Can we know something that has not been proven true?

Juwel

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(Original post by icy)
hey all

i've got a tok essay to do, and i need some ideas...

can we know something that has not been proven true?

All scientific theories are unproven. But the ones that last, and the ones we get in our textbooks, have not yet been disproved. This is why we accept these theories (not facts). Until 500 (I think) years ago we knew the world was flat...

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mikesgt2

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What about '2 + 2 = 4,' or any other mathematical truth? Has that proposition ever been proven to be true? We just take it to be true because it seems to be a necessary truth, we cannot conceive of it not being true. This does not amount to a proof, yet we rightfully consider it to be something we have knowledge of.

By the way, if you are talking about stuff like whether the sun will rise tomorrow the posh word is induction. Induction is the principle that the more times somthing as occured in the past, the more probable it's truth is. However, with the example of the sun rising, although our knowledge of the statement 'the sun rises every morning' is to be considered very probable due to numerous past instances, anything established through induction will never be certain. Induction is a principle, without which we could not live our lives, but it cannot lead to certain knowledge and cannot constitute a proof of anything. I would argue, then, that induction does not show that there are things we can know that have not been proven to be true.

If you want to read somthing about it, try http://www.ditext.com/russell/russell.html. I have found the book very heavy going and given up on it half way through, but it has some stuff about the theory of knowledge.

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Juwel

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Mathematical theories are different. Once it's proven (and Maths requires absolute proof, not just "well we haven't disproved it") it becomes a theorem (fact). Until then it's a conjecture.

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mikesgt2

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(Original post by ZJuwelH)
Mathematical theories are different. Once it's proven (and Maths requires absolute proof, not just "well we haven't disproved it") it becomes a theorem (fact). Until then it's a conjecture.

I am not talking about mathematical theories. I am talking about the very basis of mathematics. Like simple things such as 2+2=4... or things like m+n=n+m, mn=nm, m(n+k)=mn+mk... these are rightly accepted as knowledge but cannot be proven.

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++Hex++

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(Original post by mikesgt2)
I am not talking about mathematical theories. I am talking about the very basis of mathematics. Like simple things such as 2+2=4... or things like m+n=n+m, mn=nm, m(n+k)=mn+mk... these are rightly accepted as knowledge but cannot be proven.

I think a lot of maths is defined to be true. I reckon a number system of any sort is artificial really.

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++Hex++

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(Original post by mikesgt2)
Induction is a principle, without which we could not live our lives, but it cannot lead to certain knowledge and cannot constitute a proof of anything.

What about proof by induction...?

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mikesgt2

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(Original post by ++Hex++)
What about proof by induction...?

From what I understand of mathematical proof by induction, it is different to what I was refering to above.

What I was refing to was about arriving at probable principles from past experience (like that the sun will rise tommorow.) Mathematical proof by induction is not concerned with experience; rather, it assumes a general case and shows that if this is true then the next one is true. These are two different things aren't they?

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Juwel

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(Original post by mikesgt2)
I am not talking about mathematical theories. I am talking about the very basis of mathematics. Like simple things such as 2+2=4... or things like m+n=n+m, mn=nm, m(n+k)=mn+mk... these are rightly accepted as knowledge but cannot be proven.

Oh, axioms. Yeah we just take them as true, maybe someone who does Maths at degree level will tell us more...

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Vienna

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(Original post by icy)
repetition...
we assume that it will rise tomorrow, simply because it has always done so, but we cannot know for sure. repetition is not a plausible definition for truth.

thats my point.

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Vienna

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(Original post by hotnanoo)
not really he always acts like a monkey have'nt ou seen that tread tutut

acting is not being.

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Infinity

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(Original post by mikesgt2)
What about '2 + 2 = 4,' or any other mathematical truth? Has that proposition ever been proven to be true? We just take it to be true because it seems to be a necessary truth, we cannot conceive of it not being true. This does not amount to a proof, yet we rightfully consider it to be something we have knowledge of.

By the way, if you are talking about stuff like whether the sun will rise tomorrow the posh word is induction. Induction is the principle that the more times somthing as occured in the past, the more probable it's truth is. However, with the example of the sun rising, although our knowledge of the statement 'the sun rises every morning' is to be considered very probable due to numerous past instances, anything established through induction will never be certain. Induction is a principle, without which we could not live our lives, but it cannot lead to certain knowledge and cannot constitute a proof of anything. I would argue, then, that induction does not show that there are things we can know that have not been proven to be true.

If you want to read somthing about it, try http://www.ditext.com/russell/russell.html. I have found the book very heavy going and given up on it half way through, but it has some stuff about the theory of knowledge.

Well if you believe that one is in fact a single unit, then yes 2+2=4.
As far as the sun rising everyday, this would not be a probable statement, is it not a proven fact that the earth rotates while circling the sun, hence the sun appears to rise everday. Regardless it is a proven fact.

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Expression

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(Original post by ZJuwelH)
Oh, axioms. Yeah we just take them as true, maybe someone who does Maths at degree level will tell us more...

Basically axioms are the absolute corner stone of mathematics - we assume them to be true, and the results follow.

(Original post by Fermet's Last Theorem (Simon Singh, The 4th State, London 2002))
Appendix 8 - The Axioms of Arithmetic
The following axioms are all that are required as the foundation for the elaborate structure of arithmetic:

For any numbers m, n:
m + n = n + m and
mn = nm
For any numbers m, n, k
(m+n) + k = m + (n+k) and
(mn)k = m(nk)
For any numbers m, n, k
m(n + k) = mn + mk
There is a number 0 which has the property that, for any number n:
n+ 0 = n
There is a number 1, which has the property that, for any number n,
n * 1 = n
For every number n there is another number k such that:
n + k = 0
For any numbers m, n, k:
if k NOT EQUAL 0, and kn = km then m = n

From these axioms other rules can be proved. For example, by rigorously applying the axioms and assuming nothing else, we can rigorously prove the apparently obviously rule that:

If m + k = n + k, then m = n.

To being with we state that:

m + k = n + k.
Then by Axiom 6, let l be a number such that, k + l = 0, so:
(m + k) + l = (n + k) + l

Then by Axiom 2,

m + (k + l) = n + (k + l)

Bearing in mind that k + l = 0, we know that:
m + 0 = n + 0

By applying Axiom 4 we can at last declare what we set out to prove:

m = n

Hope that adds a little insight.

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Linda

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Jin, I'm disappointed in you. Looking for answers from a message board... Anyways - you should start by thinking about what is meant by "knowledge". How do we know something? How can we be sure we know something?

If something has not yet been proven true, then how can we know it? Does knowledge equate with truth? Does knowledge have to be "true" to be knowledge? Does a proposition need to be a justified true belief to be real knowledge? Does the justification have to involve proof? Is it proof?

Let's say a guy living before Galileo believe that the Earth is round. But it is not yet proven to be round. He justifies his belief by observations and experience as a sailor, and claims he knows that the earth is round. But does he really know it, if he can't prove it? (you know that 2+2=4, but can you prove it? It has been proven yes, but couldn't one say that you just believe it to be true, justifying it by coherence and correspondence theories of truth, using authority? What is the difference between you saying that you know that 2+2=4 and this guy saying the earth is round?) Later Galileo proves that the earth must be round. Can you say that Galileo knew it, but not the first guy?

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UWC student

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#34

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#34

Here's how I am looking at it

I am examining the concept of truth and the concept of knowledge. Once these two are defined (definitions are in the TOK book), I am going to examine homeopathic medications.

find something that has not yet been proven as real, yet we choose to believe it - aliens, sorcery and so on...

good luck and let me know how it went!

Hadar Meltzer

“Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth”- Sherlock Holmes.

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Linda

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(Original post by UWC student)
Here's how I am looking at it

I am examining the concept of truth and the concept of knowledge. Once these two are defined (definitions are in the TOK book), I am going to examine homeopathic medications.

find something that has not yet been proven as real, yet we choose to believe it - aliens, sorcery and so on...

good luck and let me know how it went!

Hadar Meltzer

you cant just look up a definition, you're supposed to think about it. The answer in the ToK book isn't going to be good enough.

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Jonatan

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(Original post by icy)
hey all

i've got a tok essay to do, and i need some ideas...

can we know something that has not been proven true?

From Gödel Escher Bash, an Eternal Golden Braid , by Hofstadter:

Tortoise: So what you are saying is that if two things are equal to the same they are equal to each other?

Achilles: Yes, I just wrote it down in my notebook:
A Things which are equal to the same are equal to each other

Tortoise: And we both agree that the two sides of a specific triangle may be equal to teh same.

Achilles: I have called that statement B, so we have:
A: Things which are equal to the same are equal to each other
B: The two sides of this triangle are equal to the same

Achilles: And so we may deduce:
A: Things which are equal to the same are equal to each other
B: The two sides of this triangle are equal to the same
Z: The two sides of this triangle are equal to each other

Tortoise: But might I not agree to statement A and B but still not to statement Z ?

Achilles: That would be remarkably foolish, but it is of course possible. Therefore I will addd a third statement which I should ask you to accept.

Tortois: Go ahead my dear Achilles.

Achilles:
A: Things which are equal to the same are equal to each other
B: The two sides of this triangle are equal to the same
C: If both statement A and B is correct, then statement Z is correct.
Z: The two sides of this triangle are equal to each other

Tortoise: But might I not accept A, B and C , but STILL not accept Z ?

Achilles: I suppose you could do so, even though it may be exceptionally foolish of you , but yet.....

My ( Jonatan's )conclusion: It is not possible to prove anything , regardless of the number of accepted postulates and axioms. Thus Mathematics is not absolutely proven. The proofs in mathematics seem obvious, but yet they are, just as any other proofs, only arguments which you may accept or not.

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brij

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Hi,
k, look i have included this example in my tok essay so far,
a = b
ab = b2 Multiply both sides by b
ab – a2 = b2 – a2 Subtract a2 from both sides
a(b – a) = (b + a)(b – a) Factor each side
a = (b + a) Divide both sides by (a – b)
a = (a + a) Since a = b substitute a and b
a = 2a
a/a = 2a/a Divide both sides by a
1 = 2

You guys think that this is a good example? below i jus wrote abit about Theoretically, the calculation above is correct, yet, we disproved something that is a very concrete piece of information. This raises the question whether our theory is correct or not. Can you guys help?
Also, i have one idea that may help some of you doing this essay, in physics, the michelson - morely and earth, adn speed of light and ehter and all that junk! please help me! and post some cool ideas!

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pedy1986

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(Original post by vienna95)
cognito ergo sum.

Your assuming too much. Thoughts may not require a subject.

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pedy1986

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(Original post by brij)
Hi,
k, look i have included this example in my tok essay so far, which is about 400 words!! AHHH its driving me crazy!

a = b
ab = b2 Multiply both sides by b
ab – a2 = b2 – a2 Subtract a2 from both sides
a(b – a) = (b + a)(b – a) Factor each side
a = (b + a) Divide both sides by (a – b)
a = (a + a) Since a = b substitute a and b
a = 2a
a/a = 2a/a Divide both sides by a
1 = 2

You guys think that this is a good example? below i jus wrote abit about Theoretically, the calculation above is correct, yet, we disproved something that is a very concrete piece of information. This raises the question whether our theory is correct or not. Can you guys help?
Also, i have one idea that may help some of you doing this essay, in physics, the michelson - morely and earth, adn speed of light and ehter and all that junk! please help me! and post some cool ideas!

The calculation is wrong, since a=b, therefore a-b=0, and you can't divide by 0

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elpaw

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(Original post by brij)
Hi,
k, look i have included this example in my tok essay so far, which is about 400 words!! AHHH its driving me crazy!

a = b
ab = b2 Multiply both sides by b
ab – a2 = b2 – a2 Subtract a2 from both sides
a(b – a) = (b + a)(b – a) Factor each side
a = (b + a) Divide both sides by (a – b)
a = (a + a) Since a = b substitute a and b
a = 2a
a/a = 2a/a Divide both sides by a
1 = 2

You guys think that this is a good example? below i jus wrote abit about Theoretically, the calculation above is correct, yet, we disproved something that is a very concrete piece of information. This raises the question whether our theory is correct or not. Can you guys help?
Also, i have one idea that may help some of you doing this essay, in physics, the michelson - morely and earth, adn speed of light and ehter and all that junk! please help me! and post some cool ideas!

you cannot divide by (a-b) because it is 0

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