The role of mathematics in philosophy

[removeduser_426582376423734]

How far were mathematics and philosophy linked? Great philosophers like Descartes and Russell were both innovators in maths as well as philosophy - Russell had an obscene fascination with it as 'base truth'. Any views?

[Tankbuster]

Well I do know that philosophers like Lucretius (kind of an early atheist) HATED mathematicians, because they always seemed to conclude that there had been a creator. So apparently mathematics were seen as a tool for a religious view. I'm thinking 0 times infinity = any real number.

[The Friend]

For a long time, Mathematics and Philosophy was closely related because both are arts of reason. Mathematics shows the relation between ,material objects which are viewed as quatifiable. Philosophy tries to find a relation of harmony between apparently unrelated scenarios.

Notable here is George Boole of Boolean fame. He authored the The Laws of Thought. Pertinent here is the discussion of the science of Logic, which is closely related to both Philosophy and Maths.

After the formulation of Quantum Mechanics and Uncertainty principle, ancient Eastern Philosophy has been found to bear astounding similarity to the findings of these modern sciences. Both QM and Uncertainty Principle are heavily mathematics based approaches.

[Chaigidel]

mathematics reflects the most accurate language ever discovered to describe the universe around us accurately-- mathematicians are the most religious of all scientists according to study; it is because math simply is too perfect I imagine.

[McGness]

mathematics reflects the most accurate language ever discovered to describe the universe around us accurately-- mathematicians are the most religious of all scientists according to study; it is because math simply is too perfect I imagine.

Math is not the most accurate language describing the universe, it is however the most concrete language nearly imaginable to describe how matter functions and relates in the universe. Give that matter something like life or especially consciousness and math becomes next to useless.

[Chaigidel]

but it still allows for discernment of the process, discernment of all processes; without mathematical basises no biology would be understood at all, it is the foundation of all other thought.

[Tankbuster]

Maths only work in fully described spaces with CONDITIONS posed.

If you take mathematical formulas and try to project them on the world around you, trying to understand the universe or so (as happened for example in pythagoreism or the gothic period), you get ridiculous conclusions.

@Chaigidel: back that claim up

[Gaidin]

Maths only work in fully described spaces with CONDITIONS posed.

If you take mathematical formulas and try to project them on the world around you, trying to understand the universe or so (as happened for example in pythagoreism or the gothic period), you get ridiculous conclusions.

Explain what's so ridiculous about Physics and its math theory originating in Fields.

[Axeman]

Mathematics is far from my best subject , but I know that Socrates and Plato both used Mathematical formulas to describe thier thinkings , and Socrates using the sun's shadow even accuratley measured the diameter of the earth , he was infact the first recorded person in history who claimed the world was round.

[Le Beotien]

Mathematics is far from my best subject , but I know that Socrates and Plato both used Mathematical formulas to describe thier thinkings , and Socrates using the sun's shadow even accuratley measured the diameter of the earth , he was infact the first recorded person in history who claimed the world was round.

I've never heard of that one. I think you're making a confusion with Aristarchus of Samos, who made many measurements, but to my knowledge nothing very accurate. Other scientists made similar measurements later during antiquity, sometimes with better results, but they were not philosophers (or at least, they are not known to be so).
Socrates was probably not a good mathematician though he surely had a some basic knowledge. Plato, as a well educated man, was certainly better but I don't know of any mathematic work from him.

I'll add that I don't think there are any deep connections between mathematics and philosophy. But there are some parts of philosophy where you have to master both, like philosophy of Logic or of Mathematics. People like Russell, Hilbert, Wittgenstein, etc represent this part of philosophy.
But what's the use of mathematics when it comes to ethics ? Ontology ? etc.
In fact, the only field where mathematics has proven to be useful is in philosophy of science or in epistemology, but mainly to supply examples (very common thing in antique philosophy) or to be compared to other kind of knowledge (indeed, maths have a very special status as they give apodictic proof).

[Chaigidel]

@tankbuster do something without using numbers, and mathematics -- the base chemistry of the molecules involved in organic chemistry obey things understood through mathematics.

this is like asking me to back up that the world is round, all you need to do is open your eyes ( and not in any spiritual sense)

[Le Beotien]

@tankbuster do something without using numbers, and mathematics -- the base chemistry of the molecules involved in organic chemistry obey things understood through mathematics.

Well, that is what they seem to do. And as this is a "philosophical" thread, I'll insist on this difference. We have no proof that our world follows mathematical rules. In fact, we're just using mathematics to create models of our world: that is very different. Karl Popper used to say that we're trying to impose rules to nature (I don't know the quote in English).
I know both a mathematician (a doctor) and a philosopher of science (doctor in physics too) who do not believe our world has any mathematic rule.

[Chaigidel]

but the proof is in the fact that the calculations work-- none of our science would work unless the calculations work-- thats how something is PROVEN; it is in equation, nothing is proven outside of mathematics.

yes we all have beliefs, we make choices given the evidence we have.

I didnt say mathematical "rule" I just said that mathematics exposes a basic nature in the way our reality is put together, it is shaped by balance-- as evident by how proof is found both in experiment and in equation.

[Gaidin]

[Le Beotien]

but the proof is in the fact that the calculations work-- none of our science would work unless the calculations work-- thats how something is PROVEN; it is in equation, nothing is proven outside of mathematics.

Ah ? Why would this be a "proof" ?
Here's one of my post in another thread where I explained what science is actually (based on twentieth century philosophy) and why you can't prove anything in science: http://www.twcenter.net/forums/showt...06#post3204306
(read after the parenthesis)

[chriscase]

I suppose I'm just being naive, but I think mathematics has a lot to offer philosophy. Yes, it's about building models. But so is language as well as thought. Is any model ever absolutely perfect? Probably not. But mathematics at least has its own set of criteria for the evaluation of suitability of a model, and it manages to avoid fruitless ontological thrashing. What's not to like?

[kev-o]

I have always found the golden ratio and Pi to be mysterious numbers. There is a side in math that is wonderous and brings about awe.

For instance, take the Ulam Spiral something that hasn't been fully explained.

[tco]

Well I consider Zeno and Calculus intertwined for Zeno said there is no movement. Well actually he said that to go some where you have to go somewhere and to go there you need to go half way, then you have to go have way to that where take the distance to where movement is impossible because you can only go half way. I consider calculus to prove him wrong because we can calculate instantaneous velocity thus prove him wrong.
:hmmm: At least that is how I see it,

[Juvenal]

Well, I suppose you could say that the Calculus solves Zeno's paradox because it enables you to quantify instantaneous velocity (something he was implying couldn't be achieved). However, it does not seem to be a true representation of the world because reality looks like it is fundamentally discrete and not continuous (e.g. Planck length and Planck time).

[The Friend]

Well, I suppose you could say that the Calculus solves Zeno's paradox because it enables you to quantify instantaneous velocity (something he was implying couldn't be achieved). However, it does not seem to be a true representation of the world because reality looks like it is fundamentally discrete and not continuous (e.g. Planck length and Planck time).

What is reality anyways ? That is the fundamental question Philosophers as also Mathematicians and Scientists tried to decipher since ages.

Whether it is continuity or discreteness that is reality is precisely where Science and Philosophy both make theorems and hypothesis.

In any case isnt Plank Length and Planck Time derive their major importance from the Uncertainty principle ? The Uncertainty principle itself suggests astonishing similarity between the findings of Modern Physics and Eastern Philosophy.