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

[untermensche]

What was the trains very first movement? The absolute smallest movement it was possible for the train to make?

Are you also one who claims there can be movement without an initial movement?

The first movement (relative to the track, for you relativity lovers) would not include internal movements that necessitate external movement (otherwise that would confuse "movement of" with "movement within," so I guess the smallest possible movement would be the first Planck length distance traversed.

Whatever you want to label it doesn't matter.

This isn't some paradox where things become impossible because of infinite division.

This is the simple necessity for any movement to have an initial movement. Without one there is no movement.

 

[untermensche]

It remains fascinating to me that anyone should stick to such an assumption. Yet, come to think of it, I don't remember anyone actually providing a full and detailed explanation as to why Zeno of Elea's Achilles & the Tortoise argument was wrong except the one Phil Scott just provided in this thread:



If anyone know of any previous occurrence, I'd like to know.
EB

Other than Phil's post, I haven't really seen anyone attempt to challenge UM's postulate about the "problem" of minimal initial distance.

It's not a problem. It's not a paradox of any kind.

It is a couple of simple truisms. It really is indisputable.

1. For a thing to move it must have an initial movement.

2. That movement will be the smallest movement possible.

Obviously the movement cannot be shorter than the smallest movement possible. That is an absurdity.

And if the movement is longer than the shortest movement possible it had to have made the shortest move possible first.

No problems. Simple truisms.

 

[beero1000]

It remains fascinating to me that anyone should stick to such an assumption. Yet, come to think of it, I don't remember anyone actually providing a full and detailed explanation as to why Zeno of Elea's Achilles & the Tortoise argument was wrong except the one Phil Scott just provided in this thread:



If anyone know of any previous occurrence, I'd like to know.
EB

Other than Phil's post, I haven't really seen anyone attempt to challenge UM's postulate about the "problem" of minimal initial distance.

What's the smallest positive real number? The real numbers include all the numbers greater than 0, and if a number precedes another there must have been the very first number between them. So there must be a least positive real number, or there are no non-zero real numbers...

Of course, UM will come back and say 'but we're not talking about imaginary things like numbers, we're talking about the real world', implicitly positing that the real world doesn't act in that way like real numbers do, which is what he's trying to argue, which is why he is VERY OBVIOUSLY BEGGING THE QUESTION.

 

[beero1000]

Other than Phil's post, I haven't really seen anyone attempt to challenge UM's postulate about the "problem" of minimal initial distance.

It's not a problem. It's not a paradox of any kind.

It is a couple of simple truisms. It really is indisputable.

1. For a thing to move it must have an initial movement.

2. That movement will be the smallest movement possible.

Obviously the movement cannot be shorter than the smallest movement possible. That is an absurdity.

And if the movement is longer than the shortest movement possible it had to have made the shortest move possible first.

No problems. Simple truisms.

Your truisms suffer from exceptions.

 

[untermensche]

Other than Phil's post, I haven't really seen anyone attempt to challenge UM's postulate about the "problem" of minimal initial distance.

What's the smallest positive real number? The real numbers include all the numbers greater than 0, and if a number precedes another there must have been the very first number between them. So there must be a least positive real number, or there are no non-zero real numbers...

Of course, UM will come back and say 'but we're not talking about imaginary things like numbers, we're talking about the real world', implicitly positing that the real world doesn't act in that way like real numbers do, which is what he's trying to argue, which is why he is VERY OBVIOUSLY BEGGING THE QUESTION.

Bull.

What is needed here is an argument why the real world should behave anything like an imaginary invented one.

You have things upside down.

And we are talking about movement.

Something real. Can we logically conclude with any argument that movement could be divided infinitely?

Or can that only be claimed?

 

[ryan]

Other than Phil's post, I haven't really seen anyone attempt to challenge UM's postulate about the "problem" of minimal initial distance.

It's not a problem. It's not a paradox of any kind.

It is a couple of simple truisms. It really is indisputable.

1. For a thing to move it must have an initial movement.

2. That movement will be the smallest movement possible.

Obviously the movement cannot be shorter than the smallest movement possible. That is an absurdity.

And if the movement is longer than the shortest movement possible it had to have made the shortest move possible first.

No problems. Simple truisms.

I mean how does what you say here (your "truism") present a problem for infinite division?

 

[beero1000]

What's the smallest positive real number? The real numbers include all the numbers greater than 0, and if a number precedes another there must have been the very first number between them. So there must be a least positive real number, or there are no non-zero real numbers...

Of course, UM will come back and say 'but we're not talking about imaginary things like numbers, we're talking about the real world', implicitly positing that the real world doesn't act in that way like real numbers do, which is what he's trying to argue, which is why he is VERY OBVIOUSLY BEGGING THE QUESTION.

Bull.

What is needed here is an argument why the real world should behave anything like an imaginary invented one.

You have things upside down.

I don't know if it does, I don't know if it doesn't. You are the one claiming certainty without justification.

Do you have an actual argument that does not beg the question? Maybe you can post one in its entirety so we can all see it?

 

[ryan]

Other than Phil's post, I haven't really seen anyone attempt to challenge UM's postulate about the "problem" of minimal initial distance.

What's the smallest positive real number? The real numbers include all the numbers greater than 0, and if a number precedes another there must have been the very first number between them. So there must be a least positive real number, or there are no non-zero real numbers...

Of course, UM will come back and say 'but we're not talking about imaginary things like numbers, we're talking about the real world', implicitly positing that the real world doesn't act in that way like real numbers do, which is what he's trying to argue, which is why he is VERY OBVIOUSLY BEGGING THE QUESTION.

So I was just reading about smooth infinitesimal analysis from https://plato.stanford.edu/entries/continuity/#9 (among other mathematical areas using infinitesimals). It explains how in this analysis using real numbers, there is a number x that is used instead of the arbitrarily small epsilon of a limit. It is so small that x^2 = 0, but x =/= 0, quite interesting and mind blowing for me.

 

[untermensche]

Bull.

What is needed here is an argument why the real world should behave anything like an imaginary invented one.

You have things upside down.

I don't know if it does, I don't know if it doesn't. You are the one claiming certainty without justification.

Do you have an actual argument that does not beg the question? Maybe you can post one in its entirety so we can all see it?

I'm saying if you have any movement you have to have an initial movement.

Some are saying you can have movement without an initial movement.

But without an initial movement of some length you do not have movement.

If movement remains at zero you have not moved.

The only question is: What length above zero is the smallest possible movement?

That will be the length of the movement everything that moves makes first.

 

[ryan]

I don't know if it does, I don't know if it doesn't. You are the one claiming certainty without justification.

Do you have an actual argument that does not beg the question? Maybe you can post one in its entirety so we can all see it?

I'm saying if you have any movement you have to have an initial movement.

Some are saying you can have movement without an initial movement.

But without an initial movement of some length you do not have movement.

If movement remains at zero you have not moved.

The only question is: What length above zero is the smallest possible movement?

That will be the length of the movement everything that moves makes first.

Can't it be a distance greater than 0 and still be an infinitesimal?

 

[beero1000]

I don't know if it does, I don't know if it doesn't. You are the one claiming certainty without justification.

Do you have an actual argument that does not beg the question? Maybe you can post one in its entirety so we can all see it?

I'm saying if you have any movement you have to have an initial movement.

Some are saying you can have movement without an initial movement.

But without an initial movement of some length you do not have movement.

If movement remains at zero you have not moved.

The only question is: What length above zero is the smallest possible movement?

That will be the length of the movement everything that moves makes first.

Ok, progress. Let's focus in on this claim:

But without an initial movement of some length you do not have movement.

Can you give an argument for why that has to be true?

 

[untermensche]

I'm saying if you have any movement you have to have an initial movement.

Some are saying you can have movement without an initial movement.

But without an initial movement of some length you do not have movement.

If movement remains at zero you have not moved.

The only question is: What length above zero is the smallest possible movement?

That will be the length of the movement everything that moves makes first.

Ok, progress. Let's focus in on this claim:

But without an initial movement of some length you do not have movement.

Can you give an argument for why that has to be true?

To have an actual movement requires a movement of some length.

A movement of zero length is not a movement. It is the lack of movement.

 

[beero1000]

Ok, progress. Let's focus in on this claim:

But without an initial movement of some length you do not have movement.

Can you give an argument for why that has to be true?

To have an actual movement requires a movement of some length.

A movement of zero length is not a movement. It is the lack of movement.

That's just a restatement of the claim. It is trivial to model a particle moving continuously so that it has no initial movement. Yet it moves.

You are claiming that that type of movement CANNOT be represented in the real world. Can you give an argument as to why?

 

[bilby]

What's the smallest positive real number? The real numbers include all the numbers greater than 0, and if a number precedes another there must have been the very first number between them. So there must be a least positive real number, or there are no non-zero real numbers...

Of course, UM will come back and say 'but we're not talking about imaginary things like numbers, we're talking about the real world', implicitly positing that the real world doesn't act in that way like real numbers do, which is what he's trying to argue, which is why he is VERY OBVIOUSLY BEGGING THE QUESTION.

Bull.

What is needed here is an argument why the real world should behave anything like an imaginary invented one.

You have things upside down.

And we are talking about movement.

Something real. Can we logically conclude with any argument that movement could be divided infinitely?

Or can that only be claimed?

We observe that things move. This is consistent with the mathematical explanation given, and inconsistent with your position.

 

[fast]

Ok, progress. Let's focus in on this claim:

But without an initial movement of some length you do not have movement.

Can you give an argument for why that has to be true?

To have an actual movement requires a movement of some length.

A movement of zero length is not a movement. It is the lack of movement.

But a movement of zero length only implies no "movement of," not that there is no "movement within."

 

[untermensche]

Ok, progress. Let's focus in on this claim:

But without an initial movement of some length you do not have movement.

Can you give an argument for why that has to be true?

To have an actual movement requires a movement of some length.

A movement of zero length is not a movement. It is the lack of movement.

That's just a restatement of the claim. It is trivial to model a particle moving continuously so that it has no initial movement. Yet it moves.

You are claiming that that type of movement CANNOT be represented in the real world. Can you give an argument as to why?

No. You have to address this.

How do you claim a movement took place unless some distance was moved?

It doesn't matter if we start from rest or start from an object's current position.

To get to a different position requires a movement of some length.

If you have moved a length of zero you have not moved.

- - - Updated - - -

Ok, progress. Let's focus in on this claim:

But without an initial movement of some length you do not have movement.

Can you give an argument for why that has to be true?

To have an actual movement requires a movement of some length.

A movement of zero length is not a movement. It is the lack of movement.

But a movement of zero length only implies no "movement of," not that there is no "movement within."

Movement in my little scenario was defined as movement of the train in relation to the track.

 

[untermensche]

Bull.

What is needed here is an argument why the real world should behave anything like an imaginary invented one.

You have things upside down.

And we are talking about movement.

Something real. Can we logically conclude with any argument that movement could be divided infinitely?

Or can that only be claimed?

We observe that things move. This is consistent with the mathematical explanation given, and inconsistent with your position.

We use mathematics as a PART of the models we use to MODEL reality.

There is a huge difference between the models and the real thing.

The models approximate the behavior of things in isolation. In other words abstractly.

There are no models that will predict how the leaves will blow around in your back yard.

 

[beero1000]

Ok, progress. Let's focus in on this claim:

But without an initial movement of some length you do not have movement.

Can you give an argument for why that has to be true?

To have an actual movement requires a movement of some length.

A movement of zero length is not a movement. It is the lack of movement.

That's just a restatement of the claim. It is trivial to model a particle moving continuously so that it has no initial movement. Yet it moves.

You are claiming that that type of movement CANNOT be represented in the real world. Can you give an argument as to why?

No. You have to address this.

How do you claim a movement took place unless some distance was moved?

It doesn't matter if we start from rest or start from an object's current position.

To get to a different position requires a movement of some length.

If you have moved a length of zero you have not moved.

Objects have positions at every instant in time and those positions may be different for different instants in time; movement can take place without any need for an initial movement. The math here is trivial and shows that your position is not universal among all possible models of movement, so you are making extra assumptions about which types of movement exist. It's easy to imagine a variety of different types of movement, some continuous and some discrete, that do not satisfy your claim.

You are assuming that those types of movement CANNOT be represented in the real world. That requires justification. Do you have an argument?

 

[untermensche]

Ok, progress. Let's focus in on this claim:

But without an initial movement of some length you do not have movement.

Can you give an argument for why that has to be true?

To have an actual movement requires a movement of some length.

A movement of zero length is not a movement. It is the lack of movement.

That's just a restatement of the claim. It is trivial to model a particle moving continuously so that it has no initial movement. Yet it moves.

You are claiming that that type of movement CANNOT be represented in the real world. Can you give an argument as to why?

No. You have to address this.

How do you claim a movement took place unless some distance was moved?

It doesn't matter if we start from rest or start from an object's current position.

To get to a different position requires a movement of some length.

If you have moved a length of zero you have not moved.

Objects have positions at every instant in time and those positions may be different for different instants in time; movement can take place without any need for an initial movement. The math here is trivial and shows that your position is not universal among all possible models of movement, so you are making extra assumptions about which types of movement exist. It's easy to imagine a variety of different types of movement, some continuous and some discrete, that do not satisfy your claim.

You are assuming that those types of movement CANNOT be represented in the real world. That requires justification. Do you have an argument?

How is there any movement from a position if there is no first movement from that position?

How does that occur?

If there is no first movement there is NO movement. To have a movement it has to have a length. You cannot have a movement of zero length. A movement HAS to be something not nothing.

Your objections do not make one bit of sense.

 

[beero1000]

Ok, progress. Let's focus in on this claim:

But without an initial movement of some length you do not have movement.

Can you give an argument for why that has to be true?

To have an actual movement requires a movement of some length.

A movement of zero length is not a movement. It is the lack of movement.

That's just a restatement of the claim. It is trivial to model a particle moving continuously so that it has no initial movement. Yet it moves.

You are claiming that that type of movement CANNOT be represented in the real world. Can you give an argument as to why?

No. You have to address this.

How do you claim a movement took place unless some distance was moved?

It doesn't matter if we start from rest or start from an object's current position.

To get to a different position requires a movement of some length.

If you have moved a length of zero you have not moved.

Objects have positions at every instant in time and those positions may be different for different instants in time; movement can take place without any need for an initial movement. The math here is trivial and shows that your position is not universal among all possible models of movement, so you are making extra assumptions about which types of movement exist. It's easy to imagine a variety of different types of movement, some continuous and some discrete, that do not satisfy your claim.

You are assuming that those types of movement CANNOT be represented in the real world. That requires justification. Do you have an argument?

How is there any movement from a position if there is no first movement from that position?

How does that occur?

If there is no first movement there is NO movement. To have a movement it has to have a length. You cannot have a movement of zero length. A movement HAS to be something not nothing.

Your objections do not make one bit of sense.

Your incredulity is noted, but I can think of multiple different ways that movement could happen without a smallest movement. Do you have an argument that shows why your claim MUST be true? Or is it just, "I can't see how that could happen..."?