Why mathematics is neither absolutely nor objectively "right."

[Unknown Soldier]

It's very popular these days to see mathematics as one truth we can know is objectively and absolutely right. I must disagree. A common example of this supposed absolute and objective truth is the equation 2 + 2 = 4. We are told that for all times and places, 2 + 2 = 4, no matter what! If human beings went extinct, then 2 + 2 = 4 still holds as true. If the dinosaurs had the brains, then they would have known 2 + 2 = 4. If there's an advanced civilization of extraterrestrials in the Andromeda galaxy, then they know 2 + 2 = 4.

It's not true that 2 + 2 is absolutely 4. Depending on the rules mathematicians are using, 2 + 2 = 0 might be the case. In modular arithmetic, 2 + 2 might not even be defined at all much less true. For example, in binary there is no 2.

So the truth of 2 + 2 = 4 depends on what arbitrary set of rules you are using. No absolute or objective truth can be so arbitrary. Hence in general, mathematics is neither absolutely nor objectively "right."

 

[bilby]

Hence in general, a simplistic layperson's misunderstanding of mathematics is neither absolutely nor objectively "right."

FTFY.

When you confuse simplifications for the entirety of a field, you will inevitably conclude that the entirety of the field is simplistic and wrong.

But that's not a problem with the field; It's just you being a simpleton.

Getting annoyed by it is a poor choice of response. You would do better to seek a deeper understanding of why your expectations don't match reality. Though that does carry the risk that you will be crushingly embarrassed at your own ignorance, when you look back at your earlier commentary from a future in which you are less abjectly ill-informed.

 

[Jimmy Higgins]

We've got sats in geosynchronous orbit around the planet... taking into account relativistic physics... to help guide some tiny box of metal from one street in one state, to another street in another state. This required a great deal of math to get correct.

Makes me ponder that the reflection mathematics is neither absolutely nor objectively "right" has no absolute nor objective importance.

 

[Elixir]

This would be funny if not so sad.
Verily, truth isn’t truth. For example, see Truth Social! And see binary systems to render Arabic numbers other than 1and 0 meaningless.

 

[Unknown Soldier]

We've got sats in geosynchronous orbit around the planet... taking into account relativistic physics... to help guide some tiny box of metal from one street in one state, to another street in another state. This required a great deal of math to get correct.

I don't doubt that, but I fail to see your point.

Makes me ponder that the reflection mathematics is neither absolutely nor objectively "right" has no absolute nor objective importance.

As I see it, it's always important to understand the underlying reasoning behind any discipline, mathematics included. Most people at best skim the surface of mathematics learning only techniques. Without the knowledge of the logic behind mathematics, you'll be hard-pressed to develop new mathematical techniques or prove that those techniques are reliably applicable. Do you really think that mathematicians never bothered to prove the math behind relativity?

 

[Unknown Soldier]

This would be funny if not so sad.
Verily, truth isn’t truth. For example, see Truth Social! And see binary systems to render Arabic numbers other than 1and 0 meaningless.

Are you unfamiliar with the material I presented in the OP? If so, then you are welcome to ask questions about it.

 

[steve_bank]

No one says math is absolute.

Math is logically consistent based on a set of rules and definitions. This means no matter how you write equations algebra you will always get the same answer.

A good example is Euclidean Geometry.

It is based on things like

1. A point is an infinitly small and massless.
2. A line is comprised of an infinite number of points.
3. The shortest distance between two points is a straight line.

These are abstractions. However in our non relativistic surface environment it works well in solving physical problems.

Same with plane trigonometry.

Logcally comsistent means no matter how you properly apply the rules you get the same answer.

Formal logic and its cousin Boolean Algebra are logically commitment.

 

[Jarhyn]

It's very popular these days to see mathematics as one truth we can know is objectively and absolutely right. I must disagree. A common example of this supposed absolute and objective truth is the equation 2 + 2 = 4. We are told that for all times and places, 2 + 2 = 4, no matter what! If human beings went extinct, then 2 + 2 = 4 still holds as true. If the dinosaurs had the brains, then they would have known 2 + 2 = 4. If there's an advanced civilization of extraterrestrials in the Andromeda galaxy, then they know 2 + 2 = 4.

It's not true that 2 + 2 is absolutely 4. Depending on the rules mathematicians are using, 2 + 2 = 0 might be the case. In modular arithmetic, 2 + 2 might not even be defined at all much less true. For example, in binary there is no 2.

So the truth of 2 + 2 = 4 depends on what arbitrary set of rules you are using. No absolute or objective truth can be so arbitrary. Hence in general, mathematics is neither absolutely nor objectively "right."

Not all math describes all things. (+) May mean something else.

While a particular application math will objectively fail to describe some thing, however, the fact is that math is still objectively applicable to describe to completion anything short of "perfect randomness" and even that is describable in terms of "what happened" even if "why" is inaccessible.

Math that completely describes a thing is objectively descriptive of that thing.

The better question is "can EVERYTHING be described completely with math?"

As the most fundamental laws of our universe are described with math, and this math operates on a discrete, if complicated system, yes, math is objectively "correct" and absolute.

You just can't assume you're always using such simple operations as "standard addition of integers"

Sometimes you have to view the system I terms of Lie groups and Lie Algebras.

Sometimes you have to view the system using a set with no zero property.

But it's still all just counting in various bases.

That the way you choose to apply set theory fails to describe some thing does not establish that set theory necessarily cannot describe it. All it establishes is that you don't know how to do it.

 

[Unknown Soldier]

No one says math is absolute.

In that case you agree with me that 2 + 2 is not always 4.

Math is logically consistent based on a set of rules and definitions.

That's the goal of most math, but it's a goal that is obviously not always met.

This means no matter how you write equations algebra you will always get the same answer.

I demonstrated in the OP that what you're asserting here is wrong.

A good example is Euclidean Geometry.

It is based on things like

1. A point is an infinitly small and massless.

A point is defined in geometry as a position or location. It has zero dimensions and therefore has no size. This definition like any definition is arbitrary and is made up by people.

2. A line is comprised of an infinite number of points.
3. The shortest distance between two points is a straight line.

Again, those are arbitrary definitions made up by mathematicians. As such, they have no objective truth to them.

These are abstractions. However in our non relativistic surface environment ...

What is a "non relativistic surface environment"?

...it works well in solving physical problems.

Math often does, but ask any engineer, and she or he will tell you that math is often not very helpful in solving problems in their field. The physical world is very complex and messy, and math often offers no models that can represent that complexity.

Same with plane trigonometry.

What is "plane trigonometry"?

Logcally comsistent means no matter how you properly apply the rules you get the same answer.

I suppose, but all you're doing there is showing that the rules that were made up are consistent.

Formal logic and its cousin Boolean Algebra are logically commitment.

I've studied both. I don't recall seeing the term "logically commitment" in them.

 

[steve_bank]

HeeHee, 2 + 2 = 4 is always true.

Now the usual debate over terms and meaning ensues. Define what you mean by absolute and true.

By the rules of arithmetic and I think Peano 2 + 2 by definition equals 4. It is absolutely true with true being in the logical sense.

Yes consistent, maybe you are getting it?

There is a great small paperback probably still in print. How To Read And Do Proofs. It is an easy read, I suggyou give it a try. I read it to better understand and follow theory proofs in engineering texts.

If you seriously don't understand plane and spherical trig then your math is lacking.

For me as an electronics engineer using formal logic and Boolean Algebra was routine as is the case for elctonic technicians and engineers.


Given a local function that needs to be implemented in a circuit, there an infinte number of combinations of logic functions that can implement the design. As long as the rules of Boolean Algebra are followed they will all work exactly the same. For a given set of logcal inputs the logical outputs will always be the same. That is what logicaly consistent means, no ambiguities.

Finding a minimum Boolean function for an arbitrary set of logic inputs and outputs( a truth table) is part of Boolean Algebra. The min term expression. K Maps.


Are you pulling my leg and playing games or do you not kow?

Gravnded out into space it s no longer a right triangle.

Euclidean flat surface. Spherical trig is used for air navigation around the globe. Look it up. The Great Circle

All this stufff is not abstract philosophy for me, it is what I used.

There is no answer to 'what IS math or logic'. They are a set of definitions.

Math is considered objective because it always works regardless of any subjectve bias or perception or philosophy.

The meaning of math would be subjective philosophy.

 

[Elixir]

you are welcome to ask questions

Just one:
WTF went wrong with your education?

Steve has explained your fallacy

 

[Unknown Soldier]

HeeHee, 2 + 2 = 4 is always true.

Like I already explained 2 + 2 isn't always 4. If we base on calculations on the integers modulo 3 (Z
₃), then 2 + 2 = 1. If we base on calculations on the integers modulo 4 (Z₄), then 2 + 2 = 0. The decision regarding which of these parity rules to use is arbitrary, of course.

Now the usual debate over terms and meaning ensues. Define what you mean by absolute and true.

In the context of this discussion, "absolute truth" refers to anything that's correct regardless of the situation. Many philosophers have concluded that there is no absolute truth, and that would include the "truths" of mathematics. What is true in mathematics is true by definition rather than absolutely true.

By the rules of arithmetic and I think Peano 2 + 2 by definition equals 4. It is absolutely true with true being in the logical sense.

If it's true by definition, then it isn't absolutely true.

There is a great small paperback probably still in print. How To Read And Do Proofs. It is an easy read, I suggyou give it a try.

I may. Right now I'm studying Velleman's How to Prove It, Third Edition.

I read it to better understand and follow theory proofs in engineering texts.

That's good.

If you seriously don't understand plane and spherical trig then your math is lacking.

I know that trigonometry can be used to determine the angles between planes and the angles inside a sphere. is that what you're referring to?

For me as an electronics engineer using formal logic and Boolean Algebra was routine as is the case for elctonic technicians and engineers.

I've yet to see anything in any of your posts that reflect that kind of knowledge.

Given a local function that needs to be implemented in a circuit, there an infinte number of combinations of logic functions that can implement the design. As long as the rules of Boolean Algebra are followed they will all work exactly the same. For a given set of logcal inputs the logical outputs will always be the same. That is what logicaly consistent means, no ambiguities.

Finding a minimum Boolean function for an arbitrary set of logic inputs and outputs( a truth table) is part of Boolean Algebra. The min term expression. K Maps.

What is the relevance of any of this to the topic?

Are you pulling my leg and playing games or do you not kow?

I know how to use spell-check!

All this stufff is not abstract philosophy for me, it is what I used.

Either that or you're just making it up.

There is no answer to 'what IS math or logic'. They are a set of definitions.

Then the definitions are the answers, of course.

Math is considered objective because it always works regardless of any subjectve bias or perception or philosophy.

Then use math to model human psychology.

The meaning of math would be subjective philosophy.

That's a new one on me.

 

[Unknown Soldier]

you are welcome to ask questions

Just one:
WTF went wrong with your education?

Argument weak--start cursing.

Steve has explained your fallacy...

What fallacy?
[removed]

 

[bilby]

Argument weak--start cursing.

Then if you want people to stop cursing at your arguments, you need to make them stronger.

People start cursing when you present an argument so poor that to identify and correct all of the errors and fallacies in it would require several pages of response; And to get you to understand those corrections would require a decade of remedial education.

Nobody on a discussion board owes you that amount of thankless hard work, so they're likely going to just tell you to fuck off, instead.

When all your threads attract profane and/or dismissive responses, from different respondents, the problem is almost certainly on your side, not theirs.

You're making it very clear that you're not smart enough to write a worthwhile OP; the question remains whether you are smart enough to learn that fact, and to correct it by getting an education to replace your current arrogant ignorance.

 

[Cheerful Charlie]

2+2=4. This is true. No matter what modulus you choose, what notation you use.
Binary, decimal, hexidecimal, octal. Roman numerals, Arabic numerals or Aztec numerals. Anything else does not work in real world operations. If you want a deeper understanding of this, we have the Peano axioms, Cantor's set theory. Russell and Whitehead, Frege and others to explain to you why this works. Underlying mathematics is logic.

 

[steve_bank]

HeeHee, 2 + 2 = 4 is always true.

Like I already explained 2 + 2 isn't always 4. If we base on calculations on the integers modulo 3 (Z
₃), then 2 + 2 = 1. If we base on calculations on the integers modulo 4 (Z₄), then 2 + 2 = 0. The decision regarding which of these parity rules to use is arbitrary, of course.

Now the usual debate over terms and meaning ensues. Define what you mean by absolute and true.

In the context of this discussion, "absolute truth" refers to anything that's correct regardless of the situation. Many philosophers have concluded that there is no absolute truth, and that would include the "truths" of mathematics. What is true in mathematics is true by definition rather than absolutely true.

By the rules of arithmetic and I think Peano 2 + 2 by definition equals 4. It is absolutely true with true being in the logical sense.

If it's true by definition, then it isn't absolutely true.

There is a great small paperback probably still in print. How To Read And Do Proofs. It is an easy read, I suggyou give it a try.

I may. Right now I'm studying Velleman's How to Prove It, Third Edition.

I read it to better understand and follow theory proofs in engineering texts.

That's good.

If you seriously don't understand plane and spherical trig then your math is lacking.

I know that trigonometry can be used to determine the angles between planes and the angles inside a sphere. is that what you're referring to?

For me as an electronics engineer using formal logic and Boolean Algebra was routine as is the case for elctonic technicians and engineers.

I've yet to see anything in any of your posts that reflect that kind of knowledge.

Given a local function that needs to be implemented in a circuit, there an infinte number of combinations of logic functions that can implement the design. As long as the rules of Boolean Algebra are followed they will all work exactly the same. For a given set of logcal inputs the logical outputs will always be the same. That is what logicaly consistent means, no ambiguities.

Finding a minimum Boolean function for an arbitrary set of logic inputs and outputs( a truth table) is part of Boolean Algebra. The min term expression. K Maps.

What is the relevance of any of this to the topic?

Are you pulling my leg and playing games or do you not kow?

I know how to use spell-check!

All this stufff is not abstract philosophy for me, it is what I used.

Either that or you're just making it up.

There is no answer to 'what IS math or logic'. They are a set of definitions.

Then the definitions are the answers, of course.

Math is considered objective because it always works regardless of any subjectve bias or perception or philosophy.

Then use math to model human psychology.

The meaning of math would be subjective philosophy.

That's a new one on me.

Unfortunately for me I have diabetic retinopathay, my eyesight is poor. Glasses and large text helps, I don't always catch the underline for the spell checker.

It gets more basic.


Math arose out of practical necessity. Counting.

If I put 2 potatoes and two onions in a pile how many total objects are there? Can there not be 4 objects?


You are conflating some kind of philosophizing with objective math.

My point on Boolean Algebra is that logic and objective mathematical truth is not just the purview of math and philosophy, it is everywhere. Global commence and the jet you fly on depend on math to be absolutely true.

A philosophical thought experiment.

You go into a store and pick up 3 objects to buy. You go to the checkout and yio are charged for 4 objects. You protest and the cashier says '1 plus 1 plus 1 is not always 3, sometimes it is 4".

Would yiu apy for 4 objects?

 

[Unknown Soldier]

Unfortunately for me I have diabetic retinopathay, my eyesight is poor. Glasses and large text helps, I don't always catch the underline for the spell checker.

Do you have some adaptive equipment you use to do your engineering work? I'm wondering how you can be an engineer with such poor writing skills.

Math arose out of practical necessity. Counting.

I've studied the history of mathematics, and according to what I've read, the earliest math involved time reckoning, in particular the calendar.

If I put 2 potatoes and two onions in a pile how many total objects are there? Can there not be 4 objects?

Yes, that's what we're taught to call that quantity. However, depending on the "objects" being summed, the result can be something other than 4. For example, if you add 2 clouds to 2 clouds, how many clouds do you have? You could have only one cloud! Or 2 or 3 or any number of clouds. So nature cares little for our inventions, and math like any invention does not always "work" the way we intend.

You are conflating some kind of philosophizing with objective math.

There is no "objective math," and it's very suspicious that any engineer would think so. The mathematics I've been citing on this thread, which you appear to be completely ignorant of, is known as modular arithmetic. As a reference, I'm using Linear Algebra: A Modern Introduction 3rd Edition by David Poole, pages 13-14. So the math I'm using is math that is standard and commonly accepted by mathematicians.

My point on Boolean Algebra is that logic and objective mathematical truth is not just the purview of math and philosophy, it is everywhere. Global commence and the jet you fly on depend on math to be absolutely true.

What you're saying here is a non sequitur. It doesn't follow that if math can be used to model things in the real world, then math must be absolutely true. Commerce and airplanes don't rely on what is absolutely true but rely on what is true enough.

A philosophical thought experiment.

You go into a store and pick up 3 objects to buy. You go to the checkout and yio are charged for 4 objects. You protest and the cashier says '1 plus 1 plus 1 is not always 3, sometimes it is 4".

Would yiu apy for 4 objects?

No, I wouldn't pay for what I didn't intend to buy. Stores as far as I know don't use modal arithmetic to charge for items, so 3 items are not 4 items.

But let's go with your analogy, and say you're looking for gala apples in that store. You see none on the shelves, and you ask when the gala apples will be in stock. The clerk apologizes and explains that the gala apples won't be in stock for another two hours. You look at the time and see that it's 11 o'clock Do you conclude that the apples will be in stock at 13 o'clock?

Hint: Use modal arithmetic!

 

[Elixir]

I'm wondering how you can be an engineer with such poor writing skills.

Have you looked at his profile? maybe the problem is your reading skills or lack thereof.

 

[steve_bank]

Well soldier, ad homs are the last resort of the befuddled.

You can resurrect the threads on objective versus subjective, that appears to be what you are debating.

In 60s parlance I'd say you are tripping. If there are three distinct clouds observed there are 3 clouds not 4 or 1. If they merge then there is 1 clod. To say 1 + 1 + 1 can matically equal 1 based on that is poor logic and reasoning.

Ipitrich is a mathematician. If he drops it he can explain the basis and uniqueness proof of integer counting better than I can.

Based on past poters and debates I have an idea of where you are coming from. A mix of fuzzy reasoning and philosophizing.

You said yio studied formal logic and Boolean Algebra. If you have, then you must know within those systems there can be no ambiguities. If not then they would be useless. Same with aritmetic and counting.

Your cloud example is not about counting and arithmetic. It is metaphysics. The problem with abstract conceptual metaphysics is that there is no requirement for logical consistency as there is in math.

If te OP said sometimes 1 + 1 sometimes equals 1 and then added rge clod example it would have been a different debate. I think I undertsnd what you are trying to get at, but arithmetically speaking 1 + 1 always equals 2.

Meta[aphyscs requires qualifying the meaninand intent.

 

[Unknown Soldier]

I'm wondering how you can be an engineer with such poor writing skills.

Have you looked at his profile? maybe the problem is your reading skills or lack thereof.

Are profiles somehow absolutely true while posts are not? The way I see, there can be as many lies in a profile as there are lies anywhere else.