Philosophy of Mathematics - Numbers Watch

Zuza K
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Ok, here goes...

Do numbers start from 0 and go both ways infinitely, or do they have an indefinite beginning?
OR, a counter argument, numbers are man made and have no physical substance, which means numbers do not exist, therefore mathematics is bull****?
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_gcx
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The field of mathematics is indeed human construct, that does not stop it becoming one of the most important.
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EternalLight
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The number 5 doesn't "exist" as a physical object obviously, mathematics is just a language we use to count objects.
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RDKGames
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(Original post by Zuza K)
Ok, here goes...

Do numbers start from 0 and go both ways infinitely, or do they have an indefinite beginning?
OR, a counter argument, numbers are man made and have no physical substance, which means numbers do not exist, therefore mathematics is bull****?
So you're implying that if it doesn't physically exist, it's BS?
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ThePricklyOne
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(Original post by Zuza K)
Ok, here goes...

Do numbers start from 0 and go both ways infinitely, or do they have an indefinite beginning?
OR, a counter argument, numbers are man made and have no physical substance, which means numbers do not exist, therefore mathematics is bull****?
Working numbers go both ways indefinately as a measurement, but for some people believe infinity is not a number at all.

For me, infinity is a number as it is a measurement (like 1, 2, 3....) that I use in calculations (i.e. measurement = number).
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EternalLight
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(Original post by ThePricklyOne)
Working numbers go both ways indefinately as a measurement, but for some people believe infinity is not a number at all.

For me, infinity is a number as it is a measurement (like 1, 2, 3....) that I use in calculations (i.e. measurement = number).
Infinity is not a number. If anything infinity is probably more of a flaw than a strength.
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DJMayes
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(Original post by Zuza K)
Ok, here goes...

Do numbers start from 0 and go both ways infinitely, or do they have an indefinite beginning?
OR, a counter argument, numbers are man made and have no physical substance, which means numbers do not exist, therefore mathematics is bull****?
Could you pose this question a little less vaguely? It's not clear what you are even trying to ask.

The answer to the actual mathematical portion of your question is that it depends on how you order the set of numbers (and what that set is, but I think it's fairly safe to assume you mean the real number line).

Your second part appears completely unrelated to the first part, but oh well. Whether or not numbers exist is a legitimate philosophical question but if you take a moment to consider that you're posting this question on a computer it should be entirely evident that that in no way implies mathematics is bull.

(Original post by ThePricklyOne)
Working numbers go both ways indefinately as a measurement, but for some people believe infinity is not a number at all.

For me, infinity is a number as it is a measurement (like 1, 2, 3....) that I use in calculations (i.e. measurement = number).
Where have you ever measured an infinite quantity?
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ThePricklyOne
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(Original post by AishaGirl)
Infinity is not a number. If anything infinity is probably more of a flaw than a strength.
It's a strength. Helps mankind work a whole load more stuff than before. Same with 0. Nobody today would call it a flaw, but they did in the past even calling it satanic. I guess ol' infinity would have to hang out a bit longer until it gets acceptance.

It is a number for the purpose of measurement. If it is removed from the definition I've stated in the previous sentence, then a lot of maths won't make sense.

There are more than one definition of a number. To say categorically that infinity is not a number (any definition) is not scientific IMO.
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EternalLight
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(Original post by ThePricklyOne)
It's a strength. Helps mankind work a whole load more stuff than before. Same with 0. Nobody today would call it a flaw, but they did in the past even calling it satanic. I guess ol' infinity would have to hang out a bit longer until it gets acceptance.

It is a number for the purpose of measurement. If it is removed from the definition I've stated in the previous sentence, then a lot of maths won't make sense.

There are more than one definition of a number. To say categorically that infinity is not a number (any definition) is not scientific IMO.
The problem is nothing is actually infinite, so far as we know (possibly the universe). For example consider the geometric series \frac{1}{2}+\frac{1}{4}+\frac{1}  {8}+\frac{1}{16}+\cdots = 1

While yes this does absolutely converge, it doesn't actually in the real world because you cannot have infinitely many items. The concept works, but the reality would never work.

Planck length is deemed to be the smallest physical size an object can be, that geometric series would go beyond that size, forever getting smaller which simply isn't possible. At least as far as we know.

Infinity is basically the plug that just so happens to fit the mathematical hole... in reality this is a flawed concept.

Maybe someone like RDK with more knowledge can weigh in.
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B_9710
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(Original post by ThePricklyOne)
It's a strength. Helps mankind work a whole load more stuff than before. Same with 0. Nobody today would call it a flaw, but they did in the past even calling it satanic. I guess ol' infinity would have to hang out a bit longer until it gets acceptance.

It is a number for the purpose of measurement. If it is removed from the definition I've stated in the previous sentence, then a lot of maths won't make sense.

There are more than one definition of a number. To say categorically that infinity is not a number (any definition) is not scientific IMO.
To say infinity is not a number is not scientific at all. This is simply because science is not concerned with the nature of infinity - this is mathematics which is not a science in my opinion.
Objectively though inifinity is not a number and can't be treated like one.
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ThePricklyOne
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(Original post by Zuza K)
OR, a counter argument, numbers are man made and have no physical substance, which means numbers do not exist, therefore mathematics is bull****?
Everything except the stuff that happens in the wild are man-made. By your argument, does that mean that everything man-made including you, is bullsh*t?

Scientific reasoning involves having an idea, create a model to test it, if it works - keep, if it doesn't - discard. The fact that numbers have stood the test of time and still enable mankind to make great discoveries/advances in all fields - would suggests that numbers are useful. And not bullsh*t at all.

Numbers, like language are symbols representing an idea. For mankind to advance from the stone age, we need symbols to represent more and more abstract ideas, not just the things we can experience directly (see, touch, feel etc.).
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ThePricklyOne
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(Original post by B_9710)
To say infinity is not a number is not scientific at all. This is simply because science is not concerned with the nature of infinity - this is mathematics which is not a science in my opinion.
Objectively though inifinity is not a number and can't be treated like one.
Mathematics is a squarely a science, and it underpins all the other sciences. Physics isn't going anywhere without Mathematics. It's definately a TSR popular opinion that Maths is not science. No Mathematician or Physicist holds that opinion. One of my lecturers is a physicist who's escaped the physics lab doing space research to teach Mathematics in IT. I do Mathematics in IT, but I'm getting a whole load of Physics from this dude, which goes to show there is a lot of overlap between the 2 subjects. So if Maths isn't a science, then neither is Physics.

Physics is concerned with infinity, and a lot of the maths in both Physics and Maths are the same. You do mechanics in school Maths, right? That's Physics. And Physics doesn't work if you remove all the algebra (that's Maths).
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B_9710
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(Original post by ThePricklyOne)
Mathematics is a squarely a science, and it underpins all the other sciences. Physics isn't going anywhere without Mathematics. It's definately a TSR popular opinion that Maths is not science. No Mathematician or Physicist holds that opinion. One of my lecturers is a physicist who's escaped the physics lab doing space research to teach Mathematics in IT. I do Mathematics in IT, but I'm getting a whole load of Physics from this dude, which goes to show there is a lot of overlap between the 2 subjects. So if Maths isn't a science, then neither is Physics.

Physics is concerned with infinity, and a lot of the maths in both Physics and Maths are the same. You do mechanics in school Maths, right? That's Physics. And Physics doesn't work if you remove all the algebra (that's Maths).
Mechanics is applied maths that does come under physics. Physics is dependent on maths but maths is completely independent of physics. Physics uses maths as a tool to describe results and stuff. But maths isn't the study of 'real' things/object in the world - like physics and all the other branches of science. Physics is most definitely a science - all because it used maths doesn't mean that maths has to be a science - which in my opinion would be wrong to say.
Physics would be nothing without algebra as you said but algebra would still be exactly the same without physics.
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ThePricklyOne
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(Original post by B_9710)
Mechanics is applied maths that does come under physics. Physics is dependent on maths but maths is completely independent of physics. Physics uses maths as a tool to describe results and stuff. But maths isn't the study of 'real' things/object in the world - like physics and all the other branches of science. Physics is most definitely a science - all because it used maths doesn't mean that maths has to be a science - which in my opinion would be wrong to say.
Physics would be nothing without algebra as you said but algebra would still be exactly the same without physics.
But that doesn't support your argument that Maths is not a science. Independence of one subject from another is not proof that one of the subjects is not a science. All the universities of the world agree that Maths and Physics are Science subjects (STEM).

Besides, Maths is not independent from physics. The advances made in Physics (and IT) is finding its way back into Maths. Which is why it is possible for a Physicist doing hard core Physics can jump ship and teach Maths and IT. He won't be able escape the lab coat to teach Eng Lit. Eng Lit is definately not a science (its an Arts subject and just as good as a Science IMO).
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DJMayes
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(Original post by ThePricklyOne)
But that doesn't support your argument that Maths is not a science. Independence of one subject from another is not proof that one of the subjects is not a science. All the universities of the world agree that Maths and Physics are Science subjects (STEM).

Besides, Maths is not independent from physics. The advances made in Physics (and IT) is finding its way back into Maths. Which is why it is possible for a Physicist doing hard core Physics can jump ship and teach Maths and IT. He won't be able escape the lab coat to teach Eng Lit. Eng Lit is definately not a science (its an Arts subject and just as good as a Science IMO).
lol are you using the fact Maths is a STEM subject as your argument that Maths is a Science, when STEM stands for "Science Technology Engineering and Mathematics"?
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B_9710
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(Original post by ThePricklyOne)
But that doesn't support your argument that Maths is not a science. Independence of one subject from another is not proof that one of the subjects is not a science. All the universities of the world agree that Maths and Physics are Science subjects (STEM).

Besides, Maths is not independent from physics. The advances made in Physics (and IT) is finding its way back into Maths. Which is why it is possible for a Physicist doing hard core Physics can jump ship and teach Maths and IT. He won't be able escape the lab coat to teach Eng Lit. Eng Lit is definately not a science (its an Arts subject and just as good as a Science IMO).
This is a subjective argument so you can't really say whether it is or isn't a science - but it is my opinion that maths is not a science.
What is your definition of science?
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_gcx
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(Original post by ThePricklyOne)
Mathematics is a squarely a science, and it underpins all the other sciences. Physics isn't going anywhere without Mathematics. It's definately a TSR popular opinion that Maths is not science. No Mathematician or Physicist holds that opinion. One of my lecturers is a physicist who's escaped the physics lab doing space research to teach Mathematics in IT. I do Mathematics in IT, but I'm getting a whole load of Physics from this dude, which goes to show there is a lot of overlap between the 2 subjects. So if Maths isn't a science, then neither is Physics.

Physics is concerned with infinity, and a lot of the maths in both Physics and Maths are the same. You do mechanics in school Maths, right? That's Physics. And Physics doesn't work if you remove all the algebra (that's Maths).
By IT, are you more so talking about computer science?
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ThePricklyOne
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(Original post by _gcx)
By IT, are you more so talking about computer science?
Yes. All the maths that gets into IT. There's a lot coming from Physics, such as some Maths that was used to solve a problem in Physics (observations on planets) ended up in IT, and now quantum mechanics is finding its way into IT (as in quantum computing).
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ThePricklyOne
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(Original post by B_9710)
This is a subjective argument so you can't really say whether it is or isn't a science - but it is my opinion that maths is not a science.
What is your definition of science?
My definition is the same as the one used to separate STEM subjects from Arts subjects in research and academia. But there are some Arts subjects that sits very close to Science in that they have rules that operate in a way that can be defined mathematically.
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DJMayes
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(Original post by ThePricklyOne)
My definition is the same as the one used to separate STEM subjects from Arts subjects in research and academia. But there are some Arts subjects that sits very close to Science in that they have rules that operate in a way that can be defined mathematically.
Mate I just checked my Maths degree from Cambridge

It says it's a Bachelor of Arts (BA), not a Bachelor of Science (BSc)

Help what do I do?
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