What's a number?

[Birdjaguar]

I agree that numbers don't exist in the same way that physical things exist. But perhaps existence can be defined in another way, for which numbers do exist. For instance Perfection earlier in the thread used existence to mean existential quantification, and said that the lowest prime number in a certain range may or may not exist. Surely there is a useful definition of existence that implies numbers exist.

For instance, It may be useful to say that not only physical things exist, but also physical properties, like mass. You can't point at something and say that's mass. But still it is useful to say that mass, the measure of an objects tendency to attract other objects with mass, exists. Or similarly the measure of inertia exists. A number of people have connected numbers with they physical properties of quantity and relative size.

Similarly it may be useful to say that abstract things like the id, ego, and superego, the moral compass, exist. Are numbers similar?

Such things are useful, that's why we create them. They are how we organize our thinking and as science thinking gets more complex, we create new ideas so we can talk about them more easily. Yes, by redefining existence, we can make all kinds of things "appear" and "disappear" from reality. Numbers and mathematics do exist in our minds, isn't that sufficient? What is gained by having them somehow exist outside of us?

 

[Souron]

What is gained by having them somehow exist outside of us?
We get the difference between discovery and design.

 

[Birdjaguar]

What is gained by having them somehow exist outside of us?
We get the difference between discovery and design.

It strikes me that design/creation tops discovery so discovery would be a net loss of something. The ability to fashion modern mathematics from its humble beginnings by a Sumerian temple "accountant" is pretty impressive.

I should have phrased my question differently: What is lost when the origination of numbers and mathematics is found to be ourselves alone.

 

[Millman]

Like any other science a way to define the unknown. Until all science is known it's better than pulling something out of your aaa. That's what fiction's for.

 

[Birdjaguar]

Like any other science a way to define the unknown. Until all science is known it's better than pulling something out of your aaa. That's what fiction's for.

Your post is not clear to me; could you clarify it please?

 

[warpus]

I do believe I figured all of this out a couple pages back.

 

[Birdjaguar]

I do believe I figured all of this out a couple pages back.

yeah, but those who advocated for numbers and math having an existence external to humans have been strangely quiet. From their silence, it appears that there is no case for such a thing.

 

[Souron]

It strikes me that design/creation tops discovery so discovery would be a net loss of something. The ability to fashion modern mathematics from its humble beginnings by a Sumerian temple "accountant" is pretty impressive.

I should have phrased my question differently: What is lost when the origination of numbers and mathematics is found to be ourselves alone.

What is lost is that people would not be able to agree on the conclusions. In math, the result follows from the premises.

Math is closely tied to logic, and logic is sometimes simpler than math, so perhaps this example from logic will make the point. In logic you some things can conditionally depend on others, as in p is true implies that q is true. For example, if an object emits light, then it looses energy. One of the tenants of logic is that given such a statement, if p then q, then it is also true that if not q, then not p. Following the example it would mean that if an object does not loose energy, then it does not emit light. Does the non existence of humans change that second fact? Are do any closed systems emit light? No, of course not. This is what we mean by logic and math being external to humans.

yeah, but those who advocated for numbers and math having an existence external to humans have been strangely quiet. From their silence, it appears that there is no case for such a thing.

Or it shows that we feel our case has already been made, and to explain it again would be repetition, and not likely to make you understand.

 

[ParadigmShifter]

Birdjaguar was at Woodstock so I think he is familiar with smoking some large numbers.

 

[Birdjaguar]

What is lost is that people would not be able to agree on the conclusions. In math, the result follows from the premises.

Math is closely tied to logic, and logic is sometimes simpler than math, so perhaps this example from logic will make the point. In logic you some things can conditionally depend on others, as in p is true implies that q is true. For example, if an object emits light, then it looses energy. One of the tenants of logic is that given such a statement, if p then q, then it is also true that if not q, then not p. Following the example it would mean that if an object does not loose energy, then it does not emit light. Does the non existence of humans change that second fact? Are do any closed systems emit light? No, of course not. This is what we mean by logic and math being external to humans.

Interesting.
I would say that logic (as separate from math) in built into consciousness (whatever that means). Brain development in various life forms has included a logic capable component. Dogs, cats, birds, apes, etc. all show logical thinking in various degrees. I think our ability to use logical thinking is an evolutionary trait and it appears that humans have developed great facility in using it. With it has come science, math and philosopy.

We begin perhaps in different places:

You seem to be saying (correct me if I am wrong) that the universe is put together in a "logical way" and we are discovering that "logical way" through our methods of inquiry. The logic is built in and we just bring it to light.

I am saying that the universe exists and that we are applying our evolved logical thinking skills to organize what we see in a way that makes sense to us using the senses we have. When confronted by things that don't make sense (quantum mechanics maybe) we create logical explanations that we try to make fit. Then we refit them as needed.

In both cases we end up with a pretty good description of how our brains see things. Now because they have very different sensory apparatus, dolphins and spiders see the universe differently than we do. Their senses tell them a different story about what is real and how things fit together. Spiders and dolphins fit nicely into our view, but we may not fit so nicely, if at all, into theirs. Which universes are true? Does that fact that ours appears true to us make it absolutely true? Does our evolutionary development mean that our view of things is more true than the spider's? If so, would our view be rendered obsolete if a creature has advanced beyond us and sees things very differently? Will all "life" that is capable of "studying" the universe discover the same universe which we see as real? Is that an acceptable extension of saying that logic is embedded in the universe?

The presumption of a logical foundation to the universe is the foundation that allows us to say our view of things is true (in some absolute sense). I think that that is what is lost when logic and numbers have a human origin. Now we have to start with some foundation, some locus of assumed truth or we will have trouble getting anywhere. I guess some of us are destined to choose one way some another.

Now I am not an expert on spiders, so this particular example may fail, but there are other critters i'm sure which might be a better fit. In the universe of a spider does an object that loses energy emit light? Or is his universe just incomplete? If his is, could ours be to the same extent?

I hope I haven't gone too far astray, but logical thinking and determinism made me do it.

 

[Birdjaguar]

Birdjaguar was at Woodstock so I think he is familiar with smoking some large numbers.

My sojourn at Woodstock was pretty interesting and there were large numbers there. For that weekend it was the third largest city in NY. large numbers played an important role in everyone's experience especially around the porta potties.