This is as old as Plato though. His academy supposedly had a sign saying "let no man ignorant of geometry enter here".
But it is very much bidirectional. Philosophy is necessary to understand the foundation on which mathematics sits. If you don't understand concepts like truth and existence, can you really meaningfully engage with work that deals with demonstrating truth and proving existence? The problem of universals is also very relevant as the article suggests.
When prodded, you will probably be able to infer answers for what it means to exist, or what makes something true, but those are philosophical standpoints. They have arguments and counter-arguments. They imply an entire world-view.
It's fine to make a philosophical standpoint, I think it's more questionable to do so without realizing their context, or even that you're even doing so as is often the case in the natural sciences.
If you haven't studied philosophy, you tend to be very blind to the philosophical assumptions you and everyone around you is making. This is especially a problem as STEM education is absolutely steeped in philosophical assumptions and positions without offering the language or tools to recognize and discuss them, so they sort of seep into your mind through some sort of cultural osmosis.
I think it's often perceived as though these standpoints (e.g. logical positivism) are the somehow the result of science, or inherent in the scientific process, but that's just not so. They're a means of interpreting the results, one of many.
> This is as old as Plato though. His academy supposedly had a sign saying "let no man ignorant of geometry enter here".
Sure, but by that standard most modern philosophers wouldn't be allowed in. In Plato's time philosophy was the study of everything, whereas today philosophy is what's left over now that all the useful studies have split off into their own fields.
The article points out that some philosophers also have advanced degrees in math, but it's a pretty big leap from "Some philosophers have things to say about math because they're mathematicians" to "Philosophy has things to say about math".
> If you don't understand concepts like truth and existence, can you really meaningfully engage with work that deals with demonstrating truth and proving existence? The problem of universals is also very relevant as the article suggests.
This is true, but why should I care what philosophers have to say about truth and existence? Math and science have plenty to say about truth and existence without philosophy's help.
You might call that philosophy, but that's just a semantic argument--it can just as reasonably be called math or science. Calling it philosophy is just a way for philosophers to try to get people to listen to their baseless opinions about fields they haven't gained expertise in. If I want to know what truth or existence mean in math, I'll talk to a mathematician, not a philosopher.
> I think it's often perceived as though these standpoints (e.g. logical positivism) are the somehow the result of science, or inherent in the scientific process, but that's just not so. They're a means of interpreting the results, one of many.
Is it? What are some other ways of interpreting results?
Keeping in mind that "making shit up" isn't a way of interpreting results.
> This is true, but why should I care what philosophers have to say about truth and existence? Math and science have plenty to say about truth and existence without philosophy's help.
> You might call that philosophy, but that's just a semantic argument--it can just as reasonably be called math or science. Calling it philosophy is just a way for philosophers to try to get people to listen to their baseless opinions about fields they haven't gained expertise in. If I want to know what truth or existence mean in math, I'll talk to a mathematician, not a philosopher.
Well think about this, is this really possible what you are saying?
I'll submit either truth is a definition, or it must be derived from something (like mathematics or science). I'll omit things like innate knowledge and messages from God as explanations for how we know the nature of truth as they're a bit sketchy from a scientific perspective.
If it is a definition, then the mathematicians and scientists are also spouting "baseless opinions" along with the philosophers, and trust me, everything the mathematicians and scientists said came out of a philosopher's mouth first, probably hundreds of not thousands of years ago.
If you somehow set out to derive the meaning of truth through mathematics (or science), then to avoid assuming what you're setting out to prove, your derivation must contain no truth.
> Is it? What are some other ways of interpreting results?
Sure. There's about as much basis for a material assumption as an idealistic one. The only difference is whether you're willing to assume, with ability to verify or falsify, the notion that an objective reality exists. This is of course a popular thing to believe, but it's ultimately an article of faith.
> I'll submit either truth is a definition, or it must be derived from something (like mathematics or science). [...] If you somehow set out to derive the meaning of truth through mathematics (or science), then to avoid assuming what you're setting out to prove, your derivation must contain no truth.
As someone who regards himself as a scientist, I'm quite happy to just say, "I don't know how to derive the meaning of truth" and move on. Saying "I don't know" isn't spouting a baseless opinion.
We've got enough of an operating understanding of what truth means to function. You do, too. If I punch you in the face and then tell you I didn't, you'll still be mad at me, because you know the truth. Perhaps neither of us can derive the meaning of truth, but it would seem that for practical purposes, deriving the meaning of truth isn't particularly important.
To be clear, what I'm saying here is that philosophers don't know either. Your argument is basically "other fields aren't experts on this thing, therefore philosophers are". No, they aren't. You've actually come closer to making an argument that the derivation of truth is unknowable than that philosophy knows anything about the derivation of the meaning of truth.
> If it is a definition, then the mathematicians and scientists are also spouting "baseless opinions" along with the philosophers, and trust me, everything the mathematicians and scientists said came out of a philosopher's mouth first, probably hundreds of not thousands of years ago.
That's a purely semantic trick. Thousands of years ago, the fields of mathematics and science weren't developed enough to be separate fields, so you could just as easily call those early thinkers mathematicians and scientists as you could philosophers. The thing is, a lot of ideas from thousands of years ago are just regarded as wrong. Pythagoras identified as a philosopher as much as Plato or Aristotle, but given the Pythagorean theorem has stood the test of time, mathematicians are happy to consider him as one of their own today. But neuroscientists aren't rushing to claim Plato because his idea of the separation of mind and body is flatly wrong. If any of those early thinkers are considered purely philosophers today, it's only because no other fields want them. Philosophy today is the leftover dregs of all the other fields splitting off as they matured.
> Sure. There's about as much basis for a material assumption as an idealistic one. The only difference is whether you're willing to assume, with ability to verify or falsify, the notion that an objective reality exists. This is of course a popular thing to believe, but it's ultimately an article of faith.
There's a basis for the material assumption in usefulness. Materialist beliefs let us reason about the world, and predict things. Going back to a previous example: we can both predict that if I punch you in the face it will hurt. You can't even reasonably argue with me on this, because even you don't disbelieve the materialist assumption with regards to this.
The idealist assumption arrives at no such result. You can claim that a mind exists separately from the body and the only thing that assumption allows you to do is get a philosophy degree.
EDIT: To be clear, if we ever meet in person, I will not punch you in the face. That's meant to be a clear example, not a threat. :)
I would disagree, simply because math deals with a fairly restricted sphere of inquiry, whereas philosophy might ask questions about things that mathematical logic, being restricted axiomatically, can't necessarily touch upon. But in truth, we should attempt to be interdisciplinary, I think when people work together on things and try to share their knowledge across field the most progress is made.
Absolutely not. The domain of philosophy is precisely anything which cannot be formalized with mathematics. Not only does philosophy not need mathematics, math is utterly useless for any philosophy.
The very question “Does philosophy need mathematics” cannot be answered with mathematics.
...and this is why no one needs to care about philosophy. If philosophers insist that philosophy needs neither empirical evidence nor formal proving, then all that is left is made-up bullshit.
There are plenty of people doing actual, real, non-made-up research that might be called philosophy, but since they have evidence and formal logic to prove their ideas, they generally don't have to call it philosophy.
This attitude defeats the scientific method! There’s a motivating state of inspiration prior to evidence collection. It’s the hunch. Every scientific development begins at a hunch.
More or less, what I’m referring to above, is the generalization of this “hunch”.
This is called a "hypothesis", a concept which science doesn't need philosophy to define.
As I said before, sure, you could call this philosophy, but a philosopher without any practical science experience isn't going to have anything interesting to say about it, so I'd just as soon call it "science" and cut the unqualified opinions out of the conversation.
If motion of matter can be formalized with mathematics, this rules out supernatural processes. How would you derive this conclusion without mathematics? Philosophic conclusions are often broad, so naturally they use all available tools to draw insight from.
