If I can imagine it, it's logically possible?

[Speakpigeon]

Dreams are an obvious counterexample. Dreams are often illogical yet we still succeed in dreaming them. Psychotic delusions are a similar sort of waking state counterexample.

I was obviously not talking about dreams. Nor about psychotic people. Should have I specified I am also not talking about dead people and zombies?
I'll address the question of logic/ontology of reality whenever you can come up with a decent articulation of what you mean by that.
For the rest, I think I already provided all the answers you need in my replies to other posters.
EB

 

[James R]

Again, I can't imagine this would work. And I doubt you can.
EB

I happen to know that it wouldn't work. But that hardly prevents me from imagining it working. That's half the fun of it.

 

[James R]

Sarkus:

If the ball is lifted up the slope by magnetic attraction from the initial distance, why would it then drop through the hole where the attraction is stronger? Not saying it wouldn't, just asking your opinion, or to at least explain why it would.

It's entirely possible for the ball to drop through the hole. You might need to use a physically larger magnet at the top of the slope, but in principle you could arrange for the magnetic force on the ball to be approximately constant along the entire length of the straight ramp. All that is required for the ball to drop through the hole is for the upwards vertical component of the magnetic force at the hole to be less than the downwards force of gravity at that location, which is easily arranged. At other points on the straight ramp, the necessary "extra" upwards force is provided by the normal force of the ramp on the ball - i.e. having the slope means the magnetic force doesn't have to be so strong to lift the ball up.

 

[Speakpigeon]

I happen to know that it wouldn't work. But that hardly prevents me from imagining it working. That's half the fun of it.

Sure, but my point is that it's not anything like a realistic machine. So, here, the fact that you can imagine it shows it is indeed a logical possibility. However, there is an equivocation here that needs disambiguation. The logical possibility in this case is entirely that of a chimerical machine, not of any actual machine that would work. Hence, it's fun if you like that kind of thing, but it's also pretty useless as long as you can't imagine any realistic machine.
And of course, the crucial point is that being able to imagine something that doesn't work because it is unrealistic is no counterexample to my thesis that if I can imagine it, then it is a logical possibility. The logical possibility is that of what you imagine as you imagine it. The mistake is to assume that all Santa Claus are equivalent in this respect. Well, no. If somebody could imagine a realistic Santa Claus, that would change the way we travel almost immediately. Observe that we all have some image in mind of a Santa Claus and yet nobody seems to be travelling in a sleigh pull by actual reindeer.
I hope this does illuminate for some people around here the notion of logical possibility.
EB

 

[James R]

I don't really see why you use the word "logical" in discussing the possibility of Santa delivering presents with his flying reindeer.

We appear to agree that we can all imagine such a thing happening, but that it's physically impossible. Where does logic come in to it?

I agree that the fact that you've conceived of Santa and his reindeer logically implies that it is possible to have such a conception, etc. Is that all you're saying?

 

[Speakpigeon]

Sarkus:


It's entirely possible for the ball to drop through the hole. You might need to use a physically larger magnet at the top of the slope, but in principle you could arrange for the magnetic force on the ball to be approximately constant along the entire length of the straight ramp. All that is required for the ball to drop through the hole is for the upwards vertical component of the magnetic force at the hole to be less than the downwards force of gravity at that location, which is easily arranged. At other points on the straight ramp, the necessary "extra" upwards force is provided by the normal force of the ramp on the ball - i.e. having the slope means the magnetic force doesn't have to be so strong to lift the ball up.

Yes, the vertical force on the ball is the combination of the force of reaction of the ramp, which is normal to the ramp, and the pull from the magnet, which is in the direction of the magnet and therefore parallel to the ramp given the setup.
However, the crucial point is the component of the weight of the ball which is parallel to the ramp. It is of course much less than the weight of the ball. So the pull of the magnet needs not be very strong. The smaller the angle of the slope, the less the pull needed to help the ball up the ramp.
I think the main problem though could be indeed that the ball won't drop through the hole. The pull of the magnet will increase as the ball goes up the ramp and nearer to the magnet. The ball may keep going towards the magnet rather than drop through the hole. And if you use a smaller magnet to solve this problem, then the pull of the magnet when the ball is at the bottom of the ramp won't be enough to get the ball up the ramp.
All this could very nearly work. The ball would need to have kinetic energy at the start, for example imparted by a spring at the bottom of the ramp. The friction from the two ramps should be null. The ball would need to move in a vacuum. That could last very nearly forever if the conditions were possible to obtain in the first place with such a macroscopic object and perhaps if not for the ball loosing kinetic energy through possibly some quantum effect or other, or even because of the impact of ambiant radiation on the ball itself.
In other words, we can always try to imagine how it could work realistically, but we can't.
EB

 

[Speakpigeon]

I don't really see why you use the word "logical" in discussing the possibility of Santa delivering presents with his flying reindeer.
We appear to agree that we can all imagine such a thing happening, but that it's physically impossible. Where does logic come in to it?
I agree that the fact that you've conceived of Santa and his reindeer logically implies that it is possible to have such a conception, etc. Is that all you're saying?

A proposition is logically possible if it doesn't contradict your assumptions. So, it all depends on what assumption you make to begin with. If you assume a realistic setup, i.e. if you assume that the laws of physics apply, then what is logically possible is very much constrained. It is broadly limited to what is physical possible, although not quite since we wouldn't here assume any initial conditions and initial conditions obviously would further limit the range of physically possible outcomes. However, at the extreme, there is, arguably, only one physical reality and therefore only one physical possibility, i.e. what actually is. Yet, we can only operate with a more or less limited knowledge of the current state of the physical world and so we talk of "physical possibilities" even though what we are really talking about are logical possibilities assuming the laws of nature. And then, we may choose to ignore the laws of nature altogether, in a sort of counterfactual scenario, to imagine a fanciful Santa Claus. However, the two sets of logical possibilities have nothing in common between a fanciful Santa Claus and a realistic Santa Claus.
So, the counterexamples posters have been proposing here are all ineffective because they are equivocations.
EB

 

[James R]

Yes, the vertical force on the ball is the combination of the force of reaction of the ramp, which is normal to the ramp, and the pull from the magnet, which is in the direction of the magnet and therefore parallel to the ramp given the setup.
However, the crucial point is the component of the weight of the ball which is parallel to the ramp. It is of course much less than the weight of the ball. So the pull of the magnet needs not be very strong. The smaller the angle of the slope, the less the pull needed to help the ball up the ramp.
I think the main problem though could be indeed that the ball won't drop through the hole.

I made the point that it is quite possible to arrange things so that the magnet will be strong enough to pull the ball up the slope, but not strong enough to stop it from falling down through the hole at the top of the slope.

The pull of the magnet will increase as the ball goes up the ramp and nearer to the magnet.

Typically, yes, which is why I said that in principle one could use a magnet with larger dimensions, so as to create an approximately uniform magnetic field over the entire length of the ramp. The point is that the magnetic force pulling the ball up the slope doesn't have to get stronger as the ball goes higher up.

The ball may keep going towards the magnet rather than drop through the hole. And if you use a smaller magnet to solve this problem, then the pull of the magnet when the ball is at the bottom of the ramp won't be enough to get the ball up the ramp.

To repeat, it is perfectly possible to straddle the middle ground here and arrange for a magnet that is strong enough to pull the ball up from the bottom of the ramp and to allow the ball to fall through the hole at the top.

All this could very nearly work. The ball would need to have kinetic energy at the start, for example imparted by a spring at the bottom of the ramp.

That's not necessary to get the motion going.

The issue is not that this "machine" wouldn't work as designed (though there are certain issues that we could discuss that nobody has brought up yet). The issue is rather that any such machine that you could actually construct would not result in perpetual motion of the ball. The ball would stop moving, sooner or later.

The friction from the two ramps should be null.

Not possible, in practice.

The ball would need to move in a vacuum.

That could be arranged, of course.

That could last very nearly forever if the conditions were possible to obtain in the first place with such a macroscopic object and perhaps if not for the ball loosing kinetic energy through possibly some quantum effect or other, or even because of the impact of ambiant radiation on the ball itself.

One possible small dissipative effect might be an electromagetic induction effect between the magnet and the ball, but that's unlikely to be the most important dissipative mechanism in this design.

 

[Speakpigeon]

I made the point that it is quite possible to arrange things so that the magnet will be strong enough to pull the ball up the slope, but not strong enough to stop it from falling down through the hole at the top of the slope.
Typically, yes, which is why I said that in principle one could use a magnet with larger dimensions, so as to create an approximately uniform magnetic field over the entire length of the ramp. The point is that the magnetic force pulling the ball up the slope doesn't have to get stronger as the ball goes higher up.
To repeat, it is perfectly possible to straddle the middle ground here and arrange for a magnet that is strong enough to pull the ball up from the bottom of the ramp and to allow the ball to fall through the hole at the top.

As the ball goes up the ramp, the pull from the magnet will increase regardless. Either the ball stays put at the bottom of the ramp or it will go up but then its speed will increase as it goes up the ramp and it's kinetic energy will increase. So, it's not just a static situation where the magnet's pull needs to be weak enough to let the ball drop through the hole, it's the potential energy of the ball in the magnetic field of the magnet all transformed into momentum at the hole. To mitigate, the best way would be to put the hole straight on the path of the ball. The returning curved ramp would also need to start to curve from the hole there. Thus the magnet pulls the ball through the hole and then the curved ramp redirect the ball's momentum to force the ball to go down and away from the magnet.

That's not necessary to get the motion going.

Of course not, but if the ball is at a standstill at the start, then it will return at the end of the first cycle with a speed that should not be enough to reach its initial position to be able to start a second cycle. Unless of course, perpetual motion was possible.
Think of a body in orbit around the Sun. The starting point will be the aphelion. At the end of the first orbit, the body won't be able to reach the same aphelion. The new aphelion will be ever so slightly below the first one because already during the first orbit, the body will have lost a little bit of momentum compared to a perpetual movement, and this due to all sorts of things, say, stellar dust or whatever.
This means that in the case of our unwieldy contraption here, the ball won't get up the ramp for the second cycle because it won't be able to get back to its initial starting point to begin with, unless it had some initial momentum from a spring for example.
In other words, if you believe the ball can reach it's starting point at the end of the first cycle without an initial momentum, then you should believe in perpetual motion because if it can make the first cycle, it will have to make the second and the third and nothing will possibly stop it, ever.
You're a bit naive, aren't you?

The issue is not that this "machine" wouldn't work as designed (though there are certain issues that we could discuss that nobody has brought up yet). The issue is rather that any such machine that you could actually construct would not result in perpetual motion of the ball. The ball would stop moving, sooner or later.

Sure, but if it makes the first cycle, it will go on forever, which is impossible. The ball won't make a second cycle unless it has an initial momentum. And, assuming a constant loss of momentum with each cycle, it is the magnitude of this initial momentum which will determine the "exact" number of cycles that the ball will be able to do.

Not possible, in practice.
That could be arranged, of course.
One possible small dissipative effect might be an electromagetic induction effect between the magnet and the ball, but that's unlikely to be the most important dissipative mechanism in this design

Sure, but if friction were null, you'd still have other losses of momentum and no perpetual movement.
And without an initial momentum, everything random will contribute to the ball not making it back to its initial position at the end of the first cycle.
EB

 

[Yazata]

I was obviously not talking about dreams. Nor about psychotic people.

I was the one speaking about them.

My reason for doing so is that dreams and psychotic delusions seem to be instances of imagination. If one wants to argue that the ability to imagine something implies that whatever is imagined is "logically possible", then the scope of imagination would either have to be constrained somehow, or the meaning of "logically possible" warped to something like 'possible to imagine', which would reduce your thesis to a triviality.

In my last post, I suggested modifying your original

1. "If I can imagine it, it's logically possible"

to

2. "If I can imagine it in a logical manner, then it's logically possible"

But that change threatens to render the whole thing circular.

So my question for you is, what justification can you produce for excluding dreamers and psychotics from the class of those who imagine? What kind of constraint would you place on imagination to produce whatever results you want?

Should have I specified I am also not talking about dead people and zombies?

I seem to have angered you. (That's ok, you anger me too sometimes.)

I'll address the question of logic/ontology of reality whenever you can come up with a decent articulation of what you mean by that.

If you are going to play that game, then I'll play it too. You have yet to explain what you mean by "logically possible". Possible for you to imagine? Internally consistent? Consistent with all of our existing knowledge/beliefs? An element of some huge set of states of affairs (factual and counterfactual) that might possibly exist in actual reality (even if in our reality they don't)?

It gets at the problem that seems to me to lie beneath the whole point you are trying to make.

What is the relationship between logic in the subjective psychological sense of how somebody's individual thought process unfolds (in dreams, psychosis, imagination or rational thought... we speak this way then we use phrases like "the logic of dreams"), logic in the objective formal sense in which logical proofs that are valid for me should be valid for everyone else as well, and logic in the objective ontological sense in which our employment of logic can tell us something about what can and can't be true in the reality we all share.

It's very closely related to questions of what mathematics is, why mathematics works so well in physics and why the resulting physics produces engineering that works whether it's consistent with our personal worldviews, or not. Big topics in the philosophy of mathematics and science.

For the rest, I think I already provided all the answers you need in my replies to other posters.
EB

I was providing my own opinion. I wasn't asking you for anything though I was inviting intelligent comment.

Frankly, I don't believe that you have any satisfactory answers. That's not meant as an insult because I don't either. I don't think that anyone does at this point. All of this kind of stuff remains a fundamental mystery. I'm not convinced that human beings will ever get to the bottom of it.

 

[Sarkus]

You have yet to explain what you mean by "logically possible". Possible for you to imagine? Internally consistent? Consistent with all of our existing knowledge/beliefs? An element of some huge set of states of affairs (factual and counterfactual) that might possibly exist in actual reality (even if in our reality they don't)?

I would consider something logically possible if one can start with any premises at all and, through valid logic, reach the conclusion. Although that assumes that one is working within classical deductive logic. I guess one needn't be, so it would be a case of any proposition that can be a logical consequence of another, taking into account the axioms of the system of logic in question.
Another way to look at it is if, within a system of logic, there can be a world where the proposition is true, then it is logically possible. If there are no worlds where it can be true then it is not a logical possibility.
Or some such.

 

[Speakpigeon]

I was the one speaking about them. My reason for doing so is that dreams and psychotic delusions seem to be instances of imagination. If one wants to argue that the ability to imagine something implies that whatever is imagined is "logically possible", then the scope of imagination would either have to be constrained somehow

I wouldn't need to constrain the scope of imagination. You, however, you need to use the word "imagination" properly:

Imagine
1. To form a mental picture or image of: imagined a better life abroad.

A hallucination is not an instance of imagining.
If I have a hallucination, I'm not imagining it.

So my question for you is, what justification can you produce for excluding dreamers and psychotics from the class of those who imagine? What kind of constraint would you place on imagination to produce whatever results you want?

You don't seem to have read my answers to other posters' counterexamples and criticisms...
If being able to imagine implies a logical possibility, then the logical possibility in question depends on what is imagined... Or, rather, it depends on what exactly is imagined. Dreamers and psychotics are not able to report what it is exactly, if at all, they have imagined. Even most people, including people here, don't seem able to articulate what kind of Santa Claus they can imagine.
And, as per the definition above, imagining is a voluntary act. Dreaming is not.
You'd also be unable to tell when it is psychotic people decide of the mental events taking place in their minds.

You have yet to explain what you mean by "logically possible". Possible for you to imagine? Internally consistent? Consistent with all of our existing knowledge/beliefs? An element of some huge set of states of affairs (factual and counterfactual) that might possibly exist in actual reality (even if in our reality they don't)?

???
So you haven't read my answers to other posters...
Here it is, and it's a long and detailed explanation you've missed... How come?

A proposition is logically possible if it doesn't contradict your assumptions. So, it all depends on what assumption you make to begin with. If you assume a realistic setup, i.e. if you assume that the laws of physics apply, then what is logically possible is very much constrained. It is broadly limited to what is physical possible, although not quite since we wouldn't here assume any initial conditions and initial conditions obviously would further limit the range of physically possible outcomes. However, at the extreme, there is, arguably, only one physical reality and therefore only one physical possibility, i.e. what actually is. Yet, we can only operate with a more or less limited knowledge of the current state of the physical world and so we talk of "physical possibilities" even though what we are really talking about are logical possibilities assuming the laws of nature. And then, we may choose to ignore the laws of nature altogether, in a sort of counterfactual scenario, to imagine a fanciful Santa Claus. However, the two sets of logical possibilities have nothing in common between a fanciful Santa Claus and a realistic Santa Claus.
So, the counterexamples posters have been proposing here are all ineffective because they are equivocations.
EB

So you haven't read the answers I provided.

What is the relationship between logic in the subjective psychological sense of how somebody's individual thought process unfolds (in dreams, psychosis, imagination or rational thought... we speak this way then we use phrases like "the logic of dreams"), logic in the objective formal sense in which logical proofs that are valid for me should be valid for everyone else as well, and logic in the objective ontological sense in which our employment of logic can tell us something about what can and can't be true in the reality we all share.

I didn't specify so I meant logic as most people think of it and use it. So, no, I didn't mean to talk about how somebody's individual thought process unfolds in dreams, psychosis...
But imagination and rational thought, yes, obviously.
Clearly, there's no difference between what you call the objective and the ontological senses: The conclusion of a logical inference will have ontological import if and only if the premises are believed true of the actual world. This applies to mathematical logic as well as how non-mathematicians use logic (outside the psychotics and the dead).
There is no other meaningful connection between logic and ontology, at least for our usual concept of logic.

It's very closely related to questions of what mathematics is, why mathematics works so well in physics and why the resulting physics produces engineering that works whether it's consistent with our personal worldviews, or not. Big topics in the philosophy of mathematics and science.

Sure, and this is in line with my thesis that if I can imagine it, it's logically possible.

I was providing my own opinion. I wasn't asking you for anything though I was inviting intelligent comment.

My intelligent comment here is that you should read my answers to other posters. That's also the intelligent thing to do.

Frankly, I don't believe that you have any satisfactory answers. That's not meant as an insult because I don't either. I don't think that anyone does at this point. All of this kind of stuff remains a fundamental mystery. I'm not convinced that human beings will ever get to the bottom of it.

This shows you haven't read my answers to other posters.
Your opinion might have had some value had you read my answers to other posters and articulated your possible criticisms.
I still haven't been given any reason to give up on my thesis.
And, to tell the truth, I practise what I am preaching here. I posted my thesis without trying to conceptualise it before hand. All I had was, as Descartes would have put it, a clear and distinct idea that if I can imagine it, it's a logical possibility. And now I find that I have zero difficulty conceptualising what I had merely imagined. In effect, I'm discovering after the fact the logic behind my own thesis as I answer the criticisms of other posters.
EB

 

[Yazata]

I would consider something logically possible if one can start with any premises at all and, through valid logic, reach the conclusion.

I like it. You've studied logic, haven't you?

I can imagine a "state space" (so to speak) in which a logic is operating and all the possible interpretations that our symbolism might receive (in the formal semantics sense) in that particular universe of discourse. So... if there's even one possible interpretation of all of the variables of a formal expression that are consistent with the truth of the entire expression, then its truth would seem to be a logical possibility in that particular universe of discourse. But if there's no possible interpretation of all of the variables that make the expression true, then its truth isn't a logical possibility.

https://en.wikipedia.org/wiki/Domain_of_discourse

Although that assumes that one is working within classical deductive logic. I guess one needn't be, so it would be a case of any proposition that can be a logical consequence of another, taking into account the axioms of the system of logic in question.

And there isn't any guarantee that everything that can be imagined has to unfold in a manner consistent with classical deductive (or any other) logic, is there? There's lots to suggest that it isn't true. (dreams, psychoses, fantasy etc.)

Another way to look at it is if, within a system of logic, there can be a world where the proposition is true, then it is logically possible. If there are no worlds where it can be true then it is not a logical possibility.
Or some such.

Possible worlds semantics. Again, I like it. (In some of my moods I'm actually a realist about possible worlds!)

 

[Sarkus]

I like it. You've studied logic, haven't you?

I really don't know if you're being sarcastic or not! And I'll take the question as rhetorical, 'cos I'm all for leaving what one says as the important thing, not what they have (or haven't) studied.

I can imagine a "state space" (so to speak) in which a logic is operating and all the possible interpretations that our symbolism might receive (in the formal semantics sense) in that particular universe of discourse. So... if there's even one possible interpretation of all of the variables of a formal expression that are consistent with the truth of the entire expression, then its truth would seem to be a logical possibility in that particular universe of discourse. But if there's no possible interpretation of all of the variables that make the expression true, then its truth isn't a logical possibility.

https://en.wikipedia.org/wiki/Domain_of_discourse

Haven't heard that formally described before. I've always just put that down to the axioms one works to, or if being more restrictive, to the a priori assumptions of a discussion. E.g. the agreement that one is starting from a certain assumption, such that discussion of whether that assumption is true or not is not part of the discussion.

And there isn't any guarantee that everything that can be imagined has to unfold in a manner consistent with classical deductive (or any other) logic, is there? There's lots to suggest that it isn't true. (dreams, psychoses, fantasy etc.)

Any system of logic that doesn't start with the same axioms would qualify, surely? The question to answer then is whether the axioms of classical deductive logic are necessarily true - i.e. true in all possible worlds. And as the thread suggests, is it a case that if you can imagine a system of logic where they are not true,does that mean there must be a world where they are not true?.

Possible worlds semantics. Again, I like it. (In some of my moods I'm actually a realist about possible worlds!)

I'm not sure I hold to the reality of it (but I don't reject it either, I'm agnostic on the matter), but it does help to frame notions in a way that I oft find easier to comprehend.

 

[Yazata]

I really don't know if you're being sarcastic or not!

No, no, no. It was meant as a compliment. Your remark suggested to me how I imagine (!) that many of the philosophy professors and professional logicians would approach the question.