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

[Kharakov]

The fact that you can divide it by any real number (other than 0) should be enough to show you how many times you can divide it.

That is an evasion.

No, you're supposed to use that fact to arrive at a piece of knowledge about infinity. Of course, I assumed you knew that if you divide by infinity, unless you're using the hyperreal numbering system, you get an undefined amount. My mistake- you don't know anything about infinity, do you?

 

[Speakpigeon]

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

It depends on who is talking.

For most logicians, a logical possibility is an statement that does not contain any formal contradiction, as does for example the statement "A and not A".

For other people, I wouldn't know. Most dictionaries give all sort of definitions. It's just a mess.

Still, for most logicians, then, an infinite past is a logical possibility since the expression does not formally contradict itself.

More specifically, I think it must be easy to find particular but reasonable meanings of 'infinite' and 'past' such that there is no formal contradiction.

So, here is a challenge to all those who think 'infinite past' is a logical possibility: Express the same thing using clear definitions of 'infinite' and 'past' such that there will be no formal contradiction in the result.

Beware that it will only be convincing if your definitions are sufficiently explicit and detailed, and if they do express the common usage of these words.

Posters could then vote for the best definition.

Any takers?
EB

 

[untermensche]

That is an evasion.

No, you're supposed to use that fact to arrive at a piece of knowledge about infinity. Of course, I assumed you knew that if you divide by infinity, unless you're using the hyperreal numbering system, you get an undefined amount. My mistake- you don't know anything about infinity, do you?

Hand waving.

Your claims are instantly shown to be absurd.

You don't understand that neither infinity or zero can exist in reality.

 

[untermensche]

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

It depends on who is talking.

For most logicians, a logical possibility is an statement that does not contain any formal contradiction, as does for example the statement "A and not A".

For other people, I wouldn't know. Most dictionaries give all sort of definitions. It's just a mess.

Still, for most logicians, then, an infinite past is a logical possibility since the expression does not formally contradict itself.

More specifically, I think it must be easy to find particular but reasonable meanings of 'infinite' and 'past' such that there is no formal contradiction.

So, here is a challenge to all those who think 'infinite past' is a logical possibility: Express the same thing using clear definitions of 'infinite' and 'past' such that there will be no formal contradiction in the result.

Beware that it will only be convincing if your definitions are sufficiently explicit and detailed, and if they do express the common usage of these words.

Posters could then vote for the best definition.

Any takers?
EB

How is something being shown to be impossible NOT a problem?

Is reciting the integers possible?

What makes you think the passage of infinite time is somehow more possible than reciting the integers?

"Possible" means to be able to have real existence.

Adding "logical" doesn't change that.

 

[beero1000]

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

It depends on who is talking.

For most logicians, a logical possibility is an statement that does not contain any formal contradiction, as does for example the statement "A and not A".

For other people, I wouldn't know. Most dictionaries give all sort of definitions. It's just a mess.

Still, for most logicians, then, an infinite past is a logical possibility since the expression does not formally contradict itself.

More specifically, I think it must be easy to find particular but reasonable meanings of 'infinite' and 'past' such that there is no formal contradiction.

So, here is a challenge to all those who think 'infinite past' is a logical possibility: Express the same thing using clear definitions of 'infinite' and 'past' such that there will be no formal contradiction in the result.

Beware that it will only be convincing if your definitions are sufficiently explicit and detailed, and if they do express the common usage of these words.

Posters could then vote for the best definition.

Any takers?
EB

I'll play.

1. A "clock" is a process that generates a totally ordered set T, called "time". The elements of T are called "moments".
2. A moment m "occurs before" a moment n if m is less than n. Similarly, a moment m "occurs after" a moment n if m is greater than n.
3. The "ticks" of a clock are a set M of moments, indexed by a strictly monotonically increasing function f: Z -> M
4. The "present" is the tick indexed by 0, given by f(0).
5. The "past" is the subset of T that occurs before f(0).
6. The "future" is the subset of T that occurs after f(0).
7. An "interval of time" is a connected subset of T (in the order topology).
8. An interval I of time "has a beginning" if there is a moment m of I that occurs before every other moment of I. m is called the "beginning moment" of I.
9. An interval I of time "has an end" if there is a moment m of I that occurs after every other moment of I. m is called the "end moment" of I.
10. An interval of time is "finite" if it is contained within an interval of time that has a beginning and an ending.
11. An interval of time is "infinite" if it is not finite.

 

[untermensche]

Yes it is possible to claim infinite time is possible.

It is possible to CLAIM anything is possible. Even the impossible.

But proving it is possible is impossible.

As impossible as infinite time ever passing.

 

[Juma]

Yes it is possible to claim infinite time is possible.

It is possible to CLAIM anything is possible. Even the impossible.

But proving it is possible is impossible.

As impossible as infinite time ever passing.

Define what ”infinite time is passing” means.

 

[untermensche]

Yes it is possible to claim infinite time is possible.

It is possible to CLAIM anything is possible. Even the impossible.

But proving it is possible is impossible.

As impossible as infinite time ever passing.

Define what ”infinite time is passing” means.

Passing would mean completing, finishing.

We know ten minutes can pass. The entire time can complete.

Infinite time is time that can never complete.

It cannot pass. It cannot be in the past.

 

[ryan]

That is an evasion.

No, you're supposed to use that fact to arrive at a piece of knowledge about infinity. Of course, I assumed you knew that if you divide by infinity, unless you're using the hyperreal numbering system, you get an undefined amount. My mistake- you don't know anything about infinity, do you?

Dividing anything by infinity is undefined, really?

 

[ryan]

UM, infinity is just a property. Instead of the universe having seemingly unique properties as it expands through time, imagine a universe with the property of repeating itself. With that property in mind, every human that had lived and died in this universe would have lived an infinite number of times.

 

[Juma]

Define what ”infinite time is passing” means.

Passing would mean completing, finishing.

We know ten minutes can pass. The entire time can complete.

Infinite time is time that can never complete.

It cannot pass. It cannot be in the past.

Define ”time completing”.

 

[untermensche]

Passing would mean completing, finishing.

We know ten minutes can pass. The entire time can complete.

Infinite time is time that can never complete.

It cannot pass. It cannot be in the past.

Define ”time completing”.

When the second hand moves around one time one minute of time has completed.

It has finished. It is in the past.

- - - Updated - - -

UM, infinity is just a property. Instead of the universe having seemingly unique properties as it expands through time, imagine a universe with the property of repeating itself. With that property in mind, every human that had lived and died in this universe would have lived an infinite number of times.

Properties are something that can be observed in some way.

 

[beero1000]

No, you're supposed to use that fact to arrive at a piece of knowledge about infinity. Of course, I assumed you knew that if you divide by infinity, unless you're using the hyperreal numbering system, you get an undefined amount. My mistake- you don't know anything about infinity, do you?

Dividing anything by infinity is undefined, really?

Really. (at least in the reals, and if you want division to be well-defined)

 

[untermensche]

Being undefined does not help those who claim these infinite divisions are something real.

Zero, undefined? Makes no difference.

Definitely not something real.

 

[beero1000]

It depends on who is talking.

For most logicians, a logical possibility is an statement that does not contain any formal contradiction, as does for example the statement "A and not A".

For other people, I wouldn't know. Most dictionaries give all sort of definitions. It's just a mess.

Still, for most logicians, then, an infinite past is a logical possibility since the expression does not formally contradict itself.

More specifically, I think it must be easy to find particular but reasonable meanings of 'infinite' and 'past' such that there is no formal contradiction.

So, here is a challenge to all those who think 'infinite past' is a logical possibility: Express the same thing using clear definitions of 'infinite' and 'past' such that there will be no formal contradiction in the result.

Beware that it will only be convincing if your definitions are sufficiently explicit and detailed, and if they do express the common usage of these words.

Posters could then vote for the best definition.

Any takers?
EB

I'll play.

1. A "clock" is a process that generates a totally ordered set T, called "time". The elements of T are called "moments".
2. A moment m "occurs before" a moment n if m is less than n. Similarly, a moment m "occurs after" a moment n if m is greater than n.
3. The "ticks" of a clock are a set M of moments, indexed by a strictly monotonically increasing function f: Z -> M
4. The "present" is the tick indexed by 0, given by f(0).
5. The "past" is the subset of T that occurs before f(0).
6. The "future" is the subset of T that occurs after f(0).
7. An "interval of time" is a connected subset of T (in the order topology).
8. An interval I of time "has a beginning" if there is a moment m of I that occurs before every other moment of I. m is called the "beginning moment" of I.
9. An interval I of time "has an end" if there is a moment m of I that occurs after every other moment of I. m is called the "end moment" of I.
10. An interval of time is "finite" if it is contained within an interval of time that has a beginning and an ending.
11. An interval of time is "infinite" if it is not finite.

On second thought, a technical amendment for 3: I think I want to require f to be a bijection, and I also want the domain to be allowed to be any connected (in the order topology) subset of Z containing 0.

I don't think I missed any other issues, so I think this should probably work to formally define time, at least for our purposes. It matches the standard intuition for time, allows for different ephemeral clocks in different reference frames, ticking at different (possibly non-constant) rates, discrete time or continuous time, finite or infinite, clocks can have coarser or finer ticks, we can talk about measurable lengths or durations of time by counting clock ticks, we can bring in relativity, etc.

I very much doubt these definitions imply a contradiction for the idea of an infinite past, but I think I'll enjoy watching untermensche completely bungle the attempt.

 

[ryan]

UM, infinity is just a property. Instead of the universe having seemingly unique properties as it expands through time, imagine a universe with the property of repeating itself. With that property in mind, every human that had lived and died in this universe would have lived an infinite number of times.

Properties are something that can be observed in some way.

That's your definition of property. Forget property; switch "property" with "behavior" then. Is it logical for this "big bounce" type universe to exist?

 

[untermensche]

I am looking for PROOF that infinite time in the past is possible.

Not some over-flowery CLAIM it is possible.

I do not accept this notion that there are anything but physical possibilities.

Imaginary possibilities are not possibilities unless they actually are possible.

To prove infinite time, something physical, is possible you have to prove it is physically possible.

How is it physcially possible that infinite time can have a last moment?

For centuries theologians had their pristine and non-contradictory proofs of their gods.

What was any of it worth?

 

[untermensche]

Properties are something that can be observed in some way.

That's your definition of property. Forget property; switch "property" with "behavior" then. Is it logical for this "big bounce" type universe to exist?

I was given my language. I did not invent it.

It is only possible that a finite amount of bounces have already occurred.

If infinite bounces had to occur before you could be born you would not be here.

 

[ryan]

Dividing anything by infinity is undefined, really?

Really. (at least in the reals, and if you want division to be well-defined)

Maybe if you are talking about infinity instead of infinite, but in the former case we can't be in standard math anymore.

I have to think that you and kar are teaking the rules - just a little - to rebuke UM's issue with 0.

But let it be 0 space moved at once; 0 in a strange way is more than nothing. Think of the empty set, no objects. But zero is 1 object just like a 4 is one object.

Something can take up 0 space on the number line on say position 7, but nothing cannot take up even 0 space on the number line. 0 > nothing.

Added: all numbers on the real number line take up 0 space, yet it enough space to complete a continuum.

 

[ryan]

That's your definition of property. Forget property; switch "property" with "behavior" then. Is it logical for this "big bounce" type universe to exist?

I was given my language. I did not invent it.

It is only possible that a finite amount of bounces have already occurred.

If infinite bounces had to occur before you could be born you would not be here.

Your order is bias based on conscious experience. The bounces can be said to begin today and then successively bounce infinitely into the past. A movie does not have an absolute beginning unless someone assigns one. It's all in a dimension and its order is subjective, not objective.