What makes mathematics certain knowledge?

Original post by ~MiserableLogic~

Perhaps logic and science are incorrect. What makes that an impossibility? Surely it is a valid possibility. Note how I did not state this was your position. I am committing no straw man fallacy. I am merely positing the possibilities.

Mathematics is a social concept. It was not discovered, it was invented to help us better understand other subjects like science.

Therefore saying how can maths be wrong is like saying to the mother of a child 'how do you know your child is called Bob?'. She knows its true because she assigned him that name.

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Reply 21

zoe_bartlett

Original post by ~MiserableLogic~

Philosophy and science are human constructs too. Perhaps they are internally valid or perhaps not.

Science is not a human construct.

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Reply 22

zoe_bartlett

Original post by Martyn*

“Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.” - Friedrich Nietzsche.

Good quote :-)

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Reply 23

~MiserableLogic~

OP

Original post by zoe_bartlett

Science is not a human construct.

The scientific method surely is. Ever heard of Popper's falsification principle? It was a modern turning point in philosophy of science and the scientific method in general. It simply relied upon what was evident - it is far easier to disprove something than affirm it with certainty. Only humans could construct something so elegant and yet so simple.

Reply 24

Cringe

12

mathematics can use infinity but you cant undestand it normally.

Reply 25

Post121

8

There is only uncertainty in reality because the set of reality exceeds what we can observe. However, there is no uncertainty on a set we explicitly define (necessarily by construction). Mathematics builds on/lives in such sets we explicitly define on, not the set of reality. For instance, I think up a monster with only one leg. There is no uncertainty on whether the monster has two legs because I constructed it with one leg.

Reply 26

Cringe

12

you can make functions and equations to solve problems, wheras in english you would ask questions and answer them in enghlish

Reply 27

Eboracum

18

Because Descartes says it is?

Reply 28

eeeeeh

8

maths is a human invention. maths is how we interpret patterns in the world etc. it is certain because if something doesn't fit, we simply adjust the rules. maths doesn't exist objectively outside of human interpretation!

Reply 29

Lord of the Flies

19

Original post by Eboracum

Because Descartes says it is?

Then it's probably wrong.

Reply 30

moritzplatz

12

maths isn't certain knowledge.
what is certain is that IF YOU ASSUME SOMETHING, then you can deduce a lot of other things.
this things you deduce are "certain" as long as your axioms (Assumptions) hold.
All this process rely on logical deduction.

Reply 31

Stevo112

17

Original post by ~MiserableLogic~

Why can mathematical knowledge not be doubted? What gives it the characteristic of certainty? No one has ever coherently answered this question, as far as I am aware. Everyone just seems to take for granted its certainty like they take for granted causality's existence, for instance. Please explain, in full detail, why it is certain. Preferably without utilising formulas or proofs. To wit, referencing formulas or proofs is fine but they cannot be used to elucidate this matter for uneducated individuals.

Umm say what?

x + 2 = 3

x = 1

there is no doubt that there exists a solution for x which is clearly defined... there is no doubt that x is equal to 1.

The only issue I have is to what extent mathematics may be a man-made concept whereby we have constructed a static subject where it is actually more fluid. An obvious example would be comparing the effect of gravity on large objects and the effect of gravity on quantum objects. There is a big variation and thus whilst mathematics represents an airtight model for the majority of the observable universe there is a discrepancy in certain situations.

I would therefore suggest that mathematics can most certainly be doubted and it actually should be. But for the pure mathematicians the work that they do is beyond any doubt correct and certain.

I personally think that the real mathematics of the universe is completely unlike that of what we have right now. Not many people would agree with this and certainly not those who have published elaborate proofs. Yet i'm not smart enough to prove them wrong :p:

(edited 11 years ago)

Reply 32

~MiserableLogic~

OP

Original post by Lord of the Flies

Then it's probably wrong.

(1) That is rather arrogant for you to disregard a genius' philosophical views completely.
(2) You could have validly countered his argument by pointing it than it is an appeal to authority and possibly a false one at that.

Just because Descartes suggested something it doesn't make that thing automatically right or wrong. Truth is established through evidence and reasoning, not an expert's opinion.

Reply 33

Lord of the Flies

19

Original post by ~MiserableLogic~

(1) That is rather arrogant for you to disregard a genius' philosophical views completely.
(2) You could have validly countered his argument by pointing it than it is an appeal to authority and possibly a false one at that.

Just because Descartes suggested something it doesn't make that thing automatically right or wrong. Truth is established through evidence and reasoning, not an expert's opinion.

Wow you thought I was serious? Miserable logic indeed.

Reply 34

miser

20

Mathematics is a purely logical discipline, which means that it allows one to take truths (axioms) which are by their nature self-evident, and from derive them truths which are not self-evident, but which are nevertheless demonstrably true. For mathematics, nothing needs to be taken on faith at all - not even the numbers themselves, which can be thought of (by sceptical mathematicians) to simply be concepts which are useful to us, which do not necessarily actually exist independent of human thought. Arithmetical operations (addition, multiplication, etc.) are defined in terms of procedures that can be carried out on numbers, again not as necessarily concrete ideas that exist independently of humans. So, given that we have numbers (whether we invented them or discovered them), and given that we have created various operations and notations, all the proofs that exist are essentially the recorded observation of patterns that have been discovered.

So long as everyone agrees on what numbers are and the notation that's used, all mathematical 'truth' is simply implied by the concepts everyone already shares - proofs are just non-obvious implications. You can almost say that everyone already agrees on all the proofs that exist, they just don't know they do yet.

Reply 35

ThatPerson

18

Original post by ~MiserableLogic~

Why can mathematical knowledge not be doubted? What gives it the characteristic of certainty? No one has ever coherently answered this question, as far as I am aware. Everyone just seems to take for granted its certainty like they take for granted causality's existence, for instance. Please explain, in full detail, why it is certain. Preferably without utilising formulas or proofs. To wit, referencing formulas or proofs is fine but they cannot be used to elucidate this matter for uneducated individuals.

Prove that you are alive, and that you are you. Then you will understand mathematics.

Reply 36

~MiserableLogic~

OP

Original post by Lord of the Flies

Wow you thought I was serious? Miserable logic indeed.

I have a disposition to interpret peoples' comments literally. I apologise for my neuroanantomy. :rolleyes:

And do not mock me. You are neither funny nor witty.

(edited 11 years ago)

Reply 37

~MiserableLogic~

OP

Original post by ThatPerson

Prove that you are alive, and that you are you. Then you will understand mathematics.

The former is easy to prove with empirical evidence, but the latter is probably impossible to prove. It is the major issue of self-identity.

Reply 38

Eboracum

18

Original post by Lord of the Flies

Then it's probably wrong.

Descartes knows best. So he should rule. :cool:

Reply 39

shamika

16

Original post by ~MiserableLogic~

Why can mathematical knowledge not be doubted?

I doubt it all the time!

What gives it the characteristic of certainty?

This is a different question, and one I feel is more sensible. As others have no doubt stated, mathematics follows the axiomatic method. You assume certain propositions are true (I believe philosophers have a similar concept in 'base truths') and use a series of logical steps to deduce everything else.

The interesting thing is how much you can derive from very innocent looking propositions.

Two questions arise from the current way of doing maths:

1) what are mathematical objects? I won't get into all the details, but there are two different camps: the realists purport that mathematical objects have an intrinsic existence quite outside of our mathematical language and axioms. The other camp, formalists, claim that the axioms define the mathematical objects we play with. Both views have their flaws, but if I were to choose one, I'd be quite strongly in the formalist camp.

2) how do we know the mathematics we do makes sense? This is a question where there has been a huge amount of research by mathematicians (where we call all related areas 'foundations', for obvious reasons) as well as philosophers, logicians, and even computer scientists. If you want to get into it properly, you need to learn about sets and logic rigorously.

No one has ever coherently answered this question, as far as I am aware. Everyone just seems to take for granted its certainty like they take for granted causality's existence, for instance. Please explain, in full detail, why it is certain. Preferably without utilising formulas or proofs. To wit, referencing formulas or proofs is fine but they cannot be used to elucidate this matter for uneducated individuals.

This is quite frankly a stupid thing to want. Why on earth would you want to study mathematical certainty without formulae or proofs? And why would an uneducated individual care about the mathematical certainty at all?

Mathematical proof and formulae are tools used by humans to make the underlying concepts more understandable. If you can't be bothered to learn at least something about the way they work, there is absolutely no way you should bother with your question at all!

Oh, and all people saying we should take Descartes word for it: huh? Others can't disagree because Descartes said so? Didn't realise all of the worlds philosophical questions were already ubiquitously resolved!

(edited 11 years ago)

What makes mathematics certain knowledge?

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