General Resolution Debating

[obsrvr524]

Alright, I am getting confused now Let's take it one step at a time.

My argument has no (5a) statement. That's something you inserted into my argument (you did it for the first time in this thread) and I am still trying to figure out why you did that.

I did that because YOU said that I am supposed to despite my objection.

Whatever the reason, you are NOT supposed to argue against something I didn't say.

And that is EXACTLY what I said would result if I added that in as you insisted. -vvv

What kind of response would you expect? - "That isn't what I said! I didn't say that all that is mortal is man. You are putting false words in my mouth."

I am not even sure what (5a) means, so I need your clarification.

Well zookers, why didn't you ask?

5a) But must not have such an expression for the numbers to be the same numbers.

What do you mean by "must not have such an expression"?

In order for your conclusion to be derivable from your premises, you would have to add that (5a) premise (that was implied within your conclusion). It is referring to the prior premise (5) -vvv

5) The decimal expression of \(\sum^{i−>∞}_{i=0}9×10^i\) has a digit associated with \(10^0\).

What is "\(10^0\) expression"?
Is it a reference to a digit associated with \(10^0\)?

Of course - the \(9x10^0\) term.

I was directly challenging that conclusion's "because" clause - not because of the improper presentation but because it is an incorrect assertion.

You were challenging something I did not say? :O

See? There you go.

I was disputing what you implied with your last statement of argument - one that was more than merely a conclusion. It had an implied assertion concerning that \(9x10^0\) term. That is what that (5a) addition addressed for you - to take it out of your conclusion and make it a proper assertion (premise). You had insisted that I add a statement that would correct your logic (remove the non-sequitur status).

It means a number that is all 9s - what else could it mean? - "99" - "99999" - "...999" - "999..." - "...999..." - whichever.

In that case, I agree with the conclusion of your rebuttal :O
Both \(999\dotso\) and \(\sum_{i=0}^{i->\infty} 9\times10^0\) are decimal / denary / base-10 numerals where each digit is \(9\).

The problem is, I never said the opposite of it.

Your implied assertion that the \(9x10^0\) term could not be included in my representation because it was not included in "999..." (again the 5a statement) was saying that one 9 had to be left out - the one represented by \(9x10^0\).

My argument was that no 9s are actually left out of either expression. So your implied assertion that one of the 9s must be left out of my right hand term was incorrect.

And then because your argument against my proposal was invalid, you have not yet proven my proposal to be incorrect. So come up with another argument, refute my response, or agree that the original proposal is correct.

[MagsJ]

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No balking tho, ok.. ; )

[obsrvr524]

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No balking tho, ok.. ; )

"Balking"?

balk (bôk)
v. balked, balk·ing, balks
v.intr.
1. To stop short and refuse to go on: The horse balked at the jump.
2. To refuse obstinately or abruptly: She balked at the very idea of compromise.

No one is balking - quite the opposite.

[obsrvr524]

Here's a corrected version of my argument:

The Initial Argument (Version 2)

1) Let \(X\) be a class of decimal expressions that have no fractional part, that stand for a positive number and that do not start with \(0\).

2) Any two decimal expressions that are instances of \(X\) represent one and the same number if and only if every digit in one expression is the same as the digit located at the same place in the other expression.

3) \(999\dotso\) is an instance of \(X\).

4) \(999\dotso\) has no digit associated with \(10^0\).

5) The decimal expression of \(\sum_{i=0}^{i->\infty} 9\times10^i\) is an instance of \(X\).

6) The decimal expression of \(\sum_{i=0}^{i->\infty} 9\times10^i\) has a digit associated with \(10^0\).

7) Therefore, \(999\dotso\) and \(\sum_{i=0}^{i->\infty} 9\times10^i\) represent two different numbers.

The text in red refers to additions and changes.

What I forgot to add is statement #5.

I didn't see that post.

And now I realize that I should have objected to your (4) - there actually IS a digit (or rather value) associated with \(10^0\). It is merely unseen.

[MagsJ]

-
No balking tho, ok.. ; )

"Balking"?

balk (bôk)
v. balked, balk·ing, balks
v.intr.
1. To stop short and refuse to go on: The horse balked at the jump.
2. To refuse obstinately or abruptly: She balked at the very idea of compromise.

No one is balking - quite the opposite.

It seems the joke missed you.. remember when I accused Sil of balking in one of your communism threads?
and you thought it amusingly funny..

[obsrvr524]

It seems the joke missed you.. remember when I accused Sil of balking in one of your communism threads?
and you thought it amusingly funny..

Maybe I just need to put on another pot - sorry.

[Magnus Anderson]

I did that because YOU said that I am supposed to despite my objection.

I asked you to present an argument against the validity of my argument and I suggested a way to do it. And yes, that way involved inserting a claim in my argument (but it did not involve arguing against it.)

Did you really do that?

You argued against the claim you inserted. I did NOT ask you to do that. Moreover, it appears you argued against it LONG BEFORE you inserted it in my argument.

In order for your conclusion to be derivable from your premises, you would have to add that (5a) premise (that was implied within your conclusion).

(5a) is neither an explicit nor an implicit statement of my argument. That's something you inserted. So I would prefer it if you owned it (:

If you want to claim that my argument is logically invalid and that inserting a statement such as (5a) would make it logically valid, that's fine. But in such a case, you do not have to argue against that claim. Why? Because it is NOT my claim and because your task is merely to show that my argument is invalid. Only once (and if) I add it to my argument should you consider arguing against it.

I was disputing what you implied with your last statement of argument - one that was more than merely a conclusion. It had an implied assertion concerning that \(9\times10^0\) term. That is what that (5a) addition addressed for you - to take it out of your conclusion and make it a proper assertion (premise).

No such thing was implied by the last statement of my argument.

You had insisted that I add a statement that would correct your logic (remove the non-sequitur status).

I would say you misunderstood what I asked you to do.

Your implied assertion that the \(9\times10^0\) term could not be included in my representation because it was not included in "999..." (again the 5a statement) was saying that one 9 had to be left out - the one represented by \(9\times10^0\).

I explicitly stated that the decimal expression of your number, which is \(\sum_{i=0}^{i->\infty} 9\times10^i\), has a digit associated with \(10^0\). That digit is \(9\). It is NOT excluded. It is THERE. This is stated in (6) in Version 2 of my argument and in (5) in first (but edited) version of my argument.

What does not have that digit is \(99\dot9\). That's stated in (4).

And you agreed with BOTH premises.

My argument was that no 9s are actually left out of either expression.

That contradicts (4) which you previously agreed with.

[MagsJ]

It seems the joke missed you.. remember when I accused Sil of balking in one of your communism threads?
and you thought it amusingly funny..

Maybe I just need to put on another pot - sorry.

Ah, don’t worry..

Re. the OP.. I do think that debate resolution can/will never be a one-size-fits-all resolution, across the debating board.

[obsrvr524]

Re. the OP.. I do think that debate resolution can/will never be a one-size-fits-all resolution, across the debating board.

Oh I agree. It isn't supposed to be. It is just for us analytical reductionist types who closely examine the exact logic of assertions being made.

and even at that, it would probably take a very long time before anything practical for society would come of it. But if it does succeed, you would not believe the effect it would have on the entire world - so I won't go into that.

[Magnus Anderson]

I didn't see that post.

And now I realize that I should have objected to your (4) - there actually IS a digit (or rather value) associated with \(10^0\). It is merely unseen.

Alright. My (4) states that there is no digit associated with \(10^0\) in \(999\dotso\) seen or unseen.

Perhaps you should repost your rebuttal now (:

[obsrvr524]

Perhaps you should repost your rebuttal now (:

Although it is going to be the same thing.

And I'm not sure we resolved PoO#1.

[Magnus Anderson]

We did not resolve it but we can temporarily close it and open it the next time a similar problem occurs.

I would propose the following:

1) Magnus posts Version 2 of his argument in the thread

2) Observer reviews it and then responds to it by stating agreements and disagreements and presenting an argument against one of the things he disagrees with

If you state that you disagree with the validity of my argument, but you choose to argue against something else, we'll bring PoO #1 back from the asleep.

Respond with "Yes" and I'm gonna post that new version of my argument in that thread.

[obsrvr524]

If you state that you disagree with the validity of my argument, but you choose to argue against something else, we'll bring PoO #1 back from the asleep.

I still disagree that is what happened, but we can be more careful about that concern in the future -

So yes, we can restart. Let me restate my proposal first, then your challenge - and go from there.

[Magnus Anderson]

Do it.

[obsrvr524]

Done it.

[Magnus Anderson]

I'm done too.

[MagsJ]

Re. the OP.. I do think that debate resolution can/will never be a one-size-fits-all resolution, across the debating board.

Oh I agree. It isn't supposed to be. It is just for us analytical reductionist types who closely examine the exact logic of assertions being made.

Because.. a Debater (ENTP) is a person with the Extraverted, Intuitive, Thinking, and Prospecting personality traits. They tend to be bold and creative, deconstructing and rebuilding ideas with great mental agility. They pursue their goals vigorously despite any resistance they might encounter.

and even at that, it would probably take a very long time before anything practical for society would come of it. But if it does succeed, you would not believe the effect it would have on the entire world - so I won't go into that.

Thanks..

As not an ENTP, I want to hear the outcomes and resolutions, not the whole process, tho only pivotal parts of the process.. otherwise it does my head in/things becoming boring.

[Magnus Anderson]

Point of Order #2

When I presented Version 3 of The Initial Argument you responded to it with the following post:

4) \(999\dotso\) has no explicit digit associated with \(10^0\) but it has an implicit one and that digit is \(0\).

Disagree.

The representation 999... refers only to the digit "9" being repeated endlessly.
There is no \(0\) digit involved in 999... implicit or otherwise.

I am not sure this is an acceptable response. According to James's flowchart, the proposer is supposed to state agreements and rebuttals. And what he means by "rebuttals", I believe, is "counter-arguments". There appears to be no counter-argument in the above, something you didn't make an effort to argue against in your next post where you seemingly implied that one cannot argue that something isn't present.

How else can we argue that something isn't present other than to simply state that it isn't - implying that if you still contend that it is there - show it?

Then the following discussion followed:

Are you saying that proving a negative is an impossible task?

I thought you don't subscribe to such popular but nonetheless erroneous ideas.

I didn't say that it is impossible. I said that when someone simply says that something is there and we do not see it there - there is nothing to say but - "It is not there - so show us why you think it is there".

How about presenting an argument that concludes with "Therefore, it is not there"?

Ok -

• If there was an implicit 0 digit there, I would see it
• I don't see an implicit 0 digit indicated.
• Therefore there is no implicit 0 digit present.

That is my evidentiary argument.

And when I presented a counter-argument, you responded with:

But I was hoping that you would skip that obvious argument.

If that is where you want to go and have nothing else to offer then you have expired your defense on that issue by not convincing me of your premise (4) - so the rest of that argument (version 4) is moot.

Do you have a different argument to make addressing the proposal? If so - it's time to post it.

VERY strange.

What makes you think that I "expired my defense"?

[obsrvr524]

You seem to be getting hypercritical about form. You seem to be trying to make it too hard.

Any explanation as to why one party disagrees with another is a rebuttal. There is no requirement to list definitions, premises, and therefore's. If you say the sky is blue and I say "It looks gray to me" - that is a rebuttal.

The purpose of premises in an argument is to go from things agreed upon already to more complete agreement stated in the conclusion - as if to say "since we agree on these things - we must also agree on this...". But if the premises are not agreed upon, the process of reaching agreement cannot be satisfied - and that is the whole point - to reach agreement or at minimum point out our premise conflicts (perhaps just differences of opinions, perceptions, or preferences).

So if we cannot agree on a proposed premise - for whatever reason - that entire argument is for naught. The exact structure of our rebuttal explaining why we disagree has little to nothing to do it.

There are only 3 alternatives -

1) give alternating explanations to each other in the hopes of finding agreement on premises
2) start over with an alternatively premised argument.
3) expire from that debate and start a debate over the premise

You have stated that there is an implied 0 digit. I haven't been able to identify an implied 0 digit by the explanations that you have given. If you can't think of anything else to say to convince me - we can't use the argument you proposed because we can't agree on one of your premises - find a set of premises that we can agree on.

In the end there should be a "Oh I see now" moment for one of us. But perhaps that is a "Oh I see why you think that but I think you have a false belief concerning one of those premises".

Either way we make progress.

[Magnus Anderson]

Any explanation as to why one party disagrees with another is a rebuttal. There is no requirement to list definitions, premises, and therefore's. If you say the sky is blue and I say "It looks gray to me" - that is a rebuttal.

"It looks gray to me" is not an explanation as to why one party disagrees with the other. It's merely a counter-assertion. But I suppose your point is that a mere counter-assertion should count as a rebuttal.

The purpose of premises in an argument is to go from things agreed upon already to more complete agreement stated in the conclusion - as if to say "since we agree on these things - we must also agree on this...". But if the premises are not agreed upon, the process of reaching agreement cannot be satisfied - and that is the whole point - to reach agreement or at minimum point out our premise conflicts (perhaps just differences of opinions, perceptions, or preferences).

That's news to me.

[obsrvr524]

Any explanation as to why one party disagrees with another is a rebuttal. There is no requirement to list definitions, premises, and therefore's. If you say the sky is blue and I say "It looks gray to me" - that is a rebuttal.

"It looks gray to me" is not an explanation as to why one party disagrees with the other.

Of course it is. It is saying that "the reason I disagree is because of what I see".

It's merely a counter-assertion. But I suppose your point is that a mere counter-assertion should count as a rebuttal.

A mere counter-assertion would be - "No. It is gray" - void of why I believe it is gray.

The purpose of premises in an argument is to go from things agreed upon already to more complete agreement stated in the conclusion - as if to say "since we agree on these things - we must also agree on this...". But if the premises are not agreed upon, the process of reaching agreement cannot be satisfied - and that is the whole point - to reach agreement or at minimum point out our premise conflicts (perhaps just differences of opinions, perceptions, or preferences).

That's news to me.

Well now you know.


Remember the purpose of all of this is to work out our understanding of the process and ability to mutually moderate. So it should be expected that at first we find differences to settle.

[Magnus Anderson]

Of course it is. It is saying that "the reason I disagree is because of what I see".

A mere counter-assertion would be - "No. It is gray" - void of why I believe it is gray.

That clarifies things.

[obsrvr524]

When a dispute in an OP definition arises a new debate is required - a "start over". So any questions concerning definitions should be addressed as soon as possible.