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May 3, 2007 - Freedomain Radio - Stefan Molyneux
13:25
743 Do Numbers Exist? - Mythology Part 1
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Good afternoon, everybody. Hope you're doing well.
It's Steph. It is the 3rd of May, 2007, and I'm having a little walkie-walks at lunch, and we're just going to take this I-River for another spin and make sure that it's not the I-River that's causing the crackling, which has killed the podcaster too, but rather the microphone.
So, there is a perennial problem that sort of floats around In the realm of philosophy, which is really associated with numbers.
Numbers seem to blow people's minds in rather powerful ways, so I thought I'd give some of my minor take on the question of numbers and their existence and so on, and you can count me correct.
Oh, okay, I promise I won't make any number jokes, because Lord knows the jokes involving my internal organs are only vaguely funny.
These ones are really not going to happen at all, so...
So, what is the problem that people have?
Well, the question of the existence of something is complicated for sentient, conscious organisms like, say, you and I, or at least you.
Because if you say that something exists, the question is, always, does it exist within the mind?
Or does it exist within the mind and within reality?
Or does it exist in reality but not in the mind?
So these are sort of the three options, the three overlapping circles of existence.
So, for example, something which exists within reality and within your mind is the computer or the mp3 player that you are using to listen to this podcast.
That exists in your pocket or on your desk.
And it also exists within your mind, in that when you want to listen to a podcast, you don't peel a fruit, or you don't peel an orange and hope to find the words inside.
You have this idea of the podcast within your mind.
Sorry, of the MP3 player within your mind.
It also exists within reality.
You conform your mind to reality, and hunky-dory lickety-smack, we have both things existing within the mind and within reality.
Now... The second example is things which exist in our minds but do not exist in reality, like God, like flying elephants, like numbers.
These are concepts and sometimes contradictory concepts.
A square circle is a concept.
It's a self-contradictory concept, but it's illustrative of concept problems.
So we have in that situation something which exists in our mind which does not exist.
It's all the reality, huh?
And then we have things which exist within our own minds.
Sorry, then we have things which exist within reality which do not exist within our own minds.
And these could be things like, let's say that there's some...
This is not possible, but let's imagine there was some planet just beyond Jupiter.
Maybe it is possible, I don't know.
No, we would have seen it, I'm sure. No, we'd see the gravitational effect.
There's some planet beyond Jupiter that is orbiting continually so that Jupiter is always between the Earth and this planet, right?
Or, you know, in the meteor belt between Mars and...
What is the next planet?
Jupiter? I think so.
It's a big space, no matter what it is, right?
So, you have this planet on the far side of Jupiter.
It exists in reality, but we don't know anything about it.
Like Pluto before the 1930s.
The dark, I mean. So, these are things which exist in reality, but do not exist in our mind.
It's really, unless I'm missing something pretty significant, it's that simple.
Things which exist both in reality and in our minds, like Jupiter.
Things which exist within our minds, but not in reality.
Square circles, God, numbers.
And things which exist in reality which do not exist in our minds.
The undiscovered stuff.
Life on other planets. Some certain kinds of coleosanth-type fishes at the bottom of the Mediterranean Trench.
Things which exist in reality, but which we do not have any conception of yet.
And if you sort of get that triple sort of scoop of reality concepts, then you've kind of got the whole thing nailed and I can stop and go back to work.
Actually, I don't want to go back to work. It's sunny, so let me flesh it out with some stories from my childhood.
So, if we sort of get that, then we can look at numbers and say, well, clearly, numbers exist within our minds.
There's a concept that exists within our minds, but numbers do not exist in reality.
You can sell nine apples.
You cannot say, and for an additional five bucks, I'll throw the number nine in as well.
Number nine, number nine.
So this is pretty clear to understand in that it's like money, right?
I mean, dollar bills exist.
The concept of money does not exist.
If you say to someone, I'm going to hire you, and I'm going to pay you with the idea of money.
They'd be like, great, then I'll give you the idea of work.
But nobody's going to really do anything, right?
It doesn't really make any sense. So, we've talked about concept formation before, but numbers do not exist any more than a crowd separate from the individual people exists, but that is not to say that numbers is an arbitrary and meaningless concept.
The law of gravity does not exist.
It's not inscribed anywhere on atoms.
The law of gravity does not exist in the real world, but it's not that the law of gravity is arbitrary and just you can make up whatever you want.
So, numbers, the concept does not exist in reality, but numbers are not an arbitrary concept.
You can't call Your hands, you can't count your hands and say, I have pie hands.
Ooh, pie hands. Ooh, that would be fun to eat.
As long as they regroup.
Nothing gross. So it's not arbitrary, and the reason, of course, that numbers can be accurately derived from reality is that reality is composed of atoms and space and energy.
So atoms are discrete individual things, and of course of which electrons, protons, and neutrons are discrete and individual things.
So there's atoms, and then there's space between atoms.
And of course there's gravitational forces which cause mass to be drawn towards mass.
And because of all of this, we have discrete things within the world.
And of course, because of this, we have a brain which can think of these things.
So we have discrete things in the world.
There are atoms, which are held together by strong and weak forces, and then there is space between them, and then there are other atoms, right?
There are two oranges sitting on a table.
You've got a table, which is a bunch of atoms held together by strong and weak forces.
You've got some space between them, and then you've got the oranges sitting on top of them, which are atoms, which are like atoms, right?
It's not like half an orange and half an apple.
It's a freaky thing. So you've got oranges, which are sitting on the table.
The oranges are atoms, which are like similar atoms.
Citrus atoms, I think they're called.
And they are held together by strong and weak forces.
And then there's space, and then there's another orange.
So numbers are just descriptions of atoms.
Descriptions of aggregations of atoms.
And if you've got an orange and an apple sitting there, and you say, hey, two oranges, why are you incorrect?
Are you incorrect because...
The number two is somehow enmeshed in these in some sort of platonic manner?
Well, of course not. You're incorrect because you're saying, pretty much, that this is an orange atom, and this is a collection of orange atoms, to be non-technical in the extreme, and right next to it is a collection of apple atoms.
But I'm calling them both orange atoms.
That's like attempting to drink oil.
If you think it's water, then you can drink it and be fine.
If you think it's oil, you're incorrect.
You're not going to do too well.
So, from that standpoint, what we're doing when we use numbers as a concept is we're just describing atoms.
I mean, obviously, we're not describing individual atoms, but rather two.
But we're describing aggregations of atoms as they impact our senses.
Or, of course, we can get down to more detailed...
Observations of things, if we use scientific instruments.
Or really tiny eyes.
So, numbers exist within our minds.
They do not exist in reality, but they're not arbitrary.
Because they're descriptions of the properties of matter.
An orange is an orange.
And, of course, there's the Aristotelian essence of the orange.
You know, it's an orange, not an apple.
And if it's half orange, half apple, you say it's an apple, an apponge, or whatever.
But numbers are abstractions that we give to aggregations of like atoms.
Nothing particularly complicated about that.
The aggregations of like atoms do exist within the real world, by golly.
They, honest to goodness, really are there, and they are similar, and if you measure the light coming off an orange with a spectrograph or something, then you really are going to see that it falls within the same spectrum as the orange that's next to it.
And if it falls into an entirely different spectrum, then you're going to say it's a blue-orange or something freaky like that.
But, of course, if the color that's coming off it is pure yellow and it's got little pointy bits at the end, then you say, oh, a lemon.
So, this aspect of concept formation is something that I think is relatively easy to understand.
It takes a little while to get used to this as a concept, as a way of working with...
Empirical reality, but numbers are not, at least to me, maybe there's some complication that I'm not aware of.
It certainly could be, but I try and stay clear of those, because, well, those are tough.
But we have atoms, and atoms have properties which don't change, right?
I mean, a carbon atom can be combined with other kinds of atoms to produce C4 explosives.
I'm just making stuff up. An atom can be combined with other...
It doesn't change its properties, right?
You can rip an atom apart, and it becomes a blown-up atom, but it's then a different thing, right?
So, a carbon atom doesn't spontaneously become a hydrogen atom, and then some complex molecule, and then, you know, your right arm, and then the idea of numbers in Babylonian mathematics.
An atom is an atom is an atom.
It sits there. A matter is inert.
It doesn't change unless it's acted on, and usually with considerable energy.
So, this whole question or issue is that atoms have properties.
Atoms have properties. Physical reality is stable and doesn't change unless you act upon it.
So, because atoms have characteristics in perpetuity, hydrogen atom has probably been a hydrogen atom for quite some time, billions of years.
Because atoms have stability, we can have concepts, and not only can we exist, but we can have concepts, because concepts are merely, for the most part, well, almost always, descriptions of atoms or of other concepts, which is merely, in the end result, a description of something which is material.
And where you have a concept that can never be tied to anything that is material, that is objective, you know you have a false concept.
So if you have a concept like country, how do you know that the concept country is false?
Because it doesn't describe anything particular in reality.
The atoms don't change.
There's not this massive space between Canada, the United States, and Mexico, or whatever.
And you could say Australia is a country, because it is a, I guess, a mini-continent or a landmass.
And that's fine, but then what you're describing is a geographical feature, not any sort of political entity, right?
So where you have concepts that at some point...
Do not describe matter.
God, of course, is one of these, right?
Wherever you have a concept that at some point or another does not describe matter, you know you have a false concept, a concept which has been disconnected from reality, from a description of matter or energy...
And therefore, it's false and meaningless, and it's just a made-up summit, right?
It doesn't mean anything, and that's why I continually sort of focus on applying laws of logic, which are derived from the principles of reality and matter and energy, and applying the laws of logic to concepts.
And when you come up with concepts that have no basis in material reality, why then?
My friends, you know you have a false concept, because not describing any atoms, and that's what concepts are for.
Thank you so much for listening.
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