The idea of an infinite past

[fast]

I get the message that Imaginary Numbers are just as real as Real Numbers. I support that.

What I don't get is why they're not on the same level. I don't see the need to say that Imaginary Numbers are a subset of Real Numbers. What's wrong with no Real Number is an Imaginary Number AND no Imaginary Number is a Real Number AND both Imaginary Numbers and Real Numbers are real numbers?

What do you mean by ”real number”? All numbers are properties of the human mind they are real in the same way as names are real.

I'm doubtful in the majority, but I happen to regard numbers as abstract (as opposed to concrete). Concepts or abstractions (something entirely different) may be a property of the mind, but not only do I find a distinction between concepts and what concepts are concepts of, I distinguish between abstract objects and mental abstractions.

Although I agree that numbers are real (genuine), my intended meaning by regarding numbers as real is to deny that they are imaginary. If people never came to be, numerals, like words, would not be, but the referents to which they refer are not held by the same constraints. The referent to the numeral three is the number three, and since I regard it as an abstract object, I regard it as an existent that is neither concrete nor mental.

 

[Juma]

I get the message that Imaginary Numbers are just as real as Real Numbers. I support that.

What I don't get is why they're not on the same level. I don't see the need to say that Imaginary Numbers are a subset of Real Numbers. What's wrong with no Real Number is an Imaginary Number AND no Imaginary Number is a Real Number AND both Imaginary Numbers and Real Numbers are real numbers?

What do you mean by ”real number”? All numbers are properties of the human mind they are real in the same way as names are real.

I'm doubtful in the majority, but I happen to regard numbers as abstract (as opposed to concrete). Concepts or abstractions (something entirely different) may be a property of the mind, but not only do I find a distinction between concepts and what concepts are concepts of, I distinguish between abstract objects and mental abstractions.

Although I agree that numbers are real (genuine), my intended meaning by regarding numbers as real is to deny that they are imaginary. If people never came to be, numerals, like words, would not be, but the referents to which they refer are not held by the same constraints. The referent to the numeral three is the number three, and since I regard it as an abstract object, I regard it as an existent that is neither concrete nor mental.

Of course thay are imaginary. They doesnt exist anywhere except in our imagination.
They are useful, but why shouldnt imaginary objects be useful?
I would say that our brain hardcodes ”gruoping” (the unconcious mental festure of grouping features into objects and creating sets). Numbers 1-3 has some hardwired brain representation. Then the brain has some other more complex hardwiring (pattern recognition etc) but rest of math is not just abstract but also imaginary.

 

[DBT]

You avoided my question.

I have had several dealings with you.

You have never once answered a question put to you.

Here is just another example.

I don't give a shit about your stupidity about first causes.

Since the past was finite because infinity is not a real concept, it is like trying to apply imaginary numbers to some real world quantity, then all we can observe in some way had a beginning.

That is all I know for certain on the matter.

You are still avoiding the question.

 

[Speakpigeon]

So you can in no way demonstrate a real completed infinity is possible?

And therefore you think it is rational to think it is possible?

How do you do that?

If you can't demonstrate it is possible the rational position is that it is not.

The first rational step to take is to see if we can agree on the notion of possibility.

Here is what I think it is:

I think that the notion of possibility is that of no contradiction with what we know of reality.

Can you agree with that?
EB

 

[Speakpigeon]

The other notion which you've used capital letters to denote would be "Real Numbers" and "Imaginary Numbers." These are labels or complex terms that denote a specialized meaning that is not solely gleaned from a dictionary but instead a glossary.

And dictionaries differ on this...

Some have "real number" as an entry, some don't. Even some good dictionaries don't. Even my Oxford Encyclopedic English doesn't. Those that do will all be concerned with the specialised mathematical expression, never with the phrase "real number", since its meaning can be straightforwardly inferred from the meaning of "real" and of "number".

Anyway, thanks to the both of you for addressing this point.
EB

 

[Speakpigeon]

Not all Real numbers are Imaginary, but all Imaginary numbers are Real

Do you have any definitions of "Imaginary numbers" and "Real numbers", according to which Imaginary numbers are Real?

Yes, you're right, bilby is mistaken here.

Imaginary numbers are not Real numbers. Both the Imaginary numbers and the Real numbers are subsets, and disjoint subsets (except perhaps for zero?), of the Complex numbers. And some Complex numbers will be a complex of an Imaginary number and a Real number. Those will neither be Imaginary numbers nor Real numbers.

So, not all Complex numbers are complex numbers.

Nothing's perfect, not even in the mathematical world.
EB

 

[Speakpigeon]

I get the message that Imaginary Numbers are just as real as Real Numbers. I support that.

What I don't get is why they're not on the same level. I don't see the need to say that Imaginary Numbers are a subset of Real Numbers. What's wrong with no Real Number is an Imaginary Number AND no Imaginary Number is a Real Number AND both Imaginary Numbers and Real Numbers are real numbers?

Intuition is often your best guide in life.
EB

 

[Speakpigeon]

Two different meanings of real? Plus Real.

There is real: not imaginary
And there is real: genuine
And there is Real: not Imaginary

I agree with your sentiment that Imaginary Numbers are not 'counterfeit' in any way. Their currency in the number system is just as deserving as Real Numbers.

Exactly. It's only when you combine Real and Imaginary that things start to become Complex.

No, not Complex, not really.

It's only when you combine Real and Imaginary that things start to become complex.

The Real numbers and the Imaginary numbers on their own are not complex but they are nonetheless already Complex numbers.
EB

 

[Speakpigeon]

I get the message that Imaginary Numbers are just as real as Real Numbers. I support that.

What I don't get is why they're not on the same level. I don't see the need to say that Imaginary Numbers are a subset of Real Numbers. What's wrong with no Real Number is an Imaginary Number AND no Imaginary Number is a Real Number AND both Imaginary Numbers and Real Numbers are real numbers?

What do you mean by ”real number”? All numbers are properties of the human mind they are real in the same way as names are real.

I'm doubtful in the majority, but I happen to regard numbers as abstract (as opposed to concrete). Concepts or abstractions (something entirely different) may be a property of the mind, but not only do I find a distinction between concepts and what concepts are concepts of, I distinguish between abstract objects and mental abstractions.

Although I agree that numbers are real (genuine), my intended meaning by regarding numbers as real is to deny that they are imaginary. If people never came to be, numerals, like words, would not be, but the referents to which they refer are not held by the same constraints. The referent to the numeral three is the number three, and since I regard it as an abstract object, I regard it as an existent that is neither concrete nor mental.

I would say that if what we take to be real things seem to behave consistently as if there are real numbers, then we should do well to take numbers as real.

So, we should see them as not only useful, as juma says, but as real.

Except if someone could show there is not one case of real things that seem to behave consistently as if there are real numbers.

Me, I can't do that.
EB

 

[Speakpigeon]

Unter,

I recommend you read Roger Zelazny's "Creatures of Light and Darkness".

One of my favorite characters in that book is able to instantly "be" anywhere he can imagine. Other, less endowed characters are only capable of various degrees of temporal manipulation... you seem bound to the latter state, by your own will.

Yeah, so how long before you starve to death?

You have to keep zooming here and there at the speed of light.

That's a harsh life to be sure.
EB

 

[bilby]

My apologies, but there is an error on my part in that quote (I have edited it out of my post); Imaginary numbers are both real numbers and Real numbers. Not all Real numbers are Imaginary, but all Imaginary numbers are Real, and so if Real numbers are real, Imaginary numbers must therefore also be real, because they are Real.

The question of whether Real numbers are or are not real, remains open.

I hope that helps.

Do you have any definitions of "Imaginary numbers" and "Real numbers", according to which Imaginary numbers are Real?

I am afraid not.

I was seeking confusion for comic effect, and confused myself.

- - - Updated - - -

Two different meanings of real? Plus Real.

There is real: not imaginary
And there is real: genuine
And there is Real: not Imaginary

I agree with your sentiment that Imaginary Numbers are not 'counterfeit' in any way. Their currency in the number system is just as deserving as Real Numbers.

Exactly. It's only when you combine Real and Imaginary that things start to become Complex.

Sure, but in that case, the Imaginary numbers are not a subset of the Real numbers.

Indeed.

My apologies. I stuffed up. The Imaginary Numbers are as real as the Real Numbers, but are not (as I incorrectly asserted) a subset of them.

We all make mistakes; this has been one of mine. Thank you for giving me the opportunity to correct it.

 

[untermensche]

I think that the notion of possibility is that of no contradiction with what we know of reality.

Can you agree with that?
EB

Absolutely not.

That is worthless.

It excludes absolutely nothing since we have a very partial and superficial understanding of things.

We think things cannot move faster than light but we could be wrong. That assumption is not accepted as absolute fact. Scientists test it all the time.

The rational skeptical position is that a claim that cannot be demonstrated is rejected until it can be demonstrated.

That includes claims that a real completed infinity is possible.

 

[untermensche]

You avoided my question.

I have had several dealings with you.

You have never once answered a question put to you.

Here is just another example.

I don't give a shit about your stupidity about first causes.

Since the past was finite because infinity is not a real concept, it is like trying to apply imaginary numbers to some real world quantity, then all we can observe in some way had a beginning.

That is all I know for certain on the matter.

You are still avoiding the question.

You can't read.

 

[Speakpigeon]

I think that the notion of possibility is that of no contradiction with what we know of reality.

Can you agree with that?
EB

Absolutely not.

That is worthless.

It excludes absolutely nothing since we have a very partial and superficial understanding of things.

We think things cannot move faster than light but we could be wrong. That assumption is not accepted as absolute fact. Scientists test it all the time.

The rational skeptical position is that a claim that cannot be demonstrated is rejected until it can be demonstrated.

That includes claims that a real completed infinity is possible.

Thank you for this straight answer.

So, now, can you give here a few examples of things that you think we should take as possible but that we don't actually know that they are real. I know the Eiffel Tower is possible but that doesn't help to understand how your notion of possibility is different from you notion of reality. Just a few examples will do.

Thanks!
EB

 

[untermensche]

Absolutely not.

That is worthless.

It excludes absolutely nothing since we have a very partial and superficial understanding of things.

We think things cannot move faster than light but we could be wrong. That assumption is not accepted as absolute fact. Scientists test it all the time.

The rational skeptical position is that a claim that cannot be demonstrated is rejected until it can be demonstrated.

That includes claims that a real completed infinity is possible.

Thank you for this straight answer.

So, now, can you give here a few examples of things that you think we should take as possible but that we don't actually know that they are real. I know the Eiffel Tower is possible but that doesn't help to understand how your notion of possibility is different from you notion of reality. Just a few examples. Thanks!
EB

Engineers tell us the possible every day.

But that bridge in Florida still killed, as far as I know, six people.

I don't think you understand the skepticism I am talking about. I honor skepticism over wishful thinking.

Nothing is possible until it is shown to be possible.

If you think something is possible you have to try to demonstrate it.

How does this constrain anything?

 

[Speakpigeon]

Absolutely not.

That is worthless.

It excludes absolutely nothing since we have a very partial and superficial understanding of things.

We think things cannot move faster than light but we could be wrong. That assumption is not accepted as absolute fact. Scientists test it all the time.

The rational skeptical position is that a claim that cannot be demonstrated is rejected until it can be demonstrated.

That includes claims that a real completed infinity is possible.

Thank you for this straight answer.

So, now, can you give here a few examples of things that you think we should take as possible but that we don't actually know that they are real. I know the Eiffel Tower is possible but that doesn't help to understand how your notion of possibility is different from you notion of reality. Just a few examples. Thanks!
EB

Engineers tell us the possible every day.

But that bridge in Florida still killed, as far as I know, six people.

I don't think you understand the skepticism I am talking about. I honor skepticism over wishful thinking.

Nothing is possible until it is shown to be possible.

If you think something is possible you have to try to demonstrate it.

How does this constrain anything?

Thank you for this straight answer.

So, now, can you explain what difference you see between saying that something is possible and saying that the same thing is real?

Thanks!
EB

 

[untermensche]

Thank you for this straight answer.

So, now, can you explain what difference you see between saying that something is possible and saying that the same thing is real?

Thanks!
EB

The word "real" is honorific.

It just means we can observe it or experience it.

So if we imagine a ghost we have a real experience but the object of the imagination is not real.

 

[Speakpigeon]

Thank you for this straight answer.

So, now, can you explain what difference you see between saying that something is possible and saying that the same thing is real?

Thanks!
EB

The word "real" is honorific.

It just means we can observe it or experience it.

So if we imagine a ghost we have a real experience but the object of the imagination is not real.

Thank you for this straight answer.

So, now, can you give here a few examples of physical things that you think we should take as real. Just a few examples.

Thanks!
EB

 

[untermensche]

Thank you for this straight answer.

So, now, can you explain what difference you see between saying that something is possible and saying that the same thing is real?

Thanks!
EB

The word "real" is honorific.

It just means we can observe it or experience it.

So if we imagine a ghost we have a real experience but the object of the imagination is not real.

Thank you for this straight answer.

So, now, can you give here a few examples of physical things that you think we should take as real. Just a few examples.

Thanks!
EB

Anything we can observe or experience we should take as "real". But a real experience does not mean the objects experienced are real.

 

[Speakpigeon]

Thank you for this straight answer.

So, now, can you give here a few examples of physical things that you think we should take as real. Just a few examples.

Thanks!
EB

Anything we can observe or experience we should take as "real". But a real experience does not mean the objects experienced are real.

Thank you for this straight answer.

So, now, going back to your example with the engineers, suppose you're the one paying for the construction of a bridge over a motorway (or superhighway) and ask engineers to submit their papers on their concept proposals. You end up with three different proposals for your bridge, all three about new concepts of bridge. You can pay. The three concepts all look good on paper and you like the three different engineers who submitted the proposals. Still, why should you pay for something that doesn't exist yet, that you haven't personally experienced and that you don't know yourself that it is possible?
EB