Using "proof" by induction

Should we throw out "I think therefor I am"? Not everybody can experience it, since only I experience it.

People have to use inductive reasoning to form coherent beliefs.
Get used to it.

what's wrong with induction and why is it not a valid method of proof?

Popper already solved this problem.

Basically, induction is when you assume that something will be like something else that's similar without actually checking.

Inductive is the counterpart to deductive reasoning; with deductive reasoning, the answer is absolutely certain, given the premise. With inductive reasoning, the answer is probably true but not absolutely certain.

Here are two examples of inductive reasoning; one seems correct based on intuition, but the other is obviously wrong:
1. All the swans I have seen are white. Therefor, all swans are white.
2. The speed of light has been constant whenever and wherever measured so far. Therefor, the speed of light is the same in all parts of the universe.

2 is accepted as scientific fact even though there's no actual proof that that's the case, based only on the flawed inductive reasoning.

The examples you gave are not induction. For the first one to be induction, you should say:
I've looked at every swan in the world and they were white. Therefore, all swans are white.
Now it's induction.

>Basically, induction is when you assume that something will be like something else that's similar without actually checking.
No.

If you looked at every single swan in the world, that would be deductive reasoning because the answer is certain.

It's only inductive if there is room for doubt. The typical scientist in the modern era would happily use both of those examples I used, but they would insert the word "probably" to try to avoid responsibility for their statements, like the intellectual cowards they are.

>ow an we even start to root it out?
We first need to get rid of the axiom of infinity before we can worry about that

Warning signs that somebody is a brainlet fraud scientist:
1: They use inductive reasoning
2: They use the axiom of infinity
3: They use "imaginary" numbers

Induction requires you to assume things for which you do not have specific proof. If you had good proof it would no longer be induction. That requires you to make assumptions about things which are not proven.

What I said is true, but you're upset because I phrased it in such a way that exposed how flawed induction is in the first place.

The scientific method uses inductive reasoning you fucking retarded bitch I should kill you

Just use deductive reasoning instead

Wrong. The induction hypothesis is based on a deductive relationship.
Induction only fails if the deduction is wrong.

Another way to look at it is probabilistically. We can take a sample of the universe and see whether or not the deductive process is valid.
Then we can say with confidence that a relationship is true to some accuracy.
It turns out that induction holds for any arbitrary confidence, therefore, it converges to 100% certainty.

You have the principle of mathematical induction if and only if you have the well ordering principle. So your statement is rejecting both. You should thus be able to provide a counterexample of a nonempty subset S of the natural numbers with no least element.

Seems kinda absurd, scro

>if and only if you have the well ordering principle.

learn predicative math

there are so many rationalist spooks in this post, it's unbelievable

That's what all of statistics and science is you oaf-brain retarf

People in wheelchairs cant experience running
Checkmate atheists

(OP)
>Induction is NOT a valid method of proof. Any scientific paper that uses induction is garbage and should be disposed of.
Great, so when will you get rid of your flawed, induction based computer technology and stop posting here?

It's true that inductive reasoning can only be probabilistically correct, but you are wrong in thinking that you will ever approach 100%. You might get very close to certainty, but the only way to ever be absolutely certain is with pure logic and deduction. If you ever let induction in at any stage of thought, then, like a fungus, spread out and corrupt everything else with a disgusting layer of uncertainty. It can approach certainty, but never reach it.

Incorrect. In this framework, the validity of induction is deduced. The deduction about the process is completely reliable.

In reality, everything is approximated anyways, so the validity of induction is purely metaphysical in character.
If you don't like it, don't use it. Or better yet, find a contradiction. I don't like using induction if I can help it, but goddamn is it powerful.

Why risk walking around? You don't know the ground will continue pushing back and you might fall into the center of the planet.

Mathematical induction is deductive reasoning you retards.

this. OP is the equivalent of the guy high school that would say "what if we're all in the matrix? you can't prove we aren't!". you're right but pointing this out is not interesting or valuable

>like the intellectual cowards they are.
there will always be room for doubt. you just want a reason to feel smarter than them even though you aren't. that's what this entire thread boils down to

Correct me if I'm wrong but I don't think David Hume was actually against using induction pragmatically.

Go home Popper you're drunk

>proof
that's where you fucked up
natural science doesn't prove things
that's the formal sciences, and they're not inductive.

I think this is probably something we learned in the very first week of the very first year of a science degree.

>Mathematical induction is deductive reasoning you retards.
a proof by induction is deductive reasoning, the inductive inference rules have nothing to do with deduction.

>that's the formal sciences, and they're not inductive.
then how do you come up with the inference rules

you create a deductive construct such that induction returns values.

Just like you can create a construct in which inductive reasoning produces proof. Meaning the problem of induction can be artificially removed. But then the construct doesn't say anything explicitly about nature, or external reality. Which is also a problem of the formal sciences.

>Bayesian Inductivism
This seems really intersting, is there a book or papers explaining this?

>Mathematical induction is different but also not valid.
what is this fuck retarded shit?
What board am I on?
Is this real life?

bump

>PATIENT: doctor please help. i've been bitten by a rabid dog and need a rabies shot
>DOCTOR: but how do you know he was rabid? just cause other dogs that were foaming at the mouth had rabies doesn't mean he did
>PATIENT: technically that's true but why should that matter? i need that rabies shot doc
>DOCTOR: just cause it worked for other patients doesn't mean it would work for you
>PATIENT: can you please just give me the shot?
>DOCTOR: go read a philosophy book idiot

Kek, thanks user

ITT: 2nd-year philosophy brainlets argue dogmatically about things they don't understand. Pretty pathetic - we need mods on /sci to prune this bullshit so it doesn't slide legitimately interesting threads.

interesting

Probably a Christian shitposter. They're out in droves these days, attacking impediments to faith-based brainwashing.

holy fucking brainlet

>>>/reddit/autism

This 100%. It's pretty fucking sad that people on /sci don't understand the first thing about science.

>natural science doesn't prove things
then how do we know the atomic weight of carbon? honest question

because knowledge doesn't require proof beyond all doubt.

then why liberals use the idea of ''proof beyond all doubt.'' in their court of law to establish ''what happened''

the meaning of "beyond all doubt" is very different in colloquial language and in formal language

basically you can't know shit. but that doesn't mean we can't function and understand things.

without having read this thread much, something tells me that people ITT are confusing induction as used in reference to mathematical induction with induction as used in reference to philosophy, inductive reasoning, etc.

Also the OP is demonstrably wrong but he's one-up on me because I'm taking his bait.

Absolute proof doesn't exist, but logistic evidence does.

The inductive evidence is still evidence, it's just less reliable than deductive evidence.

Same is true for abductive evidence.

To claim induction is useless (and therefore inductive evidence doesn't exist) is... well, stupid and wrong.

> He doesn't know about the principle of non-contradiction
> inb4 le quantum physics interpretations maymay
Lrn2metaphysics, dumb dumb

It's not beyond ALL doubt, it's beyond a reasonable doubt. Saying "I know it really seems like I killed my wife, but dude what if we're all just brains in a vat?" isn't a reasonable argument.

shut the fuck up

That is not the reason induction works on the naturals. The naturals have an axiom called the well ordered property. Every nonempty subset of the naturals has a least element, 'a' such that a=1, If P(k) is true then P(k+1) is true.

Then P(n) is true for every natural n>=1.

Proof: Let S be the set of naturals such that P is false. Assume there is an element in S. Then S has a least element 'a' because S is a nonempty subset of the naturals. By assertion a=/=1 so a>1. Since a is least, a-1 is not in S, then P(a-1) is true. But by property 2, P(a) must be true. This is a contradiction and thus our assumption that S is nonempty is false. S is empty and P(n) is true for every natural n>=1.

>relying on classical maths in 2017

when does summer end?

[math]
\underline{induction}
\\
\underline{1^{\circ}} \\
f(n)= 1+2+3+...+n = \frac{n(n+1)}{2} \\
\underline{2^{\circ}} \\
n\rightarrow (n+1): \\
\left \{
\begin{align*}
f(n+1)&=1+2+3+...+n+(n+1) \\
f(n+1)&= \frac{n(n+1)}{2} + (n+1) \\
\end{align*}
\right.
\\f(n+1) = \frac{n(n+1)}{2} + (n+1) \\
= \frac{n^2+n+2n+2}{2} = \frac{n^2+3n+2}{2} \\
= \frac{(n+1)(n+2)}{2} = \frac{(n+1)((n+1)+1)}{2} \\ \\
=> \text{if f(n) is ok, so is f(n+1)} \\
\underline{3^{\circ}} \\
f(1) = \frac{1(1+1)}{2} = 1

[/math]

>tfw bayesian

its fun watching you plebs squabble over induction

Not a math guy, but isn't mathematical "induction" deductive reasoning?

Yes. The name induction is a very poor choice. They should really be called recursive proofs or something like that.

>Q.E.D. OP is a retard