Monday, April 04, 2016

Is all knowledge scientific?

I don't see how it can be. In order to do science, you have to be able to do mathematics. (Ever try to pass a science course without it?) But mathematics is not science. It operates using a infinite set of non-natural entities called numbers. If there are no numbers, there's no science.

38 comments:

William said...

Of interest, it would seem that according to Pigolucci's past quick definition of scientism at

"https://scientiasalon.wordpress.com/2014/04/28/staking-positions-amongst-the-varieties-of-scientism/

as Apple dictionary's "excessive belief in the power of scientific knowledge and techniques,"
scientism is compatible with theism!

Currently, however, it seems that most scientism believers are atheists. This may be a historical accident.


jdhuey said...

Except that math is about logical relationships, not about factual knowledge of reality. That is, by itself math tells us only about itself and nothing about reality. While math is a very productive tool that science uses for developing knowledge, it doesn't contain knowledge within itself.

William said...

jdhuey,

Pigilucci's article I linked discusses this: you are excluding mathematical facts from your view of reality, which means you assume nominalism in mathematics, which is just one of many unprovable philosophical positions about reality.

grodrigues said...

@jdhuey:

"That is, by itself math tells us only about itself and nothing about reality. While math is a very productive tool that science uses for developing knowledge, it doesn't contain knowledge within itself."

First, the assertion that mathematics is not knowledge is preposterously false. Whenever a mathematician proves a theorem, whether it is Euclid proving the infinitude of primes or Pierre Deligne the Weil conjectures, something hitherto unknown becomes known. If this is not knowledge, then nothing is knowledge. In fact, you yourself admit this when you say "math tells us only about itself" (whatever the heck that means) or "that math is about logical relationships"; so it is knowledge, but knowledge about "itself" (whatever the heck that means) or "logical relationships".

Second, as William points out, Platonists and all sorts of realists deny that mathematics is not knowledge of reality (actually, depending on how exactly you cash this out, even many nominalists will), so you have to give an argument that actually establishes your claim. You have given no argument. By the nature of the case, such an argument cannot be empirical, but philosophical.

Third, labeling "relationships" as "logical" does not thereby mean that they are not real. For if they are not real, then no demonstrative knowledge is possible in (empirical) Science. But there is demonstrative knowledge in Science for otherwise there would be no science at all as even so much as testing a theory T presupposes establishing its logical entailments.

Fourth, the examples of actual *theorems* in physics (sticking to physics as it is what I know) are dime a dozen: Noether's theorem on conserved quantities, the uncertainty principle in QM, the multitude of no-go theorems, etc. It is just a matter of opening any physics textbook. So apparently, and to pick one example, the uncertainty principle in QM -- which I stress that it is a logical entailment, a theorem, of quantum mechanics -- is not knowledge about the real world. Who would a thunk it?

Cal Metzger said...

VR: "But mathematics is not science. It operates using a[n] infinite set of non-natural entities called numbers."

We could say the same thing about light wavelengths and colors -- that wavelengths aren't themselves colors, that colors aren't actually natural (physical) -- that they're subjective, qualia, incorrigible, etc. But that wouldn't change the fact that colors are related to wavelengths, in ways that are objective, reliable, and verifiable. Colors, like math, are probably derived synthetically. So while I agree that math (and colors) are not physical, they are almost certainly derived from physical experience.

VR: "If there are no numbers, there's no science."

That's like saying if there are no colors, there are no wavelengths. This doesn't seem like a tenable position.

William said...

But is there genuine knowledge of color without specific knowledge of wavelength? That is where the OP is coming from.

Legion of Logic said...

"But is there genuine knowledge of color without specific knowledge of wavelength? That is where the OP is coming from."

Exactly. Science is great at explaining functionality, but I don't need to know anything about gravity to know that if I step off a high ledge, I will die. Even the dimmest of animals know that for a fact, and they don't need science to know, either. Just experience and, in the case of humans, logic.

Joe Hinman said...

VR: "But mathematics is not science. It operates using a[n] infinite set of non-natural entities called numbers."

Cal" We could say the same thing about light wavelengths and colors -- that wavelengths aren't themselves colors, that colors aren't actually natural (physical)

the whole point is that science needs other things that are not science

Joe Hinman said...

Philosophy still owns science, on Metacrock's blog

Joe Hinman said...

knowledge is stuff you know, you can quote me on that.

Ilíon said...

"Is all knowledge scientific?"

As I keep harping -- "Is [*any*] knowledge scientific?"

Or, to be much more precise, "Is [any] scientific [statement actually knowledge]?"

Cal Metzger said...

Legion: " Even the dimmest of animals know that for a fact, and they don't need science to know, either. Just experience and, in the case of humans, logic."

That is the point. Animals know things based on experience. And that logic is a tool derived from physical experience. (If you think that only humans use logic, you're mistaken.)

Himnan: "the whole point is that science needs other things that are not science."

That's the not the claim in the OP. The claim in the OP is that 1) Math is knowledge, and 2) Math is not scientific because numbers aren't natural, 3) therefore scientific knowledge isn't based on natural entities.

I am pointing out that Math is almost certainly derived from the natural world, and thus the claim that science is based on something unnatural seems highly dubious.

B. Prokop said...

"Math is almost certainly derived from the natural world"

I don't see that at all. Even in the absence of a material universe altogether (i.e., if there really were nothing rather than something), 2 plus 2 would still equal 4. How do I come by that? Simple!

A. 2 pears plus 2 pears equals 4 pears.
B. 2 apples plus two apples equals 4 apples.
C. 2 pomegranates plus 2 pomegranates equals 4 pomegranates.
D. So it appears that the statement "2 plus 2 equals 4" is independent of the thing being counted.
E. Ergo (I've always wanted to use that word), The mathematical reality of 2 plus two being equal to 4 is independent of the natural world.

Now if you would re-word your statement to say something like "Our knowledge of Math is almost certainly derived from observing the natural world, but the reality of Math is independent of it," then I just might agree with you.

"the claim that science is based on something unnatural seems highly dubious"

There is a huge difference between "unnatural" and "non-natural". I would have no problem with asserting that science is based on non-natural (such as mathematics) entities.

Jezu ufam tobie!

Joe Hinman said...


April 05, 2016 3:52 AM
Delete


Blogger Ilíon said...
"Is all knowledge scientific?"

As I keep harping -- "Is [*any*] knowledge scientific?"

Or, to be much more precise, "Is [any] scientific [statement actually knowledge]?"


not knowledge is scientific but why is science not knowledge?

Joe Hinman said...

Himnan: "the whole point is that science needs other things that are not science."

That's the not the claim in the OP. The claim in the OP is that 1) Math is knowledge, and 2) Math is not scientific because numbers aren't natural, 3) therefore scientific knowledge isn't based on natural entities.

Not the point. The title of the piece indicates the topic is there knowledge than scientific knowledge. the rest that is a demonstration in the affirmative.

I am pointing out that Math is almost certainly derived from the natural world, and thus the claim that science is based on something unnatural seems highly dubious.

you are trying to imply that all knowledge is scientific even if it is at the most rudimentary level. If you want to get so far down in the rudimentary scale that everything is science then it's meaningless to talk about science.

animals are not doing science when the follow instinct because that's not derived from experience. It takes just experience to be science.

Joe Hinman said...

All examples of experience and natural world are not science. I can learn from trial and error to pray in Certain ways and they are answered more is that science?

grodrigues said...

@Cal Metzger:

"That's the not the claim in the OP. The claim in the OP is that 1) Math is knowledge, and 2) Math is not scientific because numbers aren't natural, 3) therefore scientific knowledge isn't based on natural entities."

That is not the argument of the OP. At all.

"I am pointing out that Math is almost certainly derived from the natural world"

Yes, you are making claims with absolutely no argument to back them up, in a futile attempt to answer an argument that was never made.

Cal Metzger said...

Grod: "That is not the argument of the OP. At all."

Sure it isn't.

Grod: "Yes, you are making claims with absolutely no argument to back them up, in a futile attempt to answer an argument that was never made."

Full of sound and fury, no doubt.

William said...

Original goal post: is all knowledge scientific?

New goal post: is all knowledge natural?

The two questions are not the same unless everything we can know is science. That may mean that when we learn to speak as children, either we are not truly acquiring knowledge of the language, or learning the language is the same as learning science.

Is that right, Cal?

grodrigues said...

@Cal Metzger:

"Sure it isn't."

Glad you agree. There may still be hope for you.

Cal Metzger said...

@William, this post is written on the heels of several discussion about Methodological Naturalism, and its role in science.

The OP reads like an attempt to divorce mathematical knowledge from its relation to the natural world, and because we agree that mathematical knowledge is a part of scientific inquiry, to demonstrate that the claim that science relies on methodological naturalism alone to be false.

No goal post moving on my part. I'm trying to cut to the chase, and clarify. If you or others here disagree then you should suggest what you think the point of the OP is.

William: "... or learning the language is the same as learning science."

If you have a way for someone to learn a language that doesn't rely on methodological naturalism -- hearing, seeing, etc., then you are free to introduce it. Languages are about as famously dependent on one's environment as anything I can think of.






William said...

Ok, you concede that all knowledge is not scientific knowledge.

Your change of subject: Mathematical knowledge is acquired using exclusively the methods of methodological naturalism.

This becomes a matter of definitions of methods, and thus kind of boring and beside the point for me..

David Brightly said...

But mathematics is not science. It operates using a infinite set of non-natural entities called numbers.

Compare:
But linguistics is not science. It operates using a infinite set of non-natural entities called sentences.

Cal Metzger said...

William: "Ok, you concede that all knowledge is not scientific knowledge."

"All knowledge is not scientific knowledge?" No, no I didn't say that. I have been addressing the specific issue of math, and its role in scientific inquiry, per the OP.

William: "Your change of subject: Mathematical knowledge is acquired using exclusively the methods of methodological naturalism."

Again, now what I said. I am pointing out that divorcing math from the natural world is a dubious claim. Hence, the conclusion that science relies on non-natural knowledge (Math) to constitute its knowledge is probably false -- because I don't buy into the notion that Math is divorce from, or not derived from, the natural world.

William: "This becomes a matter of definitions of methods, and thus kind of boring and beside the point for me."

I agree that the things you're writing about seems beside the point to me as well. I just don't think I'm the one writing them.

Joe Hinman said...

can't you see that the "natural" issue is a means of truing to reduce everything to science. But there's no basis for the claim that natural = science. Superstition might be natural too.

Joe Hinman said...

William: "Your change of subject: Mathematical knowledge is acquired using exclusively the methods of methodological naturalism."

Again, now what I said. I am pointing out that divorcing math from the natural world is a dubious claim. Hence, the conclusion that science relies on non-natural knowledge (Math) to constitute its knowledge is probably false -- because I don't buy into the notion that Math is divorce from, or not derived from, the natural world.

(1 Being natural doesn't make it science. (2) Math employs an experience of natural phenomena but is not Methodological naturalism by an stretch. We don't see numbers in the world. We don't see geometric lines. we have to abstract them. We can see them when we know to look for them but I doubt that we could pick them out of the pattern if we didn't have the abstracting ability That takes it to realm not natural and not part of science.

It's debatable as to what constitutes science anyway, the boarder you make it the less meaingful it is to claims things as scientific.

Ilíon said...

VR: "But mathematics is not science. It operates using a infinite set of non-natural entities called numbers."

Might than not be better put as: mathematics operates *on* an "infinite set of non-natural entities called numbers", using a finite set of non-natural rules?

David Brightly: "Compare: But linguistics is not science. It operates using a infinite set of non-natural entities called sentences."

Actually, "linguistics" *does not* "operate[] using a infinite set of non-natural entities called sentences."

Languages operate by a finite set of linguistic rules applied to a finite set of words ... by which operations a finite set of possible sentences may be generated in a particular language. And these entities (the rules, the words and the sentences) are indeed non-natural, albeit in not quite the same sense that numbers are non-natural entities.

Gyan said...

Illon,
By which sense of the word "natural" it is meaningful to say that (natural) numbers are non-natural?

Gyan said...

"Languages operate by a finite set of linguistic rules applied to a finite set of words"

This algorithmic view of languages, though popular in Artificial intelligence community, is entirely misleading.
For one, words are slippery and fuzzy things and meld into one another.The rules likewise to some extent. The true unit of meaning is not words but sentences.

Joe Hinman said...

there is not a finite set of words since new words can always be coined and signifiers are arbitrary, Plug in Austin and meaning is established though context and contexts are always changing.

Joe Hinman said...

:"By which sense of the word "natural" it is meaningful to say that (natural) numbers are non-natural?"

the whole idea that number "occur" in nature is silly. We can affix numbers to things by counting them but that mean numbers are {in nature" you don't look at a tree real closely and find branches have little numbers on them .This is branch 247. I can't find branch 54. Branch 54 where you?

there are no straight lines in nature. We draw the line straight. Making it a number or making a line straight is abstracting.

Ilíon said...

Gyan: "By which sense of the word "natural" it is meaningful to say that (natural) numbers are non-natural?"

Ah! Since mathematicians have used the word 'natural' in a completely different sense than V.Reppert is using the word in the OP, so as to distinguish the set of numbers with a certain characteristic from other numbers without that characteristic, therefore *I* must justify or explain V.Reppert's statement that numbers are "non-natural entities".

B. Prokop said...

I remember well a discussion I had about 2 years back with astrophysicist Dr. Ron Lee. I was floored when he told me that no serious cosmologist believes that something called the "Big Bang" actually occurred billions of years ago. The Big Bang (or, to give it its official name, the Standard Cosmological Model, or SCM) is simply a mathematical construct that helps make sense of and provides a framework for observations made in the contemporary universe. But as to what really happened at the Dawn of Time, I was told, "That's not a question for science, but for theology."

Similarly, nuclear physicists employ something called a quasiparticle to explain what occurs within matter at the subatomic level. Quasiparticles have no physical existence, but once again are merely mathematical models used to account for observations.

It turns out that quite a lot of scientific terminology is like that.

Victor Reppert said...

What I mean by non-natural, in this case, is that they have no particular location in space and time. If we maintain that whatever exists has to have a particular location in space and a particular location in time, then we have to deny that numbers exist.

Ilíon said...

^ I'm sure everyone understood that.

Joe Hinman said...

What I mean by non-natural, in this case, is that they have no particular location in space and time. If we maintain that whatever exists has to have a particular location in space and a particular location in time, then we have to deny that numbers exist.

that goes with being concepts. Like you 12 sheep they know there are 12. they probably don't count stuff. Not even so people can sleep. We have the concept of counting we fix a number.

Cal Metzger said...

VR: "What I mean by non-natural, in this case, is that they have no particular location in space and time. If we maintain that whatever exists has to have a particular location in space and a particular location in time, then we have to deny that numbers exist."

Math is useful for modeling reality. You appear to be concluding something along the lines of this: that because a map uses ink, and reality isn't entirely made of ink, then therefore we can't map reality.

Abstractions are used to model reality. We can abstract real things (Math that describes the acceleration of gravity), and we can abstract imaginary things (a painting of a unicorn). Science, and methodological realism, are the means by which we distinguish between models that are real and those that are imagined.

It seems that the only people who resist this are those who don't like the fact that scientific inquiry reveals that part of their model for reality includes things that are best explained as imaginary.

Gyan said...

VR,
"If we maintain that whatever exists has to have a particular location in space and a particular location in time"

There are modes of existence. Time exists in a different sense than a physical thing, say, this apple exists.
A man exists in one sense of the word "exists" and his humanity or his smile exists in yet another sense.
So, numbers exist in a different sense and nobody ever claims (except some theists) that "all that exists has to exist in the same sense or mode as physical things exist in."