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Numbers exist independent of human mind.

tahir.imanov
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7/11/2014 9:09:56 PM
Posted: 2 years ago
First the philosophical side: There are three explanations for numbers (also mathematical objects, relations and etc).

1. Nominalism : Numbers do not exist, they are describing objects, and used with units. 1 nut, 2 nuts, and etc. But nominalism fall down when we think about numbers such as e, pi, 3+5i, or pi^i and etc. Hence Nominalism falls. (For more information on nominalism: http://plato.stanford.edu... )

2. Fictionalism : It is the most stupid philosophy. Main idea that is numbers do not exist. They are not abstract objects, thus mathematical discourse is false. It is stupid to agre with such statement, while reading this statement. (Your PC, laptop, smartphone and etc. exist thanks to math.) (For more info on Fictionalism : http://plato.stanford.edu... )

3. Platonism: Numbers exist as abstract objects, they are non-spatial, and atemporal. It is the most rational choice. ( http://plato.stanford.edu... )

There are constants in universe which existed since the beginning of time and independent of human mind, which has certain values. (Such as G = 6.7384 * 10^(-11) * N * kg^(-2) * m^(2) ).

There will be some objections to these view, but soime of them are arguiments from ignorance (just stupid people).

1. Numerals are not numbers. They are signs to describe numbers. It doesn't matter if you use Arabic numerals (1,2,3,4,5,6,7,8,9,0 - and actually it is west Arabic numerals), or east Arabic numerals, or you made your own numerals.

2. Numerical systems - 13 pencils are always 13, it doesn't matter if you use decimal (base 10 =13), octal (base 8 = 15), hexadecimal (base 16 = D), it will not change the number (whether it is quantitive or qualitive).
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rross
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7/12/2014 12:49:13 AM
Posted: 2 years ago
At 7/11/2014 9:09:56 PM, tahir.imanov wrote:

Eh? Of course numbers don't exist independently of the mind. You've already called me stupid twice, which is not a good sign, but how can an abstract idea exist objectively?
tahir.imanov
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7/12/2014 1:16:47 AM
Posted: 2 years ago
At 7/12/2014 12:49:13 AM, rross wrote:
At 7/11/2014 9:09:56 PM, tahir.imanov wrote:

Eh? Of course numbers don't exist independently of the mind. You've already called me stupid twice, which is not a good sign, but how can an abstract idea exist objectively?

So, let me ask you a question.

Does there exist positive integers between 2 and 5?
Answer is yes (3 and 4). If you say no, then stop counting items (objects, votes).

How many positive integers (natural numbers, positive whole numbers) exist between 2 and 5.
Answer is 2. Which means abstract objects just got quantified.

Now, I want an evidence for your claim (Of course numbers don't exist independently of the mind), and I want empirical evidence.

by the way, does mind exist?
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rross
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7/12/2014 3:57:42 AM
Posted: 2 years ago
At 7/12/2014 1:16:47 AM, tahir.imanov wrote:
At 7/12/2014 12:49:13 AM, rross wrote:
At 7/11/2014 9:09:56 PM, tahir.imanov wrote:

Eh? Of course numbers don't exist independently of the mind. You've already called me stupid twice, which is not a good sign, but how can an abstract idea exist objectively?

So, let me ask you a question.

Does there exist positive integers between 2 and 5?
Answer is yes (3 and 4). If you say no, then stop counting items (objects, votes).

How many positive integers (natural numbers, positive whole numbers) exist between 2 and 5.
Answer is 2. Which means abstract objects just got quantified.

Is this the first step in your proof? Because I don't see how quantifying abstract objects has anything to do with whether or not they exist objectively.

Now, I want an evidence for your claim (Of course numbers don't exist independently of the mind), and I want empirical evidence.

You want empirical evidence for something that doesn't exist? Isn't that a contradiction?

What evidence do you have that they do exist?

by the way, does mind exist?

Let's sort out the number thing first, and then we'll move onto this. :)
Envisage
Posts: 3,646
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7/12/2014 3:57:45 AM
Posted: 2 years ago
At 7/11/2014 9:09:56 PM, tahir.imanov wrote:
First the philosophical side: There are three explanations for numbers (also mathematical objects, relations and etc).

1. Nominalism : Numbers do not exist, they are describing objects, and used with units. 1 nut, 2 nuts, and etc. But nominalism fall down when we think about numbers such as e, pi, 3+5i, or pi^i and etc. Hence Nominalism falls. (For more information on nominalism: http://plato.stanford.edu... )

2. Fictionalism : It is the most stupid philosophy. Main idea that is numbers do not exist. They are not abstract objects, thus mathematical discourse is false. It is stupid to agre with such statement, while reading this statement. (Your PC, laptop, smartphone and etc. exist thanks to math.) (For more info on Fictionalism : http://plato.stanford.edu... )

3. Platonism: Numbers exist as abstract objects, they are non-spatial, and atemporal. It is the most rational choice. ( http://plato.stanford.edu... )

There are constants in universe which existed since the beginning of time and independent of human mind, which has certain values. (Such as G = 6.7384 * 10^(-11) * N * kg^(-2) * m^(2) ).

There will be some objections to these view, but soime of them are arguiments from ignorance (just stupid people).

1. Numerals are not numbers. They are signs to describe numbers. It doesn't matter if you use Arabic numerals (1,2,3,4,5,6,7,8,9,0 - and actually it is west Arabic numerals), or east Arabic numerals, or you made your own numerals.

2. Numerical systems - 13 pencils are always 13, it doesn't matter if you use decimal (base 10 =13), octal (base 8 = 15), hexadecimal (base 16 = D), it will not change the number (whether it is quantitive or qualitive).

I haven't thought about it in great detail. But I am somewhere between a. Fictionalise and a nominalistic. Numbers don't exist objectively as some fort of entity, although they do form a logical framework of their own which describes reality, and reality roughly describes it.

Interestingly it runs into a problem on materialism that zmike pointed out to me:

P1) No physical process is determinate
P2) Formal thinking is determinate
C) Formal thinking is not a physical process

You can easily swap in 'thinking of numbers' in there. The most relevant question is how to brains undergo formal thinking physically, which will tell us a lot about the nature of numbers.
tahir.imanov
Posts: 272
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7/12/2014 4:54:55 AM
Posted: 2 years ago
At 7/12/2014 3:57:42 AM, rross wrote:
Is this the first step in your proof? Because I don't see how quantifying abstract objects has anything to do with whether or not they exist objectively.
You want empirical evidence for something that doesn't exist? Isn't that a contradiction?

I don't want evidence for something that doesn't exist. You claimed that numbers don't exist independ of mind. I want evidence for it.

What evidence do you have that they do exist?

I took all possible eplanations (numbers exist, numbers exist in mind, they don't exist) and I used elimination method.

by the way, does mind exist?
Let's sort out the number thing first, and then we'll move onto this. :)

Actually to say numbers exist in minds, and it is used to describe objects. First the existence of mind must be proven then existence of objects must be proven.
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Ajab
Posts: 395
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7/12/2014 5:08:23 AM
Posted: 2 years ago
At 7/11/2014 9:09:56 PM, tahir.imanov wrote:
First the philosophical side: There are three explanations for numbers (also mathematical objects, relations and etc).

1. Nominalism : Numbers do not exist, they are describing objects, and used with units. 1 nut, 2 nuts, and etc. But nominalism fall down when we think about numbers such as e, pi, 3+5i, or pi^i and etc. Hence Nominalism falls. (For more information on nominalism: http://plato.stanford.edu... )

2. Fictionalism : It is the most stupid philosophy. Main idea that is numbers do not exist. They are not abstract objects, thus mathematical discourse is false. It is stupid to agre with such statement, while reading this statement. (Your PC, laptop, smartphone and etc. exist thanks to math.) (For more info on Fictionalism : http://plato.stanford.edu... )

3. Platonism: Numbers exist as abstract objects, they are non-spatial, and atemporal. It is the most rational choice. ( http://plato.stanford.edu... )

There are constants in universe which existed since the beginning of time and independent of human mind, which has certain values. (Such as G = 6.7384 * 10^(-11) * N * kg^(-2) * m^(2) ).

There will be some objections to these view, but soime of them are arguiments from ignorance (just stupid people).

1. Numerals are not numbers. They are signs to describe numbers. It doesn't matter if you use Arabic numerals (1,2,3,4,5,6,7,8,9,0 - and actually it is west Arabic numerals), or east Arabic numerals, or you made your own numerals.

2. Numerical systems - 13 pencils are always 13, it doesn't matter if you use decimal (base 10 =13), octal (base 8 = 15), hexadecimal (base 16 = D), it will not change the number (whether it is quantitive or qualitive).
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Wocambs
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7/12/2014 11:33:18 AM
Posted: 2 years ago
At 7/11/2014 9:09:56 PM, tahir.imanov wrote:
First the philosophical side: There are three explanations for numbers (also mathematical objects, relations and etc).

1. Nominalism : Numbers do not exist, they are describing objects, and used with units. 1 nut, 2 nuts, and etc. But nominalism fall down when we think about numbers such as e, pi, 3+5i, or pi^i and etc. Hence Nominalism falls. (For more information on nominalism: http://plato.stanford.edu... )

2. Fictionalism : It is the most stupid philosophy. Main idea that is numbers do not exist. They are not abstract objects, thus mathematical discourse is false. It is stupid to agre with such statement, while reading this statement. (Your PC, laptop, smartphone and etc. exist thanks to math.) (For more info on Fictionalism : http://plato.stanford.edu... )

3. Platonism: Numbers exist as abstract objects, they are non-spatial, and atemporal. It is the most rational choice. ( http://plato.stanford.edu... )

There are constants in universe which existed since the beginning of time and independent of human mind, which has certain values. (Such as G = 6.7384 * 10^(-11) * N * kg^(-2) * m^(2) ).

There will be some objections to these view, but soime of them are arguiments from ignorance (just stupid people).

1. Numerals are not numbers. They are signs to describe numbers. It doesn't matter if you use Arabic numerals (1,2,3,4,5,6,7,8,9,0 - and actually it is west Arabic numerals), or east Arabic numerals, or you made your own numerals.

2. Numerical systems - 13 pencils are always 13, it doesn't matter if you use decimal (base 10 =13), octal (base 8 = 15), hexadecimal (base 16 = D), it will not change the number (whether it is quantitive or qualitive).

I don't see how 'mathematics works' means that 'mathematics exists independently of a mind'. I mean, reality exists, but reality is only quantifiable from the standpoint of a subject, quite clearly.
rross
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7/13/2014 1:21:41 AM
Posted: 2 years ago
At 7/12/2014 4:54:55 AM, tahir.imanov wrote:
At 7/12/2014 3:57:42 AM, rross wrote:
Is this the first step in your proof? Because I don't see how quantifying abstract objects has anything to do with whether or not they exist objectively.
You want empirical evidence for something that doesn't exist? Isn't that a contradiction?

I don't want evidence for something that doesn't exist. You claimed that numbers don't exist independ of mind. I want evidence for it.

See - I thought you were arguing that numbers DO objectively exist, and I think they DON'T objectively exist, which means you're the one with the positive claim, which means that you're the one who needs to come up with the evidence.

When I said that "of course numbers don't exist independently of the mind", I suppose it was just a statement of belief. I should have said, "I don't believe numbers exist objectively," but what I really mean is that I can't see any reason to believe in their existence given that they are no more than mental constructs. Or maybe I should say I can't see any reason to believe that they are more than mental constructs. Which invites you to provide a reason.

What evidence do you have that they do exist?

I took all possible eplanations (numbers exist, numbers exist in mind, they don't exist) and I used elimination method.

So you have eliminated numbers exist in the mind. But why?

by the way, does mind exist?
Let's sort out the number thing first, and then we'll move onto this. :)

Actually to say numbers exist in minds, and it is used to describe objects. First the existence of mind must be proven then existence of objects must be proven.

The way I see it is that numbers only exist in the mind, so if the mind doesn't exist then neither do numbers. So I suppose you could argue that numbers do exist but that the mind doesn't. That'd be an interesting argument to read.
Mhykiel
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7/13/2014 3:58:34 AM
Posted: 2 years ago
At 7/11/2014 9:09:56 PM, tahir.imanov wrote:
First the philosophical side: There are three explanations for numbers (also mathematical objects, relations and etc).

1. Nominalism : Numbers do not exist, they are describing objects, and used with units. 1 nut, 2 nuts, and etc. But nominalism fall down when we think about numbers such as e, pi, 3+5i, or pi^i and etc. Hence Nominalism falls. (For more information on nominalism: http://plato.stanford.edu... )

2. Fictionalism : It is the most stupid philosophy. Main idea that is numbers do not exist. They are not abstract objects, thus mathematical discourse is false. It is stupid to agre with such statement, while reading this statement. (Your PC, laptop, smartphone and etc. exist thanks to math.) (For more info on Fictionalism : http://plato.stanford.edu... )

3. Platonism: Numbers exist as abstract objects, they are non-spatial, and atemporal. It is the most rational choice. ( http://plato.stanford.edu... )

There are constants in universe which existed since the beginning of time and independent of human mind, which has certain values. (Such as G = 6.7384 * 10^(-11) * N * kg^(-2) * m^(2) ).

There will be some objections to these view, but soime of them are arguiments from ignorance (just stupid people).

1. Numerals are not numbers. They are signs to describe numbers. It doesn't matter if you use Arabic numerals (1,2,3,4,5,6,7,8,9,0 - and actually it is west Arabic numerals), or east Arabic numerals, or you made your own numerals.

2. Numerical systems - 13 pencils are always 13, it doesn't matter if you use decimal (base 10 =13), octal (base 8 = 15), hexadecimal (base 16 = D), it will not change the number (whether it is quantitive or qualitive).

Numbers do not exist. They are part of a man made system to describe reality and make accurate predictions of reality.

pi is the circumference of a circle divided by it's diameter. In reality the circle is closed and finite. But in the man made system of math the number pi is never ending. Even Math is insufficient to describe reality.

Things that exist have qualities that can be discerned. If "gdurms" has no discernible qualities it does not exist or is imperceptible to mankind.

What discernable qualities does "1" have? Without a unit it can not be described objectively. With out using it as an adjective to describe something real, "1" can only be described in relation to other numbers "2, 3, 4, 5..."

Each of those numbers, only discernible in relation to other numbers. Making the numbers a self referencing coherent system. But as a whole, indiscernible by themselves.

Therefore numbers do not exist or are imperceptible to humans.

But humans do perceive of numbers. They call it "number sense". Even when numbers do not describe something else they have a perceived influence on thought or examination of real things.

So numbers are not real. They are man made. They are not perfect representations of reality. They are consistent and "fairly enough" accurate when used correctly.
ThoughtsandThoughts
Posts: 178
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7/13/2014 6:26:52 PM
Posted: 2 years ago
At 7/11/2014 9:09:56 PM, tahir.imanov wrote:
3. Platonism: Numbers exist as abstract objects, they are non-spatial, and atemporal. It is the most rational choice. ( http://plato.stanford.edu... )


I lean toward this.

Let's take color, instead of numbers, as an example. The color blue exists independently of the human mind. Before human existence, substances could be blue without being so because of the construct of human thought. Blue is a color. Colors are observable. Let me explain how numbers are observable.

Now, numbers are a quantity. Quantities do exist; they're a measure of something. Quantities exist independently of the human mind being able to measure them. If no one occupied a room with three windows, there would still be two windows. I would argue that numbers describing how objects and substances relate to one another simply redefines what numbers are. Numbers are a certain kind of system of relations. If there are relations, then numbers exist independently of the mind.

Similarly, it could be said that, "Processes exist independently of human mind." A process is the steps taken to reach a result. One could counter argue that the definition of process simply describes a set of events. This implies that the order in which the events have happened could be random. Yet there is indeed a phenomenon in which events happen in a certain order. For instance, an amoeba splitting into two amoeba (binary fission), cannot happen like this: there are two amoeba, the amoeba splits into two, and then the nucleus divides. The correct order is an example of what we call a process. Of course its definition describes a set of events. The definition of any word essentially describes something.
ThoughtsandThoughts
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7/13/2014 6:28:39 PM
Posted: 2 years ago
If no one occupied a room with three windows, there would still be two windows.


Oh right, 3 = 2.

Haha, I meant there would still be three :P
bladerunner060
Posts: 7,126
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7/13/2014 6:33:53 PM
Posted: 2 years ago
At 7/13/2014 6:26:52 PM, ThoughtsandThoughts wrote:

Let's take color, instead of numbers, as an example. The color blue exists independently of the human mind. Before human existence, substances could be blue without being so because of the construct of human thought. Blue is a color. Colors are observable.

Strictly speaking, you are incorrect. "Colors" are merely the labels we apply to particular frequency ranges of light. While those frequency ranges would exist independently of minds, I don't think you can really say "the color" would, because what "the color" is depends on the physical characeristics of the person viewing them. Some people can see more "shades" than others, for example. So what's "orange" to one person may be "clementine" to another.
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ThoughtsandThoughts
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7/13/2014 6:41:32 PM
Posted: 2 years ago
At 7/13/2014 6:33:53 PM, bladerunner060 wrote:
At 7/13/2014 6:26:52 PM, ThoughtsandThoughts wrote:

Let's take color, instead of numbers, as an example. The color blue exists independently of the human mind. Before human existence, substances could be blue without being so because of the construct of human thought. Blue is a color. Colors are observable.

Strictly speaking, you are incorrect. "Colors" are merely the labels we apply to particular frequency ranges of light. While those frequency ranges would exist independently of minds, I don't think you can really say "the color" would, because what "the color" is depends on the physical characeristics of the person viewing them.


Ahhh, the technicalities. Hmm, perhaps I should scratch that example.

Some people can see more "shades" than others, for example. So what's "orange" to one person may be "clementine" to another.


I've always wondered if there were slight variations between people's perception of color (aside from colorblindness). Thanks for sharing =)
rross
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7/13/2014 8:07:09 PM
Posted: 2 years ago
At 7/13/2014 6:26:52 PM, ThoughtsandThoughts wrote:
At 7/11/2014 9:09:56 PM, tahir.imanov wrote:
3. Platonism: Numbers exist as abstract objects, they are non-spatial, and atemporal. It is the most rational choice. ( http://plato.stanford.edu... )


I lean toward this.

Let's take color, instead of numbers, as an example. The color blue exists independently of the human mind. Before human existence, substances could be blue without being so because of the construct of human thought. Blue is a color. Colors are observable. Let me explain how numbers are observable.

Now, numbers are a quantity. Quantities do exist; they're a measure of something. Quantities exist independently of the human mind being able to measure them. If no one occupied a room with three windows, there would still be two windows. I would argue that numbers describing how objects and substances relate to one another simply redefines what numbers are. Numbers are a certain kind of system of relations. If there are relations, then numbers exist independently of the mind.

But I suppose that the category - this is a window - is a human judgment, and for there to be two windows, we need to categorize each as a window, a discrete thing, and then decide that they are similar - both windows - and then count them.

It's an interesting example, because there can't be windows without human perception because they are produced by humans. So even if there was nobody in the room, the room would have been already produced, categorized and named by humans in the past.

Similarly, it could be said that, "Processes exist independently of human mind." A process is the steps taken to reach a result. One could counter argue that the definition of process simply describes a set of events. This implies that the order in which the events have happened could be random. Yet there is indeed a phenomenon in which events happen in a certain order. For instance, an amoeba splitting into two amoeba (binary fission), cannot happen like this: there are two amoeba, the amoeba splits into two, and then the nucleus divides. The correct order is an example of what we call a process. Of course its definition describes a set of events. The definition of any word essentially describes something.

This is a good example. From what I remember in biology, an amoeba is separated from the fluid it lives in by a membrane which allows certain molecules in and out, and to which chemicals can attach and detach, and which constantly changes shape and composition. So we define "an amoeba" as a separate and definite thing, which is our judgment, and a fairly subjective distinction. If it separates into "two" then it is human perception putting huge significance onto a particular membranous arrangement. Again, we have to separate each amoeba as a distinct thing, and then put them the same category of things and then count them.
ThoughtsandThoughts
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7/14/2014 8:33:21 AM
Posted: 2 years ago
At 7/13/2014 8:07:09 PM, rross wrote:
But I suppose that the category - this is a window - is a human judgment, and for there to be two windows, we need to categorize each as a window, a discrete thing, and then decide that they are similar - both windows - and then count them.


Well, that assumes numbers only apply to identical objects. Even two cells within the same plant may not be identical in the processes they're performing/the chemicals they're responding to. It could be said that animal kingdoms and species don't exist independently of the mind because humans have categorized and classified animals according to human judgement. But it isn't human judgment that prevents certain animals from interbreeding. This is despite the fact that all animals within a species aren't identical. Any two given giraffes may have a different set of DNA, environments, and health conditions, but no giraffe can reproduce with a snake, for instance. These categorizations have merely been defined by people.

It's an interesting example, because there can't be windows without human perception because they are produced by humans. So even if there was nobody in the room, the room would have been already produced, categorized and named by humans in the past.


If we use a simpler example, like two cells from the same plant (which I propose don't have to be exactly identical), we can say they exist without human perception because they have existed without it. Again, because numbers are simply a system of relation, only one object (or perhaps two?) needs to exist for it to relate to something else. Objects do exist independently of the mind, therefore numbers do a well.

Similarly, it could be said that, "Processes exist independently of human mind." A process is the steps taken to reach a result. One could counter argue that the definition of process simply describes a set of events. This implies that the order in which the events have happened could be random. Yet there is indeed a phenomenon in which events happen in a certain order. For instance, an amoeba splitting into two amoeba (binary fission), cannot happen like this: there are two amoeba, the amoeba splits into two, and then the nucleus divides. The correct order is an example of what we call a process. Of course its definition describes a set of events. The definition of any word essentially describes something.

This is a good example. From what I remember in biology, an amoeba is separated from the fluid it lives in by a membrane which allows certain molecules in and out, and to which chemicals can attach and detach, and which constantly changes shape and composition. So we define "an amoeba" as a separate and definite thing, which is our judgment, and a fairly subjective distinction. If it separates into "two" then it is human perception putting huge significance onto a particular membranous arrangement. Again, we have to separate each amoeba as a distinct thing, and then put them the same category of things and then count them.


Yes, but like with the classifications of animals, certain restrictions apply to amoeba that don't apply to other single-celled organisms. That's what objectifies the categorization of any two, three, etc. things. In the classification of species example, restrictions apply to reproduction.
rross
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7/14/2014 11:40:17 PM
Posted: 2 years ago
At 7/14/2014 8:33:21 AM, ThoughtsandThoughts wrote:
At 7/13/2014 8:07:09 PM, rross wrote:
But I suppose that the category - this is a window - is a human judgment, and for there to be two windows, we need to categorize each as a window, a discrete thing, and then decide that they are similar - both windows - and then count them.


Well, that assumes numbers only apply to identical objects.
Not identical, but in the same category (even if the category is "things") to count.

Also, there needs to be imposed a limit - I didn't think of that before. So, for example, if we're counting amoebas, unless we count all the amoebas in existence, we have to define a space within which the amoebas are counted.

Even two cells within the same plant may not be identical in the processes they're performing/the chemicals they're responding to. It could be said that animal kingdoms and species don't exist independently of the mind because humans have categorized and classified animals according to human judgement. But it isn't human judgment that prevents certain animals from interbreeding. This is despite the fact that all animals within a species aren't identical. Any two given giraffes may have a different set of DNA, environments, and health conditions, but no giraffe can reproduce with a snake, for instance. These categorizations have merely been defined by people.

It's an interesting example, because there can't be windows without human perception because they are produced by humans. So even if there was nobody in the room, the room would have been already produced, categorized and named by humans in the past.


If we use a simpler example, like two cells from the same plant (which I propose don't have to be exactly identical), we can say they exist without human perception because they have existed without it. Again, because numbers are simply a system of relation, only one object (or perhaps two?) needs to exist for it to relate to something else. Objects do exist independently of the mind, therefore numbers do a well.

Yeah, but I suppose my point is that a cell is not a discrete, separate, well-defined entity unless we choose for it to be. Actually, it's just a whole lot of molecules and space between presumably (I'm a bit vague on physical chemistry), and it's a human decision to define it as one thing on the basis of the cell wall or membrane.

Similarly, it could be said that, "Processes exist independently of human mind." A process is the steps taken to reach a result. One could counter argue that the definition of process simply describes a set of events. This implies that the order in which the events have happened could be random. Yet there is indeed a phenomenon in which events happen in a certain order. For instance, an amoeba splitting into two amoeba (binary fission), cannot happen like this: there are two amoeba, the amoeba splits into two, and then the nucleus divides. The correct order is an example of what we call a process. Of course its definition describes a set of events. The definition of any word essentially describes something.

This is a good example. From what I remember in biology, an amoeba is separated from the fluid it lives in by a membrane which allows certain molecules in and out, and to which chemicals can attach and detach, and which constantly changes shape and composition. So we define "an amoeba" as a separate and definite thing, which is our judgment, and a fairly subjective distinction. If it separates into "two" then it is human perception putting huge significance onto a particular membranous arrangement. Again, we have to separate each amoeba as a distinct thing, and then put them the same category of things and then count them.


Yes, but like with the classifications of animals, certain restrictions apply to amoeba that don't apply to other single-celled organisms. That's what objectifies the categorization of any two, three, etc. things. In the classification of species example, restrictions apply to reproduction.

Maybe. But I'm not sure what you're counting in this example.
ThoughtsandThoughts
Posts: 178
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7/16/2014 8:31:39 PM
Posted: 2 years ago
Well, that assumes numbers only apply to identical objects.
Not identical, but in the same category (even if the category is "things") to count.

Also, there needs to be imposed a limit - I didn't think of that before. So, for example, if we're counting amoebas, unless we count all the amoebas in existence, we have to define a space within which the amoebas are counted.


Yes, that would be the restrictions. People may not always exactly define these restrictions, but they can be rather easily implied. e.g. "I'm going to count my change." There's no need to specify what given space the change is in because the counter knows the restrictions.

If we use a simpler example, like two cells from the same plant (which I propose don't have to be exactly identical), we can say they exist without human perception because they have existed without it. Again, because numbers are simply a system of relation, only one object (or perhaps two?) needs to exist for it to relate to something else. Objects do exist independently of the mind, therefore numbers do as well.

Yeah, but I suppose my point is that a cell is not a discrete, separate, well-defined entity unless we choose for it to be. Actually, it's just a whole lot of molecules and space between presumably (I'm a bit vague on physical chemistry), and it's a human decision to define it as one thing on the basis of the cell wall or membrane.


That's completely true. But the decision to count an aspect of something as opposed to another (to use certain restrictions over another) doesn't mean numbers don't exist. We just simply choose a level (is it at the particle level, the molecule level, the cell level, the organism level, etc.?) to count at. Those levels do relate to one another because they exist.

Yes, but like with the classifications of animals, certain restrictions apply to amoeba that don't apply to other single-celled organisms. That's what objectifies the categorization of any two, three, etc. things. In the classification of species example, restrictions apply to reproduction.

Maybe. But I'm not sure what you're counting in this example.

There's nothing necessarily being counted in the species example. I was just pointing out that human judgement can be valid in terms of making categories.
Sidewalker
Posts: 3,713
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7/16/2014 9:27:27 PM
Posted: 2 years ago
If numbers exist in the absence of mind, where do they exist?
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater
Enji
Posts: 1,022
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7/16/2014 9:49:02 PM
Posted: 2 years ago
The question is "Are mathematical truths discovered or invented?" If Platonism is true, then mathematical truths exist and we can discover them through proof. The alternative is that mathematics is a human construct; we invent the rules and from them create mathematical truths. I'm inclined to believe that mathematics is largely invented.

An example of this is found in geometry. Euclid presented 5 axioms, the first four of which were self-evident definition type things, and the fifth was a less-intuitive, more complicated claim: the parallel postulate. With only the first four axioms you can prove a small range of trivial claims, but with the introduction of the parallel postulate a much wider variety of mathematical truths can be proven (for example, Pythagoras' theorem). However alternatives to the parallel postulate can also be posited which can prove unique claims, and these claims are inconsistent with those based on the parallel postulate.

This example is applicable to all areas of mathematics; a mathematical claim can only be said to be true within the set of rules with which it was proved. We can change the rules to prove different claims, but then we are no longer working in the same mathematical system. And distinct, contradictory mathematical systems are only possible if mathematics is created, not if mathematics is discovered.