Based on all the supposed benefits of doing math, it sounds like people would be better off studying philosophy. Same benefits but a much broader appeal, and far more applicable to most people's everyday lives.
When I finally "discovered" philosophy in college, I was angry that we hadn't been exposed to it at all in middle or high school. Instead, I'd been forced to waste years on things like math, biology, etc. that I had no interest in and no use for. Our history / social studies classes would be greatly improved if they incorporated more philosophy.
Real philosophy can't be limited to some set of tools or into some set of books and approaches that fits into curriculum. Philosophy is completely open ended pursuit.
I firmly believe that philosophy without mathematically oriented thinking at the core is limiting. Teaching and studying of formal logic has been traditionally part of philosophy. In practice there is no real border between philosophy and formal sciences (logic, mathematics, statistics and theoretical computer science).
Consider the problem Kant faced in Prolegomena to Any Future Metaphysics, §13. Two objects that are intrinsically alike must be interchangeable. But there are objects that are intrinsically alike and you can't exchange them.
Kant was incredible philosopher but he was thrown off by looking at his hands. Left hand and right hand seem to be intrinsically same, but you can't replace one with another. Kant concluded that things like chirality and mirror images could not be understood with intellect and reasoning using concepts. Time and space were part of sense intuition. Mathematics would disagree. Spatial intuition is not fundamental building block for reasoning about time and space. Algebra, geometry and topology are.
Many modern day problems facing humanity can be understood only as systems thinking using, probability, mechanism design, games, incentives, equilibrium, trade-off, hysteresis, etc. But many schools of philosopy still try to use tools and concepts that can't describe the system.
edit: Several important contemporary philosophers and schools of philosophy are not are in fact limiting themselves. Saul Kripke for example.
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I think philosophy should be part of curriculum in school. But it should be live philosophy centered in problem solving and rational thought. The traditional history oriented curriculum should be part of history. History of science, technology, philosophy, economics and ideas in general is more important than the narrative trough kings and power cliques.
I think this is an excellent description of where philosophy has gone wrong for me personally. I took a class in high school and found the study of what amounts to history to be rather tedious and fruitless. A close friend was a philosophy major in college and understood lots of abstractions that came from the field, but it would seem that none of them were applicable to everyday life. They were not useful or practical in any fashion.
It's very much like learning the history of mathematics without being able to e.g. solve an integral, or model a problem in the real world and make meaningful observations about the model and its relation to the subject. History is fine if it's what you're into, but the other is not taught in any widely disseminated fashion and I believe people and society are deprived as a result.
There are entire sub-disciplines of philosophy that are useful and practical for everyday decision making. Here I would disagree that you need a formal background in mathematics. Game theory, statistics and the like are certainly valuable, but they are still more a part of the engineer's or mathematician's toolkit and will be glossed over due to their rigorous technical underpinnings that are simply out of reach for many individuals. Rhetoric, critical thinking, stoicism, ethics, and the like are pretty approachable topics that have somehow been elided from the educational system in any established fashion in the US - and they used to be at the core of a liberal arts education. Great religious thinkers, politicians, and intellectuals have left a legacy of work that speaks across time and space to a modern reader.
There is an analytical strain, of what I consider a better class of philosophy - see https://en.wikipedia.org/wiki/Logical_positivism , just it tends to be in a minority among university courses. I had to seek it out.
A lot of 'continental' philosophy seems to be a mix of historical analysis, and cult-of-personality/lit-crit...
In PTAFM 13, Kant is arguing that neither space nor time are intrinsic properties of things in themselves, and basically making the point that properties like position and congruence are relational, not intrinsic. Spatial relations fit with the intuition of space, which is the form of external experience (and one should think of this as the abstract form of any space whatsoever - people tend to think that Kant is undermined by the development of non-euclidean geometries, but I think one can push the abstraction so it fits equally well). Experience of- and reasoning about spatial objects involves both intuition that corresponds with the forms of space and time (which applies to any experience whatsoever, outer or inner), and the operation of the understanding through concepts. Now, reasoning from principles which might apply to spatial objects (in the case of algebra, geometry and topology) can go through concepts alone as long as it is logical. But those principles would be meaningless for us if we didn't have experience of any spatial objects whatsoever (if we didn't have the pure intuition of space).
"Thoughts without content are empty, intuitions without concepts are blind. The understanding can intuit nothing, the senses can think nothing. Only through their unison can knowledge arise." (KrV A51).
This highlights why math generally trumps philosophy. Take any math that is similarly well known to Kant. You don't get two educated people having diverging opinions on a solution if they start with the same assumptions. Usually someone concedes; e.g. because the other side shows that the losing position implies something that everyone accepts is impossible.
In philosophy you get this all the time because people refuse to agree on definitions like truth, consciousness, goodness, evidence etc. So debates generally involve people talking past each other until someone gets bored. If we're lucky spectators will judge by popular acclamation which side won or lost. Participants rarely concede their position.
> You don't get two educated people having diverging opinions on a solution if they start with the same assumptions.
No, in this case he was mistaken in some basic assumptions about what Kant is doing in that text. The paragraph he mentioned starts with: "Those who cannot yet rid themselves of the notion that space and time are actual qualities inherent in things in themselves, may exercise their acumen on the following paradox." So in this case it isn't even the case that he is proposing something about Kant one can reasonably disagree on (like my suggestion that Kant is not undermined by the development of non-euclidean geometry, something which I would be willing to concede given evidence against it).
On the other hand, in my experience, actual debates on philosophy usually revolve around conceding some initial assumptions and then debating on what follows from them. Of course, one can always move from the internal questions about what follows from those assumptions to external questions about what follows if we rejected those assumptions, but this move is usually well motivated by internal conflicts. One might, for example, find some dilemma for which no option is acceptable, and thus be forced to retreat to discussing the assumptions. And it is not a given from the outset whether no such conflicts will arise.
The problem I got with philosophy is that it's supposed to be applied knowledge. But it's always consumed as an intellectual one.
As a result, the smartest philosophy lovers that I know are incredibly unhappy. They know so many things. But knowing something doesn't mean you are able to do anything about it.
Some becomes cynical. Other become depressed. Other procrastinate to hell.
But only those who actually take the knowledge and try to act on it, improving themself in the process, ends up happy. And once they get there, they usually don't quote much philosophy anymore, except for humorous purpose or make someone feel better.
Bottom line: it's interesting to look for the meaning of life. But it's necessary to actually stop and live your life unless you want to have the joy of Sartre, the energy of Rilke, the sense of purpose of Kant and drive of Schopenhauer. Hint: you really don't.
The problem I got with philosophy is that it's supposed to be applied knowledge.
Can you elaborate on that? On why it's supposed to be applied knowledge I mean?
To me philosophy is one of the most abstract forms of thought available, and to me abstract is the antithesis of "applied". Maybe the furthest I would go is to state that philosophy is knowledge applied recursively on itself. But that already seems an abstract formulation to me.
Because eventually, you can always go deeper and more abstract. The more you do philosophy, the less you get answers, the more you get questions, and they become less and less practical. At best it becomes absurd or pointless, at worst it becomes depressing.
However, if you use your knowledge of philosophy to actually do something in your life instead of trying to think your way into the abyss of infinite dissection, it becomes a powerful tool.
This is the main difference between very old philosophers (Seneca, Gautama, Epicurus...) and more recent ones (Kant, Sartre, Schopenhauer...). The first ones try actively to make something out of their thinking. They derive a way of life out of it. The second ones try to understand more deeply, categorize more things, raise more difficult questions.
In the end, by reading the active ones, you can feel the joy, the sense of purpose and solutions arising. If you read the other ones, you can almost picture them trying to kill themself.
I disagree. I find math much more interesting. Philosophy is vague. It's all guesses and interpretation, with the exception perhaps of pure logic. I like the purity of math. It's all a matter of preference.
The concepts you deal with in philosophy are vague, the challenge is to provide very precise analysis of these vague (fuzzy?) concepts.
But yeah I don't think one is better than the other. Each provide value.
I would actually claim that to live your best life, be an engineer. They seem to me at least to be living in that sweet-spot between the abstract, creative and the concrete.
This has a 99% probability of being absolute nonsense. Looks more like 30 years of anecdotal evidence and hearsay. Try find a credible source with actual numbers.
I'd love to know where that 99% comes from. (Or maybe I wouldn't.)
I'd say there's far more than anecdotal evidence, but not, obviously, not enough to draw necessarily firm conclusions. So I would say there's enough question to sustain further scientific inquiry. That, interestingly enough, puts us in a position at odds with one of a common traits noted among engineers, in psychological terms: 'need for closure'; which would put the 'engineering mindset' in conflict with the 'scientific mindset', due to the open-ended nature of the science. (Of course, this is only my own speculation.) Which is why we get things like this: http://cosmicfingerprints.com/ee/
I pulled the 99% out of thin air, I just wanted to emphasize how small I estimate the chances of this being true. I found one analysis [1] that found that creationist or only half as likely to be engineers as the general population, admittedly only using data from a preexisting survey as proxy for the question at hand.
Maybe it is a naive view on my side but I expect that additional education will make it less likely that one believes religious claims to be true in general and this extends to becoming an engineer and being a creationist.
But even if there was indeed a correlation of the form claimed by the Salem hypothesis, I would naturally want to look for traits that make it more likely for one to become an engineer and a creationist, not for something that causes engineers to become creationists.
You did not explicitly spell it out this way and I am inclined to think you do not think this causation exists, but your response to a comment suggesting that it might be a good choice to become an engineer at least allows the interpretation that becoming an engineer causes becoming a creationist.
And I obviously consider the idea of a causal relationship between being an engineer and being a creationist even more unlikely than that of certain traits increasing the likelihood of becoming an engineer as well as a creationist.
Not that it is unlikely in the general case that learning about X makes one more likely to also believe Y, that is actually certainly pretty common, but in the concrete case I am really unable to see which things one learns when becoming an engineer are suitable to turn one into a creationist.
Finally I am not sure what you wanted the express with the Evolution 2.0 article, but at least in the linked article the reasoning is heavily flawed.
Most philosophers are not very careful thinkers. There is a lot of circular thinking a lot of apriori assumptions and so one. Mostly the designers who are worth listening to IMO are those who broke down previously held illusions.
I always saw philosophy and maths as the same. Philosophy is what math and logic especially looks like when you're using words instead of leibnitz notation and other modern notations.
I mean, howdo you explain modus ponens without the notation? You say that not A and not B is the same as not A or B. And that's a poor transpilation from math notation to words. What if you never saw the math notation and had to use regular words?
I do as well, to some extent. However, let us never lose sight of the fact that any foundational axioms (e.g., ZFC) are decided upon on a purely philosophical basis. It is interesting to see such philosophical consideration around the "behavior" of truths when reading about Frege's early developments in propositional logic.
Like in math, it is humbling to revisit philosophy from a historical perspective and to be reminded of the cumulative impact of simple ideas (to us) that were being considered 2000+ years ago.
I agree, but there is a lot of value in approaching Philosophy from a mathematical context (both as a student and as a philosopher- c.f. Russel, Wittgenstein, et al had backgrounds in mathematics and left a huge mark on the subject).
I was a math major for much of my undergraduate career, but by my junior year I realized that I was actually only interested in the philosophy behind it. In fact, I had little interest in my freshman Philosophy 101 course, though after studying math, I realized that I would have loved to study philosophy more. As a freshman, I was enamored by math as it was this ivory tower of abstract truth.
I loved learning about what math could say and how the notation worked and the notion of formal proof etc. but slogging through proofs was abhorrent after awhile and I dropped the program. I had come to understand that math was actually just the same sort of discourse as "soft" philosophy, just formalized. Learning about counterexamples to math as a "closed system of reasoning"[0] (Godel's theorems, constructive mathematics, etc.) simultaneously ruined my perception of the nobility of math and spurred my interest in philosophy (specifically analytic philosophy and philosophy of language) and cognitive science. That's where the real "unsolvable" or "interesting" problems lay (e.g. the mind-body problem).
I would highly recommend anyone who is intellectually curious to learn and understand formal mathematics for the purposes of understand philosophy, but also to recognize when to quit (if ever!).
[0] - I may be butchering these terms, but I hope the meaning is clear
> simultaneously ruined my perception of the nobility of math and spurred my interest in philosophy
Can you explain this? Math isn't perfect, so might as well abandon all formality? This feels like "Science doesn't have all the answers, so maybe I can find them in the bible?"
I'm not sure how constructivism hinders mathematics, or Godels in the long run.
The mind-body problem is unsolvable because it rests upon vague or false assumptions; It is philosophical nonsense : "communicating badly and then acting smug when you're misunderstood is not cleverness." https://xkcd.com/169/
You could make these type of arguments over and over. How about doing multiple? Math, philosophy, music, dance, cook, workout, just do the things that you enjoy, and do meaningful things. Dance to your own damn beats whatever it is that plays in your head and tickles your fancy. last year, math it was and for about 4 months straight, I studied maths every morning, then I left it and started tooling around with the piano, then I started coding, now I'm coding and tooling with the piano again. I do have some philosophy books waiting to be read. I'm living my best life. Whilst you might have no interest in math, biology or other subjects. Some people do. I do have use for math and interest. I wish I had strong biology and chemistry background, bio engineering interests me, but I can only watch from the outside.
Math classes ramp up in a gradual way that develops critical thinking and intuition in a very small sandbox, where it's easier to appreciate the results. Thinking in, say, just the x-y plane makes it far easier to isolate relationships than philosophy, which tackles much bigger problems and gets you into controversial problems almost immediately, with no clear answers. The basic math framework is rigid and precise, whereas philosophy only gets that rigidity at much higher levels where, guess what, it starts to merge with the field of mathematical logic.
Of course, a one size approach won't fit everybody.
To me the key point is "no clear answers" in philosophy.
In math you learn to follow a series of developments, building structure that leads to statements that are true. These are the foundation for more bricks in the wall and even bigger constructions. e.g. The proof of Fermat's last theorem.
My sense of philosophy - after reading maybe a dozen of the classics, was there was little that was accepted as true. Yes, there are self-consistent chains of reasoning but the foundation blocks are more a matter of "taste", and the amount of rigor in the chains varied - complicated by the fact that human language is inherently not very precise.
True, but that is because philosophy doesn't deal with answers. It deals with a more fundamental question, the question of truth itself. Instead of providing a framework for finding singular answers to exact formulations like mathematics does, philosophy ultimately provides a framework for exploring and expanding the limits of certainty.
Please remember that the entire STEM field grew out of the questions of those philosophers you dismiss as "no clear answers": our entire scientific process (empirical theory-building) is based on the previous explorations of philosophers on truth and knowing. Similarly, both capitalism and Marxism grew out of the questions of philosophers about the structure of society.
You need questions before you can answer them. Philosophy deals with the questions. Our answers to those questions have become the main pillars of modern society.
Mathematics is also based on foundations which are in some sense a matter of taste e.g. Euclidean vs non-Euclidean geometries. IMO at a certain level of abstraction mathematics and philosophy are the same thing.
This seems like a poor curriculum rather than an actual flaw in philosophy, without the logic framework philosophy is just the history of ideas. If taught in a manner similar to math, where you learn logic tools and then build on top of them over time, I would expect similar and overlapping development.
A philosophy class teaching fundamentals in logic - taught in a way similar to math - is probably more like math in the sense of the article than philosophy in the sense of the grandparent post. The grandparent probably meant something more like a class on ethics, which doesn't really have the same style of beauty and truth that math does. This is certainly my impression after taking a few philosophy classes and a ton of math ones, including a philosophical logic class cross-listed with math.
This isn't a flaw of philosophy. Lots of fields of human study are great. Math just has some things that make it unique. But just like defining what art is, it's hard to pin down exactly what it all is.
Philosophy, as it is typically taught, contains too much historical annotation and attribution to my taste. I want the factual/logical content only, not the "Wittgenstein said this" and the "Nietzsche said that", because it almost implies that I have to choose a side.
I doubt it is because there might be no such core.
(Or rather, if you believe in the core, you are automatically a analytic philosopher? A school I have many sympathies for, but hardly the only or even mainstream of philosophy.)
For me, philosophy shows the ideals of human affairs and the the higher ideals, but it seems to suffer from too many opinions and contradictory viewpoints.
Mathematics gives you the kernel of the universe. Its a much finer grained tool that represents absolutes.
That the heat from your laptop flows in this way thoughout the air around it. As does the warmth of breath, or body heat or the heat surrounding an open flame?
And then there are logical principles that create "elegant" logical structures like in group theory, where you develop two different ways of looking at things only to find out they were one and the same all along (e.g. Lagrange's theorem).
I agree that Philosophy is important, and probably more so as you say, but a love of Philosophy and an appreciation for Mathematics is hard to beat.
Philosophy can invite discord due to the circular nature of using language to define language with the intention that this is supposed to bring clarity to our reasoning. Not to mention that the name "Philosophy" is often co-opted by charlatans to advance their brands.
But Philosophy coupled with Mathematics brings a kind of calm that's removed from language and an appreciation for simple, provable, truths.
I would like to add that in most cases it is crucial to understand philosophy behind everything. Whatever you try to learn, if you don't understand the way of thinking, don't see a roadmap, then you don't understand a subject.
In schools and colleges this is not always the case that we learn philosophy of a subject. Especially in schools. This is sad.
Why is it so hard for people to accept that it's probably a good thing not everybody wants to do exactly the same things as they do? Do you really think that if everybody focused their life on any single intellectual venture you picked, we'd live in a better (or even functioning) world? Or that people who enjoy X and don't like Y (or simply don't like it as much!) should just deal with being unhappy so you can conclude that Y is the One True Intellectual Pursuit?
I don't think that's the argument being made. But that by learning X or Y, you can add a lot of substance or perspectives to your life that you may not have had before. These 'things' more likely than not can bring many positives to aspects of your life that aren't related.
Both come from the latin "Gratia" (favor), but you can thank the extremely ambiguous prefix "in" for the confusion. Depending on the word it can act both as "into" as well as "without".
> Instead, I'd been forced to waste years on things like math, biology, etc.
Is this sarcasm?
If not, can you outline "the supposed benefits of doing math" versus the benefits of studying philosophy, that are "far more applicable to most people's everyday lives"?
I've heard a similar argument before but I'm skeptical. As a science-trained person with only a little exposure to philosophy, while philosophy uses rational arguments, etc., it seems like it's all too easy to bullshit your way out of.
My question: what does graduating with a degree in philosophy say about one's abilities, and how can you show it? (I would argue the types of problems that an upper-level science/math/CS person is expected to solve very clearly shows analytical and creative ability to anyone with a little knowledge of the subject)
The way I see it, most subjects in school focus on teaching you what to think. Philosophy focuses more on how to think.
That's obviously not true in all cases (there are plenty of dogmatic philosophies) but in my opinion it's much more common for people to teach things like math, biology, history, etc. as a series of objective, memorized facts and formulas. Doing that with philosophy is far more difficult because so much of it is subjective and relies on criticism and analysis. In that regard, learning philosophy serves as a foundation for learning all other subjects, or learning anything in life, for that matter.
I also personally believe there's more beauty in great philosophy than in any poem or song. There are plenty of Socratic dialogues, stoic passages, and political pamphlets that still give me chills when I read them.
Based on your comment I'm going to assume you've never taken a mathematics course above Calculus. Anything beyond that is the absolute antithesis of "memorized facts and formulas".
It also fails to apply to any sciences I'm aware of at the research level. Philosophy pretty much only exists at the research level, but it's also a much smaller pool of jobs than most fields.
> Doing that with philosophy is far more difficult because so much of it is subjective and relies on criticism and analysis.
Any education in a topic worth it's salt should include that once you get passed the intro courses (because the intro courses are often necessary to provide context for your analysis). Whether curricula succeed in doing so, or students engage themselves enough to do so, is another matter.
What is the philosophy behind arrow functions in JavaScript? Should I just use them blindly, or should I understand why this exists and why/when I should use it? What problem does it solve? Why?!
In my opinion every article about some aspect of programming should begin what an explanation of the philosophy behind it's development. Why does this exist? What problem does it solve? When should it be used/not used?
Totally disagree. Philosophie try to find answer to question which can't be answered. It's just a lot of energy wasted in unsolvable problems. And it is far easier. In philosophy there is no truth, everyone can be right.
Math is a lot tougher, and so, teach you discipline and rigor much better.
When I finally "discovered" philosophy in college, I was angry that we hadn't been exposed to it at all in middle or high school. Instead, I'd been forced to waste years on things like math, biology, etc. that I had no interest in and no use for. Our history / social studies classes would be greatly improved if they incorporated more philosophy.