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Notes on The Importance of Empiricism
« on: December 26, 2017, 08:25:10 PM »
After much thought about our movement, I realize that we need more concrete guiding principles. After the introduction page I would like to dedicate an entire chapter to Empericism, why it is important, and why it is the best guide to our determination of truth.

Empiricism is a philosophy that stresses the importance of experience in the attainment of knowledge, especially sensory experience.

    “All our knowledge begins with the senses, proceeds then to the understanding, and ends with reason. There is nothing higher than reason.”
    ― Immanuel Kant, Critique of Pure Reason

Empericism, in fact, forms the basis of the Scientific Method (however flawed it might be, as discussed elsewhere):

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

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Empiricism in the philosophy of science emphasizes evidence, especially as discovered in experiments. It is a fundamental part of the scientific method that all hypotheses and theories must be tested against observations of the natural world rather than resting solely on a priori reasoning, intuition, or revelation.

Empiricism, often used by natural scientists, says that "knowledge is based on experience" and that "knowledge is tentative and probabilistic, subject to continued revision and falsification."[4] One of the epistemological tenets is that sensory experience creates knowledge. Empirical research, including experiments and validated measurement tools, guides the scientific method.

However, empiricism is NOT "you have to see it to believe it." It is more like "someone must have seen or experienced it at some point for that idea to have merit". If there is no evidence behind that idea, then it can be easily dismissed. Hitchen's Razor asserts:

    "What can be asserted without evidence can be dismissed without evidence."
    ― Christopher Hitchen
« Last Edit: December 26, 2017, 09:00:56 PM by Tom Bishop »

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Re: Notes on The Importance of Empiricism
« Reply #1 on: December 26, 2017, 08:41:43 PM »
Flat Earth Theory is a Natural Science. We are Natural Scientists.

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

    "Natural science is a branch of science concerned with the description, prediction, and understanding of natural phenomena, based on empirical evidence from observation and experimentation."

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Re: Notes on The Importance of Empiricism
« Reply #2 on: December 28, 2017, 08:09:18 PM »
The Round Earth/Flat Earth debate is, at its essence, a debate of Rationalism versus Empiricism. Rationalists claim that there are significant ways in which our concepts and knowledge are gained independently of sense experience. Empiricists claim that sense experience is the ultimate source of all our concepts and knowledge.

Round Earth proponents and Round Earth astronomers, for the most part, are Rationalists. The various phenomenons that are said to exist under the Round Earth model do not have mechanisms which have been demonstrated first hand, but are assumed and argued to exist. Firstly, Round Earthers argue that there are cases where the content of our concepts or knowledge outstrips the information that sense experience can provide. Second, they construct accounts of how reason in some form or other provides that additional information about the world.

Flat Earth proponents, in contradiction, are generally Empiricists. John Locke says that our experiences tell us about the nature of reality. An explanation must be seen or experienced for it to be real. If there is no direct test of an explanation for something, then regardless of any reasoning, there is no real reason to assume that the explanation should be considered a truth. Reason does not tell us about the universe. Since reason alone does not give us any knowledge, it certainly does not give us superior knowledge. Knowledge can only be gained, if at all, by experience.
« Last Edit: December 29, 2017, 05:33:02 PM by Tom Bishop »

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Re: Notes on The Importance of Empiricism
« Reply #3 on: December 28, 2017, 10:58:24 PM »
Not only are Flat Earthers Empiricists, one could even say from a certain standpoint that the Flat Earther is the Ultimate Empiricist. What we see and experience of the world is the extent of our total knowledge. In order for an alternative explanation to have merit, it must be observed or experienced, and it is hard to argue against that.

The Rationalist argument against Empericism is that reality may present a certain perception; but how could we ever experience with what reality really is, in order to know that? Rationalists do not think we can, so we have to rely on reason. The Empiricist rebuttal to this is that the reality of the world is all we know, and so we must either make direct conclusions from what we experience or leave the subject as unknown.

The bulk of this work will show why Round Earth Theory is rationalized in many of its elements, while Flat Earth Theory is empirically determined.
« Last Edit: January 22, 2018, 06:36:27 PM by Tom Bishop »

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Re: Notes on The Importance of Empiricism
« Reply #4 on: January 23, 2018, 11:20:39 PM »
A telltale sign of rationalization is the need for multiple assertions to be true for a conclusion to have merit. Rationalists are often guilty of arguing on the basis of theory, rather than on the basis of fact. The typical rationalist argument proceeds with "if this is true, and if that is true, then this is the conclusion." Direct evidence is rarely provided, and the need for it is rationalized away entirely. It seems impossible for the rationalist to cite or provide direct evidence for a direct conclusion.

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Re: Notes on The Importance of Empiricism
« Reply #5 on: January 25, 2018, 12:39:39 AM »
This is not to say that all rationalization is bad. It is, as an admission, impossible to explore all possibilities in an investigation without using the tool of rationalization to do so. Rationalization is acceptable when used as a preliminary method to assess a truth. However, as a rule for the empiricist, the conclusion from such investigation should always favor those arguments which are the most experienced and observable, and with the least number of undemonstratable assumptions.

As a matter of integrity, the empiricist is compelled to downgrade all theories that are highly rationalized in its elements to the level of speculation and conjecture. A theory which is based on rationalization is a sign that the science that has not yet been fully settled. Anything less than direct conclusion from direct evidence speaks of speculation that that not yet been entirely vetted; perhaps due to incompetence, interference, lack of funding, or inability of technology. Regardless of reason, if a science is incomplete, how can its rationalization be considered to be a truth? Truth must follow directly from fact, and fact must be empirically determined.

While, in matters of science and philosophy, it may be fundamentally impossible to know "the" truth; the term truth, as it will be used in this work, will mean the current truth. Truths are the conclusions which are made from all available evidence, and form the base axioms with which we understand our universe. It is very possible for those axioms to be questioned and changed, and indeed, it is an absolute responsibility for every curious mind to ensure that they are constantly challenged and embettered.
« Last Edit: January 26, 2018, 02:07:05 AM by Tom Bishop »

Re: Notes on The Importance of Empiricism
« Reply #6 on: January 28, 2018, 09:16:05 AM »
I think you're conflating several things together in "rationalization", which will backfire against readers who believe in their own sense of logic.

There is nothing wrong with making logical deduction:
1. I know watering plants makes them grow.
2. I know rain drops water that is indistinguishable from the water from the tap on the ground.
3. Therefore I conclude that rain makes plants grow.

You have a valid point in that axioms that are taken must be justified and challenged. You are right that the assumptions of mathematical models should not be taken without criticism. But I believe that wholly dismissing logical deduction (such as mathematics, which is just a rigorous system for applying logical rules consistently) will not only backfire against readers, but also constrain Flat Earth in what it can do. For example, indirect measurement is accomplished through using similar triangles. It is probably more reliable than slinging a tape measure down the Willis Tower. There is no harm in applying mathematics as long as you can justify empirically that 1) your lines are straight and 2) the triangles are really similar (AA/SAS/SSS).

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Truths are the conclusions which are made from all available evidence, and form the base axioms with which we understand our universe.

This is wrong. Axioms are used in conjunction with observational/empirical evidence to derive truth. For example, an axiom that we might use is that our eyes are not being fooled by mind-controlling alien overlords, and we can use our eyes to make reliable observations. It would be circular reasoning to accept the conclusions as axioms themselves.
« Last Edit: February 01, 2018, 05:27:52 PM by Tom Bishop »

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Re: Notes on The Importance of Empiricism
« Reply #7 on: February 01, 2018, 05:28:14 PM »
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I think you're conflating several things together in "rationalization", which will backfire against readers who believe in their own sense of logic.

There is nothing wrong with making logical deduction:
1. I know watering plants makes them grow.
2. I know rain drops water that is indistinguishable from the water from the tap on the ground.
3. Therefore I conclude that rain makes plants grow.

Logic is not enough. Surely if we replaced "know" with "show" in your above assessment, it would be FAR more conclusive. This is the difference between rationalism and empiricism. Rationalists go off on tangents with what they "know" and empiricists focus on what is shown.

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You have a valid point in that axioms that are taken must be justified and challenged. You are right that the assumptions of mathematical models should not be taken without criticism. But I believe that wholly dismissing logical deduction (such as mathematics, which is just a rigorous system for applying logical rules consistently) will not only backfire against readers, but also constrain Flat Earth in what it can do. For example, indirect measurement is accomplished through using similar triangles. It is probably more reliable than slinging a tape measure down the Willis Tower. There is no harm in applying mathematics as long as you can justify empirically that 1) your lines are straight and 2) the triangles are really similar (AA/SAS/SSS).

How will it backfire on us? There is nothing wrong with using rationalized logic as a preliminary method, like you did in your example above. At this point it is considered rationalization -- speculation and conjecture. In order for it to be considered a truth it it must progress to the show stage.

We are not disregarding or limiting anything. We just have higher standards than you do.

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Truths are the conclusions which are made from all available evidence, and form the base axioms with which we understand our universe.
This is wrong. Axioms are used in conjunction with observational/empirical evidence to derive truth. For example, an axiom that we might use is that our eyes are not being fooled by mind-controlling alien overlords, and we can use our eyes to make reliable observations. It would be circular reasoning to accept the conclusions as axioms themselves.

This really depends on how you define conclusion. Your example "our eyes are not being fooled by mind-controlling alien overlords" and "we can use our eyes to make reliable observations" must be conclusions in some sense, even if you use it to make other conclusions.
« Last Edit: February 01, 2018, 08:39:29 PM by Tom Bishop »

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Re: Notes on The Importance of Empiricism
« Reply #8 on: February 02, 2018, 07:21:13 PM »
So when I observe that the sun is sinking below the horizon, and all that is visible is the top half circle of the sun, I should conclude that half of the sun must be below the horizon

Yet, from what I can understand the Flat Earth explanation for this observation is that it is essentially an optical illusion that has to do with perspective (correct me if I'm wrong).  Is that not rationalization for a direct observation from nature that wouldn't be possible in the flat earth model?
« Last Edit: February 02, 2018, 09:06:15 PM by Tom Bishop »

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Re: Notes on The Importance of Empiricism
« Reply #9 on: February 02, 2018, 09:08:41 PM »
So when I observe that the sun is sinking below the horizon, and all that is visible is the top half circle of the sun, I should conclude that half of the sun must be below the horizon

Did you observe that the half of the sun was below the horizon?

If you did not observe that, then that cannot be the direct conclusion. You are using rationalization -- a number of logical leaps and assumptions, to make your conclusion, not empericism.

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Yet, from what I can understand the Flat Earth explanation for this observation is that it is essentially an optical illusion that has to do with perspective (correct me if I'm wrong).  Is that not rationalization for a direct observation from nature that wouldn't be possible in the flat earth model?

Your idea of "wouldn't be possible" is based on rationalization that makes many assumptions about how things would or should work. If.. if.. if...

Re: Notes on The Importance of Empiricism
« Reply #10 on: February 03, 2018, 10:35:10 AM »
Did you observe that the half of the sun was below the horizon?

If you did not observe that, then that cannot be the direct conclusion. You are using rationalization -- a number of logical leaps and assumptions, to make your conclusion, not empericism.
This is pretty crazy thinking. Every time you see a car or any other object going over a hill you understand what is happening. No-one thinks "Hmm, that must be some trick of perspective" or "the object is changing shape", as infants we learn how the world works - one object goes behind another opaque object and you see it disappearing behind the object.

So in this diagram the person on the left can only see the head of the person on the right, not because of some new law of perspective but because the curve physically blocks the light from the bottom part of the person



It's pretty crazy to think "I can only see the person's head, I can't observe the rest of the person so I don't know if the rest of them is still there".

The empirical evidence that the sun is physically low in the sky at sunset is the long shadows you observe. They cannot be explained by a sun being where your model thinks it is. And if you're so fussed about empirical evidence then why not take some observations from locations with known distances between and do some triangulation to determine the distance to the sun or moon. If they're as close as you supposed you wouldn't need locations too far apart to observe measurable differences in angles.

"This is literally just a few people talking about it for a brief time every day on their spare time. That’s the flat earth movement" - Tom Bishop

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Re: Notes on The Importance of Empiricism
« Reply #11 on: February 03, 2018, 04:11:13 PM »
The fact that you are so quick to rationalize and jump to conclusions shows that you are not really much of a free thinker.

If you saw half a car sticking out of the ground it is possible that the car is half-buried. Did you think about that?

If you saw a car driving up and over a hill, how do you know that it makes it behind the hill? How do you know it was a hill? Maybe it was a cliff and you were witnessing a suicide.

While we generally know that those types of things are rare, we already have a lot of experimental knowledge about cars and hills to base our knowledge on. The same cannot be said about perspective and the sun, and so we should not make such ready comparisons. I cannot simply hop into the sun and drive it around for my video camera.

Direct evidence is necessary for a direct conclusion. Anything less is speculation and conjecture.
« Last Edit: February 03, 2018, 04:33:30 PM by Tom Bishop »

Re: Notes on The Importance of Empiricism
« Reply #12 on: February 03, 2018, 04:50:23 PM »
If you saw half a car sticking out of the ground it is possible that the car is half-buried. Did you think about that?
I quite specifically said if you saw it "going" over a hill. So as I see it go and can see less and less of it I don't think "It's got caught in quicksand!", I think "It's going over the brow of the hill, that's why I can no longer see it".
And if it was a car then as cars generally drives on roads I would assume that it is a hill and the road continues over the other side of it.
My general experience of the world is that objects disappear from the bottom as they go over a hill (which they don't on a plane, whatever Rowbotham may claim) and that roads are not built up hills which terminate in a sheer drop. I imagine people who build roads that do would get sued quite a lot by bereaved relatives.

As I said, the direct evidence of where the sun is at sunset is from the shadows it casts. Perspective does not affect the angle or length of shadows.
And if the sun and moon are as close as you suppose then you could take observations and do some triangulation to prove that.

The level of proof and direct evidence you require seems to wildly vary depending on whether it fits in with your world view or not.
All the "proofs" in ENaG are basically Rowbotham saying "this is what I have observed". That's it. And you blindly accept it.
Anything which shows the earth to be spherical you demand an absurdly high level of proof for. A level that can never really be satisfied.
You really should look into things like cognitive dissonance and confirmation bias.
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Re: Notes on The Importance of Empiricism
« Reply #13 on: February 04, 2018, 04:34:39 PM »
If you saw half a car sticking out of the ground it is possible that the car is half-buried. Did you think about that?
I quite specifically said if you saw it "going" over a hill. So as I see it go and can see less and less of it I don't think "It's got caught in quicksand!", I think "It's going over the brow of the hill, that's why I can no longer see it".
And if it was a car then as cars generally drives on roads I would assume that it is a hill and the road continues over the other side of it.
My general experience of the world is that objects disappear from the bottom as they go over a hill (which they don't on a plane, whatever Rowbotham may claim) and that roads are not built up hills which terminate in a sheer drop. I imagine people who build roads that do would get sued quite a lot by bereaved relatives.

You can only expect those things because we have a lot of experimental evidence involving cars and hills. If we had zero experimental evidence, and therefore zero emperical knowledge, then we cannot really say what is happening.

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As I said, the direct evidence of where the sun is at sunset is from the shadows it casts. Perspective does not affect the angle or length of shadows.
And if the sun and moon are as close as you suppose then you could take observations and do some triangulation to prove that.

Whatever conclusion you come up with needs to be without undemonstrated assumption. If you make an undemonstrated assumption then your conclusion becomes weaker. The more undemonstrated assumptions, the weaker the conclusion.

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The level of proof and direct evidence you require seems to wildly vary depending on whether it fits in with your world view or not.
All the "proofs" in ENaG are basically Rowbotham saying "this is what I have observed". That's it. And you blindly accept it.
Anything which shows the earth to be spherical you demand an absurdly high level of proof for. A level that can never really be satisfied.
You really should look into things like cognitive dissonance and confirmation bias.

How is asking for direct evidence for your claims an "absurdly high" level of evidence? We usually ask for some very basic evidence for things that you are resting your logic on, which is necessary to turn your speculation into knowledge.

Every single argument REers have made on this forum has been easily defeated in this manner. Every single one of them. I don't really have the time to address all of the people who come here, but when we do have a conversation, and we have had many since 2007 on the two tfes websites, touching on almost all subjects, it is pretty easy to pick where the fault is and where the assumptions are.

If you are going to argue perspective, you first need to demonstrate that perspective operates in the manner you believe it to operate on, for your argument to have merit. That is the rule for you, and that is also the rule for me. There are no double standards.

The problem is that we can just point to empirical reality that shows that in a perspective railroad track scene the perspective lines meet in the distance, for example, and therefore that is direct evidence of how perspective operates. You need to contradict that because according to your model it is impossible for those perspective lines to meet. You are arguing against reality -- an uphill battle and most disadvantageous position -- and this is really the root of all of your complaining that things are so hard and difficult for you here.
« Last Edit: February 04, 2018, 06:04:24 PM by Tom Bishop »

Re: Notes on The Importance of Empiricism
« Reply #14 on: February 05, 2018, 01:22:02 AM »

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You have a valid point in that axioms that are taken must be justified and challenged. You are right that the assumptions of mathematical models should not be taken without criticism. But I believe that wholly dismissing logical deduction (such as mathematics, which is just a rigorous system for applying logical rules consistently) will not only backfire against readers, but also constrain Flat Earth in what it can do. For example, indirect measurement is accomplished through using similar triangles. It is probably more reliable than slinging a tape measure down the Willis Tower. There is no harm in applying mathematics as long as you can justify empirically that 1) your lines are straight and 2) the triangles are really similar (AA/SAS/SSS).

How will it backfire on us? There is nothing wrong with using rationalized logic as a preliminary method, like you did in your example above. At this point it is considered rationalization -- speculation and conjecture. In order for it to be considered a truth it it must progress to the show stage.

We are not disregarding or limiting anything. We just have higher standards than you do.


My point is that you shouldn't have to do an experiment to verify the height of the Willis Tower is what the indirect measurement says it is if you accept that your lines are straight and the triangles are similar and your measurements of the small triangle are accurate. The laws of logic and mathematics dictate that any accurate direct measurement of the Willis Tower should line up with the indirect measurement, as long as what you took to be axioms (your lines are straight, similar triangles, measurement accuracy) to be true. If you did a direct measurement of the Willis Tower and got a different answer, then instead of saying that the math was wrong, you need to consider any experimental flaws in your direct measurement.
« Last Edit: February 05, 2018, 01:28:12 AM by JohnAdams1145 »

Re: Notes on The Importance of Empiricism
« Reply #15 on: February 05, 2018, 01:25:37 PM »
Whatever conclusion you come up with needs to be without undemonstrated assumption. If you make an undemonstrated assumption then your conclusion becomes weaker. The more undemonstrated assumptions, the weaker the conclusion.
Fairly reasonable, but you use undemonstrated assumptions all the time and you often cite Rowbotham who did the same.
His proofs are literally just him saying "this is what I have observed". Why is that good enough for you? Especially when it doesn't match with anyone else's observations.
No-one sees a person going away from them disappearing feet first into a flat path.
Your ridiculous claim about shadows being angled upwards because from your perspective the light appears to be below the level of your raised hand and so the "photons are angled upwards".
That is a completely undemonstrated assumption and doesn't match reality. If your hand is physically below the lamppost then the shadow will be angled downwards.
I will start a separate thread about that.

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How is asking for direct evidence for your claims an "absurdly high" level of evidence?
It isn't. It's your definition of what you regard as admissible as direct evidence which makes it so. There is plenty of direct evidence for a globe - people who have been in orbit, multiple agencies producing photos of the globe earth. But you dismiss it all as fake. You can always prove yourself right if you ignore or dismiss the evidence which shows you to be wrong.
I can't provide direct evidence that the stars are moving away from us, but if you understand spectroscopy (which you have shown you don't) and Doppler shift then it is a logical conclusion. You dismiss this as "rationalization" but you rationalize things all the time. You have no direct evidence of the "shadow object". But you claim it is there because without it lunar eclipses are not possible. There are so many problems with the model of a sun and moon rotating above a plane you have to keep rationalizing and inventing things to try and make it work.
Seasons - the sun's orbit keeps changing to a tighter and larger circle. No explanation as to what makes that happen. Lunar phases - the sun and moon keep changing altitude and no explanation there either.
Eclipses - the unobservable shadow object.
Why doesn't the sun get smaller as it goes away - some made up magnification effect which isn't observed on any other object.
Sunset - perspective. That's what apparently makes an object 3000 miles in the sky intersect the horizon.

I'm still waiting for an explanation of how the sun's rays are powerful enough to leave the sun sideways, hit the moon and reflect to the ground but the diagonal rays aren't powerful enough to reach earth so we can't see the sun at night but we can see the moon.

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Every single argument REers have made on this forum has been easily defeated in this manner. Every single one of them.
Declaring yourself right and everyone else wrong by ignoring their evidence really isn't "defeating" them.

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If you are going to argue perspective, you first need to demonstrate that perspective operates in the manner you believe it to operate on, for your argument to have merit. That is the rule for you, and that is also the rule for me. There are no double standards.
OK. Demonstrate that shadow angle is affected by one's perspective rather than the physical location of the light source and the object.

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The problem is that we can just point to empirical reality that shows that in a perspective railroad track scene the perspective lines meet in the distance, for example, and therefore that is direct evidence of how perspective operates. You need to contradict that because according to your model it is impossible for those perspective lines to meet. You are arguing against reality -- an uphill battle and most disadvantageous position -- and this is really the root of all of your complaining that things are so hard and difficult for you here.
I will address this in a separate thread in FE Debate but, in brief, you need to understand the difference between "appear to meet" and "meet". The limitations of your vision are different from reality.

Back to the topic of this thread. If you think empirical evidence is so important then why have you not taken measurements of the sun from different locations and triangulated to determine its distance?
That is your alternative explanation of the shadow experiment and it is a possible one, so verify it by empirical measurements of the sun or moon.
Yours is the claim that the sun and moon are much closer than supposed by all modern science. Prove it.
« Last Edit: February 05, 2018, 01:29:12 PM by AllAroundTheWorld »
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Re: Notes on The Importance of Empiricism
« Reply #16 on: February 06, 2018, 06:36:34 PM »

Quote
You have a valid point in that axioms that are taken must be justified and challenged. You are right that the assumptions of mathematical models should not be taken without criticism. But I believe that wholly dismissing logical deduction (such as mathematics, which is just a rigorous system for applying logical rules consistently) will not only backfire against readers, but also constrain Flat Earth in what it can do. For example, indirect measurement is accomplished through using similar triangles. It is probably more reliable than slinging a tape measure down the Willis Tower. There is no harm in applying mathematics as long as you can justify empirically that 1) your lines are straight and 2) the triangles are really similar (AA/SAS/SSS).

How will it backfire on us? There is nothing wrong with using rationalized logic as a preliminary method, like you did in your example above. At this point it is considered rationalization -- speculation and conjecture. In order for it to be considered a truth it it must progress to the show stage.

We are not disregarding or limiting anything. We just have higher standards than you do.


My point is that you shouldn't have to do an experiment to verify the height of the Willis Tower is what the indirect measurement says it is if you accept that your lines are straight and the triangles are similar and your measurements of the small triangle are accurate. The laws of logic and mathematics dictate that any accurate direct measurement of the Willis Tower should line up with the indirect measurement, as long as what you took to be axioms (your lines are straight, similar triangles, measurement accuracy) to be true. If you did a direct measurement of the Willis Tower and got a different answer, then instead of saying that the math was wrong, you need to consider any experimental flaws in your direct measurement.

There are many types of math. There are many types of mathematical models. Axioms are not infallible. Those axioms make many simple assumptions about the world, which may not be entirely true. It is not a given that the world operates on the commonly used laws and logic of mathematics. Look into Zeno's Paradox. Zeno shows that the universe cannot be mathematically continuous. He shows that space and time can't truly be represented by a number line that is infinitely divisible.

If your logic rests on the assumption that the universe is continuous, then you should be prepared to demonstrated that the universe is continuous when called on it. If you can't show that the universe is continuous, then you cannot use that assumption when making declarations such as "the sun should infinitely approach the horizon and never touch it".

Your shield that "it is commonly used math, so it must be true!" is based on fallacious reasoning; an appeal to authority. However, your authorities contradict you. Einstein has made numerous works showing that space is not Euclidean, and that Euclid was wrong in many aspects. Quantum Theory supports a non-continuous universe and also makes many arguments against Euclidean space. Why should we put our full faith into an Ancient Greek model that is thousands of years old?

If you are going to tell us that space is a continuous number line and therefore this or that should happen according to that theory, and that you need not demonstrate anything further because of "Math!", that is not acceptable. You need to show that the underlying assumptions are true. If you can't do that, then you need to abandon your line of reasoning altogether.
« Last Edit: February 06, 2018, 07:17:08 PM by Tom Bishop »

Re: Notes on The Importance of Empiricism
« Reply #17 on: February 06, 2018, 09:00:35 PM »
Tom, Zeno didn't show anything. He was mistaken in that he thought that infinitesimal quantities couldn't add up to a finite number. Through calculus we know that's not true. Additionally, since space is discrete, his argument doesn't apply.

However, since we know the relative order of magnitude that space is discretized at through experimentation, mathematics tells us that we can treat space as continuous (and that's literally what's observed in daily life). Saying that space may not be continuous on macroscopic scales essentially throws out all observational evidence that it is. Yes, that's an assumption, and most people accept it on a macroscopic scale. From that assumption, and from the assumption that our reality can be approximated as a Euclidean space (again, derived from experimentation), indirect measurement holds. If you came up with a direct measurement that went against my indirect measurement result, I'm far more likely to believe that you simply did your measurement wrong (the tape measure was blowing in the wind) than to believe that either of my axioms are wrong.

Einstein showed that space is extremely close to Euclidean, and math says that we can use Euclidean geometry in that case (with a small degree of error, much smaller than if you took a tape measure and hung it down the Willis Tower).
You are correct that you need to show that the underlying assumptions are true to invoke a mathematical model. However, these assumptions are often shown to be extremely close to reality, and mathematics says, then, that our model must be very close to reality. On the other hand, if, for example, you used direct measurement, you'll get errors far higher than what the model says. That doesn't mean that the model is wrong and that the actual height of the Willis Tower is what you saw on the tape measure; it means that you need to rethink how you're measuring.

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Offline xenotolerance

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Re: Notes on The Importance of Empiricism
« Reply #18 on: February 07, 2018, 02:39:43 PM »
Specifically, regarding the 'relative order of magnitude that space is discretized at': A Planck length is ~20 orders of magnitude smaller than most atomic nuclei.

See also:

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So how can physicists find out whether space-time is discrete or continuous? Directly measuring the discrete structure is impossible because it is too tiny. But according to some models, the discreteness should affect how particles move through space. It is a miniscule effect, but it adds up for particles that travel over very long distances. If true, this would distort images from far-away stellar objects, either by smearing out the image or by tearing apart the arrival times of particles that were emitted simultaneously and would otherwise arrive on Earth simultaneously. Astrophysicists have looked for both of these signals, but they haven’t found the slightest evidence for graininess.

Finally I recommend reviewing Tom's writeup as a form of Pyrrhonism, as it resembles this unproven ancient Greek philosopher better than any other thinker.

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Online Tom Bishop

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Re: Notes on The Importance of Empiricism
« Reply #19 on: February 28, 2018, 06:16:52 PM »
Finally I recommend reviewing Tom's writeup as a form of Pyrrhonism, as it resembles this unproven ancient Greek philosopher better than any other thinker.

That is not an accurate representation of this. From your link:

"Pyrrhonists hold nothing can be known for certain and, therefore, they remain in a perpetual state of knowing nothing."

Where did I say that it is impossible to know anything? We are saying that things can be known and conclusions can be made, but the foundations of that knowledge must be empirical.

"Ultimate Truth" is impossible, but it is certainly possible to conclude a truth from the best available evidence. The best available evidence is that which is empirically based.
« Last Edit: February 28, 2018, 06:18:35 PM by Tom Bishop »