Discussion Are math and philosophy similar?

[Nøb0dy]

Do you think math and philosophy are very similar or do you think they are two different things? If you think they are similar, why? And if you think they are different, why?

 

[CTB Dream]

Philosoph nat lang math form lang ,simil depend base topic some topic same some not. Philosoph approx word math no approx word be certain

 

[tardis]

Logic, which is a branch of philosophy, is almost entirely mathematical. Many other parts of philosophy like philosophy of science (esp. philosophy of physics), or bayesian epistemology are also really math heavy.

Math and philosophy are very similar because they are both mostly concerned with a priori facts.

They obviously also have many differences. Obviously philosophy is much broader in scope. It also doesn't rely on proofs, but also uses inductive arguments, intuition, etc.

From a practical standpoint I find math to be much more difficult because you cannot simply jump into the latest research. Every new concept builds on top of other ones, and so you really have to start from the bottom and build your way up. In philosophy, it is sometimes much easier to simply read the latest research. For example, I was able to read Korsgaard's writing about a Kantian approach to animal ethics without actually reading Kant (though I certainly suffer for it, this would not even be possible with math).

 

[Winterreise]

No similarly what so ever

 

[Pluto]

From the human perspective, reality is inherently chaotic, uncontrollable, unpredictable and unknowable. The various branches of human endeavour - not only philosophy and mathematics, but even sport and art - reflect our attempts at creating some sort of order out of the underlying mayhem.

The great US violinist Yehudi Menuhin said the following about music:
Music creates order out of chaos: for rhythm imposes unanimity upon the divergent, melody imposes continuity upon the disjointed, and harmony imposes compatibility upon the incongruous.

 

[Stylite]

It depends on the philosophy.

 

[frogboi]

I don't know if this really provides an answer but I find this scene from the movie "Pi" really interesting. It's missing a little bit of context but it is free on youtube if it interests you as well.

 

[Per Ardua Ad Astra]

Logic, which is a branch of philosophy, is almost entirely mathematical. Many other parts of philosophy like philosophy of science (esp. philosophy of physics), or bayesian epistemology are also really math heavy.

Math and philosophy are very similar because they are both mostly concerned with a priori facts.

They obviously also have many differences. Obviously philosophy is much broader in scope. It also doesn't rely on proofs, but also uses inductive arguments, intuition, etc.

Agree -

example : "Symbolic logic"

 

[CTB Dream]

Unfortunate no able tell detl ,human still no adv even small cncpt no undrstnd , Phlsph nat lang human lang one-many intrprt, math one-one intrprt, see ambgty cncpt, diff phlsph use ease relate lang human but ambgs, math use simil robot lang no ambgs.

Inhrnt ambgs This human no ease undrstnd cncpt cuz mndblw, imgn all txt all say any posbl wrong cuz lang inhrnt incnst.

 

[SexyIncél]

Do you think math and philosophy are very similar or do you think they are two different things? If you think they are similar, why? And if you think they are different, why?

Let's reframe the question: what do math and philosophy have in common?

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Definitions

What do philosophy & math mean? Such concepts are names for the benefit of university deans. Otherwise, they're not really separate. And meanings change — only nowadays do we call Newton a physicist; back in the day, he was a natural philosopher

What's philosophy? Investigating what underlies things, one meta level down. You can also think of it as "thinking about why we're doing what we're doing"

What's math? Fairly recently, it was the investigation of numbers and three-dimensional shapes. Nowadays, it's the investigation of patterns in general

We'd expect math to be similar to philosophy, when we model something one meta-level down, mathematically

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Examples

Math investigators often work with fuzzy concepts, that they define more as needed. Defining things can be philosophical

For example, "function" was a commonsense object, no precise definition, until investigators felt the pain of not having one. So they built frameworks like set theory one meta-level down

An investigator can keep any crazy imprecise definition in mind, when it's cognitively more effective to do so. But the more precise definition can strip down the concept into a form that can be used in a zillion places. And give you more confidence in your ideas

Major benefit of philosophy: see hidden connections between things. If you make something more abstract, it can apply in all sorts of situations. If you build a general framework for (say) sadomasochism, it can be used to describe any dominance hierarchy — which permeate most current societies

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Warning

People philosophize all the time, for things big and small. Each has sweet spots where they're more useful. They're all fallible and vary in quality — like anything else. Even dominant ones. Some were made for surprisingly limited purposes. Some others started as mad experiments that broke out of the lab and won hype to lure more research money

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Random thought

Speaking of calculus — isn't it weird how we downplay the intelligence of people under 25? Many countries teach calculus (the hard way) much younger, like 16-18. (Not to mention teaching math at 5)

 

[Tobacco]

Yes. They use the same logical structures to arrive at truths.

I only understood more about math proofs after studying logic and philosophy.

 

[Winterreise]

Math is an absolute science, and solid. All theorems are equivalent, and build on each other. Relations are discovered not invented. It's full of interesting strange fenomens, most of it abstract, incomprehensible and uninteresting to most people. Some of it can be applied in science, medisine, encryption.

 

[Andro_USYD]

Yes they are, kindof. In my Reading and Writing Mathematics course this holidays a lot of what came up was a whole section on logical fallacies and philosophy. It covered a lot and there's math e.g in. causation e.g. A causes B (direct causation) or A causes C which causes B(indirect causation) the point I'm getting at is that algebra is used in philosophy and mathematics and both use deductive reasoning and have theorems and axioms. It's definitely a cross over in my course.

 

[loyalskateboard]

I think so, yes. Music is also similar to math.

 

[PrematureBurial]

Yes in the sense that they both deal with abstract kinds of thinking. I mean that in a metatheoretical way. Some people are ascribing the connection specifically to the field of logic. Although the symbols are common to both, traditional philosophical logic deals with language and semantics, which is absolutely not the same core issue that mathematics approach with logical formulations. Later analytic or logical philosophy has a subfield called philosophy of mathematics, though. That's where the two actually coexist.

If you're going to do philosophy seriously you absolutely cannot shift from theory to theory without a prior well grounded basis in the history of the appropriate segments of philosophical thought that form the content of what you are researching. It would be naive to think you can grasp the entirety of two arguments like that. Unless you're reading Stoics or something.

If anyone wants to dig into philosophical branches that people consider more scientific in their approach, I'll list a few. Some are going to overlap, though. Philosophy of nature (includes time-space theories, causality, atomism,..), philosophy of science (Gestalt authors, process theory, machine versus man, psychologisms), cognitive theory (neuroscience, the extension of the mind-body problem), pragmatism, analytical philosophy (by that I do not mean the division of that versus continental, I mean complex logic formulations). There's also epistemology.

If you want to go further back in the mind-body problem, then rationalism and materialism (empiricism) are the way. Spinoza's Ethics are a phenomenal example of a philosophical axiomatic theory. Then continue with Kant and German idealism. There's a lot.

Philosophy is not necessarily focused on or grounded on a priori facts like someone else mentioned. That topic is probably prevalent in only one third of the entire philosophical canon. Mainly idealism and metaphysics/realism and the fragments of the pre-Socratics. That is if a priori is meant in the sense of an ultimate underlying reality or things in themselves. If meant in the sense of transcendental idealism, the word a priori limits us to idealism only.

Philosophy needs to be less discredited as vague or "unscientific". Not that it's dying to be considered a science in the modern casual sense of the word. It's a meta-commentary on everything and should be approached seriously.

Edit: one of my best friends is a mathematician and we have the most amazing conversations about our fields. There are a lot of common and very fruitful topics to discuss between the two, but only if you carefully stick to abstract theory and ideas.

 

[aGoodDayToDie]

I'd say they're quite similar. They both heavily use logic. Except philosophy tends to be more wordy, maths tends to use symbolic representations. Maths tends to be less disputable, whereas philosophy tends to present less concrete arguments such that there can be multiple competing, conflicting conclusions. They also seem to work together. Maths enables furthering of philosophy, and philosophy can help ground foundations of maths, explaining why maths works for us, and how far it can go given our understanding and perception of the world.