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

[Bomb#20]

I.e., every number is number plus some other imaginary conception added on. "Three" is the imaginary conception "two" plus some other imaginary conception added on, like "one". The fact that three is an imaginary conception is evidently no obstacle to the actual existence of a tree branch with three plums hanging from it. So why the heck would the fact that 2^aleph-null is an imaginary conception suddenly be some insurmountable obstacle to the actual existence of a tree branch with 2^aleph-null points between the trunk and the tip?

Every number?

What are you adding onto the conception of one?

Any number I ever added one to.

And the number six is the conception of number plus what else?

It's the conception of the number five plus the conception of the number one plus the conception of "plus".

There is nothing added to the conception of number to make any number. They are all only numbers.

Of course there is. The conception of the number -6 is the conception of 6 with the conception of "in the other direction" added on. The conception of the number 6.5 is the conception of 6 with the conception of 7 and the conception of "half way there" added on.

But infinity is the concept of number plus the concept of "going on forever".

It is more than the conception of number.

This in no way distinguishes it from negative numbers, or fractions, or irrational numbers. Every time we expanded our understanding of what a number can be we were adding a concept to the concept of number. And every time we did it there were other conservatives just like you who balked and said we were wrong to take that next conceptual step.

Not merely numbers. Conceptions on top of the conception of number. Zero is the conception of "without number" or "without value".

If that were the case then "0 degrees Celsius" would be the conception "without temperature". Zero is just the next whole number down from one.

Once you have the symbol of zero you can use it to designate something positive.

You confuse the conception of zero with a use of the symbol to represent a positive temperature. It's a creative use since it highlights the phase change.

Thank you Dr. Kelvin. If zero were the conception of "without number" or "without value" then "0 degrees longitude" would be the conception "without longitude"; but it actually just means "the same longitude as Greenwich". It's just the next whole number down from one, so it designates something that's one degree west of whatever longitude you label "1 degree east longitude". Things do not need to be positive to be measured with numbers. 0 degrees longitude is the same thing as -360 degrees longitude.

Over and over you keep objecting that infinity is imaginary; but you didn't answer my question. As you yourself pointed out, "three" is an imaginary conception that has no real world existence; and yet the fact that three is an imaginary conception is evidently no obstacle to the actual existence of a tree branch with three plums hanging from it. So answer the question. Why the heck would the fact that 2^aleph-null is an imaginary conception suddenly be some insurmountable obstacle to the actual existence of a tree branch with 2^aleph-null points between the trunk and the tip?

If my software had been sophisticated enough and someone had run the simulation long enough on a powerful enough computer, in principle the little robots could have evolved intelligence and self-consciousness.

An empty claim I don't believe for a second.

Which part of my explanation are you challenging? Are you merely denying that my programming chops are up to the task I proposed? If so I agree with you but you're missing the point -- I did say "If my software had been sophisticated enough", after all. For such more sophisticated software to exist, someone more sophisticated than me would no doubt need to write it.

So what exactly is it you're disputing? Are you seriously opining that artificial intelligence is impossible? I never took you for a believer in souls. Or are you seriously proposing that artificial intelligence is possible but only if a preexisting intelligent programmer deliberately writes it and not by the operation of mere unguided reproduction of software routines and their selection for survival? I never took you for a creationist.

And nothing about the use of computers is "dimensionless".

If you mean nothing about the use of this universe's computers is dimensionless, true, but what of it? This universe's computers are not the issue. We're discussing the possibility that this universe's dimensions are an illusion, simulated on some other universe's computer. If you have proof that any universe we might be simulated by must necessarily have dimensions of its own, show your work.

 

[beero1000]

You brought it up, unsolicited, in this very thread. It was a bit of a non sequitur anyway, but it's something everyone can picture and is easily proved, unlike abstract concepts like infinity and the shape of the universe, so I'm using it as a gauge to see if any progress can be made. Can you admit that you made a mistake and that your statement was wrong?

What I said was that between two points in space a smallest distance exists.

And that includes two points outside a sphere.

If you disagree start a thread about your incredible discovery.

Well, that answered my question. It's sad, really.

 

[Speakpigeon]

WTF is this thread about? The definition of "possible"?

IMHO, you first have to decide whether or not everything is possible. If not, then anything that doesn't happen was never possible. IOW, the very word possible is nothing more than an expression of ignorance of whether or not it will come to pass. Adding the qualifier "logically" doesn't help the situation.

In an infinite universe/multiverse over infinite time, everything is not only possible, but certain. If the universe (or its duration) is finite, then only that which actually occurs was ever "logically possible" - to say that something that never occurred was possible, is to say nothing more than that we thought it could happen.

There is nothing whatsoever "logical" about something being called possible or impossible, unless this is a psych study wherein we examine the differing opinions of fallible humans regarding specific future events.

Am I missing something?

Yes, you seem to be missing something.

Which is that the meaning of the expression 'logically possible', like that of any expression, is ultimately conventional, i.e. it means what people using the expression want it to mean. In other words, the meaning of 'logically possible' may be different from the meaning you could infer from the two words, 'logically' and 'possible'.

According to usage, then, something is said to be logically possible if it is not somehow self-contradictory.

This in itself doesn't say much. In particular, it doesn't say whether something logically possible necessarily exists or not, whether it's physically possible or not, etc.

Essentially it's all inside our heads. If it is logically possible then we can feel confortable conceiving of it, which is not the case with contradictions. Conceiving of it here just means we can think about it, use it in our reasonings etc.

Crucially perhaps, we can also assume it might very well exist for real. So, the fact that infinity is logically possible means that we are at liberty to assume infinity might exist physically, and use this assumption in our reasonings. We can do that and get away with it because it may be too difficult to prove that some thing that is logically possible but physically impossible doesn't and couldn't actually exist. Infinity is a god example. How could you prove that infinity doesn't and couldn't exist physically? You would have to try to go there and find out that there's a limit, but this will usually require more time than you have available. And so it's convenient to restrict ourselves to talking of things logically possible until such a time where we have a chance to prove they're not physically possible.

Logical possibility is a weakest of all possibilities in that it does not entail any other kind of possibility. Yet it may feel like too much to bear for some people, particularly people with a literal turn of mind. They can't stop themselves from interpreting 'logically possible' as somehow entailing, or perhaps just strongly suggesting, 'physically possible'. They feel someone is getting away with murder. It's a question of fine tuning of your personal semantic interpreter. Logically possible just means you can think of it without falling foul of logic. Nothing else.
EB

 

[untermensche]

According to usage, then, something is said to be logically possible if it is not somehow self-contradictory.

According to who?

I want names.

Infinity is a god example.

My point exactly.

 

[Elixir]

According to who?

I want names.

Infinity is a god example.

My point exactly.

Which is my own point as well. There might be an "infinity" of ways to express it.

That the term "infinity" exists is inarguable. What people mean when they use the term... who knows? At the end of the day, what they accept as logical and possible determines whether it's 'logically possible".

 

[untermensche]

I don't know where people pick up their so-called logic.

Certainly if something is a contradiction it is not logically possible.

But there is no logic to say that simply because something is not a contradiction it somehow rises to the level of being an actual possibility.

A logical possibility is something that might actually happen.

That is the only way to speak logically about real world possibilities.

Saying things that can't possibly happen are logical possibilities is absolute nonsense. It focuses only on the word "logical" and ignores everything about the word "possibility".

What is a possibility?

A logical possibility cannot be more.

 

[Kharakov]

This contradicts the very definition of the term, which you yourself could have bothered to research. As usual, a good place to start is Wikipedia's description of the meaning of the expression logical possibility:



You can, of course, seek to impose your private interpretation on the expression, but language is ultimately public, not private. If others prefer to accept its conventional meaning, then your private substitute does not matter.

You are free to argue. But this is not a rational argument.

It is not rational to claim things that are physically impossible are in any way possible. Including logically possible.

Ahh. The famed Chewbacca defense. Can any rational mind stand up to it? News at 11.

 

[Kharakov]

First off, I think we should clear up one thing here.

Is everyone, except untermensche, aware that the boundary of a finite area 2 dimensional object can be infinitely long?

 

[beero1000]

First off, I think we should clear up one thing here.

Is everyone, except untermensche, aware that the boundary of a finite area 2 dimensional object can be infinitely long?

Works in higher dimensions and non-Euclidean spaces as well. In fact, a proposed candidate for the shape of the universe is the hyperbolic  Picard topology, which has finite volume but is infinitely long. Someone should probably tell the physicists that they're wasting their time on a (physical and/or logical) impossibility, right? Just cite untermensche, he can explain it to them.

 

[Juma]

I don't know where people pick up their so-called logic.

Certainly if something is a contradiction it is not logically possible.

But there is no logic to say that simply because something is not a contradiction it somehow rises to the level of being an actual possibility.

A logical possibility is something that might actually happen.

That is the only way to speak logically about real world possibilities.

Saying things that can't possibly happen are logical possibilities is absolute nonsense. It focuses only on the word "logical" and ignores everything about the word "possibility".

What is a possibility?

A logical possibility cannot be more.

Fuck no. A logical possibility is NOT (necessarily) something that could happen.

 

[Speakpigeon]

According to who?

I want names.

http://www.thefreedictionary.com/Logical+possibility

adj
(Logic) capable of being described without self-contradiction

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

Infinity is a god example.

My point exactly.

No, your point is just vacuous.

It is vacuous because you are incoherent in your arguments.

I've given up teaching you the basics. The mere fact that you should ask references for my definition of logical possibility even though it is just the standard usage shows you know nothing of the subject except your own, weird and irrelevant preconceptions.

To say that something is logically possible is in no way saying that it is physically possible. If you want to show that something is not logically possible then show how the description is somehow self-contradictory. That it is physically impossible is just entirely irrelevant.
EB

 

[Speakpigeon]

First off, I think we should clear up one thing here.

Is everyone, except untermensche, aware that the boundary of a finite area 2 dimensional object can be infinitely long?

If by 'can be' you meant 'physically' then, no, I don't know that and I'm sure nobody does.

But if you appeal to our powers of conception, then, sure, except for untermensche of course.

But this is a needlessly difficult example. A simpler example: there is an infinity of real numbers between any two distinct numbers, be they integers, rationals or reals. But then, again, whether there's anything like a physical infinity anywhere at all is something else entirely.
EB

 

[fromderinside]

How would you characterize a vacuum where one cannot find a physical element in any predefined volume of it's extent? Let me suggest it's likely cubic parsec's would be too small a volume. It's my belief that space is so large that there are regions where no photon, no neutrino, nothing, has entered such a region in millennia.

 

[untermensche]

I don't know where people pick up their so-called logic.

Certainly if something is a contradiction it is not logically possible.

But there is no logic to say that simply because something is not a contradiction it somehow rises to the level of being an actual possibility.

A logical possibility is something that might actually happen.

That is the only way to speak logically about real world possibilities.

Saying things that can't possibly happen are logical possibilities is absolute nonsense. It focuses only on the word "logical" and ignores everything about the word "possibility".

What is a possibility?

A logical possibility cannot be more.

Fuck no. A logical possibility is NOT (necessarily) something that could happen.

Fuck yes.

There is no logic in saying things can happen that can't.

Unless you define logic as something to lead you to nonsense.

 

[untermensche]

According to who?

I want names.

(Logic) capable of being described without self-contradiction

Exactly. You have no name. You have nobody willing to stand behind that nonsense.

Why you think it is so is something I can't fathom.

And something you can prove in no way.

My point exactly.

No, your point is just vacuous.

Nothing more vacuous than claiming it is logical to say things are possible which are not.

You need to look up the word "possible" in your dictionary.

 

[untermensche]

First off, I think we should clear up one thing here.

Is everyone, except untermensche, aware that the boundary of a finite area 2 dimensional object can be infinitely long?

By observation?

By imagination?

 

[ryan]

This is a very hard-lined scientific realist approach. Are you really saying that only science has the final word on all that might exist?

If something actually exists we use science not our imagination to describe it.

But if we do use our imagination to make a prediction, or math to be more relevant to my argument, are you then saying that it must put it in the impossible category?

If so, then I think you are going way too far by making all nonscientific predictions impossible.

 

[untermensche]

If something actually exists we use science not our imagination to describe it.

But if we do use our imagination to make a prediction, or math to be more relevant to my argument, are you then saying that it must put it in the impossible category?

If so, then I think you are going way too far by making all nonscientific predictions impossible.

We apply math to concepts within models to make predictions.

Energy equals mass times the speed of light squared.

Energy, light, mass. There is more than mathematics.

2 + 6 = 8 is not a prediction of anything.

Infinity is not a description of anything. To apply it to anything in the real world is a leap.

 

[ryan]

But if we do use our imagination to make a prediction, or math to be more relevant to my argument, are you then saying that it must put it in the impossible category?

If so, then I think you are going way too far by making all nonscientific predictions impossible.

We apply math to concepts within models to make predictions.

Not really, we build a math model from experimental or observational data. Then we see where the math model goes beyond the experiments/observations in order to make predictions. Having a degree in pharmacology, don't you remember the countless labs in chemistry creating mathematical models from the experiments?

Infinity is not a description of anything. To apply it to anything in the real world is a leap.

Maybe a leap, but it is not impossible. If that is what the model predicts, and if by a miracle (but not impossible) it is complete, then we don't have to observe infinity for it to be there. The universe is always parallel with math, and possibly even governed by math.

 

[untermensche]

Can you apply the Easter Bunny to things the way you think you can apply infinity?

They are different kinds of imaginary concepts but both nothing but imaginary conceptions.