Why illogical is more... Logical!

[sandy_mcd]

It is no different than stating chemical truths such as 1 oxygen atom and 2 hydrogen atoms combine to form H2O. Or the biological truth that an animal uses ATP for energy and produces ADP in the process. Or the physical truth that objects of different weight fall at the same rate. These chemical, biological, and physical truths are self-evident, irrespective of any human existence. In fact, they preceded it by billions of years. Same with mathematical truths, they are discoverable, not man-made.

They are both independent of human construction. But there is a significant difference between the two types of conclusions. How do you decide that water is H2O? You do experiments and compare your model with the real world. That is science. How do you prove that the fundamental theorem of algebra that a polynomial of positive degree over the field C of complex numbers has a root in C? You devise a proof (a word not used in rigorous science) based on other theorems and axioms. No experiment is done with the real world to validate your conjecture. That is mathematics. And that is why mathematics is not a science in the strict sense - its conclusions are not validated by experimental testing. So it is Newton and not Gauss who is associated with apples.

[MarcusOfLycia]

Mathematics is not a science. Mathematics are an entirely human-made concept with no basis in nature or the like. You can't compare biology or chemistry to math.

I honestly can't tell, are you being facetious?

A standard reference http://www.physik.uni-wuerzburg.de/file ... wigner.pdf

Still waiting for an answer.

Here's the question again, this time don't send me papers. Just answer the question:

Without human beings, are two apples and two apples equivalent to four apples?

[MarcusOfLycia]

It is no different than stating chemical truths such as 1 oxygen atom and 2 hydrogen atoms combine to form H2O. Or the biological truth that an animal uses ATP for energy and produces ADP in the process. Or the physical truth that objects of different weight fall at the same rate. These chemical, biological, and physical truths are self-evident, irrespective of any human existence. In fact, they preceded it by billions of years. Same with mathematical truths, they are discoverable, not man-made.

They are both independent of human construction. But there is a significant difference between the two types of conclusions. How do you decide that water is H2O? You do experiments and compare your model with the real world. That is science. How do you prove that the fundamental theorem of algebra that a polynomial of positive degree over the field C of complex numbers has a root in C? You devise a proof (a word not used in rigorous science) based on other theorems and axioms. No experiment is done with the real world to validate your conjecture. That is mathematics. And that is why mathematics is not a science in the strict sense - its conclusions are not validated by experimental testing. So it is Newton and not Gauss who is associated with apples.

I never said it was a science.

Ivellious had said:
"Mathematics is not a science. Mathematics are an entirely human-made concept with no basis in nature or the like. You can't compare biology or chemistry to math."

I disagreed with the second sentence.

[Ivellious]

Marcus, to answer your question: Numbers and counting are our way of describing the amount of apples. Yes, two plus two apples is still four apples without us, but you can't apply that example to the rest of mathematics. It is abstract, not reality.

For instance, is the derivative of a polynomial power function still the same without us? No, not at all, because that concept does not exist in any sense until we create it to describe something. Is an apple still called an "apple" without humans? No. But it is still the same object (or the same amount in your example).

Mathematics is a language that we use to describe things (usually science). Say we were to run into an alien life that has described the same laws of physics as us. We use derivatives and integrals and other forms of calculus and algebra to describe physics. But it is highly unlikely that an alien would use the same language to describe it. Fundamentally, physics as a whole has not changed, but how the two sides describe it is.

[sandy_mcd]

Ivellious had said:
"Mathematics is not a science. Mathematics are an entirely human-made concept with no basis in nature or the like. You can't compare biology or chemistry to math."

I disagreed with the second sentence.

Then that is probably merely a matter of semantics. I thought you were describing math as science, which some people do.

[Byblos]

It is no different than stating chemical truths such as 1 oxygen atom and 2 hydrogen atoms combine to form H2O. Or the biological truth that an animal uses ATP for energy and produces ADP in the process. Or the physical truth that objects of different weight fall at the same rate. These chemical, biological, and physical truths are self-evident, irrespective of any human existence. In fact, they preceded it by billions of years. Same with mathematical truths, they are discoverable, not man-made.

They are both independent of human construction. But there is a significant difference between the two types of conclusions. How do you decide that water is H2O? You do experiments and compare your model with the real world. That is science. How do you prove that the fundamental theorem of algebra that a polynomial of positive degree over the field C of complex numbers has a root in C? You devise a proof (a word not used in rigorous science) based on other theorems and axioms. No experiment is done with the real world to validate your conjecture. That is mathematics. And that is why mathematics is not a science in the strict sense - its conclusions are not validated by experimental testing. So it is Newton and not Gauss who is associated with apples.

I agree with you. But again, that's a far cry from calling it a man-made language. That is what I'm objecting to.

[Byblos]

Marcus, to answer your question: Numbers and counting are our way of describing the amount of apples. Yes, two plus two apples is still four apples without us, but you can't apply that example to the rest of mathematics. It is abstract, not reality.

For instance, is the derivative of a polynomial power function still the same without us? No, not at all, because that concept does not exist in any sense until we create it to describe something. Is an apple still called an "apple" without humans? No. But it is still the same object (or the same amount in your example).

Mathematics is a language that we use to describe things (usually science). Say we were to run into an alien life that has described the same laws of physics as us. We use derivatives and integrals and other forms of calculus and algebra to describe physics. But it is highly unlikely that an alien would use the same language to describe it. Fundamentally, physics as a whole has not changed, but how the two sides describe it is.

You are simply wrong. While I do agree that mathematics is a language, it is a language that describes an underlying reality. You can change the language if you wish or invent a new one, but if by changing it you sill describe exactly the same underlying reality then you have NOT invented a new reality, only its descriptive language; you merely stated it in different terms to describe the same exact thing. It's like saying 'I'm hungry' or 'J'ai faim'. They are 2 different languages that describe the same underlying reality, that a person is hungry. While the language is man-made, the reality it describes isn't.

[MarcusOfLycia]

Marcus, to answer your question: Numbers and counting are our way of describing the amount of apples. Yes, two plus two apples is still four apples without us, but you can't apply that example to the rest of mathematics. It is abstract, not reality.

For instance, is the derivative of a polynomial power function still the same without us? No, not at all, because that concept does not exist in any sense until we create it to describe something. Is an apple still called an "apple" without humans? No. But it is still the same object (or the same amount in your example).

Mathematics is a language that we use to describe things (usually science). Say we were to run into an alien life that has described the same laws of physics as us. We use derivatives and integrals and other forms of calculus and algebra to describe physics. But it is highly unlikely that an alien would use the same language to describe it. Fundamentally, physics as a whole has not changed, but how the two sides describe it is.

Mathematics is as basic an understanding of the universe as you could ever get.

The ratio between the diameter and circuimfrence of a circle is always the same. The number of sides on various shapes are always the same. The rate of change of a curve is always the same. You can use different words to describe it, but mathematical concepts, like logical proofs, are merely necessary things that exist everywhere. 2 + 2 = 4 is always true, so anything you base on that (multiplication, for instance) is also true. Algebra is based on those concepts and is always true. Calculus is based on algebra, and that is always true.

Suggesting that mathematics is a human invention while 'science' exists even without mankind is like saying events are a human invention but the stories that are made up of events could exist without mankind.

[skakos]

Mathematics is not a science. Mathematics are an entirely human-made concept with no basis in nature or the like. You can't compare biology or chemistry to math.

All science is based on specific axioms. Indeed mathematics seem more "human-created" than other fields of science but this fundamental truth lies behind everything: All scientists start from "somewhere" in order to build...

[skakos]

Marcus, to answer your question: Numbers and counting are our way of describing the amount of apples. Yes, two plus two apples is still four apples without us, but you can't apply that example to the rest of mathematics. It is abstract, not reality.

For instance, is the derivative of a polynomial power function still the same without us? No, not at all, because that concept does not exist in any sense until we create it to describe something. Is an apple still called an "apple" without humans? No. But it is still the same object (or the same amount in your example).

Mathematics is a language that we use to describe things (usually science). Say we were to run into an alien life that has described the same laws of physics as us. We use derivatives and integrals and other forms of calculus and algebra to describe physics. But it is highly unlikely that an alien would use the same language to describe it. Fundamentally, physics as a whole has not changed, but how the two sides describe it is.

You are simply wrong. While I do agree that mathematics is a language, it is a language that describes an underlying reality. You can change the language if you wish or invent a new one, but if by changing it you sill describe exactly the same underlying reality then you have NOT invented a new reality, only its descriptive language; you merely stated it in different terms to describe the same exact thing. It's like saying 'I'm hungry' or 'J'ai faim'. They are 2 different languages that describe the same underlying reality, that a person is hungry. While the language is man-made, the reality it describes isn't.

What kind of "reality" do you describe when you say 1 + 1 = 2?
For Wittgenstein all mathematics are pure tautologies: you just say the same thing in many different ways...
Whether you write (1+1) or you write (2), you mean the same thing...

[Byblos]

What kind of "reality" do you describe when you say 1 + 1 = 2?
For Wittgenstein all mathematics are pure tautologies: you just say the same thing in many different ways...
Whether you write (1+1) or you write (2), you mean the same thing...

The reality is that even abstract (in and of themselves) objects such as numbers can and do describe underlying realities testably consistently. From the universal constants to the speed of light, etc, etc. So don't know what your point is.

[skakos]

However you must have in mind the process of reaching to scientific conclusions:

We observe and THEN we MAKE our model fit the observation.
So it is not that the model (mathematical, physical, etc) is good bevause it describes what is happening!
The model fits with what is happening because we MADE IT fit.