellectual idiots masquerading under the guise of "philosophers". Without a thorough and proper understanding of fundamental physics I think it's arrogant to the point of stupidity to try and pursue a "completeness of human understanding". I talk of physics specifically because it's my field of study, but I'm sure there are similar concepts in other branches of mathematics and natural science.

I think there are very few (if any) "important" philosophical questions that can be answered by armchair philosophising. If by philosophy we just mean a broader study of reality, then I agree. But again, I think this can be better achieved for an individual by pursuing a wide range of more academic subjects than by pursuing "philosophy" explicitly.. but maybe that says more about current teaching of philosophy than philosophy itself.

(Original post by HJ M)
If you ever watch House, one thing I remember also supports my point is in one episode when diagnosing someone the brain specialist says the problem is with the brain and House says 'well of course you're going to say that, your the brain specialist'.
And this is a valid criticism... but I contend that it is better to know lots about something than nothing about everything. Sadly, contemporary philosophers who do not specialise in more academic fields are much closer to the latter.

We want someone who is a "specialist" in the brain and the rest of the body; not someone who lacks an understanding of both the brain and the body!

(Original post by HJ M)
A lot Philosophical questions cannot simply be answered by 'hard' science. I would question the idea that a doctor is more qualified to say if it is right to kill a healthy person in order to use his organs to save six ill people. Yes, there are aspects of it that a doctor could have more bearing, but I don't think they would be more qualified. You also have to remember that most people who study philosophy, do not become full-time philosophers. Doctors, politicians, lawyers etc. are examples of groups of people who study philosophy because of these questions that arise and how they impact their work and the methodology used in philosophy.
I contend that someone qualified in medicine is more qualified to say if it is right because they better understand the consequences.

I can understand people in the professions you mention studying philosophy for the answers to those questions. But in those circumstances it is still only specific branches of philosophy e.g. moral/ethical philosophy. Metaphysics, for example, is in my opinion the epitome of useless armchair speculation.
12. (Original post by skunkboy)
How do you know Pi does exist if its exact value never be calculated? Have you ever seen its exact value?

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Have you ever seen the exact value of two? No, because it doesn't make any sense. You've seen something physical to which the exact value of two can be applied... and if that's your (uneducated) definition of what it means for a number to "exist", then there are indeed some numbers that "don't exist". But pi is not one of them, since there are many physical things to which its value can be applied.

The exact value of pi is pi. It has no finite decimal representation, but so what?
13. (Original post by skunkboy)
How do you know Pi does exist if its exact value never be calculated? Have you ever seen its exact value?

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Basically the entire premise of your argument is based on whether or not we can write the number. So by that logic grahams number doesn't exist. Grahams number +1 doesn't exist, ect ect. We could think of an astronomically large number and there wouldn't be enough time in the universe to write the number down, even in the form of so you're saying that because a number is too large for us to fully represent, it doesn't exist?
14. (Original post by KeepYourChinUp)
Why are you always asking ridiculous questions? You're not a philosopher you're just asking stupid questions as if they have some sort of meaning.
15. I think a problem with this though is that in many cases specialist knowledge is required to understand philosophical implications. And this is evident when you consider how much quantum physics has been *******ised by pseudo-intellectual idiots masquerading under the guise of "philosophers". Without a thorough and proper understanding of fundamental physics I think it's arrogant to the point of stupidity to try and pursue a "completeness of human understanding". I talk of physics specifically because it's my field of study, but I'm sure there are similar concepts in other branches of mathematics and natural science.
I think you've definitely hit a problem there with those who would consider themselves 'philosophers' but are only a detriment to philosophy. In terms of completeness of human understanding, I think what is meant by that is the understanding of how all these different areas are linked and combined within our understanding. For example, a complete understanding could involve knowing that morals, politics, knowledge, religion and the self are all combined and each have there own implications and consequences and can be examined in such a way which gives us this 'completeness' of understanding.

I think there are very few (if any) "important" philosophical questions that can be answered by armchair philosophising. If by philosophy we just mean a broader study of reality, then I agree. But again, I think this can be better achieved for an individual by pursuing a wide range of more academic subjects than by pursuing "philosophy" explicitly.. but maybe that says more about current teaching of philosophy than philosophy itself.
Active engagement is certainly important, I agree on that point. I think philosophy is definitely a worthwhile pursuit as I have previously noted and I think it is most useful when used alongside something else, not just on its own in an 'armchair'. Of course you do have those which engage in philosophy everyday and those people do contribute to our understanding and these questions which cannot be definitively answered and this is valuable.

And this is a valid criticism... but I contend that it is better to know lots about something than nothing about everything. Sadly, contemporary philosophers who do not specialise in more academic fields are much closer to the latter.
I agree, I think the phrase 'jack of all trades, but master of nothing' sums it up. I think there is a fine balance between 'subject bias' (for lack of a better term) and have subject specialism with a broad understanding of its links with other areas and implications which allows one to contribute in a vast array of ways to their specialism and philosophy.

We want someone who is a "specialist" in the brain and the rest of the body; not someone who lacks an understanding of both the brain and the body!
As I said wider specialism and understanding is invaluable, in my opinion, to making philosophy more relevant and more valuable than the way it is conducted by some people.

I contend that someone qualified in medicine is more qualified to say if it is right because they better understand the consequences.
I disagree, I think in the instance of the question I pose it's difficult to defend the idea that a doctor would be more qualified to say if it is right. In the particular thought experiment it is a trade off between one and six and the implications of that decision. Medically, a doctor may indeed be able to tell us how many patients survive, that the healthy man will probably die etc. But the doctor can't add anything that say a lawyer could to this question. A lawyer would be able to tell us the current legal interpretation of the the choices in his opinion and argue on that basis, but looking solely at the question has no bearing in terms of giving us a better argument. I would add to my previous comments that the value of outside specialism depends on what you are asking.

I can understand people in the professions you mention studying philosophy for the answers to those questions. But in those circumstances it is still only specific branches of philosophy e.g. moral/ethical philosophy. Metaphysics, for example, is in my opinion the epitome of useless armchair speculation.
A would say that it is harder to see the 'value' of metaphysics, but it does have its value and it relies on what you are asking and exploring.
16. (Original post by KeepYourChinUp)
and nothing exists in the mind of a philosopher it seems.
Tell that to Newton, Bacon, Descartes, Popper and the dozens of other scientist-philosophers.

They don't call them Cartesian co-ordinates for nothing.

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17. (Original post by ockhamsshotgun)
Tell that to Newton, Bacon, Descartes, Popper and the dozens of other scientist-philosophers.

They don't call them Cartesian co-ordinates for nothing.

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Was a joke. I regard a lot of philosophers to be extremely smart people. Note I said Philosophers are smart, not wannabe philosophers who ask silly questions. There is a difference...
18. Stop being irrational.
19. (Original post by Zen-Ali)
Stop being irrational.
Actual lol

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20. (Original post by Obiejess)
Actual lol

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