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#55
Mar2011, 01:21 AM

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Dear Dave, When you apply 1+1=2 to the real world we see around us and find that it works, isn't that the ultimate proof that 1+1=2 is true and not merely an axiom? Thank you for taking the time to answer my questions. You have been very helpful and I hope we communicate again some time. Just as aside, The statement, " I think therefor I am." is a famous statement but is incorrect. I trained in Raja and Jnana Yoga in an ashram in the 60's. We did many mental exercises that proved to me through personal experience that "I am" whether I think or not. In fact, I can realize that "I am"
more fully when my mind is completely silent. Thanks again. 


#56
Mar2011, 07:21 AM

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I looked back and found that I had said the same thing in this thread two and half years ago! 


#57
Mar2011, 10:18 AM

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Since you had restarted this thread after it had had a well deserved rest for two and half years,
While mathematics "assumes" things for one kind of mathematics, in total, it considers all possiblilties. If you want to say that mathematics alone cannot "prove" statements about nature or, say, physics, then you would be perfectly correct. That is not what mathematical proofs do. I will say the same thing I said above (and two and a half years ago!) all statements in mathematics are of the form "If ... then ...". All mathematics does is say "If" the axioms are true, then these are the things that will follow. You cannot argue that mathematics is "wrong" by arguing against the axioms, though you could argue that it is useless because we do not know whether those things are true or not. But history has shown that, indeed, mathematics is very useful! And it is useful in so many different ways specifically because it "assumes" so many different things. For any application, there is bound to be some form of mathematics that "assumes" just what you want! 


#58
Mar2011, 10:33 AM

P: 15,319

Descartes decided to see what would happen if he doubted everything. He quickly digressed to doubting his own existence. He concluded that, in order to doubt his own existence, there had to be something doing the doubting. Whatever that something is, it defines I. I'll phrase the concept within your learnings: 


#59
Mar2011, 10:44 AM

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Though it would be unfortunate to define oneself as "that which does not think"!



#60
Mar2011, 10:48 AM

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Do you see no value in saying to yourself "If I do this, what will be the consequences"? 


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