Philosophy Now Forum

alan1000 wrote: ↑Sat Dec 23, 2023 1:10 pm A recent post on this question quickly descended into levity. However, it is a genuine philosophical problem in arithmetic, so let's try again, shall we?

There are four possible answers:

0/0 = 0 (based on the intuitive supposition that only zero quantities are involved, so there cannot be a non-zero answer).

0/0 = 1 (based on the supposition that n/n=1)

0/0 = infinity (assuming 0 = h)

0/0 = Ø (the division fails because the null set is indivisible)

All four positions can be supported by respectable mathematical arguments. What's your preference?

alan1000 wrote: ↑Sat Dec 23, 2023 1:10 pm All four positions can be supported by respectable mathematical arguments. What's your preference?

alan1000 wrote: ↑Sat Dec 23, 2023 1:10 pm What's your preference?

nemos wrote: ↑Sat Dec 23, 2023 4:05 pm Nothing divided by nothing, sounds philosophical to you, not to me. Or can you somehow justify that 0 is not a nothing?
No one does anything with 0, because there is no need. It is nothing more than an empty mind-bending out of boredom that has no practical application. About the same as trying to prove that 2*2=5.

Age wrote: ↑Sat Dec 23, 2023 11:10 pm 'you' can NOT divide by zero.

nemos wrote: ↑Sat Dec 23, 2023 4:05 pm Nothing divided by nothing, sounds philosophical to you, not to me. Or can you somehow justify that 0 is not a nothing?
No one does anything with 0, because there is no need. It is nothing more than an empty mind-bending out of boredom that has no practical application. About the same as trying to prove that 2*2=5.

attofishpi wrote: ↑Sun Dec 24, 2023 2:40 am

alan1000 wrote: ↑Sat Dec 23, 2023 1:10 pm A recent post on this question quickly descended into levity. However, it is a genuine philosophical problem in arithmetic, so let's try again, shall we?

There are four possible answers:

0/0 = 0 (based on the intuitive supposition that only zero quantities are involved, so there cannot be a non-zero answer).

0/0 = 1 (based on the supposition that n/n=1)

0/0 = infinity (assuming 0 = h)

0/0 = Ø (the division fails because the null set is indivisible)

All four positions can be supported by respectable mathematical arguments. What's your preference?

I'm gonna go with A: 0/0 = 0 (nothing all the way - kind of agree with nemos)

Skepdick wrote: ↑Sun Dec 24, 2023 8:40 am

alan1000 wrote: ↑Sat Dec 23, 2023 1:10 pm All four positions can be supported by respectable mathematical arguments. What's your preference?

All of them.

Depending on the context.
Depending on what the / operator means; and depending on what 0/0 is supposed to represent/denote.

Manipulating and evaluating mathematical objects/expressions is the epitome of a designing computer algebras/symbolic computations.

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

alan1000 wrote: ↑Thu Dec 28, 2023 12:02 pm

Age wrote: ↑Sat Dec 23, 2023 11:10 pm 'you' can NOT divide by zero.

You forgot to provide supporting arguments, as required by the rules of this forum. If you can provide such arguments, I will reply.

alan1000 wrote: ↑Sat Dec 23, 2023 1:10 pmHowever, it is a genuine philosophical problem in arithmetic, so let's try again, shall we?

alan1000 wrote: ↑Thu Dec 28, 2023 12:28 pm

Skepdick wrote: ↑Sun Dec 24, 2023 8:40 am

alan1000 wrote: ↑Sat Dec 23, 2023 1:10 pm All four positions can be supported by respectable mathematical arguments. What's your preference?

All of them.

Depending on the context.
Depending on what the / operator means; and depending on what 0/0 is supposed to represent/denote.

Manipulating and evaluating mathematical objects/expressions is the epitome of a designing computer algebras/symbolic computations.

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

This is at least a philosophically intelligible reply. Skepdick is right; all of the answers are correct, on condition that one specifies the appropriate mathematical context. (I deliberately say 'one' rather than 'you', because one poster seemed to take exception to the second-person pronoun).

But is there any reason to prefer one answer over the others? Because it is obvious that, in any philosophical discourse, where apparently-conclusive arguments lead to contradictory outcomes, the enquiry must have taken a wrong turn somewhere. Is there any over-reaching argument to favour one solution over the others?

Age wrote: ↑Thu Dec 28, 2023 12:38 pm

alan1000 wrote: ↑Thu Dec 28, 2023 12:02 pm

Age wrote: ↑Sat Dec 23, 2023 11:10 pm 'you' can NOT divide by zero.

You forgot to provide supporting arguments, as required by the rules of this forum. If you can provide such arguments, I will reply.

One only has to look at a computer or calculator to come to see and understand that 'you' can NOT divide by zero.

However, and of course, if 'you' CAN divide by zero, then, please, explain HOW, EXACTLY, and what answer 'you' get/got, EXACTLY.

Now,
P1. For EVERY one else and for EVERY computer/calculator 'they' can NOT divide by zero.
P2. No one has YET shown HOW 'they' CAN divide by zero.
Therefore, until 'you', or someone else, can SHOW, EXACTLY, how 'you/they' CAN divide by zero, then 'this argument' will suffice.