What does it mean for something to be "logically possible"?

[Kharakov]

Ok, but you're being nonsensical. Nothing means the complete absence of everything. Nothing causes nothing (it has no properties that would allow it to cause something). Nothing does nothing (it does not act). Nothing doesn't change (it has no qualities to change).

If nothing exists at some future time a, at any point past time a, nothing will also exist, as there isn't anything, even a quantum mechanical physical framework, to cause something to pop into existence.

I would have thought that a moment in time is something. You can't have a moment in time when there is nothing because the moment itself is something.

I went over that a bit earlier, but I do understand your point (bilby pointed it out as well). The thing is, I said "at some future time a", so we can imagine ehhhhs existence, at which point nothing exists (even the concept of the time ehhhhh).

If I said "at time ehhhh", sure. I mean, I think that I said "future time ehhhh" on purpose, because I was thinking about what you're saying, but... I forget. And I certainly forgot when bilby pointed it out, until I read what I wrote more carefully (I just assumed that I had miss-wrote, which is pretty cray cray for me to assume about stuff I write when I'm sober).

 

[fast]

Your consciousness is coming from your parents?

That is it's beginning, yes. Of course.

We do not begin from nothing.

Oh come on, you're not that far gone! What the hell happened to English?

Might as well attribute a mosquito bite to the Big Bang.

 

[untermensche]

That is it's beginning, yes. Of course.

We do not begin from nothing.

Oh come on, you're not that far gone! What the hell happened to English?

Might as well attribute a mosquito bite to the Big Bang.

His comment was about an individual consciousness.

He was claiming it arose out of chaos. From something undefined.

It arises out of specific instructions.

 

[untermensche]

It is incredibly irrational to claim you have moved FROM infinity.

It is only possible to extend out TOWARDS infinity.

No matter how you describe a real infinity it can never be something realized. It cannot end. It can only go on and on forever.

It is irrational to say the past WAS infinite.

No real infinity can be in the past.

But this is only half of the paradox of existence. Saying this does not make a finite universe possible.

A finite and an infinite past are both equally impossible.

We are apes stuck in something we do not comprehend. Something we cannot comprehend.

Thank you for knocking down that scary strawman. No doubt he was about to embark on a onslaught of murder and pillage. You're still begging the question though.

With you everything is a strawman.

You make no points. Have no points.

We see what happens when you try.

When you try you claim nonsense like the negative integers END at zero, about the stupidest thing I have ever heard.

You add nothing.

This is beyond you. It requires thinking.

 

[untermensche]

Looking further at these claims an imaginary line somehow can start at infinity.

For those who claim knowledge of mathematics they certainly don't know any basics.

The abstract representation of the two series, the positive and negative integers, does not end at zero.

Both series don't actually begin at zero either. Zero is not a positive or negative anything. Those terms do not rationally apply to it.

The positive integers begin with the first positive integer and the negative integers begin with the first negative integer.

I have no idea if this will help people understand it is irrational to say some infinite line began at infinity and ended somewhere but it should.

 

[Phil Scott]

I'm sympathetic to the idea that the positives and negatives start at 1 and -1 respectively, in as much as the way we typically represent these objects as data has them take up less space than the positives and negatives of larger absolute value. Indeed, those larger values will typically be generated from and will recursively contain the smaller ones. This fact can be discussed mathematically on the assumption that these sorts of mathematical objects are given inductively, and inductively given stuff assumes a well-order.

In other words, even though -1 has an infinity of predecessors, it is presented before those predecessors when expressed as data, and has a smaller representation. For concreteness, here's a way to present the integers:

data PositiveInteger = One
                     | S PositiveInteger

data Integer = Zero
             | Positive PositiveInteger
             | Negated  PositiveInteger

In words, a positive integer is either 1 or the successor of a positive integer, while integers generally are either positive integers, zero or the negations of positive integers. Here, the base of any recursion you want to do over this data will bottom out at either 0, 1 or -1, which can thus be taken as the initial integers.

This is not to say that the intended ordering of the integers has -1 smaller than -2, which we get with:

smallerPositive One (S x)   = True
smallerPositive (S x) (S y) = smallerPositive x y
smallerPositive _ One       = False

smallerInteger (Negated x) (Negated y)   = smallerPositive y x
smallerInteger (Negated _) _             = True
smallerInteger Zero        (Negated _)   = False
smallerInteger Zero        Zero          = False
smallerInteger Zero        (Positive y)  = True
smallerInteger (Positive x) (Positive y) = smallerPositive x y
smallerInteger (Positive _) _            = False

But notice that the way this works is that "smallerPositive" compares the size of data, while "smallerInteger" will switch that ordering when the arguments are negative.

 

[untermensche]

Anything can be done by definition. You can say 0 is an integer by definition even though zero has features unlike any other integer.

Ultimately the point I was making is far less complicated than trying to define the integers. Logically you cannot progress from something undefined towards something defined. You cannot progress from infinity towards something. You can only progress towards infinity, not from it.

 

[fast]

The positive integers begin with the first positive integer and the negative integers begin with the first negative integer.

That sounds true enough. I'm not so sure the bold part is something you (you, untermensche) would say though. It's not consistent with your thinking. If I asked you how many chairs you put on the truck and it so happens that not only did you not put any chairs on the truck but took two off the truck, I doubt you'll agree that you put -2 chairs on the truck.

If you have $20 in the bank and write a $30 check, then assuming no fees, how much money do you have in the bank afterwards? I would expect from you an answer that denies the presence of a negative. -$10 is not something, ontologically speaking, that's in the bank. You would likely give an explanatory answer that denies $0 too, as that is not something positively there, in fact.

 

[beero1000]

I'm sympathetic to the idea that the positives and negatives start at 1 and -1 respectively, in as much as the way we typically represent these objects as data has them take up less space than the positives and negatives of larger absolute value. Indeed, those larger values will typically be generated from and will recursively contain the smaller ones. This fact can be discussed mathematically on the assumption that these sorts of mathematical objects are given inductively, and inductively given stuff assumes a well-order.

In other words, even though -1 has an infinity of predecessors, it is presented before those predecessors when expressed as data, and has a smaller representation. For concreteness, here's a way to present the integers:

data PositiveInteger = One
                     | S PositiveInteger

data Integer = Zero
             | Positive PositiveInteger
             | Negated  PositiveInteger

In words, a positive integer is either 1 or the successor of a positive integer, while integers generally are either positive integers, zero or the negations of positive integers. Here, the base of any recursion you want to do over this data will bottom out at either 0, 1 or -1, which can thus be taken as the initial integers.

This is not to say that the intended ordering of the integers has -1 smaller than -2, which we get with:

smallerPositive One (S x)   = True
smallerPositive (S x) (S y) = smallerPositive x y
smallerPositive _ One       = False

smallerInteger (Negated x) (Negated y)   = smallerPositive y x
smallerInteger (Negated _) _             = True
smallerInteger Zero        (Negated _)   = False
smallerInteger Zero        Zero          = False
smallerInteger Zero        (Positive y)  = True
smallerInteger (Positive x) (Positive y) = smallerPositive x y
smallerInteger (Positive _) _            = False

But notice that the way this works is that "smallerPositive" compares the size of data, while "smallerInteger" will switch that ordering when the arguments are negative.

Alternate conventions or abuse of notation can definitely make some situations simpler to deal with, but it's important to understand the situational context. Sure, you could start the negatives with -1, but you should also keep in mind that (like you said) if you do that you'd be counting in the reverse of the standard order - counting 'backwards'. It's by inconsistently forgetting those details that someone could get so confused about whether or not we're talking about a 'beginning' or an 'end' - kind of like saying that I'm the shortest person in the room because my head is the closest to the ceiling.

 

[beero1000]

Anything can be done by definition. You can say 0 is an integer by definition even though zero has features unlike any other integer.

Ultimately the point I was making is far less complicated than trying to define the integers. Logically you cannot progress from something undefined towards something defined. You cannot progress from infinity towards something. You can only progress towards infinity, not from it.

Looking further at these claims an imaginary line somehow can start at infinity.

For those who claim knowledge of mathematics they certainly don't know any basics.

The abstract representation of the two series, the positive and negative integers, does not end at zero.

Both series don't actually begin at zero either. Zero is not a positive or negative anything. Those terms do not rationally apply to it.

The positive integers begin with the first positive integer and the negative integers begin with the first negative integer.

I have no idea if this will help people understand it is irrational to say some infinite line began at infinity and ended somewhere but it should.

With you everything is a strawman.

You make no points. Have no points.

We see what happens when you try.

When you try you claim nonsense like the negative integers END at zero, about the stupidest thing I have ever heard.

You add nothing.

This is beyond you. It requires thinking.

Gotta love the double down. Please, explain more math to me...



The sweet sweet irony.

 

[Kharakov]

The positive integers begin with the first positive integer and the negative integers begin with the first negative integer.

I have no idea if this will help people understand it is irrational to say some infinite line began at infinity and ended somewhere but it should.

The set of integers does not begin or end, and really has little to do with a timeline, other than being an easy to understand (for educated non-morons) example of something that does not have a start or an end.

 

[Phil Scott]

Alternate conventions or abuse of notation can definitely make some situations simpler to deal with, but it's important to understand the situational context. Sure, you could start the negatives with -1, but you should also keep in mind that (like you said) if you do that you'd be counting in the reverse of the standard order - counting 'backwards'. It's by inconsistently forgetting those details that someone could get so confused about whether or not we're talking about a 'beginning' or an 'end' - kind of like saying that I'm the shortest person in the room because my head is the closest to the ceiling.

"Beginning"s and "end"s are all a bit informal though, and I prefer to actually go through the details and let formalisation speak for itself. And when you get serious about that, and build the actual models in a formal calculus, you end up with the sort of thing I describe above (which can be entered with little modification in a theorem prover for constructive type theory).

Note that in the code I provide, I do define the standard ordering of the integers, and have it that -2 < -1. I don't anywhere talk about beginnings or ends, though. I instead mention the idea of a base of induction/recursion, which in the case of models of integers, will be with 0, 1 and -1.

As for untermensche's confusion, that's some off the board stuff which I'm not interested in trying to sort out. I love the fact that you folk are still trying though.

 

[untermensche]

The positive integers begin with the first positive integer and the negative integers begin with the first negative integer.

I have no idea if this will help people understand it is irrational to say some infinite line began at infinity and ended somewhere but it should.

The set of integers does not begin or end, and really has little to do with a timeline, other than being an easy to understand (for educated non-morons) example of something that does not have a start or an end.

The integers are two separate series. The positive integers and the negatives. In both series the lowest integer is the START of the series. You cannot have a series without a start to it.

 

[untermensche]

Gotta love the double down. Please, explain more math to me...

You think the negative integers END at zero.

Hard to be more stupid.

 

[untermensche]

As for untermensche's confusion, that's some off the board stuff which I'm not interested in trying to sort out.

What needs sorting out are the claims that a series can somehow begin at infinity and move towards some fixed point.

If you agree with that one then nothing you could possibly say could have any worth.

 

[beero1000]

Alternate conventions or abuse of notation can definitely make some situations simpler to deal with, but it's important to understand the situational context. Sure, you could start the negatives with -1, but you should also keep in mind that (like you said) if you do that you'd be counting in the reverse of the standard order - counting 'backwards'. It's by inconsistently forgetting those details that someone could get so confused about whether or not we're talking about a 'beginning' or an 'end' - kind of like saying that I'm the shortest person in the room because my head is the closest to the ceiling.

"Beginning"s and "end"s are all a bit informal though, and I prefer to actually go through the details and let formalisation speak for itself. And when you get serious about that, and build the actual models in a formal calculus, you end up with the sort of thing I describe above (which can be entered with little modification in a theorem prover for constructive type theory).

Note that in the code I provide, I do define the standard ordering of the integers, and have it that -2 < -1. I don't anywhere talk about beginnings or ends, though. I instead mention the idea of a base of induction/recursion, which in the case of models of integers, will be with 0, 1 and -1.

As for untermensche's confusion, that's some off the board stuff which I'm not interested in trying to sort out. I love the fact that you folk are still trying though.

I wasn't trying to formalize it - though you could very easily define the first element and last element of a toset (and people do, even though they're usually called the minimum and maximum). The constructive models don't affect that, which is why I was saying that it's important to keep in mind the difference between 'are ordered this way' and 'are enumerated this way'. I think the distinction is much more evident in the rationals - if you wanted to enumerate them formally you certainly wouldn't do it in their standard order.

The set of integers does not begin or end, and really has little to do with a timeline, other than being an easy to understand (for educated non-morons) example of something that does not have a start or an end.

The integers are two separate series. The positive integers and the negatives. In both series the lowest integer is the START of the series. You cannot have a series without a start to it.

This is your second post here where you imply that you don't think 0 is an integer. Weird.

 

[untermensche]

"Beginning"s and "end"s are all a bit informal though, and I prefer to actually go through the details and let formalisation speak for itself. And when you get serious about that, and build the actual models in a formal calculus, you end up with the sort of thing I describe above (which can be entered with little modification in a theorem prover for constructive type theory).

Note that in the code I provide, I do define the standard ordering of the integers, and have it that -2 < -1. I don't anywhere talk about beginnings or ends, though. I instead mention the idea of a base of induction/recursion, which in the case of models of integers, will be with 0, 1 and -1.

As for untermensche's confusion, that's some off the board stuff which I'm not interested in trying to sort out. I love the fact that you folk are still trying though.

I wasn't trying to formalize it - though you could very easily define the first element and last element of a toset (and people do, even though they're usually called the minimum and maximum). The constructive models don't affect that, which is why I was saying that it's important to keep in mind the difference between 'are ordered this way' and 'are enumerated this way'. I think the distinction is much more evident in the rationals - if you wanted to enumerate them formally you certainly wouldn't do it in their standard order.

The set of integers does not begin or end, and really has little to do with a timeline, other than being an easy to understand (for educated non-morons) example of something that does not have a start or an end.

The integers are two separate series. The positive integers and the negatives. In both series the lowest integer is the START of the series. You cannot have a series without a start to it.

This is your second post here where you imply that you don't think 0 is an integer. Weird.

Not strange at all to those capable of thinking.

Zero is not positive.

How one could think it is a positive integer is the strange thing.

 

[beero1000]

This is your second post here where you imply that you don't think 0 is an integer. Weird.

Not strange at all to those capable of thinking.

Zero is not positive.

How one could think it is a positive integer is the strange thing.

Well, this is embarrassing for one of us.

 

[untermensche]

Not strange at all to those capable of thinking.

Zero is not positive.

How one could think it is a positive integer is the strange thing.

Well, this is embarrassing for one of us.

I know. Very troubling when people are so lost they think zero is positive.

Nothing positive about it. It can only be considered part of the positive integers by definition. It is not a positive anything.

 

[beero1000]

Well, this is embarrassing for one of us.

I know. Very troubling when people are so lost they think zero is positive.

Nothing positive about it. It can only be considered part of the positive integers by definition. It is not a positive anything.

Aaaannnddd, we've come full circle. I'll just post this again:

Thank you for knocking down that scary strawman. No doubt he was about to embark on a onslaught of murder and pillage. You're still begging the question though.

With you everything is a strawman.