"Maths, in university, is useless bull..."

[Kuciwalker]

Originally posted by Ben Kenobi
Have you ever done one?

Why, yes. In fact, there's a certain type of proof I've done quite often.

It's called algebra.

Not to mention that any basic geometry course teaches propositional logic proofs and geometric proofs.

Yet you freely use such terms like a priori?

I suggest you reconsider this, since many of your own standards of proof seem to be based on philosophical concepts developed by philosophers.

My standards are not rigorous. It's simply impossible to go into that level of detail.

[Ben Kenobi]

My standards are not rigorous. It's simply impossible to go into that level of detail.

That doesn't stop philosophy from being rigorous.

[Kuciwalker]

I've never seen any that is.

[LulThyme]

Originally posted by Ben Kenobi
Not really. Most algorithms require understanding of the mathematical processes involved, and tend to break the problem down into ways that the computer can understand them better.

Basically refuting your statement that writing algorithm is "Number crunching dressed up. "

[Drogue]

Originally posted by Kuciwalker
Mathematics has very rigorous standards of proof.

Indeed it does. Proves by induction, elimination, etc. would all quality as proof.

The way I see it, maths is taking given assumptions, and saying if such is true, then this is also true, as per proving identies. Philosophy does the same, with ideas. If such an idea is true, then this also means that such another idea is true. However every philosophy student I have debated with has bent this a little in order to give their argument more credance, saying that since something is true, their argument must be, when that is not necessarily so. All the mathematicians I know do not do this however, because you would have to prove why that was the case, by a set means of proof, whereas in a debate, someone would have to show it to be false.

For example, you cannot use a method of proof to show that, since the universe exists, God must exist to have created it. Or to answer any of the questions like that. In the philosophical world, there aren't certainties. When you have a mathematical system, it has rules and properties, so proves can be made. You can prove that cot^2 = cos^2 over sin^2, given the assumptions of what sin and cos mean with regards to a triangle. Without those assumptions it cannot be proven. You can do the same, with assumptions, in philosophy. However you can never prove that those assumptions are true, without basing that on more assumptions. In maths, that doesn't matter, since maths is using that particular construct to solve problems. The system is a human construction, and only valid inside that construct. In philosophy there is not the same contruct. When trying to solve the ethical dilemmas, or far reach questions about our place in the universe, or anything like that, we don't know the assumptions.

Philosophy does have rigourous proof, proving that given one thing, another is true, just like maths. What it doesn't have, is a common set of assumptions to start with, and thus even if you prove that, given the assumptions, you can never prove the assumptions, thus nothing is ever actually proven.

When it comes to practical philosophy, of actions and morals, it becomes even less able to prove. My personal philosophical beliefs come from the assumption that happiness is good, as the core pillar. While I can show, that given that happiness is good, such and such an action is also probably good, I can never prove that, since I don't know all the results of that. Hence, even with a core assumption, it is unprovable.

[Fve Crathva]

If algorithm design was just number crunching--something that computers do very well--then we must be living in a false reality generated by intelligent, self-improving computers.



SP

[Kuciwalker]

Originally posted by Drogue
The way I see it, maths is taking given assumptions, and saying if such is true, then this is also true, as per proving identies. Philosophy does the same, with ideas. If such an idea is true, then this also means that such another idea is true. However every philosophy student I have debated with has bent this a little in order to give their argument more credance, saying that since something is true, their argument must be, when that is not necessarily so. All the mathematicians I know do not do this however, because you would have to prove why that was the case, by a set means of proof, whereas in a debate, someone would have to show it to be false.

For example, you cannot use a method of proof to show that, since the universe exists, God must exist to have created it. Or to answer any of the questions like that. In the philosophical world, there aren't certainties. When you have a mathematical system, it has rules and properties, so proves can be made. You can prove that cot^2 = cos^2 over sin^2, given the assumptions of what sin and cos mean with regards to a triangle. Without those assumptions it cannot be proven.

I'd say definitions, not assumptions. Without them, it's meaningless gibberish.

[Drogue]

Definitions are assumptions. You're assuming that x means y, where x and y are a particular definition of something. You're also assuming the nature of the universe, that space is in 3 dimensions and is not bending in part of that triangle. You're using a construct, a mathematical system, to assume these things, and working within that construct. Philosophy doesn't have the same construct, save for the real world, the problem with which being nobody knows exactly what that is.

[Kuciwalker]

Definitions are assumptions. You're assuming that x means y, where x and y are a particular definition of something.

Yes, but the term definition is clearer and more precise, because you aren't making any sort of outside connection between x and y, you're simply saying "when I refer to x, I mean this thing y".

[Drogue]

Yes. That is what i mean by a contruct, a system whereby those definitions are there. If you wish your construct to be grounded in reality, as the maths construct is, relating such things to shapes, geometry and the like, then you need other assumptions, such as the ones I stated.

[monolith94]

Honestly, college level mathematics is a pure waste of my time. Cause I'm not going into engineering, or architecture, or comp sci, or anything technical related. As an English major, math is utterly superfluous.

[Kuciwalker]

English majors are superfluous

Everyone should at least know basic calculus.

[Drogue]

Originally posted by monolith94
Honestly, college level mathematics is a pure waste of my time. Cause I'm not going into engineering, or architecture, or comp sci, or anything technical related. As an English major, math is utterly superfluous.

Yes, and as a math major, the study of literature would be utterly superfluous. Your point? Maths, in the sense of all people, has a point. It may not have a point for you in particular to study it, but there is a point for people to study it.

[Ben Kenobi]

I've never seen any that is.

And you've seen all of it?

[Ben Kenobi]

Basically refuting your statement that writing algorithm is "Number crunching dressed up.

I consider calculus to be number crunching, even though most of the work is trying to define the terms.

Which is, by far, the most time consuming part of writing algorithms.