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Remove the Mysticism from Mathematics!
#1

Remove the Mysticism from Mathematics!
If you don't believe in anything supernatural then you can say that you reject metaphysics. Metaphysics is the top-level category beneath which you'll find Religion, Mysticism, Astrology, and so on. The word 'metaphysics' literally means over and beyond physics, and so a metaphysical belief is a belief in something that is supposedly beyond physical reality.
 
In religious education classes (of enlightened countries) children are allowed to decide for themselves whether or not to accept metaphysical beliefs. Sadly the same can't be said for mathematics. In mathematics all children are indoctrinated into believing that numbers are metaphysical in nature. Most of us are not even aware that we have been duped into accepting metaphysical beliefs because we simply don't associate mathematics with mysticism. But the acceptance of non-physical objects is at the very core of this subject.

Perhaps we should try to explain numbers in terms of real-world physics. For example, when we think of a number, we might claim we form a symbol or image in our brain that is accessed by a thought process. So we might conclude that a number occurs when an algorithm uses a symbol/image as a quantity. This is arguably akin to a computer process accessing a memory location where the value in that location is treated as a numeric quantity.
 
If numbers are simply 'data currently being used as a quantity by an algorithm' then there can only ever be a finite amount of them. But for over two thousand years we have been teaching our children that numbers are intangible abstract things that are not constrained by physical reality. With this metaphysical description in place, we can then blow their minds with all sorts of weird stuff that arises due to there supposedly being infinitely many of these out-of-this-world objects.
 
Children are not given the option to believe that the brain is just physical material and has no metaphysical abilities, such as the power to conceive of abstract non physical objects of which there are supposedly infinitely many. Surely it is hypocritical for someone to claim they reject all supernatural beliefs when they accept the metaphysical foundations of mathematics, isn’t it?
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#2

Remove the Mysticism from Mathematics!
Well, yea.
Shit gets a bit weird grappling with some quantum mechanics but, it's not beyond the realm of the abstract. Things just get a little confusing for some when trying to smooth out some of those abstract wrinkles.

For some, that shit takes time to grok. Shy
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#3

Remove the Mysticism from Mathematics!
Hey Extreme Finitism - head on over to the introduction section and tell us about yourself. Shy
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#4

Remove the Mysticism from Mathematics!
(02-24-2021, 03:17 PM)Extreme Finitism Wrote: If you don't believe in anything supernatural then you can say that you reject metaphysics. Metaphysics is the top-level category beneath which you'll find Religion, Mysticism, Astrology, and so on. The word 'metaphysics' literally means over and beyond physics, and so a metaphysical belief is a belief in something that is supposedly beyond physical reality.
 
In religious education classes (of enlightened countries) children are allowed to decide for themselves whether or not to accept metaphysical beliefs. Sadly the same can't be said for mathematics. In mathematics all children are indoctrinated into believing that numbers are metaphysical in nature. Most of us are not even aware that we have been duped into accepting metaphysical beliefs because we simply don't associate mathematics with mysticism. But the acceptance of non-physical objects is at the very core of this subject.

Perhaps we should try to explain numbers in terms of real-world physics. For example, when we think of a number, we might claim we form a symbol or image in our brain that is accessed by a thought process. So we might conclude that a number occurs when an algorithm uses a symbol/image as a quantity. This is arguably akin to a computer process accessing a memory location where the value in that location is treated as a numeric quantity.
 
If numbers are simply 'data currently being used as a quantity by an algorithm' then there can only ever be a finite amount of them. But for over two thousand years we have been teaching our children that numbers are intangible abstract things that are not constrained by physical reality. With this metaphysical description in place, we can then blow their minds with all sorts of weird stuff that arises due to there supposedly being infinitely many of these out-of-this-world objects.
 
Children are not given the option to believe that the brain is just physical material and has no metaphysical abilities, such as the power to conceive of abstract non physical objects of which there are supposedly infinitely many. Surely it is hypocritical for someone to claim they reject all supernatural beliefs when they accept the metaphysical foundations of mathematics, isn’t it?

Depends on how you define metaphysics IMO.

"the branch of philosophy that deals with the first principles of things, including abstract concepts such as being, knowing, substance, cause, identity, time, and space."

OR

"abstract theory with no basis in reality".

Since you don't get to define what other people mean, it might be best to ask them.
Numbers and mathematics are different things.

Quote:When we think of a number, we might claim we form a symbol or image in our brain that is accessed by a thought process. So we might conclude that a number occurs when an algorithm uses a symbol/image as a quantity

You might claim that, but what in fact you are doing, is accessing a memory, (the accessing of which is a continuing physical brain process), laid down in a learning process, over a period of time. A number doesn't "occur". Your brain accesses a memory that you learned (by trial and error) to name a "number", and for a brief period, while your brain holds the concept in consciousness, the idea of what you learned to call (that) number, is experienced by your consciousness as a "number".

We might be agreeing here ... I just use biochemistry as my tool.

Hello.
Welcome.
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#5

Remove the Mysticism from Mathematics!
(02-24-2021, 03:56 PM)Kim Wrote: Hey Extreme Finitism - head on over to the introduction section and tell us about yourself.  Shy

Hi Kim, thanks for the warm welcome. I've just written something in the introduction section that sums me up.  Smile
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#6

Remove the Mysticism from Mathematics!
Okay...

Metaphysics is defined as a  philosophy that deals with the first principles of things,
including abstract concepts such as existence, knowing, identity, space, and time.
It can also be summarised  as merely abstract theories with no basis in reality—which
is how I'd define metaphysics.

Since coherent  metaphysical beliefs are impossible to refute, it's sometimes maintained
that philosophers adhere to their metaphysical theories more out of personal disposition
and temperament rather than any empirical evidence or proofs.

A few consider metaphysics to represent what's the highest in human nature; the drive to
know and to understand the nature of the universe in which we find ourselves. Others
consider metaphysics—specifically speculative metaphysics about non-empirical and
transcendent realities—to be simply bullshit.

Kant said that we can only have knowledge of things we can experience. Accordingly, in
answer to the question, "what can I know?" Kant responded that we can know the natural,
observable world, but we cannot, however, have answers to many of the deepest questions
of metaphysics.

—And, no.  I most definitely do not accept the notions of the "supernatural" and/or the
"paranormal".  If you were to, then it makes perfect sense that you'd believe in the existence
of God or gods.        Facepalm
I'm a creationist;   I believe that man created God.
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#7

Remove the Mysticism from Mathematics!
(02-24-2021, 04:53 PM)Bucky Ball Wrote: Depends on how you define metaphysics IMO.

Yes, that can be said for any word. This is why I included a description of what I take it to mean. Note that the prefix 'meta' is the Ancient Greek word for 'over and beyond' and so the word 'metaphysics' literally means over and beyond physics. In my experience, the word 'abstract' is often used to hide the metaphysical nature of a concept because most people are happy with the word 'abstract'. This is another word that needs clarity in its definition.

Quote:Numbers and mathematics are different things.

How can you know this when neither of these two words has a generally accepted definition? I find it shocking that nobody really knows what 'mathematics' really is.

Quote:You might claim that, but what in fact you are doing, is accessing a memory, (the accessing of which is a continuing physical brain process), laid down in a learning process, over a period of time. A number doesn't "occur". Your brain accesses a memory that you learned (by trial and error) to name a "number", and for a brief period, while your brain holds the concept in consciousness, the idea of what you learned to call (that) number, is experienced by your consciousness as a "number".

We might be agreeing here ... I just use biochemistry as my tool.

If you are saying that the brain is just physical material and its operation is constrained by physics then I guess we are in agreement.

As a computer programmer for many years, I have contemplated how a machine might 'conceive of infinitely many numbers' and I've concluded that whereas it might display the words "I can conceive of infinity" this would just be words. Everything has to be finite and so any claim of being able to experience or conceive or otherwise perceive of infinity is just a bug in the internal logic. Essentially I think that anyone who believes they can work with infinite objects (such as so-called real numbers) are deluding themselves.

Quote:Hello.
Welcome.

Thanks, it's nice to talk to you. Smile
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#8

Remove the Mysticism from Mathematics!
(02-24-2021, 05:34 PM)Extreme Finitism Wrote: How can you know this when neither of these two words has a generally accepted definition? I find it shocking that nobody really knows what 'mathematics' really is.

How do you know that ? You surveyed everyone in the world ?
"Nobody" ? Really ?
I think I am satistifed using the generally accepted (ie in the dictionary) definitions.
https://plato.stanford.edu/search/search...re+numbers
https://plato.stanford.edu/entries/philo...thematics/
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#9

Remove the Mysticism from Mathematics!
[Image: 2axt05.jpg]

Holy Malarkey, Batman!
[Image: sea-stones-whimsy-7-sm.jpg]
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#10

Remove the Mysticism from Mathematics!
(02-24-2021, 05:46 PM)Bucky Ball Wrote:
(02-24-2021, 05:34 PM)Extreme Finitism Wrote: How can you know this when neither of these two words has a generally accepted definition? I find it shocking that nobody really knows what 'mathematics' really is.

How do you know that ? You surveyed everyone in the world ?
"Nobody" ? Really ?
I think I am satistifed using the generally accepted (ie in the dictionary) definitions.
https://plato.stanford.edu/search/search...re+numbers
https://plato.stanford.edu/entries/philo...thematics/


These links produce reams and reams of text Huh . I cannot extract any clear definition from these, but if you think you can then that's fine. I'm happy for us to agree to disagree. I'm not here to go to war with anyone.
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#11

Remove the Mysticism from Mathematics!
Deadpan Coffee Drinker
I feel a disturbance in the house of Cantor.

Yea, I fucking said that. Dodgy
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#12

Remove the Mysticism from Mathematics!
(02-25-2021, 02:32 PM)Kim Wrote: Deadpan Coffee Drinker
I feel a disturbance in the house of Cantor.  

Yea, I fucking said that.   Dodgy

I miss HOC.
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#13

Remove the Mysticism from Mathematics!
(02-25-2021, 02:32 PM)Kim Wrote: Deadpan Coffee Drinker
I feel a disturbance in the house of Cantor.  

Yea, I fucking said that.   Dodgy

Obviously I don't want to push my own videos, but this post is your fault because you used the C word!

Are there Infinities of Different Sizes? Of Course Not! Cantor was Wrong (The Disbeliever, Part 7)
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#14

Remove the Mysticism from Mathematics!
(02-25-2021, 05:35 PM)Extreme Finitism Wrote:
(02-25-2021, 02:32 PM)Kim Wrote: Deadpan Coffee Drinker
I feel a disturbance in the house of Cantor.  

Yea, I fucking said that.   Dodgy

Obviously I don't want to push my own videos, but this post is your fault because you used the C word!

Are there Infinities of Different Sizes? Of Course Not! Cantor was Wrong (The Disbeliever, Part 7)

Cantor came up because one of his descendants was a long time member of our forum. He passed away not long ago.
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#15

Remove the Mysticism from Mathematics!
(02-25-2021, 05:35 PM)Extreme Finitism Wrote: Obviously I don't want to push my own videos, but this post is your fault because you used the C word!

Are there Infinities of Different Sizes? Of Course Not! Cantor was Wrong...

I've never been at all mathematically inclined, as such your video left me...uh... a little confused.     Tongue

Can you please define:

"even number" =

"whole number" =

"infinity" =

And is this correct?       ∞ + 1 = ∞
I'm a creationist;   I believe that man created God.
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#16

Remove the Mysticism from Mathematics!
(02-25-2021, 06:00 PM)SYZ Wrote:
(02-25-2021, 05:35 PM)Extreme Finitism Wrote: Obviously I don't want to push my own videos, but this post is your fault because you used the C word!

Are there Infinities of Different Sizes? Of Course Not! Cantor was Wrong...

I've never been at all mathematically inclined, as such your video left me...uh... a little confused.     Tongue

Can you please define:

"even number" =

"whole number" =

"infinity" =

And is this correct?       ∞ + 1 = ∞


In mathematics you can devise your own mathematical system in which you can define anything to mean anything you like. You can even re-define terms that are well known and have meanings elsewhere in mathematics. For example, 'sum' can mean all sorts of different things in different contexts. Since you can devise your own mathematical system with your own definitions and in which you only allow 'logic' that agrees with what you want to prove, you can prove any statement you want to. You just have to be careful to make sure that none of the rules you allow in your system contradict each other, that's all. It doesn't have to make any sense in the real world, it's all just fairy tales.

Again, I don't want to push my videos, but you really need to go to my 'Karma Peny' YouTube channel and watch all my videos. I don't want to push my videos, but they will answer all your questions and more. After watching them you might come back with more questions, but before you do I recommend you ask all your family & friends to watch all the videos just in case they can answer your questions. In fact, why not get them all to share my videos on social media - I really think that would help.  Shy
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#17

Remove the Mysticism from Mathematics!
(02-25-2021, 06:10 PM)Extreme Finitism Wrote: In mathematics you can devise your own mathematical system in which you can define anything to mean anything you like. You can even re-define terms that are well known and have meanings elsewhere in mathematics. For example, 'sum' can mean all sorts of different things in different contexts. Since you can devise your own mathematical system with your own definitions and in which you only allow 'logic' that agrees with what you want to prove, you can prove any statement you want to. You just have to be careful to make sure that none of the rules you allow in your system contradict each other, that's all. It doesn't have to make any sense in the real world, it's all just fairy tales.
Um, no you can't.  A logic system that only proves one statement of mathematical truth isn't really a logic system since it's not free to prove or disprove other mathematical truths.

In a nutshell, here's why mathematics is not metaphysical -- not that it is physical, but that it's not metaphysical:

Take one equation and give it to 50 mathematicians.  You will get the same answer within any degree of accuracy you care to set, and you'll get it 50 times (absent human error).

Ask 50 theologians what the Old Testament book of Micah means to the modern mainline Protestant movement, or ask 50 astrologers to tell you the characteristics of a person born at a specific place and time, and not only will you not get the same answer 50 times, you'll get up to 50 different answers, many of which are mutually exclusive.

Numbers can't have arbitrary values.  That's part of what makes them numbers.  You can't redefine one to mean one and a half because then it's just not one anymore.  And I'm not talking about the word or the symbol we use, I'm talking about the concept -- philosophical or otherwise -- of 'one-ness'.  There doesn't need to be a concrete object I can point to that is the abstract essence of 'one' for it to be meaningful, useful, and non-metaphysical.  Physicists and chemists use the ideal gas law all the time.  That doesn't mean an ideal gas is a real thing, nor does it invalidate the law.
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#18

Remove the Mysticism from Mathematics!
(02-25-2021, 06:10 PM)Extreme Finitism Wrote: Again, I don't want to push my videos, but you really need to go to my 'Karma Peny' YouTube channel and watch all my videos. I don't want to push my videos, but they will answer all your questions and more. After watching them you might come back with more questions, but before you do I recommend you ask all your family & friends to watch all the videos just in case they can answer your questions. In fact, why not get them all to share my videos on social media - I really think that would help.  Shy

Then stop pushing them before I have to intervene. Self promotion is not allowed here. If there is an ongoing discussion, and you just can't express your view without the support of one of the videos, you can post one. So far I have seen you reference them 3 times, and you are brand new here.

Ok, carry on.
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#19

Remove the Mysticism from Mathematics!
(02-25-2021, 06:00 PM)SYZ Wrote: I've never been at all mathematically inclined, as such your video left me...uh... a little confused.     Tongue 

Can you please define:

"even number" =
Any whole number (see below) divisible by 2.

(02-25-2021, 06:00 PM)SYZ Wrote: "whole number" =
Any positive integer (no decimals or fractions) greater than or equal to zero.

(02-25-2021, 06:00 PM)SYZ Wrote: "infinity" =
That's a little tricker, as there's more than one kind of infinity (no, Cantor has not been refuted).  Infinity is a number, but it's not a number like 1, 2, 56,790,858,734, or e, and it doesn't behave like other numbers, which is relevant to your question below.

The easiest ones to grasp are [Image: 721cd7f8c15a2e72ad162bdfa5baea8eef98aab1] (aleph-null) and [Image: 78c211ce8badf4ffbf9417ecceb0ef7ab0a8caed] (aleph-1).

Aleph-null is the infinite set of all computable numbers, from the integers to calculatable transcendentals like pi and phi; it's what's said to be 'countably infinite' -- while you'll never get to infinity, you can count these numbers one after another and never miss one.

Aleph-one is the infinite set of the continuum, which includes the numbers between the members of the aleph-null set.  The proof of this is in what's called Cantor's diagonal argument, which is quite accessible even without mathematical training.  And again, it has not been refuted.  Extreme Finitism is flatly wrong in his video.  It's not a matter of 'belief' or 'choosing to reject arguments'.  Mathematical rigor and mathematical proofs are one of the few areas in which we can speak with absolute knowledge: a correct proof is a correct proof forever.  We can say that we know Fermat's Last Theorem is correct, because it was rigorously proven.  We know for all right triangles, the square of the hypotenuse is equal to the sum ot the squares of the other two sides, because it was rigorously proven.  And we know there are at least two sizes of infinities, because it was rigorously proven.

(02-25-2021, 06:00 PM)SYZ Wrote: And is this correct?       ∞ + 1 = ∞
In a word, yes.  While we're at it,  ∞ + ∞ = ∞.  Infinity doesn't behave like an integer, even though it's well-defined.

I'm going to refer you to Episode 5 of Simon Singh's Numbers, a BBC Radio podcast.  I recommend the whole series, actually -- they're all short, about 15 minutes long, covering one idea in number theory.
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#20

Remove the Mysticism from Mathematics!
(02-25-2021, 06:33 PM)trdsf Wrote:
(02-25-2021, 06:10 PM)Extreme Finitism Wrote: In mathematics you can devise your own mathematical system in which you can define anything to mean anything you like. You can even re-define terms that are well known and have meanings elsewhere in mathematics. For example, 'sum' can mean all sorts of different things in different contexts. Since you can devise your own mathematical system with your own definitions and in which you only allow 'logic' that agrees with what you want to prove, you can prove any statement you want to. You just have to be careful to make sure that none of the rules you allow in your system contradict each other, that's all. It doesn't have to make any sense in the real world, it's all just fairy tales.
Um, no you can't.  A logic system that only proves one statement of mathematical truth isn't really a logic system since it's not free to prove or disprove other mathematical truths.

In a nutshell, here's why mathematics is not metaphysical -- not that it is physical, but that it's not metaphysical:

Take one equation and give it to 50 mathematicians.  You will get the same answer within any degree of accuracy you care to set, and you'll get it 50 times (absent human error).

Ask 50 theologians what the Old Testament book of Micah means to the modern mainline Protestant movement, or ask 50 astrologers to tell you the characteristics of a person born at a specific place and time, and not only will you not get the same answer 50 times, you'll get up to 50 different answers, many of which are mutually exclusive.

Numbers can't have arbitrary values.  That's part of what makes them numbers.  You can't redefine one to mean one and a half because then it's just not one anymore.  And I'm not talking about the word or the symbol we use, I'm talking about the concept -- philosophical or otherwise -- of 'one-ness'.  There doesn't need to be a concrete object I can point to that is the abstract essence of 'one' for it to be meaningful, useful, and non-metaphysical.  Physicists and chemists use the ideal gas law all the time.  That doesn't mean an ideal gas is a real thing, nor does it invalidate the law.


Um, yes you can. This is exactly what happened with the stupid idea of 'real numbers'. Simon Stevin came up with the idea of unending decimals in 1594 and over 200 years later various mathematicians eventually concocted a system of definitions and rules revolving around the idea of 'limits' specifically devised so that we could 'prove' things like the completeness of the reals and that 0.999... equals 1. There would otherwise be no justification for the imaginary number line (aka the continuum) that is infinitely thin and infinitely divisible and which goes from minus infinity to plus infinity. We can also supposedly talk about the 'cardinality' (another meaningless fairy tale concept) whereby there are just as many infinitely small so-called points (whatever they are!) between 0 and 1 as there are between 0 and 2. To anyone not fooled by the fairy tale, this is obviously a contradiction even if everything that came before it wasn't. But no, we are allowed to include an axiom of infinity which simply declares that an infinite set exists and so infinity MUST make sense because we have defined it to be in our system! 

My daughter is a mathematician and she often gets different answers to other mathematicians. This is often because high level maths questions can be so obscure and unclear that even mathematicians can't easily agree on the 'meaning' behind these abstract non-physical concepts.

Next you talk about not being able to redefine the 'concept' of 'one-ness' and you claim to not need a concrete object to point to. But in order to share meaning with another human you need to explain what you mean by 'one-ness' and this will inevitably require references to things in our shared physical reality that another human can relate to. Also this 'concept of one-ness' is physical in nature in that it only exist if a working brain is processing data within the chemistry of the brain that your brain interprets as being 'the concept of one-ness'. It is all physical. To think that 'one-ness' is out there in the universe is to believe in metaphysics. I have another video about this (in which I talk about the idea that 'three-ness' and patterns are somehow out there in the universe)...

Does Infinity Exist? No, Infinity Does Not Exist (The Disbeliever, Part 5)
{link removed}
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#21

Remove the Mysticism from Mathematics!
Once one understands mathematics as a conceptual framework to help organize human thinking about observed phenomena, any appeal to the metaphysical is moot anyway. Mathematics is simply one language of many that allows us humans to discuss observations in shared terms.

In that sense it's not metaphysical. I can draw a right-triangle and, using a tape-measure, quantify the Pythagorean theorem. Does that mean the Pythagorean theorem is metaphysical? No. It means that the Pythagorean theorem is a useful way to define some triangles we humans observe.
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#22

Remove the Mysticism from Mathematics!
(02-25-2021, 06:10 PM)Extreme Finitism Wrote: Again, I don't want to push my videos, but .....

LMAO
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#23

Remove the Mysticism from Mathematics!
(02-25-2021, 07:30 PM)Thumpalumpacus Wrote: Once one understands mathematics as a conceptual framework to help organize human thinking about observed phenomena, any appeal to the metaphysical is moot anyway. Mathematics is simply one language of many that allows us humans to discuss observations in shared terms.

In that sense it's not metaphysical. I can draw a right-triangle and, using a tape-measure, quantify the Pythagorean theorem. Does that mean the Pythagorean theorem is metaphysical? No. It means that the Pythagorean theorem is a useful way to define some triangles we humans observe.


I agree that it began as an attempt to help organize human thinking about observed phenomena, but as Zeno and Democritus pointed out, our thinking might not always make sense in the real world. If someone travels from position A to position B and then they travel further, would it be correct to say they made the journey from A to half-way to B, then half the remaining distance to B, then half the remaining distance to B, and so on? Would it be correct to say they completed an infinite amount of journeys and then went beyond infinity to continue their journey?

If actual infinities can be completed in the real world then this is not a metaphysical position. But if there is no such thing as 'infinity' in the real world then it is a metaphysical position. Given that nobody has yet proven that an actually infinity exists or can be completed I consider it to be metaphysical until proven otherwise (in the same way that the existence of God has not yet been proven).

Also you can't draw a mathematical triangle as it would have infinitely divisible edges that were perfectly straight. Everything in the real world is granular in that it consists of a finite number of smallest parts. We've known this for over 2,000 years if we take on board the findings of Democritus and the Atomists. You can try to construct a unit square with a million smallest parts (so we define each smallest part to be one millionth of the length we define to be one unit) but you will never be able to construct a diagonal that fits perfectly.

So the Ancient Greeks could have concluded that the diagonal of a unit square cannot be constructed, and that any attempt to construct a triangle with a side of an irrational length is doomed to failure. But they went along with Plato's idea that perfect forms can be imagined and so we'll allow them. I believe this was the wrong choice. They could have said that the algorithm called 'the square root of 2' can be used to determine what length could be achieved in this case given a known 'smallest part' of length, but they chose the more 'beautiful' and 'elegant' option of accepting infinite divisibility and perfect lengths.
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#24

Remove the Mysticism from Mathematics!
(02-25-2021, 07:49 PM)Extreme Finitism Wrote:
(02-25-2021, 07:30 PM)Thumpalumpacus Wrote: Once one understands mathematics as a conceptual framework to help organize human thinking about observed phenomena, any appeal to the metaphysical is moot anyway. Mathematics is simply one language of many that allows us humans to discuss observations in shared terms.

In that sense it's not metaphysical. I can draw a right-triangle and, using a tape-measure, quantify the Pythagorean theorem. Does that mean the Pythagorean theorem is metaphysical? No. It means that the Pythagorean theorem is a useful way to define some triangles we humans observe.


I agree that it began as an attempt to help organize human thinking about observed phenomena, but as Zeno and Democritus pointed out, our thinking might not always make sense in the real world. If someone travels from position A to position B and then they travel further, would it be correct to say they made the journey from A to half-way to B, then half the remaining distance to B, then half the remaining distance to B, and so on? Would it be correct to say they completed an infinite amount of journeys and then went beyond infinity to continue their journey?

If actual infinities can be completed in the real world then this is not a metaphysical position. But if there is no such thing as 'infinity' in the real world then it is a metaphysical position. Given that nobody has yet proven that an actually infinity exists or can be completed I consider it to be metaphysical until proven otherwise (in the same way that the existence of God has not yet been proven).

Also you can't draw a mathematical triangle as it would have infinitely divisible edges that were perfectly straight. Everything in the real world is granular in that it consists of a finite number of smallest parts. We've known this for over 2,000 years if we take on board the findings of Democritus and the Atomists. You can try to construct a unit square with a million smallest parts (so we define each smallest part to be one millionth of the length we define to be one unit) but you will never be able to construct a diagonal that fits perfectly.

So the Ancient Greeks could have concluded that the diagonal of a unit square cannot be constructed, and that any attempt to construct a triangle with a side of an irrational length is doomed to failure. But they went along with Plato's idea that perfect forms can be imagined and so we'll allow them. I believe this was the wrong choice. They could have said that the algorithm called 'the square root of 2' can be used to determine what length could be achieved in this case given a known 'smallest part' of length, but they chose the more 'beautiful' and 'elegant' option of accepting infinite divisibility and perfect lengths.

Well, if you keep moving you get there sooner or later, so I'm not really enamored of the infinitely-divisible halving of distances. By that logic, I can't drive to the store, because I never get there theoretically; but the fact is that I get there. Having said that, mathematics helps me get there all the same, whether we're talking about computing distance by tire revolutions, or fuel-air mixtures in the cylinders, or what-have-you.

You realize that the computer you're typing on uses mathematics in order to post online, right? It allows satellites to relay your internet connections, processes your entries to and from numbers into English, and so on. We have used mathematics to send spaceships into orbital vectors around other planets.

The fact that a process is conceptual doesn't mean that it isn't useful in reality. Mathematics need not be material in order to be useful. And there's certainly no need to appeal to metaphysics in order to justify mathematics -- as innumerable real-world processes demonstrate, mathematical conceptualization has proven its utility.

What if no intelligent life in the Universe had evolved at all? Would gravity not operate on the inverse-square function anyway?

Math is simply a human way of organizing observations of the natural world. It doesn't imply or require any superstition for it to work.
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#25

Remove the Mysticism from Mathematics!
(02-25-2021, 07:21 PM)Extreme Finitism Wrote:
(02-25-2021, 06:33 PM)trdsf Wrote:
(02-25-2021, 06:10 PM)Extreme Finitism Wrote: In mathematics you can devise your own mathematical system in which you can define anything to mean anything you like. You can even re-define terms that are well known and have meanings elsewhere in mathematics. For example, 'sum' can mean all sorts of different things in different contexts. Since you can devise your own mathematical system with your own definitions and in which you only allow 'logic' that agrees with what you want to prove, you can prove any statement you want to. You just have to be careful to make sure that none of the rules you allow in your system contradict each other, that's all. It doesn't have to make any sense in the real world, it's all just fairy tales.
Um, no you can't.  A logic system that only proves one statement of mathematical truth isn't really a logic system since it's not free to prove or disprove other mathematical truths.

In a nutshell, here's why mathematics is not metaphysical -- not that it is physical, but that it's not metaphysical:

Take one equation and give it to 50 mathematicians.  You will get the same answer within any degree of accuracy you care to set, and you'll get it 50 times (absent human error).

Ask 50 theologians what the Old Testament book of Micah means to the modern mainline Protestant movement, or ask 50 astrologers to tell you the characteristics of a person born at a specific place and time, and not only will you not get the same answer 50 times, you'll get up to 50 different answers, many of which are mutually exclusive.

Numbers can't have arbitrary values.  That's part of what makes them numbers.  You can't redefine one to mean one and a half because then it's just not one anymore.  And I'm not talking about the word or the symbol we use, I'm talking about the concept -- philosophical or otherwise -- of 'one-ness'.  There doesn't need to be a concrete object I can point to that is the abstract essence of 'one' for it to be meaningful, useful, and non-metaphysical.  Physicists and chemists use the ideal gas law all the time.  That doesn't mean an ideal gas is a real thing, nor does it invalidate the law.


Um, yes you can. This is exactly what happened with the stupid idea of 'real numbers'. Simon Stevin came up with the idea of unending decimals in 1594 and over 200 years later various mathematicians eventually concocted a system of definitions and rules revolving around the idea of 'limits' specifically devised so that we could 'prove' things like the completeness of the reals and that 0.999... equals 1. There would otherwise be no justification for the imaginary number line (aka the continuum) that is infinitely thin and infinitely divisible and which goes from minus infinity to plus infinity. We can also supposedly talk about the 'cardinality' (another meaningless fairy tale concept) whereby there are just as many infinitely small so-called points (whatever they are!) between 0 and 1 as there are between 0 and 2. To anyone not fooled by the fairy tale, this is obviously a contradiction even if everything that came before it wasn't. But no, we are allowed to include an axiom of infinity which simply declares that an infinite set exists and so infinity MUST make sense because we have defined it to be in our system! 

My daughter is a mathematician and she often gets different answers to other mathematicians. This is often because high level maths questions can be so obscure and unclear that even mathematicians can't easily agree on the 'meaning' behind these abstract non-physical concepts.

Next you talk about not being able to redefine the 'concept' of 'one-ness' and you claim to not need a concrete object to point to. But in order to share meaning with another human you need to explain what you mean by 'one-ness' and this will inevitably require references to things in our shared physical reality that another human can relate to. Also this 'concept of one-ness' is physical in nature in that it only exist if a working brain is processing data within the chemistry of the brain that your brain interprets as being 'the concept of one-ness'. It is all physical. To think that 'one-ness' is out there in the universe is to believe in metaphysics. I have another video about this (in which I talk about the idea that 'three-ness' and patterns are somehow out there in the universe)...

Does Infinity Exist? No, Infinity Does Not Exist (The Disbeliever, Part 5)
{link removed}
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