Cooperative Principle

[Amad27]

Hello there,

Recently I have been discovering the cooperative principle and have been applying to mathematics. Consider a word problem

"A spherical balloon is inflated with gas at the
rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 centimeters and (b) 60 centimeters?" (Larson Calculus P 153)

Now I am not here to discuss the math. I have a question based on the Grice Principle.

The Grice Maxim of Quality states, don't mention what is false.

So do I AUTOMATICALLY assume that a hole in the ballon (which is NOT mentioned) doesn't exist?

Also, under what conditions can you apply Grice's Quality Law?
And WHY can you apply it to this?
Thanks

[uwot]

Hello there,

Hello to you, too.

The Grice Maxim of Quality states, don't mention what is false.

Is that true? I've never heard of it.

So do I AUTOMATICALLY assume that a hole in the ballon (which is NOT mentioned) doesn't exist?

Also, under what conditions can you apply Grice's Quality Law?
And WHY can you apply it to this?
Thanks

Well there are two other principles that may be pertinent. Firstly, Wittgenstein's dictum 'Whereof we cannot speak; thereof we must remain silent.' (Which makes me think maybe I have heard of Grice's principle.) The other is Occam's Razor: 'Do not multiply entities beyond necessity.' Until you have a reason to believe in the hole; don't.

[Impenitent]

Hello there,

Recently I have been discovering the cooperative principle and have been applying to mathematics. Consider a word problem

"A spherical balloon is inflated with gas at the
rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 centimeters and (b) 60 centimeters?" (Larson Calculus P 153)

Now I am not here to discuss the math. I have a question based on the Grice Principle.

The Grice Maxim of Quality states, don't mention what is false.

So do I AUTOMATICALLY assume that a hole in the ballon (which is NOT mentioned) doesn't exist?

Also, under what conditions can you apply Grice's Quality Law?
And WHY can you apply it to this?
Thanks

At the instant the radius is 30 cm, the radius is not increasing. It is 30 cm.

If you assume that a hole in the balloon doesn't exist, you must assume that gas is entering the balloon through other means...

"assumption is the mother of all f-ups"

-Imp

[Blaggard]

I can answer the maths question now, and without even using calculus, the associated moral question is much more tricky.

Tip: convert the integral from of f'(x) dx/dy/dz/dt to non Cartesian co-ordinates, it will help you out and try not to forget that 2 pi rad is equal to 360°.

If you want us to do your homework for you that is no fuss, if you want to ask a serious question about philosophy likewise, to do both would be somewhat egregious though.

[NielsBohr]

Hello there,

Recently I have been discovering the cooperative principle and have been applying to mathematics. Consider a word problem

"A spherical balloon is inflated with gas at the
rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 centimeters and (b) 60 centimeters?" (Larson Calculus P 153)

-Hi Amad27,

Actually, it is rather physics. To help you in this problem, something tells me that there is a slowing down tense, which itself increase with the square of the radius. (So you have an inflation, but decreasing more and more until the equilibrium makes the speed of inflation to be zero.)

Now I am not here to discuss the math. I have a question based on the Grice Principle.

The Grice Maxim of Quality states, don't mention what is false.

So do I AUTOMATICALLY assume that a hole in the ballon (which is NOT mentioned) doesn't exist?

Also, under what conditions can you apply Grice's Quality Law?
And WHY can you apply it to this?
Thanks

Actually, I do not know Grice's Law, but am working in databases conception - what is not less useful about the data of an instruction.

An intermediate principle, mention that we have to tell All the truth And Only the truth.

This is the same in instruction.

If the instruction seems to be general, you shall keep its generality - you cannot infer a hole. Unless we tell you that you have an entering flow, and an output flow, what would make the hole bi-directional - or two hole for input and output.

After that, I guess you would demand if the gas entering goes trough a hole ?

It depends. If you were to consider all a system with several sub-systems, knowing: a balloon, and pressured gas in bottle, and a pipe.

If you consider all the system: you have obviously no hole, such as it is closed.
If you consider only the sub-system "balloon", you have a hole.

Obviously again, considering the whole system can help by invoking general laws, as mass conservation, and conservation of energy.

You instruction seems to be summarized about this - don't tell much about some "pressured bottles".

But if you start with a atmospherical pression, you can re-find - due to the numerical flow - the initial pressure in the bottles...

In an extension, without an atmospherical pression, you can pose a (constant) external initial pression: p0.

And then, infer on it (bottles pression decreasing until equilibrium). But you shall expect a square decrease of the inflation (function of balloon's radius) due to you experience in life with balloons - we know that the inflation shall stop (or even a break of the balloon if you invoke its superficial tension) - but in this case, you shall mention your "synthetical" experience.

I can re-find some notions about soap bubble tension. This could help to know if effectively the tension is a square function of radius.

[NielsBohr]

Amad27,

I tried anyway your problem to consider it completely.

There is much time I have not done physics, so be tolerant.

I was about to consider a complete (closed) system - the temperature being constant, I could invoke the law of perfect gases. But this was about to consider more parameters than disponible laws.

Moreover, we don't have the tension of the balloon. But - with experience - we know that a balloon is not as a soap bubble: when it is empty, it does not have a volume of zero...

Finally, we have to consider the sub-system with some basic thermodynamics - knowing, the input flow. Because of the conservation of matter, it is obvious that you have a hole. But it doesn't really matter, because the flow being constant, it does not depend from its section.

So these consideration report rather to a (simplified) mathematical problem, than a physical one - you was right.

Here are my calculus - I do not give any guarantee, of course:
dV=d(4/3πr^3) - where ^ means "power", r: radius, π: Pi (constant)
=4/3πd(r^3) = (4/3)π*3*r^2 dr
So dV = 4πr^2dr

You search dr:

dr = dV/(4πr^2).

Nevertheless, the input flow being constant, the volume increase proportionally with time,

dV = Flow * dt

Finally,
dr = (Flow/4πr^2) dt.

At the point (a), you replace r with r(a) (30 cm = 0,3m), and
at the point (b), replace r with r(b) (60cm).

As expected, the inflation will decrease as a negative exponential, with the square of the radius.

[NielsBohr]

The Grice Maxim of Quality states, don't mention what is false.

So do I AUTOMATICALLY assume that a hole in the ballon (which is NOT mentioned) doesn't exist?

Also, under what conditions can you apply Grice's Quality Law?
And WHY can you apply it to this?
Thanks

Amad,

I re-read your questions.

Grice's Law is:

False-->do not mention. That is not equivalent at all to "not mentioned-->false".

I invited you nevertheless not to specify your instruction. Nevertheless, you obviously can invoke some laws, or a physical reasoning.

The most important is to write literally your reasoning, as commenting your equations.

If you give only equations - without a draw, without verbose - the teacher do not necessarily know where to go, how to follow you.

So write your reflexions.