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

[untermensche]

You began at conception. The exact instant is hard to pinpoint but within a year your beginning is easy to pinpoint.

Is it? You are the result of a merge of a part of the process you know as your father and the process you know as your mother. There is no point in space time where you begin from nothing. It is more like as two roots of a tree combined and slowly growed into a new trunk. It is a new think because we classifies things.

I never said things could begin from nothing. Only that all things that we can experience, every particle, has a beginning.

You are the result of the fertilization of one cell by another. A life that exists that did not is a beginning.

What exact moment the fertilization takes place is unknown but in most cases it can easily be known within a month.

I am not claiming the universe could begin from nothing. Only that it needs a beginning and incidentally it seems to have one.

 

[fromderinside]

It would be better if you took the whole construction.

The whole construction is this absurd idea of an event happening that has no beginning.

That is what saying "time with no beginning" implies.

If one has no need for a beginning then one is free to say time is.

True.

If you could show me something that had no beginning then we could say it is something real.

Beginnings imply some causal reason for time to appear.

No beginning implies time never appears.

I think the whole point of using "The world is governed by (or is under the sway of) determinism if and only if, given a specified way things are at a time t, the way things go thereafter is fixed as a matter of natural law" is to use a point in time as a reference for how things are going to be thereafter. If time has no beginning there are still points in time after which etc. .....


What you do is transpose properties of events on the measure time. One need not understand the beginning of time to say an event occurred at time t as do those who define the meaning of determinism. Thus if one specifies t₁ one can say how things are at time t₂​.

 

[Juma]

I am the person that thinks that no infinity can be expressed. No infinity can exist. No infinity can already be in the past.

No. You have stopped thinking. You have stopped analyzing your own reasons.
Sad.

 

[untermensche]

I am the person that thinks that no infinity can be expressed. No infinity can exist. No infinity can already be in the past.

No. You have stopped thinking. You have stopped analyzing your own reasons.
Sad.

It is simple minded and stupid to claim that infinite events occurred in the past.

If an event doesn't start there can be no event.

 

[beero1000]

I am the person that thinks that no infinity can be expressed. No infinity can exist. No infinity can already be in the past.

No. You have stopped thinking. You have stopped analyzing your own reasons.
Sad.

How could he have stopped if he never began?

 

[Speakpigeon]

Yes, and that's a good point.

It also shows how complex our notions can be.

Finite intervals of time like this are just ordinary intervals from which you just remove one or both ends.

And if time is continuous like the Reals, there's a bijection between for example an infinite past in the usual sense and a finite interval of time, however small, that would have no beginning, as long as time is really infinitely divisible like the Reals, which maybe it is not (and quite plausibly, the past is not infinite either).

So, now, you'd have to offer another way to define the notion of infinite past so as to make the distinction with the case above.

Can you do that? You're the specialist here I guess.
EB

I don't think that's a problem, because the particular elements used to define the set T don't really matter (by construction). We could use any other set T' that is order isomorphic to T (like in your example (0,1) and R), and there won't be any difference in the results other than the labels used to describe moments in time, e.g. there is no operational difference between moments in time labeled with all of the real numbers and moments in time labeled with the real numbers from (0,1). What matters is the speed at which that the labels are passed by our clocks during those moments.

Specifically, I didn't define a time metric to measure the 'length' of time, so the elements of T (the moments in time) are just labels and don't need to be numbers at all. Even if T consists of numbers, it doesn't necessarily follow that a length on intervals T gives the appropriate metric we use to measure time. That's why I included the term 'ticks' for the clock.

If I had to define length for an interval of time, I would use clock ticks (as we do in real life) - for a given time interval, the number of ticks within the interval determines the length of the interval of time (up to the precision of your 'clock'). Then, an infinite interval of time would be one that contains an infinite number of 'ticks'. A nice aspect of this definition is that it is equivalent to the topological definition I gave originally, as long as the interval under consideration contains at least one tick of the clock (or even any moment between two ticks, but whatever ).

Ok, it's good enough for me.

Still, do you realise your metric consists in having a finite set (ticks) describe an infinite one (a bounded interval of real numbers)? Although I guess rational numbers similarly describe the set of real numbers.

Yet, only the metric so obtained makes physical sense, i.e. what matters is the finite number of ticks so obtained, not the infinity of points in the bounded interval so measured.

I wonder if the notion of metric in this case really makes sense. It seems to me that it only makes sense because real numbers already have a ready-made metric, which is provided by the subset of integers.

But think of a set of things with the same kind of infinity as real numbers but without numeric labels. How would you get them the kind of metric considered above? I guess one thing missing would be the ordering real numbers have. So, let's say we consider space, or more precisely all locations (points) along a continuous line taken in ordinary space, and assume it has the same kind of infinity as the real numbers have. And it's ordered. Yet, I think any metric would in fact be arbitrary since space doesn't come pre-labelled, at least if it's indeed continuous (not discrete like N for example).

Ok, it's a bit of a derail, so mods can prune it from here if necessary.
EB

 

[Speakpigeon]

I think we just don't know.
It's at least conceivable that time isn't a fixed frame within which events would occur forever at the same rate.
Maybe time is dependent on something else and is somehow occurring possibly at different rates. And if all events in our universe still occurred at the same rate relatively to each other, we wouldn't notice the change of rate of time itself.
In this case, apparent time, the one we would be able to observe wouldn't be the real time envisaged here. A second on our clocks might take one day a million years of real time and only a nanosecond the following day, and we would not be able to tell. If all our clock are similarly affected, and us with them, and everything else in our universe, we wouldn't be able to tell.
EB

I think something might have gotten lost in the translation. I want a persistent ever enduring time interval (a second) that cannot succumb to effects of the real world. I want a perfect second, like the one we have with my super duper state of art watch.

There are 365 1/4 days in a year, but a second isn't based on that. A second is 1/60 of 1/60 of 1/24 of 365 days; otherwise, a second wouldn't be what elixir said.

- - - Updated - - -

Also, if something happens and a year passes in 364 days, the formula is to be rejected and replaced with a recalculation where the second remains constant and the number days in a year changes keeping the weird number elixir gave consistent and ever enduring.

The thing is, if all interactions in the universe are uniformly affected by the slowing down effect of some fundamental and universal phenomenon then nobody would notice or indeed could possibly notice. Our seconds would still look like they take a second to elapse even though they would in fact take longer. Still, that would keep you happy because you wouldn't notice either.
EB

 

[beero1000]

I don't think that's a problem, because the particular elements used to define the set T don't really matter (by construction). We could use any other set T' that is order isomorphic to T (like in your example (0,1) and R), and there won't be any difference in the results other than the labels used to describe moments in time, e.g. there is no operational difference between moments in time labeled with all of the real numbers and moments in time labeled with the real numbers from (0,1). What matters is the speed at which that the labels are passed by our clocks during those moments.

Specifically, I didn't define a time metric to measure the 'length' of time, so the elements of T (the moments in time) are just labels and don't need to be numbers at all. Even if T consists of numbers, it doesn't necessarily follow that a length on intervals T gives the appropriate metric we use to measure time. That's why I included the term 'ticks' for the clock.

If I had to define length for an interval of time, I would use clock ticks (as we do in real life) - for a given time interval, the number of ticks within the interval determines the length of the interval of time (up to the precision of your 'clock'). Then, an infinite interval of time would be one that contains an infinite number of 'ticks'. A nice aspect of this definition is that it is equivalent to the topological definition I gave originally, as long as the interval under consideration contains at least one tick of the clock (or even any moment between two ticks, but whatever ).

Ok, it's good enough for me.

Still, do you realise your metric consists in having a finite set (ticks) describe an infinite one (a bounded interval of real numbers)? Although I guess rational numbers similarly describe the set of real numbers.

Yet, only the metric so obtained makes physical sense, i.e. what matters is the finite number of ticks so obtained, not the infinity of points in the bounded interval so measured.

The tick set can be finite or infinite, as long as it's countable - which I think is the 'physical sense' of ticking clocks. It's possible to use the general definition to get weird sets of ticks that are bounded, yet lie within unbounded time, that we could imagine might correspond to time 'slowing down' so that the ticks of a regular clock essentially stop (e.g. relativistic effects from a clock accelerating to light speed). I want to allow those unless there's a reason not to.

I wonder if the notion of metric in this case really makes sense. It seems to me that it only makes sense because real numbers already have a ready-made metric, which is provided by the subset of integers.

Right, I could have just used the integers, but I was trying to anticipate complications of time measurement NOT being uniformly distributed like the integers in the reals.

But think of a set of things with the same kind of infinity as real numbers but without numeric labels. How would you get them the kind of metric considered above? I guess one thing missing would be the ordering real numbers have. So, let's say we consider space, or more precisely all locations (points) along a continuous line taken in ordinary space, and assume it has the same kind of infinity as the real numbers have. And it's ordered. Yet, I think any metric would in fact be arbitrary since space doesn't come pre-labelled, at least if it's indeed continuous (not discrete like N for example).

Ok, it's a bit of a derail, so mods can prune it from here if necessary.
EB

All you need is a total ordering on a set. Numbers are easy to use because they come prepackaged with an ordering already, but it isn't too hard to come up with examples of things that aren't labelled with numbers. For example, think of all infinite 'words', like ABABCABCD... and we say one such sequence is bigger than an another if it comes after it in the alphabetical ordering.

 

[Speakpigeon]

All you need is a total ordering on a set. Numbers are easy to use because they come prepackaged with an ordering already, but it isn't too hard to come up with examples of things that aren't labelled with numbers. For example, think of all infinite 'words', like ABABCABCD... and we say one such sequence is bigger than an
another if it comes after it in the alphabetical ordering.

Space presumably is totally ordered. At least that's how we think of it. But it doesn't come with predefined labels. So when we think maybe we are measuring space, in fact we are measuring something else, which is the coincidence between two material things, for example a ruler and a plank of wood. So, our measures of space is in fact the measuring of material things in space. Similarly for time, we measure the duration not of time itself but of one thing, say a movie, relative to another, say, clock ticks.

Anyway, I'm not sure where I'm going with this.
EB

 

[untermensche]

No. You have stopped thinking. You have stopped analyzing your own reasons.
Sad.

How could he have stopped if he never began?

View attachment 12894

Always nice to hear from the children in the crowd.

When they have no arguments they post their little cartoons.

The idea of something progressing that never begins it's progression makes sense to these types.

 

[fromderinside]

Is anyone considering things that are only piece-wise continuous. Each segment has the property of being  Infinitely divisible in each  continuum.

Just sayin'

I think we've got consensus that infinite as logically possible.

 

[untermensche]

It is a strange logic that says things that are impossible are possible.

It takes a special kind of "education" to see possibilities in clear impossibilities.

 

[untermensche]

What it seems to me is there are going to be those who are convinced things can be made possible by very feeble human claims no matter what you say to them.

They have their grammar and their language and with it they think they can bring dragons into existence.

It's called a magic spell. Shared delusion.

What is clear is that nobody can show how things "without beginning" are actually a rational category of existence. They can't produce anything that has no beginning. Not one particle.

But things like that don't seem to bother some people much.

Can they describe one aspect of "no beginning"? Can they produce one bit of logic to show how progression of events can occur without a start to the events?

At one time people took this idea of the impossibility of infinite events and just put their invented god into the picture as the answer. They were primitive and superstitious.

But at least they could clearly see what is clearly obvious.

To have any event you must have a start to it. For something to move it must begin to move.

You cannot finish infinite events. It is like reciting the integers. There is no end to them.

 

[Speakpigeon]

Is anyone considering things that are only piece-wise continuous. Each segment has the property of being  Infinitely divisible in each  continuum.

Just sayin'

Aren't space and time each "piece-wise continuous", at least in our ordinary conception of them?

I think we've got consensus that infinite as logically possible.

Yes, we do, but no wonder because it's almost 'a truth universally accepted', so I wouldn't expect any of us here to come up with the 'killer blow'.

What is rather interesting is that reality probably doesn't feature any infinity at all, and more to the point I don't think we could even observe infinity as such if it was in front of us. And yet we have no problem conceiving of it.

Somewhat like we can conceive of God, in fact! Terrific!

Can you conceive of God?
EB

 

[untermensche]

I think we've got consensus that infinite as logically possible.

Yes, we do, but no wonder because it's almost 'a truth universally accepted', so I wouldn't expect any of us here to come up with the 'killer blow'.

It is not.

Only a peculiar individual accepts that things which are physically impossible are in any way possible. The idea of a "possibility" has been distorted beyond recognition.

I do not know from where this nonsense arises. From where this cancer grows.

The idea of continuity breaks down into absurdity when it is applied to the real world. That is what all these so-called paradoxes demonstrate.

You can't apply the concept to reality.

And nobody tries.

They merely claim it is possible.

As if claims ever made anything possible.

 

[untermensche]

This thread begins with me asking for a demonstration that mere claims of a possibility arise to the level of a real possibility.

And it has progressed to the point where some have now claimed the putting forth of statements amounts to creating a possibility, ignoring reality and the nature of reality. I asked in my initial post:

How does logic make things possible?

Some have shown me their so-called logic. It resembles the logic that proved the gods are possible.

I have yet to see how any of it makes anything possible.

Where is the proof or argument that an infinite amount of time is actually possible to have already passed?

How do we say that physical impossibilities are somehow logically possible?

That is the focus of this thread.

Not some derail about the admiration of statements that prove nothing.

 

[Speakpigeon]

UM, you already had all the explanations one would need to understand what 'logically possible' means. We could always improve on what has been said but I think it's not really that difficult to understand.

I repeat below an exchange between PyramidHead and beero which does the job well enough.

Logic deals with the relationship between concepts, not the relationship between concepts and the real world. The usefulness of logic is that it allows us to rule certain things out without having to check the real world. For something to be logically impossible, it must be self-contradictory, like a square circle or a married bachelor. We don't have to hold onto a sliver of doubt that somewhere in the universe, there may be a square circle. The concept of "square" contradicts the concept of "circle", so under those definitions we can be 100% positive that no such thing exists. Other than cases like that, nothing is logically impossible.

In casual language, "logic" is often used as a substitute for clear-headedness or common sense. That's a different sense of the term, and asking if something is logical by that definition may give you a different answer. It won't be a very useful answer, though. Common sense is often wrong. That's why we have science and philosophy.

Math nit pick: You should think carefully about defining 'square' and 'circle' before you say 'square circle' is self-contradictory. Lots of interesting metrics out there...

That goes to Bomb's point about clear definitions, I suppose. Assume simple Euclidean geometry, then.

I can complete a bit by saying that the above is good enough for everyday logic.

If we wanted to talk about formal logic, only a formal contradiction can show some statement is logically impossible, such as for example, 'X and not X'.

As it is, the statement 'X is God and X exists' does not contain any formal contradiction so it's logically possible.

The real question is whether the word 'God' means the same thing to different people, but there, we have to fall back on things like dictionaries and usage, which seems good enough to me.

Unless we wanted to start quibbling about every other word people will use, and then we might just as well stop talking altogether.
And clearly, you don't look like you're going to do that any time soon.

So do go on and on.
EB

 

[beero1000]

As a senior citizen was driving down the freeway, his phone rang. Answering, he heard his wife's voice urgently warning him, "Herman, I just heard on the news that there's a car going the wrong way on Highway 401. Please be careful!"

"It's not just one car," said Herman, "It's hundreds of them!"

In addition, on the standard model of the relation between these kinds of modalities the logical possibilities are the most inclusive; they include any proposition that sheer logic leaves open, no matter how otherwise impossible it might be. The metaphysical possibilities are the logical possibilities that are also allowed by the natures of all of the things that could have existed. The physical possibilities are the logical and metaphysical possibilities that are also allowed by the physical laws of nature. On the standard model, the following nesting relation holds:

 

[untermensche]

 

[untermensche]

UM, you already had all the explanations one would need to understand what 'logically possible' means.

It is clearly a religious term so I may have heard what some sect says about it. So what?

I dismiss their empty claims as quickly as I dismiss all unsupported claims.

People and their religions. Hard to separate the two.

First you claim that contradictions are a no no. Then by some miracle being impossible and a huge can of worms that makes no sense isn't a contradiction. It takes a special kind of deliberate blindness to not care about things like that.

Possibilities are what can actually happen. If something can happen it is logically a possibility, a logical as opposed to illogical possibility. An logical impossibility is something that cannot happen.

We learn about possibilities through science and experiment.

Not by sitting in an empty room writing statements that have a certain grammatical quality to them. Not with any magic spells.