Thread: Do numbers exist or are they figments of our imagination?

I'm honestly not sure what category of science this question falls under but I've narrowed down to either philosophy, mathematics, or physics.I'm sure most or all who read this, are familiarized with Zeno. (Some call him a philosopher others a nut) please look it up if you don't.According to Zeno's paradox movement is impossible, due to the infinite middle points between any two position so no matter how fast Achilles ran he couldn't catch the turtle in the paradox. I realized that similar logic could be applied to whole numbers. To get from 0-1 you first have to get to 0.5. And before achieving 0.5 you must first encounter 0.25 and so on for infinity. There are an infinite number of numbers between 0 and 1. Do whole numbers exist? And between each decimal is an infinite number of minuscule decimals. So do numbers exist or are they figures of our imagination? Is counting even a possibility?

Originally Posted by Dreamraider

There are an infinite number of numbers between 0 and 1.
...
And between each decimal is an infinite number of minuscule decimals.

Correct. That is why it is impossible to count the real number using integers.

Is counting even a possibility?

If you think it is not possible, please feel free to send me all your money and I will count it for you.

And, oh look: post #2. I think that answers the question.

Thank you, strange.

Zeno's paradox isn't actually a paradox, it was just a result of not knowing how to sum an infinite series yet.

Originally Posted by TheObserver

Zeno's paradox isn't actually a paradox, it was just a result of not knowing how to sum an infinite series yet.

It seems to hold up to the def. of a paradox -A seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true. (Google dic.)Paradox is just a secondary qualitative value for a "seemingly contradictory statement". Which is ergo a paradox. Unless your willing to contend with the definition.

If you are going to accept the "seemingly contradictory" definition, then Zeno's paradox doesn't make movement impossible, just "seemingly impossible". And, of course, movement is possible in reality. As for counting.

There is an interesting question as to whether mathematics is invented or discovered. I think most mathematicians (and, hopefully, most sensible philosophers) think it is discovered. So in that sense mathematics (and therefore numbers) exist.

I would be more inclined to think that mathematics was a method of modelling invented to keep us safe. If I was to take unknown amounts of reagents and just splash them together any old way. Or indeed to make my maths unreadable when writing a formula. People could get hurt if you were to screw with the formulas of chemical reactions can you imagine the trouble you could cause... What if I baked an apple tart and sprinkeled a load of crushed apple pips on the top for garnish?

Why?? Do you know the output of that particular function?

I think it's confusing to try to tackle two different questions:

1) Do numbers exist; and

2) What is the modern resolution of Zeno's paradoxes; and are they really resolved?

I'd like to answer #1.

Numbers are an abstraction of the human mind. They don't exist in the physical world. But they exist as abstract entities in our minds; and as a collective agreement among ourselves.

Let me give an analogy. How about a business contract? Let's say you rent an apartment. You sign a lease, which is a legally enforceable agreement between you and the landlord. In the legal system, it falls under contract law.

Now, does a lease exist in the physical world? Well of course a physical representation of the lease exists; namely, the piece of paper. But the piece of paper isn't the lease. The actual lease is the agreement between you and another person; and the entire legal system, consisting of thousands of years of precedent in many places and many cultures, regarding the renting of property. Both you and the landlord know that the least must be honored or else consequences will occur. The consequences derive from the collective human agreement to have laws and courts. If you ever stop to think about it, civilization itself is very abstract. It's not real; it's a collective agreement. A collective delusion, if you like. But we all agree to agree; and then we can do business; and then we can improve our standard of living through commerce.

Numbers are in exactly the same category. They are stories we make up from our minds. But by agreeing collectively to these stories, they become real in the sense that they have real world consequences. When you go to work, you get some money. One dollar, say. The value of that dollar is an illusion. A dollar is a piece of paper, intrinsically worth the amount of heat it would generate if you burned it to keep warm. The only reason a dollar can buy you something is because there is a general agreement among humans that there's a thing called money; and that money can be represented by intrinsically worthless pieces of paper.

Numbers are abstract creations of our mind. But they have real meaning in the real world; by virtue of our collective agreement that they do.

But once you start to think about it, there are quite a lot of things in the same category. Law, justice, politics. Letters that form words and have meaning in our minds. Are words physical? No, they're abstract. And yet they are real.

Originally Posted by someguy1

I think it's confusing to try to tackle two different questions:

1) Do numbers exist; and

2) What is the modern resolution of Zeno's paradoxes; and are they really resolved?

I'd like to answer #1.

Numbers are an abstraction of the human mind. They don't exist in the physical world. But they exist as abstract entities in our minds; and as a collective agreement among ourselves.
Numbers are abstract creations of our mind. but they have real meaning in the real world.

I do agree with the above.
I am not clear as to why Zeno's paradoxes have anything to do with the question asked, by Dreamraider, in the opening post of this thread.
I must add that I believe mathematics was invented, and not discovered.

Originally Posted by fiveworlds

Or indeed to make my maths unreadable when writing a formula.

Which is what you do all the time.

I think the question of whether numbers are "real" or "exist" depends on what you mean by those words.

But numbers (and mathematics) are clearly a representation of something in the real world. We count things because they are countable. We measure time and space because they are measurable.

If you picked two apples from a tree and gave them to Xrag from the planet K't'fg he would acknowledge that he had two (or "fg!rsth" as he would say) apples. He could give one to his sister (Zxda) and he would know he had one and she had one. So the basic ideas would be common.

Although, I heard a discussion about this with some mathematicians and one suggested that if there was an intelligent alien species who were fluid (gaseous or "pure energy") then our advanced math (calculus and fluid dynamics) might be their basic arithmetic and it took their equivalent of Newton (or Leibniz, if you prefer) to come up with the shocking concept of "integers" - which can only be mastered after several years of post-grad study...

I think the consensus, after the flurry of independence proofs in the 60's, is that Mathematics is invented; a game played by humans with nothing better to do. Is under this assumption that the unreasonable effectiveness of Mathematics in the physical sciences takes its full strength, why should the game of mathematics be any more useful at explaining the universe than the game of tick tack toe?

what about figures, cube , triangle, sphere etc. is it not only human imagination to form different figures? illusion came to reality.

numbers, figures etc can only be justified in ones mind?

Originally Posted by PhDemon

Yeah, it's all imagination, those shapes don't appear in nature at all...

i know , they appear naturally. but there are infinite shapes, in anybody's mind, which dont appear in nature. should we insist that those are real?

Originally Posted by PhDemon

If you made sense at any point it might be worth a serious reply. But you don't, so it isn't...

The word "so" is confusing me. Let P be the statement "Dreamraider makes sense" and Q be the statement "It is worth a serious reply". In the first sentence of your post, you state that P (maybe) implies Q. In your second statement you claim and infer . This is, however, a logical fallacy, as Sorry, but I had to

Originally Posted by PhDemon

. It was a reply to Precious Parts though. I don't think any of their posts have any meaning...

Is that 1 or 0?

Originally Posted by thyristor

Originally Posted by PhDemon

. It was a reply to Precious Parts though. I don't think any of their posts have any meaning...

Is that 1 or 0?

With the picture gone, this obviously doesn't make any sense anymore.

Originally Posted by Neverfly

A logical fallacy as this is certainly nothing to roll one's eyes at . Suppose that in a particular legal system there are two crimes, and , respectively, both individually resulting in the death penalty. Let R be the statement "P has committed crime " and let S be the statement "P is given the death penalty". Hence . Suppose it is found that P has not committed crime while P is convicted of committing crime . We hence incorrectly infer and P goes free.

Originally Posted by PhDemon

Sorry about that, I removed the picture as I didn't think the F word in that size font would go down too well... (0 though :-P).

Probably a good call

Originally Posted by Strange

There is an interesting question as to whether mathematics is invented or discovered. I think most mathematicians (and, hopefully, most sensible philosophers) think it is discovered. So in that sense mathematics (and therefore numbers) exist.

I want to share a thought on this one, though I realize I could be wrong.

I think One is discovered and the rest of the "mathematics" is invented.

For example, a person can spot an object which no one else has noticed before. This only means that this object was discovered, since it existed even before anyone had noticed it. Now let us say another one of the same kind of object was spotted, then we would normally say that we have found "two" of this kind of objects. We say "two objects" because we know 1+1=2, and it is always so. There can never be "1+1=3" so we would not see "1+1=2" is an invention.

But there is another way to see this whole scenario. It can also be seen as: In reality there is one object that exists and another one of the same kind exists, yet another one and another one could exist,all as single individual objects. At this point we invent math and say there are "4" of these objects. We do this to make it easier on us to keep a track. If these objects were to gain consciousness, they would each consider themselves to be individuals and would not say "there are four of me"(though there are more of its kind in existence). Just like all of us are humans but we would not say there are six billion of me (though there are six billion humans). We invented the addition so to make life easier for us. But in reality there is one and another one, yet another and so on.

[QUOTE=Faithfulbeliever;431305][QUOTE=Strange;430912]There is an interesting question as to whether mathematics is invented or discovered. I think most mathematicians (and, hopefully, most sensible philosophers) think it is discovered. So in that sense mathematics (and therefore numbers) existI want to share a thought on this one, though I realize I could be wrong.I think One is discovered and the rest of the "mathematics" is invented.(/quote )Faithful believer, how do you explain zero? Ancient Indian civilizations deserve credit for "discovering" that.

[QUOTE=Dreamraider;432257][QUOTE=Faithfulbeliever;431305]

Originally Posted by Strange

There is an interesting question as to whether mathematics is invented or discovered. I think most mathematicians (and, hopefully, most sensible philosophers) think it is discovered. So in that sense mathematics (and therefore numbers) existI want to share a thought on this one, though I realize I could be wrong.I think One is discovered and the rest of the "mathematics" is invented.(/quote )

Faithful believer, how do you explain zero? Ancient Indian civilizations deserve credit for "discovering" that.

I don't think I would be the right person to explain anything in this particular matter. When I read strange's post about this "interesting question" a thought entered my mind and I typed it in.

Thread like this can use a little humor sometimes, so here it is.....

....Although zero is considered as a number in mathematics for various reasons, but in real world the value of it can be equated to 'nothing' OR 'something which is hidden and will remain hidden forever'. Something that somehow exists but remains hidden forever is only possible if it cannot be discovered or invented for eternity. So in real life real value of zero is neither discovered nor invented! It is only as is a "0" .

Originally Posted by Faithfulbeliever

....Although zero is considered as a number in mathematics for various reasons, but in real world the value of it can be equated to ... 'something which is hidden and will remain hidden forever'.

No it can't.

So in real life real value of zero is neither discovered nor invented! It is only as is a "0" .

Wrong again.
We're talking about the concept of 0 which was discovered, not the "value".

As for your claim that you "think One is discovered and the rest of the "mathematics" is invented", maybe you should consider that, because 1 "exists" the rest of mathematics is a concomitant of 1, ergo, that's discovered too and not invented.

I find it interesting that mathematics might be considered by some to have been discovered, as though it has some sort of independent existence like a buried object waiting to be unearthed.

Originally Posted by Ledger

I find it interesting that mathematics might be considered by some to have been discovered, as though it has some sort of independent existence like a buried object waiting to be unearthed.

I agree. If I believed in the discovery, rather than the invention, of mathematics surely I could argue that everything had been discovered rather than invented.
As to the opening question I would say that numbers are mathematical abstractions and so do not exist in the physical world. I would prefer to describe them as extremely valuable products of the human mind rather than "figments of our imagination".

Originally Posted by Halliday

I agree. If I believed in the discovery, rather than the invention, of mathematics surely I could argue that everything had been discovered rather than invented.
As to the opening question I would say that numbers are mathematical abstractions and so do not exist in the physical world. I would prefer to describe them as extremely valuable products of the human mind rather than "figments of our imagination".

But then one must answer the question of why mathematics is so incredibly useful in everything we do; from counting our change at the grocery store; to probing the mysteries of the cosmos.

After all, The Cat in the Hat is a fine piece of invented fiction too. But it doesn't seem to have nearly the degree of universal applicability and -- dare I say it -- necessity in the affairs of humans.

Originally Posted by someguy1

Originally Posted by Halliday

I agree. If I believed in the discovery, rather than the invention, of mathematics surely I could argue that everything had been discovered rather than invented.
As to the opening question I would say that numbers are mathematical abstractions and so do not exist in the physical world. I would prefer to describe them as extremely valuable products of the human mind rather than "figments of our imagination".

But then one must answer the question of why mathematics is so incredibly useful in everything we do; from counting our change at the grocery store; to probing the mysteries of the cosmos.

After all, The Cat in the Hat is a fine piece of invented fiction too. But it doesn't seem to have nearly the degree of universal applicability and -- dare I say it -- necessity in the affairs of humans.

And thus the diversity of human constructs.

Originally Posted by someguy1

Originally Posted by Halliday

I agree. If I believed in the discovery, rather than the invention, of mathematics surely I could argue that everything had been discovered rather than invented.As to the opening question I would say that numbers are mathematical abstractions and so do not exist in the physical world. I would prefer to describe them as extremely valuable products of the human mind rather than "figments of our imagination".

But then one must answer the question of why mathematics is so incredibly useful in everything we do; from counting our change at the grocery store; to probing the mysteries of the cosmos.After all, The Cat in the Hat is a fine piece of invented fiction too. But it doesn't seem to have nearly the degree of universal applicability and -- dare I say it -- necessity in the affairs of humans.

believe it or not there is a whole branch of philosophy that covers that very topic. It states that all knowledge is only good, true, or right as long it is useful. When we value rhymes, limericks, and poorly drawn hallucinatory bears more than numbers we will thus substitute them for numbers and math as a whole.but it's deeper than that. Look at the Arabic numerals we have now. They had to substitute some other number system(probably roman) which is now utterly useless unless describing a world war or Super Bowl.

Originally Posted by Dreamraider

believe it or not there is a whole branch of philosophy that covers that very topic. It states that all knowledge is only good, true, or right as long it is useful.

But Hardy, one of the greatest mathematicians of the 20th century, said that the best math was entirely useless.

A Mathematician's Apology - Wikipedia, the free encyclopedia

And many mathematicians feel that way, too. Certainly the vast majority of modern research mathematics is very far removed from anything anyone would consider useful. Just consider the endless sequence of transfinite cardinals: an infinite hierarchy of infinite numbers, each infinitely greater than the previous one. Of what use are they?

And even math that eventually becomes useful, often does so only after decades or even centuries. Non-Euclidian geometry was first discovered by Gauss in the 1820's; and only found practical use when it turned out to be just the thing to express Einstein's theory of relativity in the early 1900's.

The subject of algorithms for factoring numbers was studied by the ancients; yet was utterly without any possible, conceivable use for millennia. But when computers were invented, the theory of factoring large numbers became the basis of public key cryptography, underlying all modern Internet security.

So if the only math that were done (or allowed, or funded, or taught) was math known to be useful; we would be missing out not only on a lot of very beautiful and important math; but also on math that would eventually become useful ... even after two thousand years of uselessness.

Finally, there may be some philosophers who hold that a thing in this world only has value to the extent that it's useful.

Many others would disagree. What's the use of a beautiful sunset? An ugly sunset would serve the same function.

Originally Posted by Dreamraider

Originally Posted by someguy1

Originally Posted by Halliday

I agree. If I believed in the discovery, rather than the invention, of mathematics surely I could argue that everything had been discovered rather than invented.As to the opening question I would say that numbers are mathematical abstractions and so do not exist in the physical world. I would prefer to describe them as extremely valuable products of the human mind rather than "figments of our imagination".

But then one must answer the question of why mathematics is so incredibly useful in everything we do; from counting our change at the grocery store; to probing the mysteries of the cosmos.After all, The Cat in the Hat is a fine piece of invented fiction too. But it doesn't seem to have nearly the degree of universal applicability and -- dare I say it -- necessity in the affairs of humans.

believe it or not there is a whole branch of philosophy that covers that very topic. It states that all knowledge is only good, true, or right as long it is useful. When we value rhymes, limericks, and poorly drawn hallucinatory bears more than numbers we will thus substitute them for numbers and math as a whole.but it's deeper than that. Look at the Arabic numerals we have now. They had to substitute some other number system(probably roman) which is now utterly useless unless describing a world war or Super Bowl.

That branch of philosophy doesn't state what you mentioned, a philosopher writing in a subject area covered under that branch put forth what you mentioned. That was just one philosopher's thoughts on the subject.

discusion becoming philosophical. can somebody explain in simple terms. just request

Originally Posted by Precious part II

discusion becoming philosophical. can somebody explain in simple terms. just request

Numbers are a mental abstraction, widely agreed to by society.

Widely accepted mental abstractions have tangible effects in the world: consider law, for example.

But mental abstractions aren't physical objects. Law books are subject to gravity; but the law isn't.

Likewise numbers are not physical objects. The number 5 is not bound by the law of gravity. But the number 5 still has impact in the physical world, due to the widespread human agreement on its meaning.

Originally Posted by someguy1

Originally Posted by Dreamraider

believe it or not there is a whole branch of philosophy that covers that very topic. It states that all knowledge is only good, true, or right as long it is useful.

But Hardy, one of the greatest mathematicians of the 20th century, said that the best math was entirely useless.

A Mathematician's Apology - Wikipedia, the free encyclopedia

And many mathematicians feel that way, too. Certainly the vast majority of modern research mathematics is very far removed from anything anyone would consider useful. Just consider the endless sequence of transfinite cardinals: an infinite hierarchy of infinite numbers, each infinitely greater than the previous one. Of what use are they?

And even math that eventually becomes useful, often does so only after decades or even centuries. Non-Euclidian geometry was first discovered by Gauss in the 1820's; and only found practical use when it turned out to be just the thing to express Einstein's theory of relativity in the early 1900's.

The subject of algorithms for factoring numbers was studied by the ancients; yet was utterly without any possible, conceivable use for millennia. But when computers were invented, the theory of factoring large numbers became the basis of public key cryptography, underlying all modern Internet security.

So if the only math that were done (or allowed, or funded, or taught) was math known to be useful; we would be missing out not only on a lot of very beautiful and important math; but also on math that would eventually become useful ... even after two thousand years of uselessness.

Finally, there may be some philosophers who hold that a thing in this world only has value to the extent that it's useful.

Many others would disagree. What's the use of a beautiful sunset? An ugly sunset would serve the same function.

So, maybe you would agree that mathematics and philosophy have something in common. Some of us feel compelled to acquire knowledge or play with numbers, but are not compelled to be particularly useful in any particular sense.

Originally Posted by DaBOB

So, maybe you would agree that mathematics and philosophy have something in common. Some of us feel compelled to acquire knowledge or play with numbers, but are not compelled to be particularly useful in any particular sense.

I've never said math and philosophy don't have something in common. I don't recall the question coming up.

However, "Do numbers exist?" is not a mathematical question. It's purely a question of philosophy.

Originally Posted by someguy1

Originally Posted by DaBOB

So, maybe you would agree that mathematics and philosophy have something in common. Some of us feel compelled to acquire knowledge or play with numbers, but are not compelled to be particularly useful in any particular sense.

I've never said math and philosophy don't have something in common. I don't recall the question coming up.

However, "Do numbers exist?" is not a mathematical question. It's purely a question of philosophy.

Ha, I guess I missed a question mark. I was bringing the question up.

The second sentence was intended as an example of my meaning.

Originally Posted by DaBOB

Ha, I guess I missed a question mark. I was bringing the question up.

The second sentence was intended as an example of my meaning.

Oh I see. Well IMO math is one thing and philosophy of math is another.

Math philosophy is about "are numbers real," and "Is math invented or discovered," and "Is math just a meaningless game played with pencil and paper according to formal rules, or is there a Platonic universe of math out there that we are trying to understand?"

Math itself is about ... well, consider Wiles sitting up in his attic for seven years trying to crack Fermat's last theorem. He was doing highly advanced math, trying to solve the problem. I doubt he spent any time asking, "Are numbers real?"

Now it's possible that some mathematicians, in their spare time, ask themselves these questions. But when they do, they are doing philosophy, not math.

So I would say no. Philosophy of math is not math and vice versa. Just as the philosophy of science is not science.

Originally Posted by Dreamraider

I'm honestly not sure what category of science this question falls under but I've narrowed down to either philosophy, mathematics, or physics.I'm sure most or all who read this, are familiarized with Zeno. (Some call him a philosopher others a nut) please look it up if you don't.According to Zeno's paradox movement is impossible, due to the infinite middle points between any two position so no matter how fast Achilles ran he couldn't catch the turtle in the paradox. I realized that similar logic could be applied to whole numbers. To get from 0-1 you first have to get to 0.5. And before achieving 0.5 you must first encounter 0.25 and so on for infinity. There are an infinite number of numbers between 0 and 1. Do whole numbers exist? And between each decimal is an infinite number of minuscule decimals. So do numbers exist or are they figures of our imagination? Is counting even a possibility?

Those, all were wise people to think much before about the future than, rest of us. No, doubt even if you'ld have proposed you number theory, you today, not only you but anyone could have made an long impression of great person. It's all about what ? when ? how? and why ? these basic question are ment to be answered for rest modificaion world is there to make changes.
That's it !!
Good Luck with your search to find best answer.

But are there quantities? Or am i asking the same thing?

Numbers can be said to exist since physics is consistent and can be modelled by mathematics - numbers.

Only natural numbers and rationals can exist on level 1 of reasoning. Level 1 is the "what-it-is" level. Infinity can exist only on level 2 which is the "what-is-the-relation" level.

Originally Posted by talanum1

Numbers can be said to exist since physics is consistent and can be modelled by mathematics - numbers.

Only natural numbers and rationals can exist on level 1 of reasoning. Level 1 is the "what-it-is" level. Infinity can exist only on level 2 which is the "what-is-the-relation" level.

So how come physics is riddled with things like pi and phi?

I see both sides of the argument but that's nothing new..... this is quite interesting though Plants Avoid Starvation at Night By Doing Basic Math and seems to fall on the side of it there to be discovered and this guy has an informative clip but has a slightly irritating affect:
Is Math a Feature of the Universe or a Feature of Human Creation? | Idea Channel | PBS - YouTube

Similar philosophical questions, also not very new or original: Can all science be reduced to math?
Aren't the borders between sciences blurry and artificial? Isn't math actually the most interdisciplinary theory of everything? Don't you think that knowledge that cannot be mathemati(ci)zed doesn't count as exact science, although it can be empirical science?

Originally Posted by hdjur_jcv

Similar philosophical questions, also not very new or original: Can all science be reduced to math?
Aren't the borders between sciences blurry and artificial? Isn't math actually the most interdisciplinary theory of everything? Don't you think that knowledge that cannot be mathemati(ci)zed doesn't count as exact science, although it can be empirical science?

I would prefer the phrase "modeled using" rather than "reduced to."

In other words we can model Newtonian gravity with the equation G * m1 * m2/r^2.

That doesn't mean that the essence of gravity is some guy in the sky with a calculator multiplying out the values of the variables. Rather, humans can get a very good approximation to the observed behavior of gravity using Newton's famous formula. The actual cause and essence of gravity is still a mystery, with the Higgs only the latest mathematical model. The map is not the territory; the model is not the thing itself.

What I'm saying is that I'm troubled by the phrase "reduced to." When we model natural phenomena with math, we are not explaining the underlying causes of the phenomena; rather, we're only creating a mathematical model.

Am I reading too much into your use of "reduced to math?"

Let me toss in another example. We can use Newton's theory of optics (that Newton really got around!!) to explain the colors of the rainbow. But when we look at a rainbow in the sky, is our experience of the beauty and wonder "reduced to" math? No, I'd say not. Rather, i'd say that math gives us a model of why the colors are what they are; but the rainbow itself is much more than that. The beauty and wonder are not modeled by the theory of diffraction.

counting is possible... but numbers dont exist.. they r just values...
and values dont exist

World English Dictionary

Exist:

-vb

to have being or reality; to be

to eke out a living; stay alive; survive: I can barely exist on this wage

to be living; live

to be present under specified conditions or in a specified place: sharks exist in the Pacific

philosophy

a. to be actual rather than merely possible

b. to be a member of the domain of some theory, an element of some possible world, etc

Originally Posted by someguy1

Originally Posted by hdjur_jcv

Similar philosophical questions, also not very new or original: Can all science be reduced to math? Aren't the borders between sciences blurry and artificial? Isn't math actually the most interdisciplinary theory of everything? Don't you think that knowledge that cannot be mathemati(ci)zed doesn't count as exact science, although it can be empirical science?

I would prefer the phrase "modeled using" rather than "reduced to." In other words we can model Newtonian gravity with the equation G * m1 * m2/r^2.That doesn't mean that the essence of gravity is some guy in the sky with a calculator multiplying out the values of the variables. Rather, humans can get a very good approximation to the observed behavior of gravity using Newton's famous formula. The actual cause and essence of gravity is still a mystery, with the Higgs only the latest mathematical model. The map is not the territory; the model is not the thing itself.What I'm saying is that I'm troubled by the phrase "reduced to." When we model natural phenomena with math, we are not explaining the underlying causes of the phenomena; rather, we're only creating a mathematical model.Am I reading too much into your use of "reduced to math?"Let me toss in another example. We can use Newton's theory of optics (that Newton really got around!!) to explain the colors of the rainbow. But when we look at a rainbow in the sky, is our experience of the beauty and wonder "reduced to" math? No, I'd say not.

it does, depending on wether the singularity has occurred and wether your name is Neo.

Originally Posted by someguy1

Am I reading too much into your use of "reduced to math?"

I meant to ask there (probably in a strange way) if reductionism makes math the fundamental queen of sciences.
It is a different question from that if mathematical abstractions are real things or fictions that are just very good at describing, depicting or modeling of reality, or whatever other verb you would like to use here. Which is actually not very serious question, because there is no big difference between these two characterizations. More fun would be to ask if elementary particles are real things or fictions that are just very good at..., because we expect from them much more to be real than we do from numbers and points. After all, something fundamental must be real, something that we didn't invent.

Originally Posted by someguy1

The map is not the territory; the model is not the thing itself.

I usually believe more to what I see on the ground than to that what I read from the map. Hence, yes, territory is more real than its map. But this doesn't have much to do with those questions. I didn't ask if reality can be reduced to math. The question was if other sciences, which all for them selves try to describe reality, can be reduced to math. Or logic, or whatever is more fundamental.

Maybe I should have said instead: "After all, something real must be fundamental, something that we didn't invent."
Does that sound better?

Originally Posted by hdjur_jcv

I usually believe more to what I see on the ground than to that what I read from the map. Hence, yes, territory is more real than its map. But this doesn't have much to do with those questions. I didn't ask if reality can be reduced to math. The question was if other sciences, which all for them selves try to describe reality, can be reduced to math. Or logic, or whatever is more fundamental.

Oh yes, you're right. Not asking about reality, just other sciences. Well actually I don't know. I suppose physics can be reduced to math ... yet we know that physicists often use math that's not yet been made logically rigorous by mathematicians. I suppose that a physicist might say that they use math, but they would not think that physics is being reduced to math ... because physics requires physical intuition that often goes beyond the current technology of math. I'm thinking of Newton inventing calculus 200 years before calculus could be made rigorous; or renormalization in quantum physics, which was not (still is not? I'm not sure) mathematically rigorous.

In other words I think a physicist would say that physics is much more than math, in that the physicist must have physical intuition, and then needs to invent the math he needs to work out the theory.

If all you had was math, you couldn't figure out any physics because you would not have the results of the experiments. So I don't think you can reduce physics to math. Physics requires experiments and physical intuition.

Pi and phi is not in the physics, it is in our attempt to understand it.

We can only measure rational numbers.

Originally Posted by talanum1

Pi and phi is not in the physics, it is in our attempt to understand it.

What?
Please support this claim.

We can only measure rational numbers.

We don't measure numbers.
If you mean that measurements we make of objects are only of rational numbers then what's your point?

I'd say that the natural numbers are answers to the question "how many?". And I wonder if all mathematical objects can be characterised as answers to (carefully posed) questions.

Then, the questions are invented and the answers discovered.

Somewhere I read a response by a professional mathematician (maybe John Wheeler, or VonNeumann, ...etc.) to the question, "What is mathematics?". His reply, " a manipulation of symbols". I have never read a more concise response, before or since. Not being sure of whom to quote doesn't matter since the truth is in the statement, not the person. The symbols used are a form of shorthand, which can be expanded into meaningful statements in a common language. The preference of math over common language is its restricted grammar or syntax.
Counting was probably the first example of applied math, out of necessity. An agricultural environment would require an inventory of livestock, and tracking the seasonal variations for crops. The natural/counting numbers (positive integers) as formed by Peano type rules, are just symbols representing multiples/sets/collections of elements without regard to their properties. This perspective shows numbers as a convenient accounting tool. A practical procedure could be as simple as making a one to one pairing of pebbles in an urn to a flock of sheep taken into the field. Upon returning, any excess of pebbles would indicate a loss of sheep.
Despite the success of math, applied or theoretical, because of its abstract nature, there should be a disclaimer stating 'all things mathematical, may not correspond to reality'.
We gonna generalize now.
Knowledge is representing the universe in terms of mental constructs (models). This is not by choice but because we enter a preexisting world with no knowledge, and perceive it indirectly. All geometric forms, points, lines, circles. spheres, etc. are not found beyond the mind. As an example, consider the shoreline where water meets the land. From 1 mile up it seems a distinct boundary, but at 500' it's constantly changing, (as we would expect from a dynamic system). Now zoom in on the surface of a small ball bearing in the form of a sphere to the resolution of molecules. From chemistry we know molecules are discrete objects separated by space. Where is the circular cross section of the sphere that is the bearing? It's not there and never was there. Then there is the simple example where three sticks are placed end to end to form a closed figure. Ask what the figure is, and normally the response is 'a triangle'. Remove one stick and ask 'where is the triangle? '.
The mind has a need/propensity to contain things for various reasons such as order, analysis, reference, simplification, control, etc. From here it's a short side trip to the concept of zero.
Set theory defines '{}' the empty set, as containing no elements, which seems to agree with '0', the numerical symbol for zero, i.e. nothing. To elaborate on human activities involving abstractions, there are games with geometric forms that define boundaries, lines and signs on roadways directing traffic, intangible pathways for air traffic control, etc. Any activity outside those boundaries is considered illegal. The key word here is 'boundary' or 'container' as represented by zero. Empty set is a contradiction of terms. If there are no elements, there cannot be a set. Sets are identified by their elements, which qualify as members by their properties. What properties would the non-existent elements have? Container is the preferred term because containment is common practice in most human activities. When defining numbers it becomes necessary to distinguish the container from its contents. In a base x system of representation, the value of 0 as a place holder is obvious, but not so for other reasons. During the development of basic number theory, someone thought 0 should be a number (to make everything uniform?, except it's a lack of number!), ...so much for reason. Maybe we should send in the counting sheep. If that hadn't happened, we wouldn't keep getting nonsense questions like, 'what is x/0?', or all its variations. If x + 0 = x, it's the same thing as doing nothing, a totally redundant operation. There is an unbridgeable gap from 0 to 1, i.e. you can't get something (1) from nothing (0). They are distinct concepts, each with a distinct purpose.

"None" seems to me to be as possible an answer to "how many?" as "one", "two", "three", and the rest.

Originally Posted by Faithfulbeliever

Originally Posted by Strange

There is an interesting question as to whether mathematics is invented or discovered. I think most mathematicians (and, hopefully, most sensible philosophers) think it is discovered. So in that sense mathematics (and therefore numbers) exist.

I want to share a thought on this one, though I realize I could be wrong.

I think One is discovered and the rest of the "mathematics" is invented.

For example, a person can spot an object which no one else has noticed before. This only means that this object was discovered, since it existed even before anyone had noticed it. Now let us say another one of the same kind of object was spotted, then we would normally say that we have found "two" of this kind of objects. We say "two objects" because we know 1+1=2, and it is always so. There can never be "1+1=3" so we would not see "1+1=2" is an invention.

But there is another way to see this whole scenario. It can also be seen as: In reality there is one object that exists and another one of the same kind exists, yet another one and another one could exist,all as single individual objects. At this point we invent math and say there are "4" of these objects. We do this to make it easier on us to keep a track. If these objects were to gain consciousness, they would each consider themselves to be individuals and would not say "there are four of me"(though there are more of its kind in existence). Just like all of us are humans but we would not say there are six billion of me (though there are six billion humans). We invented the addition so to make life easier for us. But in reality there is one and another one, yet another and so on.

You are discussing measurement (counting) and the concept of plurality (the relation of the multple to the unit/ the whole to a part). The object is almost certainly composite, therefore the 'unit' is by definition.
The unit is defined for practical reasons or convenience . Only in physics are there apparent natural units (until someone dicovers they have a structure).

Originally Posted by phyti

Originally Posted by Faithfulbeliever

Originally Posted by Strange

There is an interesting question as to whether mathematics is invented or discovered. I think most mathematicians (and, hopefully, most sensible philosophers) think it is discovered. So in that sense mathematics (and therefore numbers) exist.

I want to share a thought on this one, though I realize I could be wrong.

I think One is discovered and the rest of the "mathematics" is invented.

For example, a person can spot an object which no one else has noticed before. This only means that this object was discovered, since it existed even before anyone had noticed it. Now let us say another one of the same kind of object was spotted, then we would normally say that we have found "two" of this kind of objects. We say "two objects" because we know 1+1=2, and it is always so. There can never be "1+1=3" so we would not see "1+1=2" is an invention.

But there is another way to see this whole scenario. It can also be seen as: In reality there is one object that exists and another one of the same kind exists, yet another one and another one could exist,all as single individual objects. At this point we invent math and say there are "4" of these objects. We do this to make it easier on us to keep a track. If these objects were to gain consciousness, they would each consider themselves to be individuals and would not say "there are four of me"(though there are more of its kind in existence). Just like all of us are humans but we would not say there are six billion of me (though there are six billion humans). We invented the addition so to make life easier for us. But in reality there is one and another one, yet another and so on.

You are discussing measurement (counting) and the concept of plurality (the relation of the multple to the unit/ the whole to a part). The object is almost certainly composite, therefore the 'unit' is by definition.
The unit is defined for practical reasons or convenience . Only in physics are there apparent natural units (until someone dicovers they have a structure).

Well, yes I was talking about counting and counting is a form of measurement and measurements are invented by humans. Counting is also the very basic math, since all we do while counting is add a number (or unit count) to the available number(s). So counting can be viewed as simple addition. If we were to view the entire universe as one single entity and everything within it as a part or structure of One Whole, then how can "number count" of different parts of One Singular Entity can be viewed as a discovery? Is it not apparent that we humans invented the number count of units as a measurement within this singular entity we call universe?

Originally Posted by Faithfulbeliever

Well, yes I was talking about counting and counting is a form of measurement

Is it?

and measurements are invented by humans

What nonsense.
Animals have to be able measure (judge distances).
And a number of (non-human) creatures can count - for example crows (and presumably other corvidae) know how to "chunk".

So counting can be viewed as simple addition.

So counting is arithmetic then, and not measuring?

If we were to view the entire universe as one single entity and everything within it as a part or structure of One Whole, then how can "number count" of different parts of One Singular Entity can be viewed as a discovery?

Except those different parts are discrete elements.
You're inventing a premise - "universe as a singular whole" in order to support your own (speculative) conclusion.

Is it not apparent that we humans invented the number count of units as a measurement within this singular entity we call universe?

Not at all.

Originally Posted by Dywyddyr

Originally Posted by Faithfulbeliever

Well, yes I was talking about counting and counting is a form of measurement

Is it?

and measurements are invented by humans

What nonsense.
Animals have to be able measure (judge distances).
And a number of (non-human) creatures can count - for example crows (and presumably other corvidae) know how to "chunk".

So counting can be viewed as simple addition.

So counting is arithmetic then, and not measuring?

If we were to view the entire universe as one single entity and everything within it as a part or structure of One Whole, then how can "number count" of different parts of One Singular Entity can be viewed as a discovery?

Except those different parts are discrete elements.
You're inventing a premise - "universe as a singular whole" in order to support your own (speculative) conclusion.

Is it not apparent that we humans invented the number count of units as a measurement within this singular entity we call universe?

Not at all.

The link you posted kind of explains the difference between the "numbers as measurements" and "numbers as counts", but I had only said: "the counting itself is a form of measurement". For example, when we simply count objects, we do it so we can know the number of such objects available. So how can counting be not considered as a form of measurement?

Animals do judge the distances, but is that same as actually doing the measurement? Can the animal actually measure the distance in terms of COUNTING? Let us say there is a distance of 50 yards between a lion and a zebra, then lion will definitely judge the distance it terms of the closeness he has gained to zebra for a hunt, but can the lion actually count in terms of any measurement at all? Well, no animal knows about the human inventions such as "yards, KM, Miles" etc.

Anyway, let us just agree for a minute that counting is not a measurement. Tell me then, how is the simple addition not an invention, regardless of it being a form of measurement or not?

Human body is composed of many different parts yet we consider it to be one body, but you have trouble accepting the universe as one entity? So what if there are objects in the universe which are separated by space? Is not each particle within every atom in our body separated by space? There is so much we do not know about the universe, then how do you even know if the objects in universe somehow has an influence on all other objects in it or not?

And finally, my post was meant as more of a question to Phyti and not a speculative conclusion. I asked him because his posts have clarity and to me it looks like his posts are unbiased. On other hand you seem to have a serious problem with my screen name, as that's how it appears looking at all your responses to my posts. Id that's not the case and you think all my posts are nonsensical then please put me on your ignore list. Anyway this is my last and final response to you.

Originally Posted by Faithfulbeliever

The link you posted kind of explains the difference between the "numbers as measurements" and "numbers as counts", but I had only said: "the counting itself is a form of measurement".

In other words there are (at least) two distinct ways of looking at numbers. One is counting, one is measuring - which does not support "counting is (a form of) measuring".

For example, when we simply count objects, we do it so we can know the number of such objects available. So how can counting be not considered as a form of measurement?

What are we measuring?

Animals do judge the distances, but is that same as actually doing the measurement?

Huh?
They can "measure" well enough to judge whether the target is in leaping range.
I.e. make a direct comparison between two distances.

Well, no animal knows about the human inventions such as "yards, KM, Miles" etc.

Oops, they're simply the designations we apply to specified units of distance.

Tell me then, how is the simple addition not an invention, regardless of it being a form of measurement or not?

Oh wait.
Since YOU are the one claiming that addition is an invention then you should be the one to support it. (I already pointed out - post #31 - that "because 1 "exists" the rest of mathematics is a concomitant of 1").

Human body is composed of many different parts yet we consider it to be one body, but you have trouble accepting the universe as one entity?

Oops. Apples and oranges.

So what if there are objects in the universe which are separated by space? Is not each particle within every atom in our body separated by space? There is so much we do not know about the universe, then how do you even know if the objects in universe somehow has an influence on all other objects in it or not?

Oh dear. I'm not even going there.

On other hand you seem to have a serious problem with my screen name, as that's how it appears looking at all your responses to my posts.

Really?
Where have I brought up your screen name?
Where I have argued against anything other than what you have written?
Paranoid much?
There certainly is some invention happening in this thread. You do what eisegesis means, don't you?

Id that's not the case and you think all my posts are nonsensical then please put me on your ignore list.

And let your nonsense go unchallenged?
Hardly.

Anyway this is my last and final response to you.

IOW you're not going to reply to any posts I make pointing out your errors?

PS: I note you didn't make any mention whatsoever of this point - And a number of (non-human) creatures can count.
Maybe because it wrecks your argument?

Originally Posted by Faithfulbeliever

On other hand you seem to have a serious problem with my screen name, as that's how it appears looking at all your responses to my posts.

On consideration, there's probably a whole thesis for someone studying psychology on the subject of why would someone choose that particular user name for posting on science forum.
Overweening hubris?
A metaphorical death wish?
An inability to read which way the wind is blowing?

I don't want to say much about whether or not numbers exist "out there" or whether they are merely human inventions as I just don't know. I am inclined towards the latter view, but it does have problems. If numbers are human inventions, it seems odd that they should have simple features which humans don't understand or are unable to account for. I am thinking of such things as Goldbach's conjecture. The mysterious nature of these features does suggest that there is something to do with numbers "out there" that we haven't yet discovered.
Back to square 1.

Originally Posted by Faithfulbeliever

The link you posted kind of explains the difference between the "[FONT=Verdana, Arial, Helvetica, sans-serif][COLOR=#000000]numbers as measurements" and "numbers as counts", but I had only said: "the counting itself is a form of measurement". For example, when we simply count objects, we do it so we can know the number of such objects available. So how can counting be not considered as a form of measurement?

Because, as that article explains, counting and measurement are not the same thing.

Tell me then, how is the simple addition not an invention, regardless of it being a form of measurement or not?

Because it exists in nature, whether we apply numerals or words to it?

Human body is composed of many different parts yet we consider it to be one body, but you have trouble accepting the universe as one entity? So what if there are objects in the universe which are separated by space? Is not each particle within every atom in our body separated by space? There is so much we do not know about the universe, then how do you even know if the objects in universe somehow has an influence on all other objects in it or not?

Everything in the universe is influenced (even if insignificantly) by everything else. So what? You have one body; within that you have one heart, two kidneys, billions of cells, etc. I'm not sure what point you are trying to make.

Originally Posted by Dywyddyr

You do what eisegesis means, don't you?

I didn't. Thank you.

And a number of (non-human) creatures can count.

And babies can count before they can speak or have had much chance to learn/invent anything.

And some animals can measure, using their own units, and then communicate those measurements to others. (The bee's "waggle dance" is the obvious example.)

hdjur_jcv #50
"Can all science be reduced to math? "

Since math is the language used by the sciences in the course of measurement, the answer would be no.

someguy1 #51
"What I'm saying is that I'm troubled by the phrase "reduced to." When we model natural phenomena with math, we are not explaining the underlying causes of the phenomena; rather, we're only creating a mathematical model."

I agree and will add, modeling is typically in geometric forms, with relations/measurements expressed in math terms. Science can only study what it can measure.

Regarding a question lurking in the background: Are abstractions (including numbers) real or imagined?
Define reality as: the behavior of the universe independently of the mind.
Define perception as: the mental image of the universe formed from sensory input. The image is not the universe, but the mind is an object in the universe, therefore the images are also real and physical in this sense, but only in the viewers mind. There are also exceptions such as an hallucinogenic drug producing mental images that have no physical counterpart outside the mind.

Zeno's Paradox - Achilles

Zeno did not argue that motion is impossible.
Using a geometric progression, he divides a distance into a series of smaller distances.
This progression is a continuing process or iteration loop and therefore by it's definition never ends. To move a fraction of a distance requires the same fraction of time needed to move the whole distance. This is inferred or explicitly stated such as, "while Achilles moves to...", i.e. the motions are simultaneous.
The key is, if both distance and time are divided in the same ratio, the closing speed is still constant and the time required to complete the motion is a simple division of (initial separation)/(difference in speed). This solution makes no use of an infinite series.
By definition an infinite (unending) series that converges to a limit (which is what he actually defined) can never equal the limit without contradicting itself. (this is another issue in number theory)
Zeno was arguing that the concept of continuous space and time led to illogical results.

Originally Posted by Strange

Originally Posted by Faithfulbeliever

The link you posted kind of explains the difference between the "[FONT=Verdana, Arial, Helvetica, sans-serif][COLOR=#000000]numbers as measurements" and "numbers as counts", but I had only said: "the counting itself is a form of measurement". For example, when we simply count objects, we do it so we can know the number of such objects available. So how can counting be not considered as a form of measurement?

Because, as that article explains, counting and measurement are not the same thing.

Tell me then, how is the simple addition not an invention, regardless of it being a form of measurement or not?

Because it exists in nature, whether we apply numerals or words to it?

Human body is composed of many different parts yet we consider it to be one body, but you have trouble accepting the universe as one entity? So what if there are objects in the universe which are separated by space? Is not each particle within every atom in our body separated by space? There is so much we do not know about the universe, then how do you even know if the objects in universe somehow has an influence on all other objects in it or not?

Everything in the universe is influenced (even if insignificantly) by everything else. So what? You have one body; within that you have one heart, two kidneys, billions of cells, etc. I'm not sure what point you are trying to make.

We have one body and as you said within that we have various organs and billions of cells. The reason I had mentioned the body as example in my previous post was to demonstrate how the whole of universe can be viewed as a one singular entity although it has variety of different objects within it; just as we view our body as 'one' regardless of its structure.

You say addition (number counts) exists in nature. I think saying that 'addition' exists in nature is similar to saying units such as "Miles, KM, Meters...etc" exists in nature. In reality there only exists the distance between point 'A' and point 'B'. We invented the above mentioned units to measure that distance. Nature as nothing to do with such measurements, the only thing present in nature is the distance. Similarly nature offers us a variety of different objects with this one singular universe. Nature does not do the counts of this various objects, we do the counts so to keep track of these huge variety that nature has to offer us. We do it because of our own limited ability of perception, while the nature itself is far greater. Another point is that we do not even know if our universe is infinite, and if it is infinite with infinite objects present within it, then the objects in it would be simply beyond any counts and attempting to count the infinity would be just insanity. So, the point I was trying to make is, nature only offers us our great universe and a variety of objects within it and we apply the number counts to these objects to keep up with the nature, hence invent math!

(on side note: If we all accept this concept of plurality within singularity, it would be much easier for us to accept the nature's way of one singular human species with plurality within, consequently much less man made problems!)

Originally Posted by Faithfulbeliever

We have one body and as you said within that we have various organs and billions of cells. The reason I had mentioned the body as example in my previous post was to demonstrate how the whole of universe can be viewed as a one singular entity although it has variety of different objects within it; just as we view our body as 'one' regardless of its structure.

Apples and oranges.
Again.

I think saying that 'addition' exists in nature is similar to saying units such as "Miles, KM, Meters...etc" exists in nature.

Then your thinking is faulty.

In reality there only exists the distance between point 'A' and point 'B'. We invented the above mentioned units to measure that distance.

We invented the names - not the distance.

Nature as nothing to do with such measurements, the only thing present in nature is the distance.

Not quite: variation in distance counts in nature i.e. the "measurement".

Nature does not do the counts of this various objects

Wrong.
Nature "counts", for example, electrons in an orbital. Nature "counts" arms on a snowflake. In short: nature "counts".

We do it because of our own limited ability of perception, while the nature itself is far greater.

Nope.

Another point is that we do not even know if our universe is infinite, and if it is infinite with infinite objects present within it, then the objects in it would be simply beyond any counts and attempting to count the infinity would be just insanity.

Entirely beside the point.

hence invent math!

You obviously haven't read JonG's post #69. (Or you've decided to ignore it because you can't reply in a worthwhile manner).

(on side note: If we all accept this concept of plurality within singularity, it would be much easier for us to accept the nature's way of one singular human species with plurality within, consequently much less man made problems!)

And off to La La Land we go...

Originally Posted by Faithfulbeliever

We have one body and as you said within that we have various organs and billions of cells. The reason I had mentioned the body as example in my previous post was to demonstrate how the whole of universe can be viewed as a one singular entity although it has variety of different objects within it; just as we view our body as 'one' regardless of its structure.

I'm still not sure why you think that is relevant. Even if we regard the universe as "one" it is still made up of many things that can be counted.

You say addition (number counts) exists in nature. I think saying that 'addition' exists in nature is similar to saying units such as "Miles, KM, Meters...etc" exists in nature. In reality there only exists the distance between point 'A' and point 'B'. We invented the above mentioned units to measure that distance.

Again, you are confusing counting and measuring. We have already established, quite clearly, that they are not the same thing. Yes, we invented arbitrary units in which to do measuring but, again, that is irrelevant. You can measure without using any such units (just ask the ancient Greeks).

Addition is also not the same as counting. Addition occurs in nature and many animals can count (as noted, you seem to ignore this).

So, the point I was trying to make is, nature only offers us our great universe and a variety of objects within it and we apply the number counts to these objects to keep up with the nature, hence invent math!

Counting is not math. Non-human animals can count. There is one moon in the sky and 100 billion stars in the galaxy whether anyone counts them or not.

(on side note: If we all accept this concept of plurality within singularity, it would be much easier for us to accept the nature's way of one singular human species with plurality within, consequently much less man made problems!)

I have no idea what that means.

Originally Posted by Strange

Originally Posted by Faithfulbeliever

We have one body and as you said within that we have various organs and billions of cells. The reason I had mentioned the body as example in my previous post was to demonstrate how the whole of universe can be viewed as a one singular entity although it has variety of different objects within it; just as we view our body as 'one' regardless of its structure.

I'm still not sure why you think that is relevant. Even if we regard the universe as "one" it is still made up of many things that can be counted.

You say addition (number counts) exists in nature. I think saying that 'addition' exists in nature is similar to saying units such as "Miles, KM, Meters...etc" exists in nature. In reality there only exists the distance between point 'A' and point 'B'. We invented the above mentioned units to measure that distance.

Again, you are confusing counting and measuring. We have already established, quite clearly, that they are not the same thing. Yes, we invented arbitrary units in which to do measuring but, again, that is irrelevant. You can measure without using any such units (just ask the ancient Greeks).

Addition is also not the same as counting. Addition occurs in nature and many animals can count (as noted, you seem to ignore this).

So, the point I was trying to make is, nature only offers us our great universe and a variety of objects within it and we apply the number counts to these objects to keep up with the nature, hence invent math!

Counting is not math. Non-human animals can count. There is one moon in the sky and 100 billion stars in the galaxy whether anyone counts them or not.

(on side note: If we all accept this concept of plurality within singularity, it would be much easier for us to accept the nature's way of one singular human species with plurality within, consequently much less man made problems!)

I have no idea what that means.

I think, "can be counted" does not automatically mean counting exists it nature itself. Weather the counting is done by human or animal is irrelevant. Counting is simply a way which is invented to keep up with the plurality that nature has to offer, within its own singularity. Just like you said Moon is 'one' and 'billions' of stars, however counting is not done by the nature itself. Counting is only done by creatures. If there are no conscious beings left in nature, then although billions stars will be in existence, but the concept of counting them will not be in existence, since the counting is an invention. Not seeing 'counting' as 'addition' or viceversa does not help your point of view.

Whatever units did the ancient Greeks used to do measurements does not matter. If they had their own invented units, it does not support that measurement occurs in nature itself. Nature is simply 'As Is'.

Anyway, I hold the opinion that math is invented and you are of opinion that it is discovered. Not agreeing is okay, and not the end of the world for either one of us!

Originally Posted by Faithfulbeliever

I think, "can be counted" does not automatically mean counting exists it nature itself. Weather the counting is done by human or animal is irrelevant. Counting is simply a way which is invented to keep up with the plurality that nature has to offer, within its own singularity. Just like you said Moon is 'one' and 'billions' of stars, however counting is not done by the nature itself. Counting is only done by creatures. If there are no conscious beings left in nature, then although billions stars will be in existence, but the concept of counting them will not be in existence, since the counting is an invention. Not seeing 'counting' as 'addition' or viceversa does not help your point of view.

Whatever units did the ancient Greeks used to do measurements does not matter. If they had their own invented units, it does not support that measurement occurs in nature itself. Nature is simply 'As Is'.

Anyway, I hold the opinion that math is invented and you are of opinion that it is discovered. Not agreeing is okay, and not the end of the world for either one of us!

I'm not intending to change the subject, but I want to ask this question in order to understand your point of view.

In the earth-moon system, there are two bodies. Clearly the concept of "two" and the idea of counting are human abstractions. [Ignoring for the moment the fact that animals have a sense of number]

Before there were humans, were the earth and moon attracted to each other according to the law of gravity?

Is the law of gravity inherent in reality, but counting not? Do you distinguish these cases?

Originally Posted by Faithfulbeliever

I think, "can be counted" does not automatically mean counting exists it nature itself.

No. But it DOES mean that the "numbers" are there in nature to be counted.

Weather the counting is done by human or animal is irrelevant.

Because if it wasn't irrelevant you'd have to admit that your "human invention" claim is wrong. Got it.

Counting is simply a way which is invented to keep up with the plurality that nature has to offer, within its own singularity.

Specious crap.

Whatever units did the ancient Greeks used to do measurements does not matter. If they had their own invented units, it does not support that measurement occurs in nature itself.

Correct.
The units don't support that argument, but the facts do, as shown.

Anyway, I hold the opinion that math is invented and you are of opinion that it is discovered. Not agreeing is okay, and not the end of the world for either one of us!

Ah, the old cop out.
"I've been shown exactly how much and where I'm wrong, so let's agree to disagree before I have to admit my error".
Your opinion is unsupported by the facts.
It's that simple.

Originally Posted by someguy1

Originally Posted by Faithfulbeliever

I think, "can be counted" does not automatically mean counting exists it nature itself. Weather the counting is done by human or animal is irrelevant. Counting is simply a way which is invented to keep up with the plurality that nature has to offer, within its own singularity. Just like you said Moon is 'one' and 'billions' of stars, however counting is not done by the nature itself. Counting is only done by creatures. If there are no conscious beings left in nature, then although billions stars will be in existence, but the concept of counting them will not be in existence, since the counting is an invention. Not seeing 'counting' as 'addition' or viceversa does not help your point of view.

Whatever units did the ancient Greeks used to do measurements does not matter. If they had their own invented units, it does not support that measurement occurs in nature itself. Nature is simply 'As Is'.

Anyway, I hold the opinion that math is invented and you are of opinion that it is discovered. Not agreeing is okay, and not the end of the world for either one of us!

I'm not intending to change the subject, but I want to ask this question in order to understand your point of view.

In the earth-moon system, there are two bodies. Clearly the concept of "two" and the idea of counting are human abstractions. [Ignoring for the moment the fact that animals have a sense of number]

Before there were humans, were the earth and moon attracted to each other according to the law of gravity?

Is the law of gravity inherent in reality, but counting not? Do you distinguish these cases?

I do not see a reason to deny that law of gravity exists in nature, so I have no reason to deny their influence on each other before any living beings existed. (In my previous posts I have even acknowledge that billions of stars would still be in existence even if there were no beings with conscious to do the counting.) I have somewhere in one of my previous posts also acknowledge that 1+1 is always 2 and it can never be 3, hence we do not see this equation as an invention. But the point I have been arguing all along is, who came up with this whole deal of 1+1= ? in the first place. Does this question exist in nature? Is this question itself not an invention? Law of gravity is in nature, but does the nature also calculate that '1' planet (earth) and its '1' satellite (moon) adds up to '2' objects or is it that the creatures who does the calculation to keep up with the plurality of nature? The point I am trying to make is really simple: within the singularity of nature, there exists a vast variety and to keep up with its vastness, each conscious creature according to its own ability invents a way to keep up with nature.

Originally Posted by Faithfulbeliever

The point I am trying to make is really simple: within the singularity of nature

I still don't understand why you are going on about this "singularity of nature" thing as if it were somehow relevant.

each conscious creature according to its own ability invents a way to keep up with nature.

Right. So it is not a human invention after all. And we do it to "keep up with nature" - that would be because numbers exist in nature. Thank you.

Originally Posted by Strange

Originally Posted by Faithfulbeliever

The point I am trying to make is really simple: within the singularity of nature

I still don't understand why you are going on about this "singularity of nature" thing as if it were somehow relevant.

Because that means if we all join hands and sing Kumbaya while hugging bluebirds every single problem in the universe will be solved.

Originally Posted by Strange

each conscious creature according to its own ability invents a way to keep up with nature.

Right. So it is not a human invention after all. And we do it to "keep up with nature" - that would be because numbers exist in nature. Thank you.

Oh good! so finally we kind of agree upon something. "Methods are invented by living creatures to keep up with the variety that nature has to offer"!

Zeno's Paradox - Achilles

Zeno did not argue that motion is impossible.
Using a geometric progression, he divides a distance into a series of smaller distances.
This progression is a continuing process or iteration loop and therefore by it's definition never ends. To move a fraction of a distance requires the same fraction of time needed to move the whole distance. This is inferred or explicitly stated such as, "while Achilles moves to...", i.e. the motions are simultaneous.
The key is, if both distance and time are divided in the same ratio, the closing speed is thusl constant and the time required to complete the motion is a simple division of (initial separation)/(difference in speed). This solution makes no use of an infinite series.
By definition an infinite (unending) series that converges to a limit (which is what he actually defined) can never equal the limit without contradicting itself.
Zeno was arguing that the concept of continuous space and time led to illogical results.

Predators such as a lion don't need to measure distance. That's why of all those that have been tagged for tracking, none were found carrying a tape or laser. I would more likely expect to find night vision goggles.
They make judgments about the circumstances at the moment, based on past experience. They remember that they succeed in bringing down an unhealthy animal more often than a healthy one. They don't overpower elephants very often. If the mother of the young water buffalo is nearby, it's better to look elsewhere. Just as with humans, life is a learning experience.
The behavior in the animal kingdom is primarily instinctive/programmed, with the ability to adapt to the environment. If it’s not instinctive, it’s behavior learned from parents or other siblings. Despite their good or bad experiences, they still behave the same, year to year, generation to generation. Isn't it great to have so much diversity as humans!
In their defense, animals are very under-rated as to their abilities.

Originally Posted by phyti

Predators such as a lion don't need to measure distance.

No?

That's why of all those that have been tagged for tracking, none were found carrying a tape or laser. I would more likely expect to find night vision goggles.

Well duh!
How do you think lion-taggers supplement their income? By selling tapes and laser rangers of dubious provenance.

They make judgments about the circumstances at the moment, based on past experience.

Oh wait!
What is measurement?
It's a comparison (judgement) of one length (or whatever) with another.

They remember that they succeed in bringing down an unhealthy animal more often than a healthy one.

Yeah.
They also, for example, remember that they have never succeeded in leaping half a mile ¹ to catch unhealthy prey, but that something 3 feet away ² is do-able. Between those distances judgement, comparison and measurement ³ is crucial.

1 Although I concede that "half a mile" wouldn't be the terminology the lion uses ⁴, it's a human terminology ⁵.
2 Or, lion-wise, "easy-peasy".
3 Measurement doesn't have to be nanometre-precise, it simply has be sufficiently accurate for the purpose intended.
4 In lion-speak it's called "far too f*ckin' far to jump".
5 And only particular humans at that.

Originally Posted by Faithfulbeliever

Originally Posted by Strange

each conscious creature according to its own ability invents a way to keep up with nature.

Right. So it is not a human invention after all. And we do it to "keep up with nature" - that would be because numbers exist in nature. Thank you.

Oh good! so finally we kind of agree upon something.

Only if you agree that numbers exist in nature and were not invented by man. I don't think I agree with anything you have written, otherwise.

Originally Posted by Strange

Originally Posted by Faithfulbeliever

Originally Posted by Strange

each conscious creature according to its own ability invents a way to keep up with nature.

Right. So it is not a human invention after all. And we do it to "keep up with nature" - that would be because numbers exist in nature. Thank you.

Oh good! so finally we kind of agree upon something.

Only if you agree that numbers exist in nature and were not invented by man. I don't think I agree with anything you have written, otherwise.

In that case, I'll just rewrite what I already written above , "its okay to not to agree......"

(Phyti, your posts on here has led me to some very interesting links, I'll be doing a lot of reading when my work schedule allows me to do so. Thanks)

Originally Posted by Faithfulbeliever

"its okay to not to agree......"

Why do people (especially those in the wrong) think this is in any way a valid response?
“Everyone is entitled to his own opinion, but not to his own facts.”

Do numbers exist or are they figments of our imagination?

This question appears to boil down to a definition of "exist".

1) If we consider that something which exists must be at some place at some time, then material bodies and radiation exist, but abstract entities such as numbers don't as they have no location. However, this restrictive view of existence is at odds with how the word "exist" is generally used. For example, many people would claim that poverty exists, but poverty is abstract and has no location in the known universe. (However, one could regard the statement that poverty exists as a woolly extrapolation from the fact that poor people exist and they do have a location).

2) If we consider that numbers do not exist and that, for example, in referring to five cows in a field the number five is simply a label invented by human beings, then we have to account for the fact that there is more to 5 than it being a label. It isn't like the label "poverty" because it has properties such as being a prime number and these properties seem to be unrelated to its role as a label.

So if numbers exist, where do they exist? This might seem like a silly question to some, but to believe that something has an existence outside the human mind, but that there is no location where it exists, suggests that it exists is some sort of undefined spiritual universe.

Originally Posted by JonG

suggests that it exists is some sort of undefined spiritual universe.

Auugh!
"Conceptual universe" possibly.
But "spiritual"?

Originally Posted by JonG

Do numbers exist or are they figments of our imagination?

This question appears to boil down to a definition of "exist".

1) If we consider that something which exists must be at some place at some time, then material bodies and radiation exist, but abstract entities such as numbers don't as they have no location. However, this restrictive view of existence is at odds with how the word "exist" is generally used. For example, many people would claim that poverty exists, but poverty is abstract and has no location in the known universe. (However, one could regard the statement that poverty exists as a woolly extrapolation from the fact that poor people exist and they do have a location).

2) If we consider that numbers do not exist and that, for example, in referring to five cows in a field the number five is simply a label invented by human beings, then we have to account for the fact that there is more to 5 than it being a label. It isn't like the label "poverty" because it has properties such as being a prime number and these properties seem to be unrelated to its role as a label.

So if numbers exist, where do they exist? This might seem like a silly question to some, but to believe that something has an existence outside the human mind, but that there is no location where it exists, suggests that it exists is some sort of undefined spiritual universe.

I was only talking about 'existence' in terms of something which can be touched, smelled, heard, seen or tasted. If one takes the understanding of 'existence' to a completely next level which is beyond this petty understanding I mentioned above, then its a whole different story! You are lucky you did not get attacked from all directions for even writing the word I highlighted in your post. I appreciate your input!

Originally Posted by Faithfulbeliever

I was only talking about 'existence' in terms of something which can be touched, smelled, heard, seen or tasted.

In other words you were making a completely specious argument and disputing something that no one here has even put forward.
Well done.

If one takes the understanding of 'existence' to a completely next level which is beyond this petty understanding I mentioned above, then its a whole different story!

Quite.
Maybe you should read that story, and then try participating.

Originally Posted by Dywyddyr

Originally Posted by phyti

Predators such as a lion don't need to measure distance.

No?

That's why of all those that have been tagged for tracking, none were found carrying a tape or laser. I would more likely expect to find night vision goggles.

Well duh!
How do you think lion-taggers supplement their income? By selling tapes and laser rangers of dubious provenance.

They make judgments about the circumstances at the moment, based on past experience.

Oh wait!
What is measurement?
It's a comparison (judgement) of one length (or whatever) with another.

They remember that they succeed in bringing down an unhealthy animal more often than a healthy one.

Yeah.
They also, for example, remember that they have never succeeded in leaping half a mile ¹ to catch unhealthy prey, but that something 3 feet away ² is do-able. Between those distances judgement, comparison and measurement ³ is crucial.

1 Although I concede that "half a mile" wouldn't be the terminology the lion uses ⁴, it's a human terminology ⁵.
2 Or, lion-wise, "easy-peasy".
3 Measurement doesn't have to be nanometre-precise, it simply has be sufficiently accurate for the purpose intended.
4 In lion-speak it's called "far too f*ckin' far to jump".
5 And only particular humans at that.

The point is, judgment of distance is not the primary factor. The lion doesn't know how long the chase will be, and it's success does not depend on the initial distance. It's a very dynamic scenario which will require more judgments and reaccessments as it proceeds, with experience the dominant factor.

I am not implying animals don't have a sense of distance and quantity, but that they have no need of a formal number or measurement system, i.e. it's a 'fly by the seat of your pants' thing.

Originally Posted by JonG

Do numbers exist or are they figments of our imagination?

This question appears to boil down to a definition of "exist".

1) If we consider that something which exists must be at some place at some time, then material bodies and radiation exist, but abstract entities such as numbers don't as they have no location. However, this restrictive view of existence is at odds with how the word "exist" is generally used. For example, many people would claim that poverty exists, but poverty is abstract and has no location in the known universe. (However, one could regard the statement that poverty exists as a woolly extrapolation from the fact that poor people exist and they do have a location).

2) If we consider that numbers do not exist and that, for example, in referring to five cows in a field the number five is simply a label invented by human beings, then we have to account for the fact that there is more to 5 than it being a label. It isn't like the label "poverty" because it has properties such as being a prime number and these properties seem to be unrelated to its role as a label.

So if numbers exist, where do they exist? This might seem like a silly question to some, but to believe that something has an existence outside the human mind, but that there is no location where it exists, suggests that it exists is some sort of undefined spiritual universe.

Regarding a question lurking in the background: Are abstractions (including numbers) real or imagined?
Define reality as: the behavior of the universe independently of the mind.
Define perception as: the mental image of the universe formed from sensory input. The image is in the mind which is an object in the universe, therefore the images are also real and physical in this sense, but only in the viewers mind. There are also exceptions such as an hallucinogenic drug producing mental images that have no physical counterpart outside the mind.

Originally Posted by phyti

The point is, judgment of distance is not the primary factor.

Then you're confused.
The point is that the lion has to be able to judge, and actually make that judgement, whether or not the target is in range or not before it jumps.

The lion doesn't know how long the chase will be, and it's success does not depend on the initial distance. It's a very dynamic scenario which will require more judgments and reaccessments as it proceeds, with experience the dominant factor.

What?
We're talking here, specifically, about making a leap.

I am not implying animals don't have a sense of distance and quantity, but that they have no need of a formal number or measurement system, i.e. it's a 'fly by the seat of your pants' thing.

Regardless of whether it's "formal" or not there is a comparison made - target at distance "X", ability to leap distance "Y".
If X <= Y then the lion can leap (or more probably it's somewhat fuzzier, since it's not that precise, if X~<= Y then leap).
Two distances are compared - that is a measurement.
Comparison is the basis of measurement.
Whether the basis of comparison is a formal, standardised unit, or an estimate made from experience, is largely irrelevant.

[QUOTE=Faithfulbeliever;441833][QUOTE=Strange;441822][QUOTE=Faithfulbeliever;441796]

Originally Posted by Strange

each conscious creature according to its own ability invents a way to keep up with nature.

(Phyti, your posts on here has led me to some very interesting links, I'll be doing a lot of reading when my work schedule allows me to do so. Thanks)

Wanted to add this earlier, but got behind.

Faithfulbeliever #64
“Well, yes I was talking about counting and counting is a form of measurement and measurements are invented by humans. Counting is also the very basic math, since all we do while counting is add a number (or unit count) to the available number(s). So counting can be viewed as simple addition. If we were to view the entire universe as one single entity and everything within it as a part or structure of One Whole, then how can "number count" of different parts of One Singular Entity can be viewed as a discovery? Is it not apparent that we humans invented the number count of units as a measurement within this singular entity we call universe?”

Dywyddyr # 65
His response to #64
…and the continuing exchange.

Measurement in a very general sense: to compare an object to a reference object (standard) to evaluate a property /relation. The color of an object could be compared to a set of color samples, with the resulting value being a word representing a color. A quality control program might use a go-nogo gage to select defects, a yes or no result. These are examples of measurements not involving counting.
For this thread, measurement will determine how much or how many. The standard or 'unit of measure' (um) depends primarily on the physical nature of the subject measured. Discrete objects can be counted individually or as sets, such as a pair of shoes (based on anatomy), or a set of golf clubs (based on the game). Food has multiple um such as ounce, pound, gram, kilogram, liter, etc., allowing for convenient sized packaging. For the purpose of simplification, we have the astronomical unit (A.U.) and the light year (ly), for extra large distance measurement.
Even though matter is in discrete forms, a fluid can be defined as continuous, with a uniform density, and measured via a defined volume of space. This is more efficient and practical than counting molecules.
To measure the length of an object one end is aligned to the zero mark on a ruler, and the label of the mark nearest the other end is the length. If the marks were not labeled, they would be counted, and if marked, they would have been counted for the correct labeling. Counting is at least a requirement of measurement involving numerical results.

These few examples should show the um is whatever it's defined to be, and has no special significance beyond serving a specified purpose. The universe by definition is all possible things discovered or not. If we switch to discussing a galaxy, i.e. a part of the universe, then we are no longer considering the universe as a unit, but a composite object. The words that represent the entities discussed, universe, galaxy, star, etc, represent units, only within a certain context.