Mathematics is the only language that is understood by all and does not accept any lies. So it is a universal measurement to prove the truth of things.
Shaden M H Mubarak If mathematics were understood by all, mathematics education would be a lot easier and the discipline would attract more people. The history of mathematics is full of disputes and negotiations. Sure, mathematics does not accept any lies, in the sense that errors in proofs or formulations, or shortcomings in conceptualizations, are eventually discovered, so mathematics as a discipline is self-correcting. But mathematics is not unique in that regard; empirical science is self-correcting too.
Mathematics is a subject for mind & brain & we know that Mathematics consists of 3 -R'S -Reading ,Writing ,& Arithmetic & as an academic interest I have expressed my views under the captioned'' Mathematics -3-R'S -Reading -Writing & Arithmetic
which I submit herewith for your perusal with a request to offer your valuable opinion
Thanks
I'll put in my two cents, even though this question is quite old. At the heart of science is the hypothesis test, right? Well, what is the hypothesis test? Simple put, it's a statistical version of proof by contradiction. All we're doing is taking empirical data and saying "assuming this theory, how likely is it for us to get this data?" Preprint The Basics of Hypothesis Tests and Their Interpretations
Furthermore, our theories themselves are largely just mathematical models, with some narrative attached. So I wouldn't say that mathematics is so much the language of science as science is an extension of mathematics.
Daniel Goldman RE: "All we're doing is taking empirical data and saying... "
To me this doesn't quite sound the right way around. How would you relate your claim to, for example, the 1919 eclipse test of general relativity? Didn't the theory or hypothesis entail (i.e. predict) that given certain initial conditions etc. such-and-such should be observed? The likelihood of the prediction given the hypothesis was established before any data was collected; that's why the data functions as a test of the hypothesis. You make it sound as if a bunch of data is collected and then attempts are made to fit theories to the data after the fact, almost like induction.
Mathematics is explicitly language of 'Science' and implicitly language of 'Philosophy' or 'Religion'
Karl Pfeifer, what's established before is the probability of all distributions. Theories generate hypotheses, which are basically the probability distribution of potential outcomes for a given experiment. Theory->hypothesis->observation is the deductive form of scientific inquiry. So yes, the theory tells us what our expectations are. But then we see what observation we actually have, and the probability of that specific observation occurring.
Daniel Goldman So T generates H which predicts O with pr PO. Suppose the data D is way outside the margin of error for O, so H fails the test. But you are saying that the real point of the test is just to tell us “pr PD , given T” rather than the status of H?
I see why “pr PD , given T” might perhaps be interesting in its own right because of underdetermination of theory by data, but I take it that's not your point.
Karl Pfeifer, the goal is to falsify T. But here's where things get fuzzy, and you have numerous debates such as frequentist vs Bayesian debates. The easiest way to falsify the theory is to attach the following assumption: our observation is not unusual (we can establish what we mean by using a given p-value).
So now you have true proof by contradiction, as we assume T and that our observation won't be unusual.
We can easily clarify that Mathematics is the language in which Science is written.
Mathematics is the language of science only, the Greeks have linked holiness with philosophy and mathematics, but there is no scientific evidence to support it
Pankaj Tomar
Philosophy and religion benefit from the achievements of science.
I think that the many mathematicians work on problems that help us understand and interpret the natural world. For example, the discovery of the world "Isaac Newton" of the basic rules of movement; thanks to the progress made in the calculus. While some mathematical disciplines (applied mathematics) aim to help us understand physical entities in the real world. Others (algebraic geometry) focus mainly on the development of pure mathematical knowledge. Although this knowledge was often found, its applications in the real world were known only later. Thus all mathematical investigations must aim to explain the natural world.
I think at least some small areas or activities in mathematics must, like chess, be merely a recreational pastime. Even if real world applications are found, there is often more mathematics done than would have been needed for that purpose, e.g. when mathematicians refine their proofs simply to make them more elegant.
I agree with @Piyali Mitra. Throughout the history of Western and Asian thought, there have been 2 great competing epistemologies: rationalism, which is modeled on geometric proofs; and empiricism, which relies on measurement and observation. Rationalism leads to religion, philosophy, and math; empiricism leads to science.
Math, philosophy, and religion all claim to provide absolute, eternal, incontrovertible truths. Science does not. Any scientist who claims to have found an incontrovertible truth is confused. Many, many scientists have used mathematical theorems to draw erroneous conclusions, because the theorem is true only in the abstract world of math, and they map the world onto the model, or the model's conclusions back into the real world, incorrectly or imprecisely.
(One common error is to fail to test whether the assumptions made by a statistical test are correct for the dataset. Another is to fail to disprove the null hypothesis, and then conclude you have disproved the hypothesis.)
The remarkable inefficacy of philosophy has always been because it is rational. Its method is to begin with a logical formalism to represent the world (in Platonic, Hegelian, and Marxist dialectic, natural language is presumed to be a formal logic, and words to correspond to categories clearly defined by necessary and sufficient conditions), choose a set of unquestionable axioms, then deduce things from this. This never works, partly because the axioms are usually wrong, and partly because foundationalism is epistemologically incorrect and insufficient, but mainly because there is no attempt to validate the conclusions by mapping them back onto the real world and checking the results, because the logic is too vaguely defined to do such a mapping, and because the physical world is presumed to corrupt anything in it, so that failure to validate an eternal truth in the physical world doesn't disprove it.
We can define the union of religion and philosophy as the set of belief systems which are invulnerable to empirical disproof.
What about math? Is it vulnerable to empirical disproof?
Well, yes and no. You can't measure the sum of angles of a triangle, get 180.01 degrees, and conclude with mathematical rigor that we live in a non-Euclidean universe. But if you got 230 degrees, you'd know something was wrong with your theorem about the sum of triangle angles. Much math, especially geometry, is clearly-enough defined that it's easy to identify erroneous "proofs" by finding counter-examples.
Science is concerned with reducing the error of predictions in the physical world. Math is a useful tool, but there was math millenia before there was science. All of scientific methodology is concerned with how to /apply/ math to the real world: how to write down measurements, how to understand errors in measurement, what constitutes a hypothesis, what statistical truth means, what probability means, how to represent physical change mathematically, and so on. Math itself is a tool used by science. On its own, without any empirical validation of mathematical results in the real world, math would be as unreliable as religion and philosophy, because mathematicians are only human.
We can see this in some advanced math which can't be empirically tested. Take Goedel's first incompleteness theorem. It's inherently untestable. How is it that the theorem is taken to prove what formal proofs are? To be a correct proof about the nature of proofs, it would necessarily be circular. Close study of the theorem leads one into a maze of semantics. At best, it relies on the suspiciously philosophical assumption (or definition) that the sum of an infinite sequence, or the result of an infinite computation, has the same ontological status as a rational number. So the incompleteness theorem, which is presumed to be math, is also philosophy--a language game based on arbitrary choices about semantics, leading to an untestable conclusion. I would not be surprised if it turns out to be wrong.
Both Mathematics and Theology are two areas which are dear to me.
I had been a mathematics students originally then I switched to theology and eventually graduated in the area. I have to admit that to my mind, it all depends on one's perspective of things (i.e. from which angle/s a person is willing to view things). Provided that I love both areas, I was able to delve deeper into theology because I had "the mathematical lenses" on so to speak especially when things became pretty abstract to digest. The exemplary subject that I remember studying for this way, was metaphysics
In fact, it has always fascinated me that Aristotle, a pagan, was able to arrive to the notion of god my using science (reason) and logic, in his book on metaphysics.
Brenda Prato Some philosophers have used mereology and topology to analyse theological notions, e.g:
- Bartłomiej Skowron, “The Explanatory Power of Topology in the Philosophy of God”. God, Truth and Other Enigmas, edited by M. Szatkowski (Walter de Gruyter Verlag, 2015), 241-253.
- Also see https://plato.stanford.edu/entries/location-mereology/ The entries for Hud Hudson in the bibliography should be especially relevant.
Karl Pfeifer thanks for the references, this was actually very interesting!
Most of us know that there are thousands of languages all across the globe. ... Math is the only language that is shared by all civilizations regardless of culture, religion, or gender. 2 + 2 will always equals four, Pi is always approximately 3.14 no matter what country you are in
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