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June 29th, 2014, 11:34 AM   #31
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Originally Posted by bobsmith76 View Post
I am new to mathematics in the sense that I'm only starting to independently read books on higher maths, mostly mathematical logic and set theory. I came to math from philosophy, usually it's the other way around. I wanted to prove my philosophical arguments and I discovered that I had better find out how mathematicians prove their arguments. To my astonishment I found that many mathematical arguments are enormously slipshod. I have now become a very radical logician and reject many of the axioms that most logicians accept. Consequently, I have come to be quite skeptical of many mathematical arguments. The discussion I want to generate here is in your opinion how much bluffing goes on in the mathematics community? Let's describe what bluffing is:

x bluffs about y means x knows that x does not understand y and x says something so that z will believe that x understands y.

E.g. Jim bluffs about Godel's theorem means Jim knows that he does not understand Godel's theorem and Jim says something so that Ryan will believe that Jim understands GT.

Let's contrast bluffing with another form of intellectual fallacy: self-deception. Self-deception is like bluffing but not exactly.

x deceives themself about y means x believes x understands y but x never tests x to determine if x really understands y and x does not understand y.

E.g. I deceived myself that I proved the Continuum Hypothesis means I believe I understand the Continuum Hypothesis but I never tested myself to determine if I really understood the Continuum Hypothesis and I do not understand the Continuum Hypothesis.

I think self-deception is much more widespread than people are willing to admit. I have personal experience with self-deception because there have been numerous times when I wrote up all these logical symbols on paper and thought I had proven something and didn't bother to test them for months but then when I tried to get a computer to process the symbols it turns out that I had just built a house of cards.

I think there is a lot of self-deception in the mathematics community mostly because mathematicians are not forced to use their symbols to solve real world problems.
We deceive ourselves at all levels. As brilliant as mathematics is at solving real world problems, it still isn't the complete answer. Our mathematics cannot solve highly complex problems containing an extraordinary amount of variables or dimensions. Our universe is unpredictable therefore there are no clear cut conclusions we can derive out of the use of mathematics. There is an element of unpredictability in everything we measure. It's something us humans have to accept.

Your actions today may seem sound, but tomorrow those actions may lead to unforeseen and undesirable results.

Humans will make mistakes as problems are mostly multi-dimensional - not linear. The fact that we deceive ourselves and tend to judge books by their covers is not very surprising.

We like to use phrases such as should've, could've, would've and what if - but they're probably not as useful as we think they are. Hindsight is something that we experience after ourselves or others have made mistakes, but unfortunately - it can't change the past.

We seem to be passengers on this journey through life. We usually behave differently after making mistakes. That is why the best mode of reasoning is to question ourselves and our beliefs, ask questions and constantly revise the methods we use to solve problems. The scientific method allows us to do this.

Logic is useful, but it should be used under the framework of the scientific method.

Last edited by perfect_world; June 29th, 2014 at 11:50 AM.
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June 29th, 2014, 12:07 PM   #32
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If someone were to tell me they understand mathematics, I'd have to ask them what sort of mathematics they understand. They'd have to be more specific. Let's say they claimed to understand basic mathematics up to GCSE level... What I'd do is ask them to provide me with evidence to back up those claims.

To consider the evidence I'd have to be competent at doing basic mathematics up to GCSE level myself. If I were to give them challenging GCSE questions to answer, I'd have to be able to answer those challenging questions with a high degree of accuracy.

If I were to ask them for evidence in the form of a qualification certificate, I'd have to know what an original education certificate looks like. I'd also have to make sure that they are who they really say they are.

It would be very hard for someone to convince me that they understand something that they truly don't understand. There would be so many ways to figure out whether they were telling the truth or not.

I won't believe claims until I'm given the evidence that back up those claims - especially when trying to make important decisions.

The more weight there is to a piece of evidence, the more believable it can become.

Last edited by perfect_world; June 29th, 2014 at 12:12 PM.
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June 29th, 2014, 12:25 PM   #33
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On the other hand, if someone were to tell me they were a chemical engineer - and let's say I knew nothing about chemical engineering, I wouldn't be in the position to figure out whether they were telling the truth or not.

Reliable sources would have to help me figure out whether that person was being honest or not. At first I would not reach any conclusions and I would keep my mind open to the possibility that the person was lying or maybe telling the truth.

I wouldn't jump to any rash conclusions.
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July 5th, 2014, 06:36 AM   #34
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I have no idea what that picture is about.
Does anybody here knows what the picture is about?
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July 5th, 2014, 06:46 AM   #35
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Originally Posted by perfect_world View Post
Humans will make mistakes as problems are mostly multi-dimensional - not linear.
Since this is a math forum I feel obliged to point out that multi-dimensional is orthogonal to linear: you can be multi-dimensional and linear, multi-dimensional and nonlinear, single-dimensional and linear, or single-dimensional and nonlinear.
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