Why does mathematics works?

[Speakpigeon]

What I grant you is that Newton's laws don't describe what we can measure as well as does the theory of general relativity. All that means is that the mechanics of the presently observable universe can be more precisely measured. That does not make the relations between Force, mass, and acceleration devised by Newton false. When scientists and engineers use Newtons theory to measure requirements and trajectories of devices traveling between bodies one cannot say the theory is false. Theory has come to be a process where one set of generalizations are superseded by another set generalizations when more information comes available. It is not a win lose proposition. In fact units of measure which are derived using Newton's laws are still set as standards of measurement for weight, mass, length and local time.

Mankind still uses systems of measurement dating to egyption times before any theory of relations between object and motion were derived. Not even those those measure are falsified.

You should back off from a philosophical principle that the advocate of that principle came to reject. It makes you look, well, stuck in a world where scientific method is frowned upon.

 Scientific_method

The scientific method is an empirical method of acquiring knowledge that has characterized the development of science since at least the 17th century. It involves careful observation, applying rigorous skepticism about what is observed, given that cognitive assumptions can distort how one interprets the observation. It involves formulating hypotheses, via induction, based on such observations; experimental and measurement-based testing of deductions drawn from the hypotheses; and refinement (or elimination) of the hypotheses based on the experimental findings.

Theories are targets for experimental test. And as theories come to comver more information it will be superceded by the more powerful theory. That does not mean previous theory is wrong. Usually it means there is more infomatin that can be explained by another formulation.

That doesn't even address my point.

Just more sophistry and equivocation.
EB

 

[fromderinside]

To your point: From  Scientific law

Scientific laws summarize the results of experiments or observations, usually within a certain range of application. In general, the accuracy of a law does not change when a new theory of the relevant phenomenon is worked out, but rather the scope of the law's application, since the mathematics or statement representing the law does not change. As with other kinds of scientific knowledge, laws do not have absolute certainty (as mathematical theorems or identities do), and it is always possible for a law to be contradicted, restricted, or extended by future observations. A law can usually be formulated as one or several statements or equations, so that it can be used to predict the outcome of an experiment, given the circumstances of the processes taking place.
Laws differ from hypotheses and postulates, which are proposed during the scientific process before and during validation by experiment and observation. Hypotheses and postulates are not laws since they have not been verified to the same degree, although they may lead to the formulation of laws. Laws are narrower in scope than scientific theories, which may entail one or several laws.^[3] Science distinguishes a law or theory from facts.^[4] Calling a law a fact is ambiguous, an overstatement, or an equivocation.^[5] The nature of scientific laws has been much discussed in philosophy, but in essence scientific laws are simply empirical conclusions reached by scientific method; they are intended to be neither laden with ontological commitments nor statements of logical absolutes.

We've moved way past falsification is how scientific thought progresses. In fact according to the article on Popper in the Stanford Encyclopedia of Philosophy https://plato.stanford.edu/entries/popper/

Popper’s final position is that he acknowledges that it is impossible to discriminate science from non-science on the basis of the falsifiability of the scientific statements alone; he recognizes that scientific theories are predictive, and consequently prohibitive, only when taken in conjunction with auxiliary hypotheses, and he also recognizes that readjustment or modification of the latter is an integral part of scientific practice. Hence his final concern is to outline conditions which indicate when such modification is genuinely scientific, and when it is merely ad hoc. This is itself clearly a major alteration in his position, and arguably represents a substantial retraction on his part:

 

[Speakpigeon]

To your point: From  Scientific law

Scientific laws summarize the results of experiments or observations, usually within a certain range of application. In general, the accuracy of a law does not change when a new theory of the relevant phenomenon is worked out, but rather the scope of the law's application, since the mathematics or statement representing the law does not change. As with other kinds of scientific knowledge, laws do not have absolute certainty (as mathematical theorems or identities do), and it is always possible for a law to be contradicted, restricted, or extended by future observations. A law can usually be formulated as one or several statements or equations, so that it can be used to predict the outcome of an experiment, given the circumstances of the processes taking place.
Laws differ from hypotheses and postulates, which are proposed during the scientific process before and during validation by experiment and observation. Hypotheses and postulates are not laws since they have not been verified to the same degree, although they may lead to the formulation of laws. Laws are narrower in scope than scientific theories, which may entail one or several laws.^[3] Science distinguishes a law or theory from facts.^[4] Calling a law a fact is ambiguous, an overstatement, or an equivocation.^[5] The nature of scientific laws has been much discussed in philosophy, but in essence scientific laws are simply empirical conclusions reached by scientific method; they are intended to be neither laden with ontological commitments nor statements of logical absolutes.

We've moved way past falsification is how scientific thought progresses. In fact according to the article on Popper in the Stanford Encyclopedia of Philosophy https://plato.stanford.edu/entries/popper/

Popper’s final position is that he acknowledges that it is impossible to discriminate science from non-science on the basis of the falsifiability of the scientific statements alone; he recognizes that scientific theories are predictive, and consequently prohibitive, only when taken in conjunction with auxiliary hypotheses, and he also recognizes that readjustment or modification of the latter is an integral part of scientific practice. Hence his final concern is to outline conditions which indicate when such modification is genuinely scientific, and when it is merely ad hoc. This is itself clearly a major alteration in his position, and arguably represents a substantial retraction on his part:

This confirms what I said:

1. "Scientific laws summarize the results of experiments or observations, usually within a certain range of application"

Usually within a certain range of application, absolutely, and Newton's Law of Gravitation was deemed universal.

Newton's law of universal gravitation
Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
https://en.wikipedia.org/wiki/Newton...al_gravitation

So, it's perfectly fine to change the scope of Newton's formula, that is, reduce it, but then it's not longer universal and therefore it's no longer the same law. The name, "Newton's law of universal gravitation", would be misleading.

2. "In general, the accuracy of a law does not change"

In the case Newton's law of universal gravitation, the accuracy was changed. Before Mercury, it was thought perfectly accurate. After Mercury, it progressively became accepted as not accurate.

3. "As with other kinds of scientific knowledge, laws do not have absolute certainty"

Yes, and therefore, if scientific knowledge is at all knowledge, it's not knowledge of the real world. To know that p means that p is true, not that you're not certain that p is true.

4. "The nature of scientific laws has been much discussed in philosophy, but in essence scientific laws are simply empirical conclusions reached by scientific method; they are intended to be neither laden with ontological commitments nor statements of logical absolutes."

To say that you know p is to say that p is as you know it, and thus this carries ipso facto an ontological commitment. If scientists don't intend laws to carry any ontological commitment, they should not pretend, explicitly or implicitly, that scientific knowledge is knowledge of the real world.

5. Popper’s blah-blah-blah

That's entirely irrelevant. Scientific claims that carry any ontological commitment are subject to falsification, like it or not. Science doesn't have to imply any ontology, but then claiming that science is knowledge of the real world does carry ontological commitments and is therefore subject to falsification.

Science has no epistemological privilege. The human brain has been tested by 525 million years of natural selection over the entire biosphere and science isn't going to beat that any time soon. All that science can hope to achieve is to improve the scope, reliability and precision of our beliefs. But the nature of scientific beliefs is absolutely exactly the same as the nature of any idiot's beliefs, namely, they are beliefs, not knowledge.

Clearly, you are unable to understand what I say. I don't remember you ever making any relevant comment.
EB

NOTE
And by the way, you never replied to my post here. So, here it is again. Try it:

Logic is derivative of language which leverages off human capacity to produce varied sounds. That it has some structure, also a human capability, in no way means it is fundamental to that capacity no more than that one to produce varied sounds. It is an invention in the same way a language by a tribe is an invention with little other meaning about human capacities than to demonstrate their variety and breadth.

And how do you think you immediately infer, without even thinking about it, that any one particular cat you see for the first time will have all the characteristic behaviours of cats: mewing, purring, etc. You don't know this cat. Yet, you will immediately believe it has a number of characteristic behaviours.

That's true of cats and it's true of just about everything you will look at. You will infer properties you don't actually know that the thing has on the basis of your experience of similar but actually distinct things. One particular cat isn't the other cats. Yet, you immediately infer it has all the properties you believe cats have.

For a scientist, you really understand next to nothing about human beings and reality generally. You're obviously a specialist of some sort, but you are an utterly incompetent thinker. You're not the only one, far from it, but you beat the competition hands down. You are dogmatic. You compensate for your inability to think by being dogmatic. That's a way of life for you. You breathe dogma in and out. You can't express yourself outside dogma. You are a very sad example of the stupidity of mankind.
EB

Looking in a mirror doesn't help you at all. Cats? Immediately? Without thinking? Really? My early memories contradict your assertions in that I knew nothing about cats when I first saw them so that eliminates instinct. Being around cats for some time lead to improvements of my ability to characterize them with little thought but that certaining isn't intuition. Rather it is the result of experience and learning-response process improvement as many psychologists as early as Thorndike determined propelled by the neural function of association and other capacities.

As for the rest you hold words like thinking as precious without understanding anything about what makes one come to some conclusion about a category called thinking. You glibly come to some conclusion that "you immediately infer it has all the properties you believe cats have". No you don't. You presume things based on extensive experience with living things that are totally wrong or inaccurate which you have taken to mean something you wish to argue about.

BS in BS out.

Can you confirm yes or no that you don't accept that we all immediately infer on seeing a cat we've never seen before that it will display the characteristic behaviour of the kind we remember from previous experience with cats?!

Yes or no?
EB

 

[fromderinside]

Theories may be universal. To call a law universal presumes something scientists never presume, that all is known. What applies to 'fact' applies to 'universal'

scientific laws are simply empirical conclusions reached by scientific method; they are intended to be neither laden with ontological commitments nor statements of logical absolutes

Picking and choosing are not included in the scientific method. The orbit of mercury became a problem after Newton is simply outside the scope of Newton's statement that F=ma as further research proved.

Your bolded question it is not a scientific query thus its outside our discussion. Consider it akin to Popper's conclusions about Psychoanalytic statements as not being 'science'. Hell. It's simply philosophical game playing of the worst sort. I'm a retired sensory psychologist which implies I should be aware of the stuff in your query. Look. I'm stamping my feet!

You don't have a philosophical point, a mathematics point nor a scientific point. What's your point?

Seems to me that even philosophers should respect statements and methods mathematicians and scientists work by when they are discussing their methods and work. Popper only applies to a very limited area of scientific endeavor. It does not apply to scientific law which is clearly a building rather than an prohibiting domain. Constrain yourself to that. Had you done so you never would have brought up universal with law since only theory can claim such magnitude of explanation. The key to science for law making is observation of the observable.

 

[Speakpigeon]

Theories may be universal. To call a law universal presumes something scientists never presume, that all is known. What applies to 'fact' applies to 'universal'

scientific laws are simply empirical conclusions reached by scientific method; they are intended to be neither laden with ontological commitments nor statements of logical absolutes

Picking and choosing are not included in the scientific method. The orbit of mercury became a problem after Newton is simply outside the scope of Newton's statement that F=ma as further research proved.

Your bolded question it is not a scientific query thus its outside our discussion. Consider it akin to Popper's conclusions about Psychoanalytic statements as not being 'science'. Hell. It's simply philosophical game playing of the worst sort. I'm a retired sensory psychologist which implies I should be aware of the stuff in your query. Look. I'm stamping my feet!

You don't have a philosophical point, a mathematics point nor a scientific point. What's your point?

Seems to me that even philosophers should respect statements and methods mathematicians and scientists work by when they are discussing their methods and work. Popper only applies to a very limited area of scientific endeavor. It does not apply to scientific law which is clearly a building rather than an prohibiting domain. Constrain yourself to that. Had you done so you never would have brought up universal with law since only theory can claim such magnitude of explanation. The key to science for law making is observation of the observable.

LOL
EB

 

[steve_bank]

A law undergoes immense scientific scrutiny. That’s not to say a law cannot be proven false, but in the case of Newton’s laws of motion, the scientific community has not stamped it as false; in fact, it’s still a law! We just recognize the scope of its applicability now.

Nicely put!

 

[Deepak]

Thus, we don't really know whether mathematics works since we don't know if it works for things we haven't been able to observe yet.

This seems like equivocation to me. Math can be used to model the real world, and we may find that models eventually get disproven, but that doesn't mean that the math stopped working, simply that it wasn't an effective model of the natural process it purported to describe. Let's forget the esoterica of scientific laws, and instead imagine a field where I count mushroom caps protruding from the ground, and conclude that there are X distinct fungal organisms. I go out day after day, year after year and count the number of mushroom caps. My children do it. Their children do it. Then one day some distant descendant decides to dig up the ground and finds that for any X number of caps, they all protruded from a single fungal organism.

Did that disprove the mathematical process of counting, or how the process of counting was applied to the physical world? Is that really a failure of math?

 

[fast]

A law undergoes immense scientific scrutiny. That’s not to say a law cannot be proven false, but in the case of Newton’s laws of motion, the scientific community has not stamped it as false; in fact, it’s still a law! We just recognize the scope of its applicability now.

Nicely put!

Thanks.

There’s still something going on that I haven’t adequately addressed though, and I’m not quite sure how to, as I haven’t truly wrapped my head around everything yet. I’ve searched through some hard to find links that is starting to add clarity, but still, things are just not tightened down yet.

 

[Speakpigeon]

Thus, we don't really know whether mathematics works since we don't know if it works for things we haven't been able to observe yet.

This seems like equivocation to me.

There are three senses of equivocal.

equivocal
adj
1. capable of varying interpretations; ambiguous
2. deliberately misleading or vague; evasive
3. of doubtful character or sincerity; dubious

So, which do you mean?

Math can be used to model the real world, and we may find that models eventually get disproven, but that doesn't mean that the math stopped working, simply that it wasn't an effective model of the natural process it purported to describe. Let's forget the esoterica of scientific laws, and instead imagine a field where I count mushroom caps protruding from the ground, and conclude that there are X distinct fungal organisms. I go out day after day, year after year and count the number of mushroom caps. My children do it. Their children do it. Then one day some distant descendant decides to dig up the ground and finds that for any X number of caps, they all protruded from a single fungal organism.

Did that disprove the mathematical process of counting, or how the process of counting was applied to the physical world? Is that really a failure of math?

Of course not.

Apparently, you just read this line and ignored the rest.

Should I repeat my post, or maybe you could read it again?
EB

 

[fast]

There are three senses of equivocal.

equivocal
adj
1. capable of varying interpretations; ambiguous
2. deliberately misleading or vague; evasive
3. of doubtful character or sincerity; dubious

So, which do you mean?

Math can be used to model the real world, and we may find that models eventually get disproven, but that doesn't mean that the math stopped working, simply that it wasn't an effective model of the natural process it purported to describe. Let's forget the esoterica of scientific laws, and instead imagine a field where I count mushroom caps protruding from the ground, and conclude that there are X distinct fungal organisms. I go out day after day, year after year and count the number of mushroom caps. My children do it. Their children do it. Then one day some distant descendant decides to dig up the ground and finds that for any X number of caps, they all protruded from a single fungal organism.

Did that disprove the mathematical process of counting, or how the process of counting was applied to the physical world? Is that really a failure of math?

Of course not.

Apparently, you just read this line and ignored the rest.

Should I repeat my post, or maybe you could read it again?
EB

I read what he said, and I didn’t think “equivocation” was spot on, but it was close enough to make me think “conflation” would have been a better fit given what he was trying to communicate.

 

[fromderinside]

What are we actually saying when we resort to "...given what he was trying to communicate" you just tried to produce a single organism responsible for all those caps.

I find mental experiments often conveniently leave out verifiable, a SM requirement.

 

[Jimmy Higgins]

Thus, we don't really know whether mathematics works since we don't know if it works for things we haven't been able to observe yet.

Drove to work in an automobile and am working inside a structure that is over 100 years old, and using the Internet to send this message.

I think the math works.

 

[Speakpigeon]

I read what he said, and I didn’t think “equivocation” was spot on, but it was close enough to make me think “conflation” would have been a better fit given what he was trying to communicate.

Rather, he thinks my post is all three: ambiguous, evasive and dubious. That is, his explanation shows he didn't understand what I said and rather than work his brain he prefers to question my me and post.
EB

 

[Speakpigeon]

Thus, we don't really know whether mathematics works since we don't know if it works for things we haven't been able to observe yet.

Drove to work in an automobile and am working inside a structure that is over 100 years old, and using the Internet to send this message.

I think the math works.

You believe that and it's fine.

But I'm quite sure you don't actually know that, though.

Which is also fine. I don't either and I'm still alive and using the Internet to prove it.
EB

 

[Deepak]

There are three senses of equivocal.


So, which do you mean?



Of course not.

Apparently, you just read this line and ignored the rest.

Should I repeat my post, or maybe you could read it again?
EB

I read what he said, and I didn’t think “equivocation” was spot on, but it was close enough to make me think “conflation” would have been a better fit given what he was trying to communicate.

https://www.txstate.edu/philosophy/resources/fallacy-definitions/Equivocation.html

So math models reality, the model is wrong, therefore the model is the thing that failed because it doesn't reflect what's actually happening in reality.

That is, Newtonian mechanics might be incorrect in that we live in a relativistic world - but it's not the math that's wrong, but the mapping of the math onto the real world.

 

[fast]

There is something strange about laws. It takes a lot for something to become a law. Once the arduous process yields what can be called a law, it ferociously holds its title no matter what the future may bring. It couldn’t have gotten the crown unless it was useful and somewhat predictive. New information that gives one reason to tweak a law doesn’t dethrown it from keeping its title as a law.

 

[fast]

There are three senses of equivocal.


So, which do you mean?



Of course not.

Apparently, you just read this line and ignored the rest.

Should I repeat my post, or maybe you could read it again?
EB

I read what he said, and I didn’t think “equivocation” was spot on, but it was close enough to make me think “conflation” would have been a better fit given what he was trying to communicate.

https://www.txstate.edu/philosophy/resources/fallacy-definitions/Equivocation.html

So math models reality, the model is wrong, therefore the model is the thing that failed because it doesn't reflect what's actually happening in reality.

That is, Newtonian mechanics might be incorrect in that we live in a relativistic world - but it's not the math that's wrong, but the mapping of the math onto the real world.

I understood you earlier. Great example btw!

If I come up with a formula to predict the occurance of a phenomena in nature and the prediction becomes skewed, that is no good reason to think that numbers are faulty or that mathematics is bunk. Rather, it says something about the formula. For instance, that it predicts to the same level of accuracy and precision as it always has. Perhaps it’s not perfectly matching up with the phenomena occurring in nature, but that’s a function of the reflective variance from the model to what it’s a model of—but certainly not indicative of inferior numbers or inabilities for math to stand in great fashion as the language of the universe.

 

[Speakpigeon]

So math models reality, the model is wrong, therefore the model is the thing that failed because it doesn't reflect what's actually happening in reality.

That is, Newtonian mechanics might be incorrect in that we live in a relativistic world - but it's not the math that's wrong, but the mapping of the math onto the real world.

And this shows again you didn't understand my post.

Should I cross my t's?
EB

 

[Speakpigeon]

https://www.txstate.edu/philosophy/resources/fallacy-definitions/Equivocation.html

So math models reality, the model is wrong, therefore the model is the thing that failed because it doesn't reflect what's actually happening in reality.

That is, Newtonian mechanics might be incorrect in that we live in a relativistic world - but it's not the math that's wrong, but the mapping of the math onto the real world.

Your link gives the following definition:

The fallacy of equivocation occurs when a key term or phrase in an argument is used in an ambiguous way, with one meaning in one portion of the argument and then another meaning in another portion of the argument.

Please exhibit the part of my post where you think I am equivocating.
EB

 

[fast]

Thus, we don't really know whether mathematics works since we don't know if it works for things we haven't been able to observe yet.

Drove to work in an automobile and am working inside a structure that is over 100 years old, and using the Internet to send this message.

I think the math works.

You believe that and it's fine.

But I'm quite sure you don't actually know that, though.

Which is also fine. I don't either and I'm still alive and using the Internet to prove it.
EB

Of course he knows it. That’s not outlandish in the slightest. He drove to work, and he did so in an automobile (drove, not worked). He worked in the building, and the building is over a hundred years old. What’s not to know? Okay, so let’s say it’s not true the building is over 100 years old and is only a tad over 99. So what, he got that wrong! He thought he knew and didn’t; assuming it’s under 100 years old, it’s not like he knew and then didn’t. He never knew in the first place!

But what about the rest? If it’s true that he drove in an automobile, then his highly justified belief with no contravening evidence, what’s so scary to an admission that doesn’t merely believe but in fact knows? Because HIS BRAIN doesn’t have direct tactile observatory powers and CAN ONLY detect some model-like mentally internal percept of what MIGHT be a distortion of what’s out there in the world? Silly. Silly, silly, silly.