Scientific research

But the word 'science' hasn't always had the present meaning.

Aristotle wrote in Greek, while the word 'science' is derived from the Latin 'scientia' by way of the medievals. Aristotle would have used the word 'epistimi'.

In ancient times both words meant pretty much what we mean by the word 'knowledge'. (Hence 'epistemology', the theory of knowledge.) The ancients and the medievals used these Greek and Latin words to refer to any body of knowledge, however diverse and unlike each other they were. Theology was considered a science, in fact the most exalted of the sciences, as it was knowledge of God.

So sure, Aristotle probably did use a phrase that meant 'knowledge of quantity' in Greek. But that doesn't imply that he was trying to communicate our modern understanding of the word 'science'. Our concept of 'science' today refers largely to natural science and is a product of the 17th century Scientific Revolution and its wider cultural aftermath.

Which leaves mathematics in kind of a problematic position. Mathematics is often associated with natural science, especially with physics which would be pretty much impossible without math, even though mathematics is very unlike natural science. Despite mathematics being fundamental and indispensible to many sorts of science, it isn't even clear what mathematics' subject matter is or how human beings come to know about it in the first place. Mathematics does seem to possess objectivity, since valid proofs concocted by mathematicians here in my California remain valid in your Paris, Exchemist's London and even in China! (Believe it or not.) Nobody can really explain why that is either. When we employ mathematics in astrophysics, we are assuming that it remains valid over billions of light-years.

More of the mysteries the constantly surround us.

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Fair enough but people still thought of mathematics as a science well after Aristotle, and I also quoted people from the period where most scientists came to regard empirical sciences as the prototype for science. And I agree with them. I only disagree that mathematics should be considered not empirical or that physics and mathematics are in fundamentally different positions in respect to empiricism.

Sorry I can't join you in your quandary, I'm not conflicted about any abject paradox regarding the nature of mathematics because I don't assume your assumptions. To me, there is no problem whatsoever. Mathematics is an empirical science and that's also pretty obvious, too. I tend to see the root of this paradox in the ideological conflict that existed at the time of Galileo between the bourgeoisie in Europe, who very much wanted to move forward, and the Church, who wanted to stay put. People argue today as if we were still in the 16th century and that gives them very nice blinders to ignore the evidence. There's a comical effect to it, too. It is also rather sad. The top of the notch of scientists today can't seem to be able to make sense of what it is they are doing, or indeed what Copernicus and Galileo exactly did. I would encourage you to make Copernicus an example to follow. Brought up in the dogma of the Church, he came across an idea and decided it was indeed a good idea that could explain logically the appearance of things. I guess that's all we need to remember.
EB

 

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Why does the concept of mathematics disturb you?
Don't we have a saying "if it looks like a duck, walks like a duck, quacks like a duck, you can assume you are looking at a duck", without any questions about a duck presenting a problematic concept of waterfowl.

If it looks like mathematics, if it functions like mathematics, if it yields reliable results mathematics, why should it be problematic that abstract mathematics is a real aspect of spacetime fabric.

Just like saying "that bird is a duck", why not say; "the universe is of a mathematical nature"?

Mathematics is not some rare or exotic phenomenon. Everything in the universe has a mathematical aspect to it.
That is undeniable.
https://www.pbs.org/wgbh/nova/video/the-great-math-mystery

 

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I deny it, so it's not "undeniable".
EB

 

Can you name anything which does not have a mathematical aspect to it?

Try to do science without maths....what do you get?

Do you deny that all things in the universe consist of patterns, except where chaos reigns. Even then patterns will emerge from chaos.

An orderly self-assembly is by its very essence mathematical in nature. Any "system" is a mathematical pattern.

Please note that I am not proposing that human mathematics is represented in nature. On the contrary, I propose that nature's mathematics can be symbolically represented with human mathematics....difference.

 

In ancient and medieval times, 'science' basically meant 'body of knowledge'. Calling mathematics a body of knowledge is uncontroversial. So is calling religious doctrine a body of knowledge. But identifying these with what people today think of as 'science' is probably misleading. People today mean something more than merely a 'body of knowledge' when they say 'science'. Understanding what that "something more" involves is one of the places where we should direct our attention. It's the subject of the philosophy of science.

Understanding 'science' to mean nothing more than 'body of knowledge' suggests that there isn't any single answer to your question about the "essential characteristics" of "scientific research". Knowledge of different subject matters might be acquired in totally different ways, ranging from reading and accepting religious scriptures and the teachings of one's religious tradition, through intellectual intuition and logical deduction, to observation and experiment in the physical world. There likely isn't any single common denominator.

Sure, the rationalists in particular did that. (Given your avatar, you may be partial to their approach.) Many of them took Euclidean geometry to be the paradigm of an ordered body of knowledge. In their mind, mathematics and its proof structure was indeed the ideal science. So many early modern philosophical/scientific writers adopted the style of trying to deduce all of the propositions of their subjects as theorems from an initial set of axioms. Empiricism and experimental science kind of appeared as a counter-current in opposition to that. Their belief was that we will never know about physical reality unless we look.

I'm not conflicted either. I'm just acknowledging the existence of the philosophy of mathematics. It isn't a matter of paradox so much as simply recognizing that many questions about the nature of mathematics still remain unanswered. And it's exceedingly unlikely that questions about what kind of reality a 'group' or a 'ring' has, or how mathematicians can acquire knowledge of such things, can be answered in the same way that we discover extra-solar planets, describe earthquakes or elucidate the biochemistry of photosynthesis.

 

They are proceeding without proof.

 

This seems pertinent to the discussion.

https://undsci.berkeley.edu/article/mathematics

 

A "body of knowledge" would be identified by what it is you are supposed to know. In the case of the science of nature, you're supposed to know something about nature. In the case of religion, you're supposed to know something about God, whether that's true or not. So, what do you think people meant when they thought of mathematics as a body of knowledge? According to your interpretation, it seems mathematicians wouldn't have anything to know. Yet, people in ancient times thought of mathematics as a body of knowledge. This is the paradox you have to explain.

I'm not identifying. I'm well aware that people think of science as physics and then possibly a few others like chemistry, mathematics being at the far end of the spectrum. What I am saying is the people in the ancient times, and a few individuals since, got it right against the majority, as happens so often.

I don't think you would want to search for "more than merely a body of knowledge", unless you want to look into how God makes sure we get it right.
Physicists see physics as a body of knowledge and are mostly sceptical about everything else.
What people will be looking for are what methods specific to a particular discipline qualifies it in their view as a body of knowledge. This is likely to turn into finding the convenient justification promoting your own discipline to the status of body of knowledge while expressing doubts about other disciplines.

You mean that being logical about the inferences you allow is optional?! You mean mean that facts are optional?! Good Grace.
I would say myself that logic and facts are certainly necessary. If you don't have something logical to say, then it certainly isn't science. And then you need to be able to identify the facts you allow. That's definitely a minimum.
Tell me if you see something else.

Something like that, yes, and I would agree, but that's usually what most people do, even perfect idiots.

Sure, but different sciences all have specific methods.
Physics requires maths and maths requires logic. If you accept those as actual bodies of knowledge, then knowledge of what?
EB

 

That's interesting, thanks.
EB

 

Yeah, it is, good job!

So, for example...

Focuses on the natural world?
Often math is seen as dealing with entities that have parallels in the natural world but don't themselves exist in that world. Unlike, say, ants or atoms, the number two is not generally viewed as a physical entity, but as a powerful abstraction that can be used to describe physical entities. On the other hand, one could also argue that mathematical abstractions arise directly from the natural world — that the fact that two ants plus two ants yields a set of four ants is simply a description of how objects exist in the natural world.​

No. Mathematics is the formal description of our perception of nature, not a description of nature itself.

Still, good try.
EB

 

TY, I certainly agree with that succinct definition, however,
When we speak of universal constants, we speak of inherent natural values and functions (potentials), which exist outside human observation.

While human mathematics are subjectively descriptive of our observations, we cannot ignore the fact that we are able to make scientifically "objective" conclusions from our observation.

2 + 2 = 4 = true (by any form of symbolic abstraction). Nature does not present the mathematical equation as written, but the algebraic equation does represent the natural equation that two physical objects plus two more of the same physical objects equals four of that specific physical object.

This is a universal relationship between two universal constant functions: "addition" and "multiplication" (x + x = 2x)

And so IMO, it is with all algebraic formulas and equations, which represent universal functions for all values (a - z)

While actual numbers are purely human symbols, they do abstractly and arbitrarily represent universal values.

 

When we speak of a tree, we certainly mean an actual tree that exists out there in the world as a real thing with branches and leaves. Does that mean we should regard the natural world as made of words?
Inherent my ass.
EB

 

amen

 

No, that's what I just told you. Fundamentally Nature does not have words, nor numbers, nor human language. It is a permittive condition and does "recognize" values and functions (potentials) and allows for the formation of patterns, intrinsic as well as extrinsic.

When we speak of a tree we speak of a mathematical pattern. The universe does not understand the word "tree", it understands only the tree's inherent patterns of values and functions. This is how a tree stays alive and grows and converts solar energy into "food" and produces fruit and seeds which have the genetic potential to root (establish) and begin the growth of a new tree.
Each tree only one of an infinite number of repeating patterns of enfolded potentials becoming explicated in reality. The inherent fractal geometry of Nature.

The world does not have words or numbers, it has values and functions. The intrinsic quantities and qualities of physical objects and functional fields.

Nature does have it's own mode of communication, i.e. provides a permittive condition for interaction of physically precise atomic and molecular behaviors based on the extant values and functions in play. It is the mode of communication and interactions which are observable and quantifiable into symbolic representations, which we have named "mathematical values and functions" and formalized in the symbolic languages of numbers and equations.
Unless mathematical values and functions are present, nature is unable to produce repeating communication and interaction and establishment of patterns.

Human Mathematics are the symbolic representation of Natural values and functions. And apparently we are using the correct representative symbolisms and logic of Universal values and functions, to be able to accurately describe natural phenomena and even to make predictions on what and when Natural behaviors will produce a specific result.

 

Interesting. In quantum mechanics, there are mathematical descriptions of nature which we don't perceive. We can't perceive any of it either, ever.

Is QM a description of nature "itself"? Or doesn't anyone really know?

 

I also wonder what "perception of nature" is described by the Binomial Theorem, for example.

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Fair enough. Let me rephrase: Mathematical scientific theories are formal conceptual models meant to explain our perception of nature, not nature itself.
EB

 

I'd rephrase that as conceptual models which explain perceptions of nature, but which we can't conclude are not descriptions of "nature itself" if we don't really know what "nature itself" is (given all we can reasonably say is the models are good ones).

So how did you conclude this? Where did the concept arise? Was it in your mind, and where is that? Is your mind a part of "nature itself", and can you perceive this, IOW?

 

Quantum mechanics seems to me to be very instrumentalist.

https://en.wikipedia.org/wiki/Instrumentalism

In other words, what quantum mechanics seems to do is provide a way to predict (the probabilities of) observational outcomes when observational variables are plugged into the mathematical apparatus. It's a calculating device.

It's still hugely unclear what's really happening down there in the microscale of physical reality that makes these particular mathematical formulas successful and makes experimental results turn out as they do. That's what the various interpretations of QM seek to elucidate.

So despite QM's undoubted practical successes, its physical basis remains very mysterious. It's been a century now, and nobody really seems to understand it (yet).