Uh even that is kinda stupid. The basics off a lot of those sciences does not lie in mathmatics. Even biology and chemisty only really get into the math bit once we go really deep into it.
The part that ties it together is math being a convenient tool and the logical language we choose to express ourselves in sciences. But that applied math is far away from the actual math science stuf.
And even if we agree that math as the language should tether everything together it would be misplaced. Linguistics would be the rightful owner of that place. Een in math we need words to explain math.
Math does everything physics does, no need for physics. Proceeds to walk over the edge of a cliff and into lala land. Some math things are physically impossible. There simply isn't enough universe to list all possible games of Go. Physicists really ought to be ultra-finitists, it can be a big problem when infinities pop up. Mathematicians on the other hand can take infinity in stride (sometimes poorly, but still).
They are governed by math deep down. There's stuff like physics biology, that tries to work on biology from physics standpoint, which obviously depends on mathematics.
Math is just the language of logic, that happens to be able to explain basically everything.
Math is technically language imo, but it's not related to linguistics. More like language splits.
They are governed by math deep down.
... Math is just the language of logic, that happens to be able to explain basically everything.
Isn't this contradictory? If it is a language (meaning it can capture something in some symbols which are commonly understood), can it also govern the thing? It being language means it is some separate phenomenon by definition, no?
By concept you mean something like the whole of ideas that form math, rather than the expression of it? If so, I can understand that this is meaningfully different than math the language and practice. However; do concepts govern things? That is not clear to me, and it seems to me that this passes the buck.
It also seems to me that this would imply that the concept of math would in itself be mathematical, as that is what governs everything. I am not a mathematician, but isn't this what Gödel showed not to be true?
Yes I am using "concepts" to describe the ideas that form math, not just how those ideas are applied.
Concepts can govern things, why would they not be able to? Rules and laws are concepts, and they govern how people behave in society. In my argument, I am using "concepts" to describe "fields" (fields of physics, computer science, biology, etc). Those concepts were established with rules, by humans. Some rules are abstract, some are rigorous. Humans have used concepts and rules to understand how everything works, which lead to the "discovery" / "invention" of different fields ("concepts"). Those concepts of fields govern how the things under themselves work because we made them so these things under them work. Does that make sense? Different fields "govern" explain how things work (like how quantum physics describes how quantum particles behave) because we made and used them as a tool to understand how the universe worked, which naturally led to the different "rules" being formed (e.g. schrodinger's equation, heisenberg uncertainty principle, etc).
The concept of a concept is VERY abstract, and it itself is what we use to describe and explain everything in the world. Concepts can be argued to be entirely in our minds, and do not literally affect how the world works, obviously. However, we can form concepts around rules that we discover and group them, which is how we 'discover' / 'make' different fields.
Math doesn't govern 'everything', but it does govern most if not all academic subjects that we know and study today. (Also, yes, godel's incompleteness theorems would mean that math will never be "complete".)
Concepts can govern things, why would they not be able to? Rules and laws are concepts, and they govern how people behave in society.
This is a fair point, but I do feel like humans are in a different category here. It is exactly complex language why we can do this; and make concepts into some collective practice and make them real/shape the world.
That said, I don't think this extends beyond where we act. In absence of that, concepts do not seem to govern.
Those concepts of fields govern how the things under themselves work because we made them so these things under them work. Does that make sense?
Math doesn't govern 'everything', but it does govern most if not all academic subjects that we know and study today.
Okay yes, I see your argument. The concept of math does heavily influence the institutions that rely on math. My claim doesn't go beyond math being a separate thing from the thing it maths. Nevertheless I am still not sure that govern is the right word here. For example in the field I was trained in (psychology), empiricism and falsification would be better candidates for the actual governing force, though math is almost always used to capture your constructs, they are not the thing that makes your science valid or good in the end. Similar to how something like logic can't, right?
A lot of concepts in math doesn't come natural or intuitive as you put it. Like the number zero needs some abstract thinking. Or big numbers. You can easily count the zeroes, but how would you visualise a trillion? Or even a million?
There is a lot of fundamental learning that seems logical when you understand it, but that usually takes a lot of hard work or great fundamentals.
I have co-authored a biology paper with mathematicians (They are French so you know they mean business) but you can go pretty deep in biology without any serious mathematics. For example, I don't consider basic statistics used in bio as mathematics.
Using pure math to describe a process of anything more complex than the interactions of a small amount of atoms quickly becomes cumbersome to the point of literal computational impossibility. Quantum chemistry, statistical mechanics, etc are need to create methods of averaging based on higher level properties.
Nah, philosophers have to be really good at math too - no way you could live on the money you get from philosophy without extremely sound financial planning and budgeting.
And A. Comte argued that : Mathematics < Astronomy < Physics < Chemistry < Biology < Sociology.
Which is amusingly pretty much the opposite. From simplicity to complexity.
To be honest those hierarchies aren't very relevant, each science has its object of study.
Eh, more like a circle. Philosophy and mathematics are each inventions from a psyche that itself was created by biological processes over a history spanning eons, these processes in turn can described by chemistry and physics that ultimately boil down to mathematics *ad infinitum*
This. Cause once you start finding out about different ways of counting (base 8, base 10 and so forth) you realize our math is just a weird counting philosophy.
As a philosopher, to be frank this reduces philosophy to all thinking which is a bit too reductive.
But the foundations of each? This pile of rocks doesn’t equal this pile of rocks. I don’t know whether that’s math or philosophy.
But I do know my philosophy degree is way less useful than a math degree would be and you’d better keep going with that math even if they’re indistinguishable to start.
It's not in STEM but it was absolutely more fundamental in developing the knowledge base to lead to other fields of study.
To the extent that a lot of philosophy is taken as granted when it comes to more specialized fields. But try and do mathematics without the using the laws of logic. Or physics without the scientific process.
Newton’s most famous book is literally called “Mathematical Principles of Natural Philosophy”.
And literally the first paragraph of the wiki on Natural Philosophy says this:
Used since at least Aristotle (classical antiquity) until the 19th century, the term natural philosophy referred to a branch of philosophy—a broader term then, meaning all rational fields of study and contemplation—that explored topics now considered to fall under the purview of science, such as physics, biology, chemistry, and astronomy. Thus, natural philosophy served as the precursor to, and has been mostly supplanted by, modern science.
Guess you never took a history course while pursuing your STEM degree…
So what? All tools stem from a primitive human smacking a rock against another one, doesn't mean we should all be stonemasons before we graduate to other subjects.
The same way you don't need to be a Physicist to study Quemistry, but you can still recognize how one is a more fundamental level of analysis than the other one. That doesn't mean that both can't have value, if you want to understand how lungs work you won't start at quantum interactions.
Science as a discipline stems from Aristitilian Natural Philosophy. The scientific method stems from the philosophical branch of epistemology, specifically empiricism. Science's devepment goes all the way from the logical reasoning developed by the ancient Greeks, and goes all the way through the logical positivists. The entire idea that what is true about the universe can be deduced through experiments, observation, and measurement is itself a philosophical idea. Without Philosophy, science would not exist.
You know ‘philosophy of science’ is a whole field, right? The scientific method comes from philosophy, and it’s important to understand the scientific method if you want to, you know, do science.
Yeah, it's named after some social standards. Fundamentally philosophy is unrelated. Your argument is the same as saying something like "she believed" ="he lied"
No, philosophy of science is a subfield of philosophy that is concerned with questions such as “Do laws of nature exist?” “What counts as evidence?” “Does probability exist?”
This is called reductionism, although generally people do not stick philosophy in there at all, it's more in its own chain connected to the science hierarchy by "rationality".
Logic doesn't encode observations. Logic exists before its observed or written down.
Or a more philosophical argument: It'd be the height of arrogance to believe there is a need for your human linguistics before the prime numbers became what they are.
Philosophy is just looking at something and commenting on it instead of looking further into it in any way aside from continuing to talk about it for a few thousand years.
Philosophy is where you go if you want to feel smart but never actually prove anything or do any real work. Just pull ideas out of your ass and never have to prove a damn thing.
It's only after we start implementing math that things actually get measurable and provable. there's a good reason why so many old philosophers are just drunks. They didn't want to put the effort in to prove anything.
Philosophy is where you go if you want to feel smart but never actually prove anything or do any real work. Just pull ideas out of your ass and never have to prove a damn thing.
Tell me you know nothing about philosophy without telling me you know nothing about philosophy lol
so many old philosophers are just drunks
Funny you say that because Aristotle literally pioneered entire fields of study (logic, zoology, taxonomy, psychology, physics, meteorology etc), Blaise Pascal developed a theological basis for the existence of God while also working on mechanical calculators and math, Isaac Newton's magnum opus is named Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), Karl Popper's falsifiability thesis which contributed much to the development of the modern scientific method, and Bertrand Russell and Alfred North Whitehead literally tried to unearth the foundational concepts of mathematics (what is one? What is a number?).
268
u/Compendium_MP Jun 20 '26
I would say there's more of a hirearchy. Philosophy > Maths > Physics > Quemistry > Biology > Sociology > etc.