There are seriously people who believe mathematics isn't based on observation

>there are seriously people who believe mathematics isn't based on observation

observe pi

Good argument. Infinite objects are hard to observe but the more we can observe that system the closer we get to pi.

>Sources of knowledge

Sciences that use deduction and induction as their methods do not generate new knowledge, they just study stuff that is alredy there.

Mathematicians didnt create any new knowledge when they first realized 2+2 was 4. 2+2 was 4 even before anyone noticed because it logically derives from the initial axioms.

>Thirdly, Peirce argued that abduction is the logical inference by which new knowledge could be obtained: \Abduction consists in studying the facts and devising a theory to explain them. Its only justi cation is that if we are ever to understand things at all, it must be in that way.

So sciences who produce new knowledge are those who use abduction like philosophy.

Im not saying that one is better than the other but you should stop talking shit you dont know about.

It's funny because this is actually a little paradox

>A: I can know anything by observing and by comparing
>B. Okay. How long is this line?
>A: Let me see that. Oh it continues beyond that horizon.
>B: Yes. It is infinite. No matter how far you walk, you will never see the end of this line.
>A: So you are saying "observe this object that you can't observe because you can't observe it?".
>B: Yes. I'm a clever boy.

>do not generate new knowledge, they just study stuff that is alredy there.

I don't think you understand the difference between knowing vs existing.

Come on, lets not be too semantic. I clearly understood what he meant.

Imagine you have 3 pieces of "knowledge"
>A = 5
>B = 10
>and C = A*B
You do the multiplication and finding out C = 50. Is this a 4th line of 'knowledge'? Or should we have a different word for it?

Now imagine there already existing every piece of "knowledge" in the universe. Can humans generate more pieces of "knowledge" by observation and deduction? I don't know.

>having an apparently sufficiently good reason to believe it is infinite
>implying this isn't what observation is all about

A number defined by Archimedes as being between 3 and 1/7 and 3 and 10/71sts

He proves it using a 92 sided figure inscribed in the circle.

>B: This line is infinite.
>A: How do you know?
>B: Recursive reasoning. Whenever you seem to find the end-point of the line, the line extends itself with 1 meter.
>A: So how do you know the recursion will apply forever?
>B: Because what I've observed it keeps on going! Uh shit. Uhh I mean... it doesn't. It only does recursion when I try to observe it beyond it's end-point.
>A: So you observation *causes* it to grow?
>B: Yes.
>A: So if you don't observe it, it doesn't grow?
>B: It's environment will always observe it and cause it to grow.
>A: So the environment is infinite too and growing infinitely to every direction?
>B: Yes.
>A: Then what separates finite and infinite object?
>B: Nothing. We are all just subset of one infinite object.
>A: Then why is the world changing?
>B: It's not. Nothing is changing in the world.
>A: Okay, that makes sense. I guess you've convinced me!

>Math isn't science

Veeky Forums BTFO

>Abduction consists in studying the facts and devising a theory to explain them.
That's pretty similar to induction

Mathematical objects are inspired by analogies to observational phenomena, but they have no ontological commitments to them.

The most basic example being circles and [math]\pi[/math].

derp. pi is literally worked out from the observation that circles have a fixed ratio of diameter to circumference.

$\pi $

[latex]\frac{1}{2}[\latex]

\frac{1}{2}

Mathematics doesn't use inductive reasoning. The principle of induction is in fact deductive.

Observe this

*whips out dick*

=1.2mm

>mm

A unit in math? No, no, no. That's called science.

>A dick is unit of length. Dick has no other properties then it's length and the length fully defines the dick.

You ment:
dick length = 1.2 mm

its not

mathematics is axiomatic. please stop posting these threads as if they make any meaningful difference to mathematics or to the discovery/invention of new mathematics.

Mathematics is nothing more than philosophical preponderance and associating some form of thought to different fields of study in order to understand them from a calculable perspective. There's a reason math stemmed from philosophy. Because it's a subset of philosophy. Which is okay, but you have to understand that fact.

>Infinite objects are hard to observe
Wrong. They are impossible to observe.

Pi is finite m8

In the most abstract sense though, nothing is changing.

I like your little dialogues, by the way.

Perfect circles, which do not provably exist in reality.

I hink mathematical objects can exist in a vacuum, and that they physical phenomenon we model are analogies for those higher ideas. Like Plato's true forms or whatever they're called (not Platonic solids)

I's argue physics straddles both categories.

Inference != Observation

There is also another problem with that picture. Empirical reasoning should be inside logical reasoning. That is to say, all those sciences are subsets of mathematics.

Why do I say this? Well, take physics. Lets say that you have 2 laws expressed as equations that you "proved" empirically. Now that you know they are true, through logical reasoning and mathematical reasoning you can first, re-arrange terms in those equatons. Example:
If you proved empirically that a*b = c then, without carrying out new experiments, you can say that also a = c/b. That is logical reasoning merged with empirical reasoning

Two: You can mix laws mathematically.
Example:
If you have a=b*c and a=x*y as two laws you proved empirically then you can also say
b*c = x*y without needing to carry out new experiments. Logical reasoning.

Science fags, stop pretending you are not a subset of pure mathematics.

Why is OP a brainlet?

Kant called
He wants his false dichotomy back

>C: You niggas need to get some pussy. Damn!

you fucking moron
do you know what similarity is?

all squares have the same ratio of perimeter to radius even if the squares have different radii or perimeters. The ratio of perimeter to radius for a square is 4*sqrt(2)
that's the story for all regular n-gons: there is some unique number for that n-gon which is the ratio of its perimeter to radius
A circle is just a regular infinity-gon. You can't actually draw an infinity-gon in the physical universe, but you can mathematically approximate the ratio of its perimeter to its radius and the answer is 2*pi
It's not a fucking inference, it's an observation, because you can "observe" how the ratio from perimeter to radius changes as you increase the number of sides

>all those sciences are subsets of mathematics.
lmao no

source?

>but you can mathematically approximate the ratio of its perimeter to its radius and the answer is 2*pi
We can observe a pattern in the ratio as the number of sides increases, and then INFER there is a number (which we can not directly observe) called pi, and that this ratio approximates 2*pi.
Mathematics often benefits from real-world observation, but the underlying reasoning is logical, rather than empirical. We will never observe pi, but we can construct it logically and use it in further mathematical statements.

Mathematics is impossible without Symbol, which is immaterial, non-local, and non-individual.

Also, Noumena are the only source of knowledge.