So, metaphysics then.

[pErvinalia]

The 'problem' is that it's not clear what a unity is in regards to counting. Is a cloud 1 object, or is it multiple objects?

[Hermit]

The 'problem' is that it's not clear what a unity is in regards to counting. Is a cloud 1 object, or is it multiple objects?

That is no more of a problem than defining a crowd. Earth is crowded with bazillions of bacteria and trillions of insects. There was a crowd of 175,000 people at the recent Glastonbury festival. A bus might be crowded with 20 people. Three's a crowd. A metaphysical problem might be crowding my mind. A cloud might be a barely perceptible whisp of water droplets or a humongous bank of an advancing thunderstorm. Units are rarely precisely defined, and even they may change over time. The metre used to be defined by some length of a piece of very inert metal resting in a Paris museum. Now it is defined by x vibrations per second of some crystal.

[mistermack]

The 'problem' is that it's not clear what a unity is in regards to counting. Is a cloud 1 object, or is it multiple objects?

That is no more of a problem than defining a crowd. Earth is crowded with bazillions of bacteria and trillions of insects. There was a crowd of 175,000 people at the recent Glastonbury festival. A bus might be crowded with 20 people. Three's a crowd. A metaphysical problem might be crowding my mind. A cloud might be a barely perceptible whisp of water droplets or a humongous bank of an advancing thunderstorm. Units are rarely precisely defined, and even they may change over time. The metre used to be defined by some length of a piece of very inert metal resting in a Paris museum. Now it is defined by x vibrations per second of some crystal.

It's defined by a combination of time (presumably given by the crystal) and the speed of light.
The distance traveled by light in a vacuum in a measured period.

I don't know much about metaphysics. From what I remember, it started off as woo, and progressed into some kind of science. Although not the testable-by-experiment science. So it's claim to be science is shaky. But that doesn't mean it's futile. It's just not in that particular bracket.
That's just my impression of it, it might be something else entirely.

[JimC]

With at least the majority of organisms, the skin or exoskeleton is a pretty defined boundary. We have very little difficulty in counting most organisms (slime-moulds could get a little tricky, I suppose)

On the dog and scent thing, it's not going to confuse a hunting dog - he'll pounce on the actual organism, not its scent trail...

I certainly not saying that every aspect of physical reality has clear, discrete boundaries. But there are plenty that do, and enumerating collections of them is not a waffly, vague process, it is very clear-cut indeed. All of this, to me, is saying that the numbers of a given set of physical objects is an empirical fact about that collection of object, which gives the number concerned a reality which is not just an abstraction.

Interesting, are clouds physical objects? or are they merely a collection of water droplets?

Yeah, this is what I was getting at with the galaxy super-clusters (because I couldn't think of a good example at the macro scale we exist at).

@Jim you explained away the dog, adequately, as it relies on sight as well as scent. But bats and other animals that don't rely on sight would presumably form different boundaries to us.

To take the bat example first; a bat relying on ultrasound to detect a moth would still perceive it as a localised object with boundaries; certainly enough to grab and eat it in mid-air... Sure, the sensory modality is different, which poses interesting questions in terms of bat consciousness, but no issues as far as the discreteness of the flying invertebrates it perceives, IMO.

With clouds, etc. I did say that not all situations in the physical world present us with clear-cut examples of discreteness, only that there are sufficient examples so that sets of discrete, physical objects exist. Hermits point about naming a collection of water droplets as a cloud is fair enough in a pragmatic sense, though many such examples (e.g. a "beach") do not have obvious boundaries; it may be that the set of "beaches" in Australia is not, in principle, countable...

All of this, to me, is saying that the numbers of a given set of physical objects is an empirical fact about that collection of object, which gives the number concerned a reality which is not just an abstraction.

That sounds a bit wibbly to me. What else is there other than materials and ideas? Is there some other form of "stuff"?

Take a situation with a collection of 9 pebbles, clustered together but separate and countable. Then take a second situation a little way off of 8 pebbles of a similar type. Each pebble has a set of physical properties which can be measured to some level of accuracy. So does each cluster of pebbles, but the most obvious measurable quantity of the 2 clusters is the number of discrete entities they contain.

Now, once we leave off counting actual discrete objects in sets we can use our senses to examine, and start blithely tossing around numbers without a physical referent, we have made (dare I say it) metaphysical leap...

[Xamonas Chegwé]

The 'problem' is that it's not clear what a unity is in regards to counting. Is a cloud 1 object, or is it multiple objects?

That is no more of a problem than defining a crowd. Earth is crowded with bazillions of bacteria and trillions of insects. There was a crowd of 175,000 people at the recent Glastonbury festival. A bus might be crowded with 20 people. Three's a crowd. A metaphysical problem might be crowding my mind. A cloud might be a barely perceptible whisp of water droplets or a humongous bank of an advancing thunderstorm. Units are rarely precisely defined, and even they may change over time. The metre used to be defined by some length of a piece of very inert metal resting in a Paris museum. Now it is defined by x vibrations per second of some crystal.

Actually, its definition now is "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second."

I think you were confusing its definition with that of the second, which is defined as "the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."

[JimC]

The 'problem' is that it's not clear what a unity is in regards to counting. Is a cloud 1 object, or is it multiple objects?

That is no more of a problem than defining a crowd. Earth is crowded with bazillions of bacteria and trillions of insects. There was a crowd of 175,000 people at the recent Glastonbury festival. A bus might be crowded with 20 people. Three's a crowd. A metaphysical problem might be crowding my mind. A cloud might be a barely perceptible whisp of water droplets or a humongous bank of an advancing thunderstorm. Units are rarely precisely defined, and even they may change over time. The metre used to be defined by some length of a piece of very inert metal resting in a Paris museum. Now it is defined by x vibrations per second of some crystal.

Actually, its definition now is "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second."

I think you were confusing its definition with that of the second, which is defined as "the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."

Some interesting issues here. Now, given that we are talking about a quantum transition, this will involve a discrete amount of energy, which should be fixed, not variable. Measured in appropriate units, will the number involved be rational or irrational? The amount of energy will determine the wavelength of the photon released, and hence its frequency and period. Again, will these figures be rational (possibly even integers, if we are talking a frequency), or irrational?

I'm actually not sure...

[Xamonas Chegwé]

The 'problem' is that it's not clear what a unity is in regards to counting. Is a cloud 1 object, or is it multiple objects?

That is no more of a problem than defining a crowd. Earth is crowded with bazillions of bacteria and trillions of insects. There was a crowd of 175,000 people at the recent Glastonbury festival. A bus might be crowded with 20 people. Three's a crowd. A metaphysical problem might be crowding my mind. A cloud might be a barely perceptible whisp of water droplets or a humongous bank of an advancing thunderstorm. Units are rarely precisely defined, and even they may change over time. The metre used to be defined by some length of a piece of very inert metal resting in a Paris museum. Now it is defined by x vibrations per second of some crystal.

Actually, its definition now is "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second."

I think you were confusing its definition with that of the second, which is defined as "the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."

Some interesting issues here. Now, given that we are talking about a quantum transition, this will involve a discrete amount of energy, which should be fixed, not variable. Measured in appropriate units, will the number involved be rational or irrational? The amount of energy will determine the wavelength of the photon released, and hence its frequency and period. Again, will these figures be rational (possibly even integers, if we are talking a frequency), or irrational?

I'm actually not sure...

Surely, whether the number is rational or not depends on the units.

Wavelength = hc/E, where h is Planck's constant, c is the speed of light and E is the energy of the photon. Pick appropriate units for these and you can make any wavelength rational, or even an integer. But that doesn't really make it special. Just as the metre and the second aren't special - just arbitrary choices.

[pErvinalia]

The 'problem' is that it's not clear what a unity is in regards to counting. Is a cloud 1 object, or is it multiple objects?

That is no more of a problem than defining a crowd. Earth is crowded with bazillions of bacteria and trillions of insects. There was a crowd of 175,000 people at the recent Glastonbury festival. A bus might be crowded with 20 people. Three's a crowd. A metaphysical problem might be crowding my mind. A cloud might be a barely perceptible whisp of water droplets or a humongous bank of an advancing thunderstorm. Units are rarely precisely defined, and even they may change over time. The metre used to be defined by some length of a piece of very inert metal resting in a Paris museum. Now it is defined by x vibrations per second of some crystal.

Yeah, but that doesn't really help to address the claim that numbers are physical because unities are supposedly obvious in the natural world. I'm saying that they are only obvious because of our specific evolutionary history. Those unities might be totally different with a different evolutionary history - for example echo-locating bats, or pelagic fish with bilateral lines that school as one whole.

[pErvinalia]

With at least the majority of organisms, the skin or exoskeleton is a pretty defined boundary. We have very little difficulty in counting most organisms (slime-moulds could get a little tricky, I suppose)

On the dog and scent thing, it's not going to confuse a hunting dog - he'll pounce on the actual organism, not its scent trail...

I certainly not saying that every aspect of physical reality has clear, discrete boundaries. But there are plenty that do, and enumerating collections of them is not a waffly, vague process, it is very clear-cut indeed. All of this, to me, is saying that the numbers of a given set of physical objects is an empirical fact about that collection of object, which gives the number concerned a reality which is not just an abstraction.

Interesting, are clouds physical objects? or are they merely a collection of water droplets?

Yeah, this is what I was getting at with the galaxy super-clusters (because I couldn't think of a good example at the macro scale we exist at).

@Jim you explained away the dog, adequately, as it relies on sight as well as scent. But bats and other animals that don't rely on sight would presumably form different boundaries to us.

To take the bat example first; a bat relying on ultrasound to detect a moth would still perceive it as a localised object with boundaries; certainly enough to grab and eat it in mid-air... Sure, the sensory modality is different, which poses interesting questions in terms of bat consciousness, but no issues as far as the discreteness of the flying invertebrates it perceives, IMO.

If you limit it to objects in clear air, then yes. But what about a tree growing against a rocky cliff? Does it discern the tree as a discrete entity or just another part of the cliff?

With clouds, etc. I did say that not all situations in the physical world present us with clear-cut examples of discreteness, only that there are sufficient examples so that sets of discrete, physical objects exist. Hermits point about naming a collection of water droplets as a cloud is fair enough in a pragmatic sense, though many such examples (e.g. a "beach") do not have obvious boundaries; it may be that the set of "beaches" in Australia is not, in principle, countable...

Sure, but our "common sense" approach to defining boundaries is due to our evolutionary history. Another type of sensory animal with a different evo history, would categorise things differently.

All of this, to me, is saying that the numbers of a given set of physical objects is an empirical fact about that collection of object, which gives the number concerned a reality which is not just an abstraction.

That sounds a bit wibbly to me. What else is there other than materials and ideas? Is there some other form of "stuff"?

Take a situation with a collection of 9 pebbles, clustered together but separate and countable. Then take a second situation a little way off of 8 pebbles of a similar type. Each pebble has a set of physical properties which can be measured to some level of accuracy. So does each cluster of pebbles, but the most obvious measurable quantity of the 2 clusters is the number of discrete entities they contain.

Now, once we leave off counting actual discrete objects in sets we can use our senses to examine, and start blithely tossing around numbers without a physical referent, we have made (dare I say it) metaphysical leap...

That doesn't really answer the question. I'm claiming that there are only two types of "things" - physical/material, and ideas. So numbers have to be either one or the other. Unless there is some other type of "stuff" out there that it can be.

[Hermit]

The 'problem' is that it's not clear what a unity is in regards to counting. Is a cloud 1 object, or is it multiple objects?

That is no more of a problem than defining a crowd. Earth is crowded with bazillions of bacteria and trillions of insects. There was a crowd of 175,000 people at the recent Glastonbury festival. A bus might be crowded with 20 people. Three's a crowd. A metaphysical problem might be crowding my mind. A cloud might be a barely perceptible whisp of water droplets or a humongous bank of an advancing thunderstorm. Units are rarely precisely defined, and even they may change over time. The metre used to be defined by some length of a piece of very inert metal resting in a Paris museum. Now it is defined by x vibrations per second of some crystal.

Yeah, but that doesn't really help to address the claim that numbers are physical because unities are supposedly obvious in the natural world. I'm saying that they are only obvious because of our specific evolutionary history. Those unities might be totally different with a different evolutionary history - for example echo-locating bats, or pelagic fish with bilateral lines that school as one whole.

You'll need to reword that post for me. I don't get what you are driving at. Until then, all I can say that unities are not obvious in the natural world. They are what we say they are - ultimately arbitrary and changing. I tried to indicate that with "crowd" and "metre". As for numbers being real, that depends on what you mean with real. I say numbers are not real insofar as they are abstractions we make when we, say, contemplate the presence of two apples, two cows, two cars, two anythings and what these things have in common. On the other hand numbers are real in so far as they enable us to predict things like tides, eclipses and the next time Tony Abbott says something outrageously stupid.

[pErvinalia]

You basically agree 100% with what I have said in the thread. JimC is claiming that numbers are more than just abstractions, and he is pointing to the 'obviousness' of unities and boundaries in the natural world as to why they are more than just abstractions. I'm arguing against that, and by what you've written here, you would argue against that too.

[Hermit]

You basically agree 100% with what I have said in the thread. JimC is claiming that numbers are more than just abstractions, and he is pointing to the 'obviousness' of unities and boundaries in the natural world as to why they are more than just abstractions. I'm arguing against that, and by what you've written here, you would argue against that too.

Insofar as I can make out what you are saying, I guess I do, but unless I have misinterpreted this statement by JimC, he also agrees:

Take a situation with a collection of 9 pebbles, clustered together but separate and countable. Then take a second situation a little way off of 8 pebbles of a similar type. Each pebble has a set of physical properties which can be measured to some level of accuracy. So does each cluster of pebbles, but the most obvious measurable quantity of the 2 clusters is the number of discrete entities they contain.

Now, once we leave off counting actual discrete objects in sets we can use our senses to examine, and start blithely tossing around numbers without a physical referent, we have made (dare I say it) metaphysical leap...

[pErvinalia]

He was dodging the point. Read his earlier stuff. He is clear that he thinks numbers are somewhat equivalent to physical objects.

[Hermit]

He was dodging the point. Read his earlier stuff. He is clear that he thinks numbers are somewhat equivalent to physical objects.

Did he actually say that "numbers are somewhat equivalent to physical objects"? I don't recall reading anything of the sort. Best leave it to Jim to clarify now.

[pErvinalia]

Yeah, he can clarify. I've got to get packing and moving. He's wibbling a bit, and claiming that numbers are somewhere between the physical and ideas. I don't reckon there is anything else other than the physical and ideas. But if there is, I'm open to hearing about it.