Ok, then at best this is a useless classificatory dispute that is basically arbitrary. At worst, this is just an effort to distract from the point about which you're clearly mistaken, i.e. the idea that there is "proof" in the run of ordinary non-abstract science as opposed to always defeasible theories. If you disagree with this, you're well outside the mainstream of scientific opinion and have quite a lot of argumentative work to do, which would involve overturning quite a lot of basic stuff in philosophy and methodology of science. Imprecise statements that don't clearly amount to anything, such as "Mathematical constants can be discovered in a scientific background," won't cut it.
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Ok, then at best this is a useless classificatory dispute that is basically arbitrary. At worst, this is just an effort to distract from the point about which you're clearly mistaken, i.e. the idea that there is "proof" in the run of ordinary non-abstract science as opposed to always defeasible theories. If you disagree with this, you're well outside the mainstream of scientific opinion and have quite a lot of argumentative work to do, which would involve overturning quite a lot of basic stuff in philosophy and methodology of science. Imprecise statements that don't clearly amount to anything, such as "Mathematical constants can be discovered in a scientific background," won't cut it.
balancing a simple chemical equation would not be possible if mathematics was just mere philosophy.
As far as I know, chemistry constitutes a huge part of both our shared reality and science as well. Believe it or not, the universe is written in formulas.
however yes, it's the same pointless debate where I need to state the obvious for the billionth time, my bad. have a nice day
You cannot distinguish mathematics as such from scientific applications of mathematics, as made manifest where you discuss balancing a chemical equation. You take this failure on your part to reflect something obviously true about the nature of science and mathematics. What more is there to say? The difference here should be blindingly apparent. It's as if you think anything expressed in quantitative terms should be classified as mathematical rather than scientific, or as some nebulous hybrid of the two, regardless of its factual content. This is utterly ridiculous.
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Hey, I'm not nearly as knowledgeable as you regarding Math and especially physics, but I wanted to pose a question that I would earnestly like answered, in your opinion.
My interest is in your statement that Math represents the reality in which we live; I love math, and I always used to think that too, and that was one thing that was so cool about it, I thought. But when I was taking Calc 2, I had a short conversation with my professor about Vector spaces (A class my dad said he took when he was in college. What I know about it is that it involves looking at "n" dimensions. You probably know this already, but apparently in math there can theoretically be any number of dimensions, using the arbitrary variable n to represent the number (like how what we see on a graph with just an X and Y axis represent 2-d, whereas our world is 3-d, and on paper a third axis would be represented by Z, if I recall correctly). Basically, if memory serves, my professor expressed to me that Vector spaces didn't hold a lot of meaning for her in the physical world, but they meant a whole lot in terms of theoretical mathematics.
This conversation made me question the degrees to which mathematics can be considered to actually equal reality. I wanted to know if you had any thoughts about this.
Also, this is just semantics, but being OCD like I am, I feel the need to point it out; I'm pretty sure Math and Science aren't separate things... Math IS a Science, just like Physics, Chemistry, Biology, etc.
Anyways... Thanks in advance!
Edit: Oh, also.... I know that proofs are done in Logic as well as Math. Unless you want to say that Math and Logic are the same thing, which.... I don't know if that can be said or not. I thought Logic was a form of applied math.
I dunno... Maybe I'm just getting too hooked on semantics. And I haven't studied any of this shit in like 8 years.
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Mathematics can be classified as an abstract, or non-empirical, science. If one takes science to necessarily involve empirical inquiry, as I do, however, then mathematics isn't a science.
If one considers something like the process by which Fermat's last theorem was proven, it's apparent that it didn't involve empirical evidence. The proof was confirmed as correct in the light of the reasoning of multiple mathematicians, which relies in the end on intuitive cognition, not in the light of empirical work. Compare the process by which evolution by natural selection came to be the favored model of biological evolution over, e.g., Lamarckianism -- much empirical work involved.
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Well as I understand it, empiricism is based on what you can "detect," for lack of a better word, with your 5 senses. So in that sense, of course math wouldn't be considered empirical. But as KCN seems to have been emphasizing, it is critical in our use of analyzing things empirically. And if you feel that way about Math, what about Logic? That must not be an empirical science either, am I wrong? No disrespect to you, thanks.
As I understood it, he/she was describing the overlapping of the factual content you are talking about with a proper mathematical formula, and vice versa. Hence unifying both sides
What about you, do you think that Math is fully able to describe the physical world, and that it is an empirical science? I'd really like to know what people (who know more about math and physics than I do) think about this.
Well, there's a full branch of applied mathematics called "mathematical physics", so I'd say that lagrangian mechanics, statistics, classical mechanics, quantum theories as well are definitely a thing and do a good job in representing what's happening out there.
They're more than an useful approach to our external reality. I'd say that's the only one, since we cannot really rely on anything else to verify any hypothesis.
I see. That's useful information. So would it be fair to say that there are other branches of (non applied, i.e. theoretical) mathematics that can't be relied upon to explain things in our external reality?
The point you miss is that if it's false hope what's the loss? If they go to nothingness how has believing for comfort hurt them? You are again confounding issues. There is a difference between believing in something out there and being some religious pusher of policy. Despite what you think and r/atheism likes to believe, most people who believe aren't out there knocking on doors or trying to brainwash anyone else. I say that as an agnostic who things nothing is most likely...but isn't so arrogant to say "well the evidence doesn't show anything so there is nothing".
I just cannot understand the sort of atheists that says "there is nothing" and science proves i or cannot accept that the two may not be mutually exclusive. They tend to confound religion with a possible creator and for those who claim critical thinking as a skillset I can't grasp this. It's often young people or people who were religious and discovered atheism later and are flexing their minds trying to solidify their views so I tend to cut them some slack. But in the end anyone on either side who can't say "nobody really knows" is being dishonest in my view.
the loss is about recognizing that the main content of beliefs -- requiring less cognitive involvement than a thorough research-- might be easily transmitted, like memes, to other people who will often start to believe in them especially if they don't have tools to defend against the same old wishful thinking.
What I mean is that it's important that people learn to think with their own brains, without being influenced by supposed supernatural "third parties" that by chances of sheer luck help people out. Superstition is a very bad thing, being rooted in ancestral fears it extends all over concepts of social life that might not involve just religion, and you see its effects every day especially on the news.
Maybe false mathematical proofs presented to fool people who haven't adequate skills to recognize the trickery.
You just can't separate people believing in something unproven from religious politics can you? You seem to actually believe that someone must "accept the ugly truth that there is nothign because nothing has been show to be true" regardless of how much pain that brings them. I can tell you have never been around sick and dying people because the selfish view of "you need to face facts" is all about you...feeling smart and superior...not about empathy and the suffering person. There is a huge diffrence between trying to get religious influence out of human rights and preaching militant atheism. It pains me to see most people do the latter. Simple fact is you don't know what is or isn't anymore than some uneducated person in a cave. The question is too big and science can't get there yet. Just because you have more of an understanding of physics or cosmology than they do doens't mean there isn't a god or creation. it's an open question and I am getting tired of both sides declaring truth with the same tactics.
Here is the "truth". Nobody knows. If you declare on one side or the other and then try to "debate" why the other side is incorrect and your position is the "correct" one then you are being dishonest. I love science but it is a process and doesn't end...it's not a snapshot in time that lays out all reality. People who use science as an intellectual weapon and claim some position of overarching truth based on current knowledge are as bad as people who claim that position based on a 2000+yo book written and edited by countless people. Both sides want control and safety and fear the unknown. Rather than trying to come to terms with that unknown they attack the other side to feel more in control. Nobody knows...none of us. If you can't face that then that's your failure not anyone else's.
It's not about "me", it's about us as a whole.
I personally would avoid a societal system where the mental attitude towards superstitions is something so peculiar that it impacts the whole community, because religious people who keep their beliefs to themselves without proselytizing or giving their 'blessings' to the whole neighborhood
are quite a few.
It would be way more interesting if deities received the same treatment as Marvel superheroes. Something you can admire and fabricate a narrative upon, yet not something so strikingly important that you have to give up on your critical thinking.
It's not the first time that for some unknown reason you point the finger at me implying that I haven't seen the sufferer, let alone I've been a sufferer. I'm just not inclined to lie to myself or others, when somebody needs comfort a hug, a smile, playing music or reading a book to who's dying can be good ways to spend the last moments together.
My sense of the provenance of this dispute is that KCN wanted to justify his incorrect use of the term "proof." It simply isn't controversial that "proof" is a concept reserved for mathematics and logic (I failed to include the latter before), and isn't part of empirical science. Empirical scientists don't "prove" things, they gather evidence and build defeasible theories via hypothesis construction and testing. This fact has led to the realization that empirical scientific theories are pervasively underdetermined: "Underdetermination is a thesis explaining that for any scientifically based theory there will always be at least one rival theory that is also supported by the evidence given, and that that theory can also be logically maintained in the face of any new evidence." "This is a result of our inability to completely understand or gain access to the whole set of empirical evidence for any one particular situation or system, and therefore our acceptance that new evidence could be made available at any time. This thesis maintains that since there is no method for selecting between our two (or more) valid solutions, the validity of our conclusion is always in question." https://www.rit.edu/cla/philosophy/quine/underdetermination.html
KCN's response to this being noted was to try to implausibly elide mathematics and science, without appreciation for the obvious fact that application of mathematics in science is distinct from mathematics as such.
Yes, logic is an abstract, or non-empirical, discipline, like mathematics. This seems undeniable to me, but if you want details, see this paper: https://pdfs.semanticscholar.org/d124/3542b263f9a807871adf4803e0c096dd21ad.pdf.
Here are some passages that may help clear up some of the confusion surrounding these topics. Consider the following from philosopher Elijah Chudnoff:
"Abstract reality encompasses the necessary, normative, infinite, and abstract as in non-spatiotemporal and causally inert. Mathematics, metaphysics, and morality are about it. Concrete reality encompasses the contingent, non-normative, finite, and concrete as in spatio—and/or—temporal and/or causally efficacious. Physics, psychology, and history are about it. These seem like fairly natural groupings. It might be that there are some tough borderline cases such as time itself or the universe as a whole . . . ."
Consider also the following from mathematician and philosopher Neil Tennant:
"Philosophy is a conceptual discipline. Its method is introspective and reflective. It is based on our intuitions and on our grasp of the meanings of our words. Yet it aspires now, after two and a half millennia of refinement, refutation and re-thinking, not to be provincial to any particular language. Nor is it confined to any particular historical period, cultural milieu, socio-political system or religious affiliation. Philosophy strives to be of universal appeal, to any rational intellect, human or otherwise. In that regard, it is a lot like Mathematics. Philosophy tries not to depend on empirical considerations, even though one of its main contemporary aims is to come to mutually enlightening terms with natural science."
"Mathematics and natural science both aim at the truth. Mathematics aims at necessary truths about abstract structures and objects. Natural science, by contrast, aims at law-like truths about the various natural kinds of physical objects and events forming the causal order in space and time."
Again, the fact that empirical scientific facts are often expressible in mathematical terms does not make them part of mathematics as such. In their work, engineers rely on facts that are the province of physics in everything they do; this doesn't entail the absurd idea that there's no principled distinction to be drawn between engineering and physics -- they're separate disciplines for a reason. KCN clearly just didn't want to be wrong about the concept of proof, and so kicked up this nonsense effort to run mathematics and empirical science together, such as to make it somehow illegitimate to say that proof is exclusive to mathematics (and logic) and doesn't feature in empirical science.
To further illustrate the point, take KCN's example of the speed of light. KCN apparently believes that the speed of light is a mathematical fact, or exists in some nebulous borderland between mathematics and physics. Anyone who knows about the history of the discovery of the speed of light knows that it was discovered via empirical work, and is simply expressed in quantitative terms (if you're unfamiliar with the history, see this: https://en.wikipedia.org/wiki/Speed_of_light#History). The processes by which it was discovered, those of empirical science, are clearly highly distinct from the processes that lead to advancement in mathematics (consider my earlier example of the proof of Fermat's last theorem). Mathematical proofs don't involve observational data, for example. To say that the speed of light somehow falls under the umbrella of mathematics because it is quantitatively expressed is about as silly as saying that any fact expressed in a language should be classified as a linguistic fact.
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