Math is quite literally the most empirical science that exists
Empirical: “Verifiable or provable by means of observation or experiment.”
Ever heard math isn’t invented it’s discovered? Math isn’t about trying to make something new, it’s about trying to make things that were already there obvious.
You’re heading deeper into the philosophy/study of knowledge which is called Epistemology.
What I think you’re trying to say is you think there’s a divide between sciences which deal with making models about “reality” and testing them versus the sciences like logic and abstract mathematics which constructively discover truth by deriving it from previous truths (axioms/theorems).
However, in a very general sense, any logic whatsoever—written symbolically or in natural language—is mathematics. Making the assumption “matter/energy is not created nor destroyed” and then using that assumption (axiom) to derive “momentum must be conserved in a collision” is mathematics just as much as it is physics. Any time you build ideas on/using a “scientific model” you are using logic/mathematics.
Literature isn’t logic, but if you want to describe literature rigorously you will be using a logical system. All science is based on logic.
The scientific method is literally just proving/disproving a logical implication (the hypothesis) using axioms (model assumptions and evidence) to construct a proof (research paper).
Anyway, we’re off from your original statement. You were wondering if math counts as a science. Anything rigorously studied is science.Even in math, hypotheses are formed and tested and occasionally proven wrong.
Non-euclidean space, irrational numbers, Gödels incompleteness theorems, Tarski’s undefinability problem, etc. are all examples of when widely accepted scientific models of sets or geometry or logic etc. were tested and eventually disproven, leading to the creation of new models. That is science.
The symbols/notations were invented and axioms are arguably arbitrarily chosen, but the consequences of those axioms are undeniably discovered not invented
Math is quite literally the most empirical science that exists
Empirical: “Verifiable or provable by means of observation or experiment.”
Ever heard math isn’t invented it’s discovered? Math isn’t about trying to make something new, it’s about trying to make things that were already there obvious.
I’m not sure that’s right. Science in all the definitions I see talk about explaining phenomena or talk about explaining nature/society.
Math can be used in those pursuits, but exists outside of that definition and is not strictly a requirement for science.
You’re heading deeper into the philosophy/study of knowledge which is called Epistemology.
What I think you’re trying to say is you think there’s a divide between sciences which deal with making models about “reality” and testing them versus the sciences like logic and abstract mathematics which constructively discover truth by deriving it from previous truths (axioms/theorems).
However, in a very general sense, any logic whatsoever—written symbolically or in natural language—is mathematics. Making the assumption “matter/energy is not created nor destroyed” and then using that assumption (axiom) to derive “momentum must be conserved in a collision” is mathematics just as much as it is physics. Any time you build ideas on/using a “scientific model” you are using logic/mathematics.
Just because a lot of science uses math doesn’t mean Science=Math.
A simple example - “I’m going to name this ant species I discovered the Leggy Ant.” - Science (Entomology) sans math.
That’s called Class Logic
(It’s math)
I mean if you’re just going to subsume everything under “logic”, then there really isn’t a point in having anything but math.
You can use math to understand literature, but no ones going to agree Math=Literature.
Literature isn’t logic, but if you want to describe literature rigorously you will be using a logical system. All science is based on logic.
The scientific method is literally just proving/disproving a logical implication (the hypothesis) using axioms (model assumptions and evidence) to construct a proof (research paper).
Anyway, we’re off from your original statement. You were wondering if math counts as a science. Anything rigorously studied is science.Even in math, hypotheses are formed and tested and occasionally proven wrong.
Non-euclidean space, irrational numbers, Gödels incompleteness theorems, Tarski’s undefinability problem, etc. are all examples of when widely accepted scientific models of sets or geometry or logic etc. were tested and eventually disproven, leading to the creation of new models. That is science.
The debate as to whether math is invented or discovered was never settled and never will be settled
The symbols/notations were invented and axioms are arguably arbitrarily chosen, but the consequences of those axioms are undeniably discovered not invented