The Liar's paradox

[James R]

Similarly whenever you see a + b this is identical to b + a.
This is referred to as the cumulative property of addition.

I thought that was the commutative property.

 

[Baldeee]

I thought that was the commutative property.

It is.
I blame spellcheck on my ****ing Asus Memo Pad.
Once the "error" is accepted the first time, it seems to correct every other occurrence it comes across.
And I was in too much of a hurry to check.
Me bad.

 

[Baldeee]

well.... show it...
where is the math?
link perhaps?

The force of gravity between two objects at a given distance apart (r) is given as F = G M1 M2 / r^2 where G is the gravitational constant, and M1 and M2 are the respective masses of the objects.
This formula helps calculate the acceleration due to gravity at the earth's surface on an object:
F = Ma, so the gravitational force on an object with mass M1 at the earth's surface will be given by G M1 M2 / r^2 where M2 is the mas of the earth, and r is the radius.
This gives roughly 9.81 m/s^2 - at the surface.
However, differentiate that force with respect to the radius and you end up with dF/dr = -2 G M1 M2 / r^3
This is the rate of change of the force as you get higher (as r increases).
If your intention is simply to match this gravitational force with thrust so that the net acceleration is zero and the object thus climbs with the same velocity, these equations will help you achieve that.

Remember we are discussing things in absolute terms... Heisenberg comes close, as does Maxwell but they are not quite on the nail IMO.

What do either of these two have to do with the price of eggs?

Facts:
An object can not move away from a source of attraction by applying less energy.

Yes it can.
Think about it: if the attractive force reduces with distance then, assuming you have an upward velocity at the start, by applying the same force up you will gradually start to accelerate away, as the net force upwards increases.
If you apply zero force upward then you will decelerate and fall back to the source.
There is thus, even using this simplistic conceptualisation, a point between zero thrust and maintaining the initial thrust level at which the thrust can reduce in line with the decreasing attractive force such that the velocity can remain constant.

You have to apply more energy to move into a position requiring less energy.

It's not discrete blocks but a continuum.
Otherwise you'll keep arguing Zeno's paradox and insist that the sum of an infinite sequence can't be reached.

...a more+less paradox exists if you seek a steady, non-accelerating velocity away from a source of attraction. This is forced upon us as an outcome of the inverse laws.

No, it really isn't.

 

[Quantum Quack]

The force of gravity between two objects at a given distance apart (r) is given as F = G M1 M2 / r^2 where G is the gravitational constant, and M1 and M2 are the respective masses of the objects.
This formula helps calculate the acceleration due to gravity at the earth's surface on an object:
F = Ma, so the gravitational force on an object with mass M1 at the earth's surface will be given by G M1 M2 / r^2 where M2 is the mas of the earth, and r is the radius.
This gives roughly 9.81 m/s^2 - at the surface.
However, differentiate that force with respect to the radius and you end up with dF/dr = -2 G M1 M2 / r^3
This is the rate of change of the force as you get higher (as r increases).
If your intention is simply to match this gravitational force with thrust so that the net acceleration is zero and the object thus climbs with the same velocity, these equations will help you achieve that.
What do either of these two have to do with the price of eggs?
Yes it can.
Think about it: if the attractive force reduces with distance then, assuming you have an upward velocity at the start, by applying the same force up you will gradually start to accelerate away, as the net force upwards increases.
If you apply zero force upward then you will decelerate and fall back to the source.
There is thus, even using this simplistic conceptualisation, a point between zero thrust and maintaining the initial thrust level at which the thrust can reduce in line with the decreasing attractive force such that the velocity can remain constant.
It's not discrete blocks but a continuum.
Otherwise you'll keep arguing Zeno's paradox and insist that the sum of an infinite sequence can't be reached.
No, it really isn't.

Again thanks for taking the time to post.
Unfortunately I disagree and would like to discuss it further at some time in another thread. The detail required is off topic.

Regardless IMO the math required to prove a paradox would mean that the reciprocation of equivalence would have to be broken. Thus a paradox can never be proven in math.

x+(-)x = 0 =/= x+(-)x
is I believe a way to show a paradox by revealing the zero in the middle as being both relative and absolute.

 

[Speakpigeon]

Is this how you usually speak to women, lovey?

I speak English as it is spoken, and better than most here, I dare say.
EB

 

[Speakpigeon]

It is a paradox, and there's no solution.

Are you sure?
If so, how could you possibly be sure?

Should? You're asking us to make some kind of moral judgment about the possibility of a logical proof? Seems a bit odd.

???
Seems we really don't speak the same kind of language.
"Should" doesn't necessarily signal a moral judgement.
Here, there's obviously nothing "moral" about it.

Should
3. used to express expectation or probability: He should be here soon. I should know by tomorrow

9. (vagueness) You use should in expressions such as I should think and I should imagine to indicate that you think something is true but you are not sure: I should think it's going to rain soon.

7. (formal) You use should in conditional clauses when you are talking about things that might happen: Should you be fired, your health benefits won't be cut off.

EB

 

[James R]

Are you sure?
If so, how could you possibly be sure?

No, I'm not sure. No more sure than any of the philosophers who have spent a couple of millennia debating the matter.

I don't think you're going to settle the matter here and now.

???
Seems we really don't speak the same kind of language.
"Should" doesn't necessarily signal a moral judgement.

It's usually about moral obligation, at least when it comes to the actions of human beings.
I concede that, when applied to abstract concepts, it probably expresses expectation or probability, as you say.

You asked:

Finally, do you think it should be possible to prove there is in fact no paradox.

If you meant "Do you expect it will be possible to prove there is in fact no paradox?" or "Do you think it is likely that a proof that tehre is in fact no paradox will be discovered?", then my answer in both cases is: no.

I could be wrong, of course. That's what not being sure means.

 

[Speakpigeon]

You asked: If you meant "Do you expect it will be possible to prove there is in fact no paradox?" or "Do you think it is likely that a proof that tehre is in fact no paradox will be discovered?", then my answer in both cases is: no.

OK, so perhaps you could look up what Wiki says: https://en.wikipedia.org/wiki/Liar_paradox
There are a number of interesting resolutions proposed. Tell me if there's any you could agree with.
EB

 

[iceaura]

OK, so perhaps you could look up what Wiki says: https://en.wikipedia.org/wiki/Liar_paradox
There are a number of interesting resolutions proposed.

All of them depend on converting directly, assuming an equivalence, between the "sentence" and a logical statement - which you explicitly excluded, in post 6.

So none of them apply to the OP here.

 

[Speakpigeon]

All of them depend on converting directly, assuming an equivalence, between the "sentence" and a logical statement

Prove there is "equivalence".

assuming an equivalence, between the "sentence" and a logical statement - which you explicitly excluded, in post 6. So none of them apply to the OP here.

I didn't do that. Quote me when you allege I said something.
EB

 

[iceaura]

Prove there is "equivalence".

It's assumed, not proven, in your link.
You excluded it, so the link does not apply.

I didn't do that. Quote me when you allege I said something.

Post 6 of this thread, as cited.

 

[Speakpigeon]

Sorry, you'd need to learn to articulate your point and quote people.
EB

 

[fess]

'This sentence is false" is completely self-referential. There is no information in it to be true or false. It makes no sense

 

[TheFrogger]

If the sentence is false, then the WHOLE statement can be considered to be untrue, but in order for this to be considered, the statement must BE CONSIDERED TO BE TRUE!

 

[RainbowSingularity]

Second, if you think it is not a paradox, please explain briefly why.

it is mathematics

Finally, do you think it should be possible to prove there is in fact no paradox.

the nature of the paradox lies in the mind of the perceptual field of comprehension by predisposition.
this is not a paradox
a paradox is not a state of lack of understanding or miss interpretation.
a paradox is a confluence of opposing reality as express terms of compliant scientific data define.
this makes a paradox.
thus science is the nature to define the paradox, not psychology.
a paradox of thought is the nature to not comply with rules of thought.
this makes the real paradox the paradox of implied meaning.
a claytons paradox

you now heave the reality of 3 things
1 a paradox
2 a lack of understanding or miss interpretation
3 an opposing opinion

 

[TheFrogger]

This sentence is false: 1=0.

 

[Write4U]

This sentence is false: 1=0.

The paradox lies in the "whole sentence".

Therefore to say (1 = 0) is a false sentence in its entirety and thus not (1 = 0), which presents an unsolvable paradox......

p.s. however at quantum this paradox may disappear due to "superposition" of all four possible paradoxical states to become true under different circumstances.....

 

[TheFrogger]

I understand your conclusion Write4u. The, "false" is part of the statement.

The array of statements would be:

This statement is true...
This statement is false...
It is not this statement that is true...
It is not this statement that is false...

 

[Speakpigeon]

'This sentence is false" is completely self-referential. There is no information in it to be true or false.

Good points.
And that's the points of it.

It makes no sense

I makes sense to me and it apparently made sense to many of the mathematicians and philosophers who have discussed it since the first Paradox of the Liar 2,500 years ago.
The sentence is grammatical. It is a very simple sentence. We understand what it means. It is talking about something real, i.e. itself.
So, I take your point that there is a problem but certainly not that it makes no sense. That's a cop out. The easy answer when you are unable to articulate what the problem is.
EB

 

[Speakpigeon]

If the sentence is false, then the WHOLE statement can be considered to be untrue, but in order for this to be considered, the statement must BE CONSIDERED TO BE TRUE!

Problem solved?
EB