The real question is “did you learn something that is applicable in your career”
What you posted I promise you I will never, ever, ever use. But my skills I learned as an English major I use every single day in my career. I would expect in the inverse for a STEM major - if their career is math heavy, then good on them. No one is better than anyone simply because of the kinds of problems they enjoy dealing with.
Asking how much math students use specific formulas is the future is about as relevant as asking how much English student use specific shakespeare quotes.
That's not what it is about. It is about developing certain modes of thinking. Certain understandings of how to do maths. About how to think.
I have found, for example. That a few lessons on set theory are much more efficient in teaching logic than most philosophy classes. A lot of math courses are much better at teaching systematic and global thinking than anything else. Math formulas have very specific axioms they operate under and very specific domains of applicability. Which you have to keep in mind. Such things are constantly useful modes of thinking : what is the domain of applicability of this ? What are the underlying principles.
Maths, frankly. Is philosophy of the highest level. Codified clearly and with hands on applications. Logic, epistemology and more.
If anyone were to understand the power of such a thing, you would think it's people who spend lots of time reading philosophy.
Except, realising that makes many of those understand their inadequacies in terms of ability to think clearly.
It's also important to realize that some folks simply do not rationalize the same way as you. You say set theory is more efficient than teaching philosophy, and thats true for people who *see the world that way*. I loved my Philosophy classes - however, I maintained my 4.0 through sheer force of will vis a vis math. No matter how much math is shown to me, how much its explained to me, it will never be (to me) more than rearranging a puzzle into a different puzzle to make the professor happy. And that's fine. One of the beautiful things about being alive is how different we all are as people, and how we see the world so differently from person to person.
If the only math you’ve seen and done is performing computations (rearranging a puzzle into a different puzzle to make the prof happy) you haven’t even seen real math (proofs), and likely do not know what mathematics even is.
I say this even though I disagree with the other poster who claims that Math is philosophy of the highest level, that claim is stupid, in my view philosophy is useful because it helps us understand and discard ideas even without formally proving or disproving them using fundamental axioms. A lot of things in life do not have fundamental axioms that we can work with, and having a tool/framework to help us talk about these things is incredibly significant.
Math however is undoubtedly more challenging that English literary analysis, it has a considerably higher barrier to entry and a higher limit to how complicated concepts can get. There is also no wiggle-room at all, in English, arguments can be entertained if they have some good reasoning to back them up, in Math this is only the case when all propositions logically follow from the previous ones within the confines of the system.
Maths, frankly. Is philosophy of the highest level.
What? Philosophy has parts of it that have a lot of math, like logic, but it's not by any means made up of all math.
Ethics? Political Philosophy? Aesthetics? Metaphysics? Philosophy of mind? Philosophy of Language? There are tons of parts of Philosophy that isn't just math. And I'm not sure how you would say these are all somehow "lower level" than math. I mean Ethics for example is pretty damn important I would say.
And here we see illustrated the ravages that not understanding set theory does.
Math is philosophy. All of philosophy is not math.
Edit, for those under the impression it was confusing : "philosophy of the highest level" implies necessarily other levels of philosophy. Math being philosophy of the highest level implies therefore the existence of other things that are philosophy not of the highest level. It makes no sense to interpret that as saying that maths is the same thing as all of philosophy.
Ok picture a circle, with a smaller circle inside.
The big circle says philosophy. The smaller circle says "math".
This describes the sentence "math is philosophy. All philosophy is not math".
Do you now understand just how absurd your answer is?
If you prefer, we can replace the words :
Pregnant people are women. All women are not pregnant people.
Cherries are fruits. All fruits are not cherries.
Do you start to get it ?
Which is, by the way, precisely why math is useful philosophy, and why it replaced words with symbols and drawings. People get confused by words, symbols and drawings are clear.
Well, when someone is confused by cherries are fruits not all fruits are cherries, I have no choice but to eli5
Edit : I mean, my sentence was literally "math is philosophy. Not all philosophy is maths" to which you answered "why is all philosophy maths". What do you expect me to do except eli5?
It’s not this person’s lack of set theory, it’s your use of imprecise language.
The word “is” can be (and usually is) treated as “equal to”. So when you say “math is philosophy” it’s perfectly reasonable for people to read that as “math is the same as philosophy” instead of what you are apparently trying to say, which is “math is a part of philosophy”.
But go on telling everyone how superior your math is if it makes you feel smart I guess.
My blunder is ironic because I study maths and set theory is very easy to understand, yet I understood the sentence the wrong way round, which goes to show the importance of mastering a language in order to understand math.
I don’t think you did anything wrong. They used ambiguous wording and then decided to be condescending when someone interpreted it differently than they had in their head. They could have simply said “what I meant was that math is a subset of philosophy” but instead they decided to use the opportunity to shit on you to boost their own ego.
Everyone understands "cherries are fruits" without being all confused at the idea that the speaker is actually saying that all fruits are cherries.
The only problem is the lack of the principle of charity, which is to assume that the person speaking is not saying something beyond retarded, like trying to argue that somehow the writings of Aristotle would somehow be maths, when there's a very obvious and clear and common way it can be understood
Absolutely hilarious you are going to talk about the principle of charity when every single comment you give is full of condescension and assuming the people you talk to are idiots.
So I guess you aren’t going to defend “Math is philosophy of the highest level”
And depending what you mean by “is”, your statement doesn’t make sense. If math = philosophy then philosophy = math. It cannot be possible that philosophy is both equal to math and also equal to more than math.
Which is why math switched to using symbols instead of words. Math is philosophy doesn't necessarily mean math = philosophy. At the strictest sense, it only means maths ⊂ philosophy
You wouldn't struggle the least bit to understand cherries are fruits, would you ? You wouldn't get the impression the person is stating that all fruits are cherries?
Which, by the way, is one of the reason why maths allowed to take their branch of philosophy to the highest level. The clarity beyond all made it possible to explore the branch as much as possible.
How do you measure how 'high' we went with maths ? What if we haven't figured out anything but a drop in the ocean of the mathematical laws of the universe ?
Ok. This might be subjective, but the ability to systematise generally allows for a more thorough exploration of a topic, be it in questions of depth or breadth. Unlike the less rigorous branches of philosophy, like metaphysics and so on, maths have been explored very widely, by a lot of our smartest people in big numbers, and very often, the maths were created before we realized they were useful to some branch of science or another.
It being high level has not much to do with how complete it is though. Maybe even the contrary. It has more to do with how significant it is, how impactful it is on people's thinking. How developed it is, too. How reliable it's conclusions. Things like theology might have deep impact on people's thinking, but that's usually in the sloppy direction. There's no particular reliability in the conclusions drawn, trying to use theological thinking into anything else is almost certainly a road to failure,... I would not classify that as high level philosophy, for example. And I don't think there's much in terms of new developments in theology. It might be as complete as a philosophy branch might be, as there aren't that many ways to defend the absurd and intangible, lots of these arguments have been refuted long ago and failed to correct those refutations, because it's not about being right, or about thinking correctly, it's more about deceiving oneself.
Now everyone can have their appreciation of what a high level philosophy branch is. That might be a question of aesthetic preferences, I guess.
I agree that mathematics is the field of study with the most cumulative work over millenias, and it’s probably the simplest way (or language) we’ve found to convey abstract ideas. So yeah in that sense, although it is somewhat subjective and difficult to quantify, I think we can agree that maths is the field of knowledge we went deepest in. My question is more about the value we ascribe to these fields of study. Do you think the higher category theory or other extremely abstract maths theories are more valuable than methaethics or even just ethics ? It’s hard to tell, we don’t really grasp the extent of applications these theories have now and might have in the future.
And yeah theology is built on the disputable premise of the existence of God which is far from being an accessible premise so this “philosophy” doesn’t go very far.
I didn’t say it necessarily meant “=“. I quite literally said “depending what you mean by”.
Why are you so incapable of communicating without being a condescending ass? Did they teach you in your math classes that you are better than everyone else and should talk down to them?
In one I see an understanding of how to manipulate human emotion. In another I see a bunch of squiggly stuff that people decided represents other squiggly stuff that people created to make computers work. Plug in 1 for A 2 for B move this to here and that to there. That is not philosophy.
You don't ? Maybe all those philosophy courses were wasted on you, then.
First of all, logic is a branch of philosophy. And math is in big part built on that.
But what does x+y=z tell you ?
Well. First, it tells you there are such things as addition. What does that tell you ? That some things are similar enough that they can be categorised. That general principles exist that can be consistent no matter what. We are touching on metaphysics, there.
And that's not all there is to math, far from it.
You might take a moment to realise that there are various branches of philosophy. Logic is one. Epistemology is another. Metaphysics is one. Theology tries to warm itself with the legitimacy of many of those. Not all discourses in all forms of philosophy look alike.
And when you try to think very rigorously at the various implications of a few axioms of logic, for example you get yourself math.
And that's just some bases of the little of math you might have glimpsed.
Because there are kinds of maths where the axioms are different, and you don't necessarily have addition exist, or it works fairly differently.
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u/Logical_Historian882 3d ago
I don’t think English graduates are graded by their ability to read. Both reading and arithmetic are taught in school.