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

[Kharakov]

Our mental representation of space is continuous. But maybe there's no space at all, just our mental representation of certain relations between real things.

Are you going down the "no actual space because you can't prove that there is" route, or do you have some evidence for your claims? You'd be knocking down a lot of astrophysics with whatever scientific know-how you're hiding from the rest of the world.

We can observe that the universe is continuous and connected by..well, looking around us. The only real discrete boundaries are transition points in gradients of fields. These boundaries are "discrete", as they set definite boundary points between one direction of a gradient and another.

Do you mean you believe volume is fake? Do you think that gravitational interactions that depend on the stress energy tensor (simplified: mass/energy in a volume of space) are fake? Do you think we live in a simulation (another thing that nobody can prove is false)?

Maybe volume only exists in our mental representation of reality.

To understand that you cannot exclude entirely the possibility that you are living in a simulation is to understand that your mental representation may be essentially arbitrary as to likeness. That is to say, reality may well be seriously different from our mental representation of reality.

Sure it is. That's why we mine, eat, farm, fish, build houses, create GPS satellites that take into account relativistic effects, etc... because reality isn't real.

I fail to see why real time would have to be continuous. All we need is a simple rule to explain how time behaves and see if this can explain empirical data. And real time does not need to be anything like what we think of time as being. Our intuitive representation of time may well be almost entirely irrelevant.

Ehh. Look around. You see a clockwork orange ticking away, or are things smoothly transitioning? Even a computer uses flow of fields, gradients, etc. to make its "clockwork" calculations. The same principles used in electrical computers can be used in water based computers... so, the point is, even computers use smooth properties to simulate discrete properties.

I'm definitely not saying discrete conditions exist in nature, nor am I saying that there are an infinite amount of discrete boundaries in nature (if untermensche sees this). After all, every transition in gradient direction in nature is a discrete, unitary (single/quantum) boundary.

I thought this point was now well understood after Quantum Physics and Relativity!

Relativity rests upon connected, continuous spacetime. I don't know if there is a formulation for discrete spacetime?

 

[Kharakov]

Do you beg the question while you're beating your wife?

There isn't a shortest possible distance. There are transition points (where a gradient switches directions) in nature, but they have no length.

Otherwise, all things in nature are smooth/continuous (except for transition points).

You're refusal to answer the question is not my anything. You have failed to address the question twice. That is telling. Nothing can move without making the smallest possible move first.

I doubt nothing moves- it doesn't exist.

In continuous reality, there is no smallest possible move.

 

[Kharakov]

See what it is you're doing when you ask about the applicability of the word "logical" to the word "possibility". You'd be doing the same thing as asking what does "free" to do with "will" or "red" to do with "men" or "jumbo" to do with "peanut."

A logical possibility is not some kind of in the same sense possibility that has some quality of being logical. After all, physical impossibilities are logically possible -- even if not a possibility of the logical variety--whatever that might mean.

I once used logically possible to mean logically possible and got in an argument with someone about it.

 

[fast]

I wish you could see what I see. You can't treat an adjective as fully applicable when it's purpose is for distinction in name only. You must treat the two-worded term "logical possibility" as a name in its own right and not look to the individual meanings of the terms as if it calcuably gives rise to what "logical possibility" means. It's the same thing with "free will." The individual words are akin to a business name. It clues us in, but it doesn't tell the whole story.

You are doing the very thing you should be doing by questioning what is so logical about a purported possibility, but once you learn that a logical possibility (a term in its own right with its own specific meaning) is not a logical possibility (a kind of possibility that is logical) and recognize the ambiguity, you should drop what only appears to be intentionally conflating them.

You are not amazing me when you point out the absurdity of calling an impossibility as something possible. A physically impossible event surely is impossible, but it can nevertheless quite correctly be called possible (save for contradictions). It's easier to see when the ambiguity of the name is removed and replaced with a term that is less misleading. (Recall my previous post substituting jumbo peanuts with Strain 78).

Let's try another route:
If I refer to all women over 60 as red men, then no amount of logic is going to make it so that women are men, let alone red, but if I refer to all women over 60 with a proper name (oh say, Red Men), the meaning is stipulative. If it becomes apart of common usage, the meaning of red men (adjective and noun) will be vastly different than the proper name that gained notoriety red men (to not be treated as two one worded-terms but instead as one two-worded term.

See what it is you're doing when you ask about the applicability of the word "logical" to the word "possibility". You'd be doing the same thing as asking what does "free" to do with "will" or "red" to do with "men" or "jumbo" to do with "peanut."

A logical possibility is not some kind of in the same sense possibility that has some quality of being logical. After all, physical impossibilities are logically possible -- even if not a possibility of the logical variety--whatever that might mean.

What is a possibility?

Is it something you just have to imagine?

If I imagine something how is the thing imagined a possibility? I already imagined it.

In what universe is it a possibility?

I am in South Carolina right now. Also, I am not in South Carolina right now. That's contradictory. Because it's contradictory, it's not possible. It lacks consistency. They can't both be true. Imagine it all you want, it's still logically impossible.

I am in South Carolina right now. Also, I am in Florida right now. That's not contradictory. It's not true that I am in both places right now, but it's not contradictory. Imagination has nothing to do with it. The key is whether there is or isn't a contradiction.

Logical possibilities include contraries (physically possible or otherwise), but contradictions they do not.

 

[DBT]

You tell me.

Is it rational to say the universe has imaginary qualities?

Whether the universe is infinite or not, the possibility of infinity cannot be dismissed. Certainly not because you say so but cannot give a logical argument to support your assertion.

I am arguing AGAINST the irrational idea that movement can be divided infinitely. Or that anything real can be divided infinitely.

It is an idea that instantly becomes an absurdity.

Your remark was absurd. You said; ''It is impossible for an object to make the smallest movement possible'' when it should have been clear that the inclusion of 'possible' means that this is indeed the smallest possible movement, hence not impossible.

 

[Speakpigeon]

An infinitesimal is a point on a line, a line on a plane (infinitesimal area), a plane in a volume (infinitesimal volume)....

They aren't necessarily without size. An infinitesimal hypervolume could still take up a lot of space.

A moment in spacetime is.....

Me, I always thought that by 'point' we all meant 'without size', or, 'with zero dimension'.

While 'volume' was supposed to mean a three-dimensional quantity (or above).

So, a point in this sense could not possibly take "a lot of space", at least if a lot of space is not a zero-dimensional thing.

Same for a line. I thought lines where one-dimensional spaces, i.e. zero-volume 'spaces'.

Er, same for planes (except airplanes). No three-dimensional volume either.


So, basically, I think you are thinking of infinitesimals in a way that's very different from what Newton, Leibnitz and others had in mind.

But you seem to be in the semantic neighbourhood of ryan, and probably of many modern mathematicians.

I mean, these people just seem to have re-defined the notion of infinitesimals out of recognition. Newton would be aghast.



No wonder we can't understand each other if we're constantly re-defining the words we use out of recognition.

It should be noted that this seems to happen for a lot of basic terms, like 'consciousness', 'qualia', etc.
EB

 

[Speakpigeon]

Sorry, I think you're trying to dress your intuitive understanding of the issue as a properly logical or rational argument. No good. Either n somehow gets to equal infinity at some point and then your sum equals 1 or it doesn't (and you're now saying it doesn't) and then only the sum's limit equals 1.

"As n goes to infinity" is the same as saying all n of the naturals. There are an aleph 0 infinity numbers in the set of the naturals, yet n never actually equals aleph 0 in the set.

If I go to New York, the idea is that at some point I will be in New York. So, "n goes to infinity" suggests that n will somehow be infinite in value. Not so if I express thing using the concept of limit. So, n may well tend towards a limit without ever reaching it. So, the two expressions are not equivalent. There's no n in N which is infinite, so, contrary to your claim here, saying "n goes to infinity" does not suggest "all n of the naturals".

Nah, I'm pretty sure that if Newton, Leibnitz or any of the others had thought of infinitesimals in this way they would have specified this number, that you say infinitesimals are supposed to represent, straight away. So, why didn't they? Shyness? Lack of time? They didn't know of the zero? What?

What value is lim n-->infinity c/n

Think about it this way. If I start at 0 and don't gain any distance, I have moved 0 distance. I get a dot on 0, but at least I moved an infinitesimal. If I don't even start at 0, then I don't even get a dot. I gain no distance, not even an infinitesimal.

That wasn't my question.

So, I can only assume you couldn't explain why all these great minds didn't get it right where you, on the other hand, did.
EB

No, it's because set theory hadn't been invented yet.

And then what? How would that prove that Newton's notion of infinitesimals was somehow incoherent?

I certainly fail to see how the idea that infinitesimals are all null could possibly be coherent. Why even talk of infinitesimals if they were null. Talk of zero instead and you will save time.

And of course, adding 0 to anything won't do what infinitesimals could do at the time of Newton and Leibnitz.

Anyway, it seems you don't even understand what I'm talking about.
EB

 

[Speakpigeon]

I'm not really so sure that the word "logical" can even be applied to the word possibility.

I wish you could see what I see. You can't treat an adjective as fully applicable when it's purpose is for distinction in name only. You must treat the two-worded term "logical possibility" as a name in its own right and not look to the individual meanings of the terms as if it calcuably gives rise to what "logical possibility" means. It's the same thing with "free will." The individual words are akin to a business name. It clues us in, but it doesn't tell the whole story.

You are doing the very thing you should be doing by questioning what is so logical about a purported possibility, but once you learn that a logical possibility (a term in its own right with its own specific meaning) is not a logical possibility (a kind of possibility that is logical) and recognize the ambiguity, you should drop what only appears to be intentionally conflating them.

You are not amazing me when you point out the absurdity of calling an impossibility as something possible. A physically impossible event surely is impossible, but it can nevertheless quite correctly be called possible (save for contradictions). It's easier to see when the ambiguity of the name is removed and replaced with a term that is less misleading. (Recall my previous post substituting jumbo peanuts with Strain 78).

Let's try another route:
If I refer to all women over 60 as red men, then no amount of logic is going to make it so that women are men, let alone red, but if I refer to all women over 60 with a proper name (oh say, Red Men), the meaning is stipulative. If it becomes apart of common usage, the meaning of red men (adjective and noun) will be vastly different than the proper name that gained notoriety red men (to not be treated as two one worded-terms but instead as one two-worded term.

See what it is you're doing when you ask about the applicability of the word "logical" to the word "possibility". You'd be doing the same thing as asking what does "free" to do with "will" or "red" to do with "men" or "jumbo" to do with "peanut."

A logical possibility is not some kind of in the same sense possibility that has some quality of being logical. After all, physical impossibilities are logically possible -- even if not a possibility of the logical variety--whatever that might mean.

I agree with your point about the meaning of complex expressions, obviously. Yet, I believe this does not do justice to the semantic of 'logical possibility'.

As I see it, UM making two mistakes, not just the one you insist on in your discussion here. First, he takes the notion of possibility to be that of physically possibility, something your analysis does not cover.

A physical possibility is just something which may be true in the sense that we don't know of any physical fact preventing it from being true. That is, we don't know of any physical contradiction preventing it from being true. For example, I can say that it is a physical possibility that the Eiffel Tower is right now in London because I can't see it from where I am now and it's at least conceivable to dismantle the Eiffel Tower and ship it to London, if only for a short period of time. But if I'm standing at the foot of the Eiffel Tower right now and looking up at it, I will probably think that if it is in Paris right now, it can't be in London right now, and that would be a physical impossibility.

Clearly, logical possibilities don't work like this. A logical possibility is something that might be true in the sense that I don't know of any formal contradiction to it being true. Clearly, this does not mean, imply or suggest in any way that if it is logically possible then it is also physically possible, or that we can conceive of how it would be true physically. It just means that there is no formal contradiction in the formal expression of the idea. So, it is a logical possibility that the Eiffel Tower is right now in New York while the Statue of Liberty is right now in Moscow. And I would still think of those as logical possibilities even if I was right now looking at the Eiffel Tower in Paris or at the Statue of Liberty in New York.

The two notions are nonetheless linked in the sense that a logical impossibility is also ipso facto a physical impossibility and that a physical possibility is ipso facto a logical possibility.

That being said, clearly, the notion of possibility probably originally meant 'physical possibility'. But it's also true that the notion of 'logical possibility' de facto extended the semantics of the word 'possibility' beyond its original physical implication so that today, it can be used to mean logical possibility and is so used by philosophers (if not by many people outside philosophy).

Ultimately, UM is guilty of ignoring what people who use the expression mean by 'logical possibility'. His attitude is very much in line with his usual posture so we're not going to be too surprised here.

What is more difficult is to tell whether his posture is related to some cognitive disposition, for example some form of 'pathological literalism', which I suspect is the case, or if it is merely a sort of temperamental posture, for example an excessive love for constant contrariness, perhaps linked to some imbalance in hormones and such.

We all have our issues, though, so we can sort of try to accommodate those of others. We're here also to learn things and we do count on other people for that.
EB

 

[Speakpigeon]

You're refusal to answer the question is not my anything. You have failed to address the question twice. That is telling. Nothing can move without making the smallest possible move first.

I doubt nothing moves- it doesn't exist.

In continuous reality, there is no smallest possible move.

Unless you want to count not moving at all as moving over a null distance.

Such a move would be the smallest possible move, right?

Unless you would want to count any backward move as smaller than any forward move.

In which case the smallest possible move would have to be a move backward over an infinite distance. Which wouldn't be physically possible because of the limitation of the speed of light.

Unless the end of time does exist at some point infinitely away into the future.

Unless UM would say that if so then time is not without end and therefore no infinite, and therefore...

Hey, I have to go.
EB

 

[untermensche]

What is a possibility?

Is it something you just have to imagine?

If I imagine something how is the thing imagined a possibility? I already imagined it.

In what universe is it a possibility?

I am in South Carolina right now. Also, I am not in South Carolina right now. That's contradictory. Because it's contradictory, it's not possible. It lacks consistency. They can't both be true. Imagine it all you want, it's still logically impossible.

I am in South Carolina right now. Also, I am in Florida right now. That's not contradictory. It's not true that I am in both places right now, but it's not contradictory. Imagination has nothing to do with it. The key is whether there is or isn't a contradiction.

Logical possibilities include contraries (physically possible or otherwise), but contradictions they do not.

Human expressions can be contradictory.

But something is either possible or it is impossible.

Human expressions have nothing to do with that.

Logic involves human expressions not real possibilities.

 

[untermensche]

You're refusal to answer the question is not my anything. You have failed to address the question twice. That is telling. Nothing can move without making the smallest possible move first.

I doubt nothing moves- it doesn't exist.

In continuous reality, there is no smallest possible move.

Then continuous "reality" is a fantasy.

Because in the real world when any thing moves it moves the shortest possible distance first.

It has to.

 

[ryan]

"As n goes to infinity" is the same as saying all n of the naturals. There are an aleph 0 infinity numbers in the set of the naturals, yet n never actually equals aleph 0 in the set.

If I go to New York, the idea is that at some point I will be in New York. So, "n goes to infinity" suggests that n will somehow be infinite in value. Not so if I express thing using the concept of limit. So, n may well tend towards a limit without ever reaching it. So, the two expressions are not equivalent. There's no n in N which is infinite, so, contrary to your claim here, saying "n goes to infinity" does not suggest "all n of the naturals".

Look, I think everyone goes through this; I certainly did. To this day the logic of it bothers me. How can there be an infinite number of natural numbers without n finally equalling infinity? But that's what we are told. If you Don't like it, be a constructivist.

And then what? How would that prove that Newton's notion of infinitesimals was somehow incoherent?

I certainly fail to see how the idea that infinitesimals are all null could possibly be coherent. Why even talk of infinitesimals if they were null. Talk of zero instead and you will save time.

And that just may be why 0 is used instead.

How did an invention like 0 evade great thinkers and Greek mathematicians? It's all obvious now, but...

 

[Phil Scott]

If I go to New York, the idea is that at some point I will be in New York. So, "n goes to infinity" suggests that n will somehow be infinite in value. Not so if I express thing using the concept of limit. So, n may well tend towards a limit without ever reaching it. So, the two expressions are not equivalent. There's no n in N which is infinite, so, contrary to your claim here, saying "n goes to infinity" does not suggest "all n of the naturals".

Look, I think everyone goes through this; I certainly did. To this day the logic of it bothers me. How can there be an infinite number of natural numbers without n finally equalling infinity? But that's what we are told. If you Don't like it, be a constructivist.

Or a moral subjectivist.

 

[fast]

I wish you could see what I see. You can't treat an adjective as fully applicable when it's purpose is for distinction in name only. You must treat the two-worded term "logical possibility" as a name in its own right and not look to the individual meanings of the terms as if it calcuably gives rise to what "logical possibility" means. It's the same thing with "free will." The individual words are akin to a business name. It clues us in, but it doesn't tell the whole story.

You are doing the very thing you should be doing by questioning what is so logical about a purported possibility, but once you learn that a logical possibility (a term in its own right with its own specific meaning) is not a logical possibility (a kind of possibility that is logical) and recognize the ambiguity, you should drop what only appears to be intentionally conflating them.

You are not amazing me when you point out the absurdity of calling an impossibility as something possible. A physically impossible event surely is impossible, but it can nevertheless quite correctly be called possible (save for contradictions). It's easier to see when the ambiguity of the name is removed and replaced with a term that is less misleading. (Recall my previous post substituting jumbo peanuts with Strain 78).

Let's try another route:
If I refer to all women over 60 as red men, then no amount of logic is going to make it so that women are men, let alone red, but if I refer to all women over 60 with a proper name (oh say, Red Men), the meaning is stipulative. If it becomes apart of common usage, the meaning of red men (adjective and noun) will be vastly different than the proper name that gained notoriety red men (to not be treated as two one worded-terms but instead as one two-worded term.

See what it is you're doing when you ask about the applicability of the word "logical" to the word "possibility". You'd be doing the same thing as asking what does "free" to do with "will" or "red" to do with "men" or "jumbo" to do with "peanut."

A logical possibility is not some kind of in the same sense possibility that has some quality of being logical. After all, physical impossibilities are logically possible -- even if not a possibility of the logical variety--whatever that might mean.

I agree with your point about the meaning of complex expressions, obviously. Yet, I believe this does not do justice to the semantic of 'logical possibility'.

As I see it, UM making two mistakes, not just the one you insist on in your discussion here. First, he takes the notion of possibility to be that of physically possibility, something your analysis does not cover.

A physical possibility is just something which may be true in the sense that we don't know of any physical fact preventing it from being true. That is, we don't know of any physical contradiction preventing it from being true. For example, I can say that it is a physical possibility that the Eiffel Tower is right now in London because I can't see it from where I am now and it's at least conceivable to dismantle the Eiffel Tower and ship it to London, if only for a short period of time. But if I'm standing at the foot of the Eiffel Tower right now and looking up at it, I will probably think that if it is in Paris right now, it can't be in London right now, and that would be a physical impossibility.

Clearly, logical possibilities don't work like this. A logical possibility is something that might be true in the sense that I don't know of any formal contradiction to it being true. Clearly, this does not mean, imply or suggest in any way that if it is logically possible then it is also physically possible, or that we can conceive of how it would be true physically. It just means that there is no formal contradiction in the formal expression of the idea. So, it is a logical possibility that the Eiffel Tower is right now in New York while the Statue of Liberty is right now in Moscow. And I would still think of those as logical possibilities even if I was right now looking at the Eiffel Tower in Paris or at the Statue of Liberty in New York.

The two notions are nonetheless linked in the sense that a logical impossibility is also ipso facto a physical impossibility and that a physical possibility is ipso facto a logical possibility.

That being said, clearly, the notion of possibility probably originally meant 'physical possibility'. But it's also true that the notion of 'logical possibility' de facto extended the semantics of the word 'possibility' beyond its original physical implication so that today, it can be used to mean logical possibility and is so used by philosophers (if not by many people outside philosophy).

Ultimately, UM is guilty of ignoring what people who use the expression mean by 'logical possibility'. His attitude is very much in line with his usual posture so we're not going to be too surprised here.

What is more difficult is to tell whether his posture is related to some cognitive disposition, for example some form of 'pathological literalism', which I suspect is the case, or if it is merely a sort of temperamental posture, for example an excessive love for constant contrariness, perhaps linked to some imbalance in hormones and such.

We all have our issues, though, so we can sort of try to accommodate those of others. We're here also to learn things and we do count on other people for that.
EB

Good post!

The term, "physical possibility" implies "logical possibility," but the inverse is not true. If I speak of a physical impossibility with no contradictions and ask if what I speak of is possible, the trained logician will correctly answer yes, as all non-contradictory physical impossibilities are logically possible. Clearly, the term, "possibility" is ambiguous. The term, "logical possibility" is of a much broader scope.

However, there is more than mere ambiguity at play here. The terms themselves are deceptive. We use the term, "physical" to clarify which possibility we're speaking of, and we use the term, "logical" to clarify as well. We need to distinguish between them somehow!

What would you say to the logican that says a non-contradictory physical impossibility is not logically possible? Well, we'd say he is mistaken. But, what if he retorts that by "possibility" (when he says not logically possible) that he means it in the other sense (the sense we mean when we speak of physical possibilities)? I would respond, then why the hell did you clarify which sense of term you were using if you didn't mean it in that sense.

That would be like me saying, "is doing X morally right in the legal sense of the word right." Moreover, "is X logically possible in the physical sense of the word possible?" This brings me to the additional confusion (and thus more than mere ambiguity) between complex expressions and how perceived meaning differs for those suffering from 'pathological literalism'.

He asks, "what is so logical about it?" We refer to physically impossible events and announce to the world that they are possible. Logically possible, at that! Literalism, at it's finest.

The problem, however, is deeper than that, as he frequently (very frequently) mentally alters the meaning of many (many) terms--simple terms even. He's in the grip of a theory that underlies an alteration of meaning.

 

[Kharakov]

Hey, I have to go.

Point taken.

 

[Kharakov]

In continuous reality, there is no smallest possible move.

Then continuous "reality" is a fantasy. Because in the real world when any thing moves it moves the shortest possible distance first.

There is no shortest possible distance in the continuum. It's all connected man.... whoa.

 

[Kharakov]

And that just may be why 0 is used instead.

How did an invention like 0 evade great thinkers and Greek mathematicians? It's all obvious now, but...

I remember someone here once joked "0, the only real infinitesimal."

 

[Phil Scott]

And that just may be why 0 is used instead.

How did an invention like 0 evade great thinkers and Greek mathematicians? It's all obvious now, but...

I remember someone here once joked "0, the only real infinitesimal."

It certainly satisfies the definition I gave earlier.

The reason that the Greeks didn't have zero is because their numbers were literally measurable geometric objects, usually line segments. It's not clear why zero would be of use here, and what Descartes did by discovering algebraic geometry, complete with zero and negatives, was hardly obvious (he didn't just come up with the idea of a graph).

 

[Kharakov]

Umm, weren't merchants using zero and negatives way before geometers?

 

[Phil Scott]

Umm, weren't merchants using zero and negatives way before geometers?

I believe the Chinese are often credited with inventing the convention of red and black for negative and positive respectively, and I think it was before geometry. But I'm not going to compare the tallying of merchants and debt collectors with the pioneers of pure mathematics. It's not clear why Greek mathematicians and geometers would have found zero and negatives useful.