So, metaphysics then.

[Mr.Samsa]

He's getting at the same thing I was I think when I mistakenly described metaphysics as non-physical/empirical. It is indeed that, but not that alone as it's obviously more than that. So in that sense, numbers don't exist - i.e. we can't see, touch, feel them. They are ideas as opposed to physical objects. They certainly exist as concepts, the same way that logical statements and evidence exist.

There are actually a large number of mathematicians and physicists who would disagree with the claim that mathematical concepts aren't real, existent, physical things. I mentioned Max Tegmark above as a joke but he actually believes the fundamental fabric of the world is mathematics. Not that it can be modelled or described by maths, but that it literally is maths.

[pErvinalia]

Yeah, I've heard such claims, and I think even JimC holds to some small part of this view (that numbers are real things). It doesn't make sense to me. Numbers are categories, categories are inventions of our minds. I wouldn't deny that numbers are highly relevant to our interactions with the natural world. I just deny that they are "real" in a physical sense.

[JimC]

however for certain definitions of existent/nonexistent, my description of metaphysics about sums it up. It's odd that one has to adopt a metaphysical stance to describe metaphysics.

Fair point, I guess if by "existent" we mean something like physical or observable or measurable, etc, then those things might still be consistent with what you've said (but I imagine there'd be a few annoyed mathematicians after hearing that numbers don't exist).

He's getting at the same thing I was I think when I mistakenly described metaphysics as non-physical/empirical. It is indeed that, but not that alone as it's obviously more than that. So in that sense, numbers don't exist - i.e. we can't see, touch, feel them. They are ideas as opposed to physical objects. They certainly exist as concepts, the same way that logical statements and evidence exist.

Numbers can be a property of a set of real objects, however. If there are 10 sheep in that field, then, in that context, the number 10 (by counting) is an empirically measurable property of that set of sheep.

[Robert_S]

however for certain definitions of existent/nonexistent, my description of metaphysics about sums it up. It's odd that one has to adopt a metaphysical stance to describe metaphysics.

Fair point, I guess if by "existent" we mean something like physical or observable or measurable, etc, then those things might still be consistent with what you've said (but I imagine there'd be a few annoyed mathematicians after hearing that numbers don't exist).

He's getting at the same thing I was I think when I mistakenly described metaphysics as non-physical/empirical. It is indeed that, but not that alone as it's obviously more than that. So in that sense, numbers don't exist - i.e. we can't see, touch, feel them. They are ideas as opposed to physical objects. They certainly exist as concepts, the same way that logical statements and evidence exist.

Numbers can be a property of a set of real objects, however. If there are 10 sheep in that field, then, in that context, the number 10 (by counting) is an empirically measurable property of that set of sheep.

Sheep and non-sheep are just aritrary made-up divisions; probably invented by the matriarchy. Free your mind, the matrix has you.

[JimC]

however for certain definitions of existent/nonexistent, my description of metaphysics about sums it up. It's odd that one has to adopt a metaphysical stance to describe metaphysics.

Fair point, I guess if by "existent" we mean something like physical or observable or measurable, etc, then those things might still be consistent with what you've said (but I imagine there'd be a few annoyed mathematicians after hearing that numbers don't exist).

He's getting at the same thing I was I think when I mistakenly described metaphysics as non-physical/empirical. It is indeed that, but not that alone as it's obviously more than that. So in that sense, numbers don't exist - i.e. we can't see, touch, feel them. They are ideas as opposed to physical objects. They certainly exist as concepts, the same way that logical statements and evidence exist.

Numbers can be a property of a set of real objects, however. If there are 10 sheep in that field, then, in that context, the number 10 (by counting) is an empirically measurable property of that set of sheep.

Sheep and non-sheep are just aritrary made-up divisions; probably invented by the matriarchy. Free your mind, the matrix has you.

Actually, they were invented by the Welsh...

[pErvinalia]

however for certain definitions of existent/nonexistent, my description of metaphysics about sums it up. It's odd that one has to adopt a metaphysical stance to describe metaphysics.

Fair point, I guess if by "existent" we mean something like physical or observable or measurable, etc, then those things might still be consistent with what you've said (but I imagine there'd be a few annoyed mathematicians after hearing that numbers don't exist).

He's getting at the same thing I was I think when I mistakenly described metaphysics as non-physical/empirical. It is indeed that, but not that alone as it's obviously more than that. So in that sense, numbers don't exist - i.e. we can't see, touch, feel them. They are ideas as opposed to physical objects. They certainly exist as concepts, the same way that logical statements and evidence exist.

Numbers can be a property of a set of real objects, however. If there are 10 sheep in that field, then, in that context, the number 10 (by counting) is an empirically measurable property of that set of sheep.

Yeah, but they aren't physical things themselves. To create a number from nature we first have to categorise and set boundary limits around objects. Only then can we introduce the concept of numbers.

[JimC]

however for certain definitions of existent/nonexistent, my description of metaphysics about sums it up. It's odd that one has to adopt a metaphysical stance to describe metaphysics.

Fair point, I guess if by "existent" we mean something like physical or observable or measurable, etc, then those things might still be consistent with what you've said (but I imagine there'd be a few annoyed mathematicians after hearing that numbers don't exist).

He's getting at the same thing I was I think when I mistakenly described metaphysics as non-physical/empirical. It is indeed that, but not that alone as it's obviously more than that. So in that sense, numbers don't exist - i.e. we can't see, touch, feel them. They are ideas as opposed to physical objects. They certainly exist as concepts, the same way that logical statements and evidence exist.

Numbers can be a property of a set of real objects, however. If there are 10 sheep in that field, then, in that context, the number 10 (by counting) is an empirically measurable property of that set of sheep.

Yeah, but they aren't physical things themselves. To create a number from nature we first have to categorise and set boundary limits around objects. Only then can we introduce the concept of numbers.

Some parts of physical reality are a little fuzzy, but other objects are, for all practical purposes, discrete. Their own nature gives them boundaries, and we can sense them easily. Once they are perceived, they can be counted, and the count is an objective measurement of a defined set of those discrete objects.

[pErvinalia]

Those boundaries aren't set by nature, per se, they are set within our brains. Of course, we evolved in nature, so it's probably not a surprise that our minds are good at modelling nature. But can we conceive of something where the boundary is there because it makes sense from an evolutionary human perspective, but different from another perspective? I guess at the macro scale, things are more defined. But as we get to the micro scale, things start getting a bit fuzzier. What about at galactic+ scales? Super clusters of galaxies. Does it make any more sense to count galaxies individually in a super cluster than it does to consider a tree not one entity but a collection of individual entities (like leaves + bark + wood + etc...)?

I don't know the answers to these questions.

[pErvinalia]

Just to continue on a bit from that... Where do we set boundaries and why do we set them? Does it make sense to set the boundary of an animal at its skin, but not the scents being emitted by that animal? I've particularly got dogs in mind, as they rely massively on scent as a form of identifying other things. So, from a human perspective, where we are dominated by the sense of sight, we form boundaries on visual cues. But a dog might form a different boundary, and taking it even further an echo-locating bat might form totally different boundaries again.

[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.

[Scott1328]

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?

[MiM]

Some parts of physical reality are a little fuzzy, but other objects are, for all practical purposes, discrete. Their own nature gives them boundaries, and we can sense them easily. Once they are perceived, they can be counted, and the count is an objective measurement of a defined set of those discrete objects.

I distinctly remember making an equivalent claim previously somewhere here on Ratz. Then FBM took up the stance rEv is now taking

[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.

[pErvinalia]

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"?

[Hermit]

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

Clouds are a collection of water droplets. We name collections of water droplets. What's that name? Oh, right. It's "clouds". What exactly is the problem with that?