**Regarding the Claims! Claims! Claims! stream and the ternary system.**

*or ternarinception*

Let’s employ some programming skills with ternary operators and a bit of logic and see where it gets us.

**definitions and notation**

Before I get into the argument let me set up some tools. You can skip or glance over these, but they're there if you need them later.

We assume that it is only possible to hold one of three positions on any proposition

A = Accept

B = Reject

C = Abstain

Given any proposition P one can then make three derived propositions P' of the form:

PA ⇔ position on P is 'Accept'

PB ⇔ position on P is 'Reject'

PC ⇔ position on P is 'Abstain'

The ternary system must then be applicable to each of those statements but must retain logical consistency, so each statement must infer meaning about the other statements.

PA ⇔ PAA ∧ PBB ∧ PCB

In other words:

*Accepting P is equivalent to Accepting PA AND Rejecting PB AND Rejecting PC*

And the relation can be written as:

PAA ⇔ PBB ∧ PCB

*Accepting PA is equivalent to Rejecting PB And Rejecting PC*

In other words:

*Accepting P is equivalent to neither Rejecting nor Abstaining from P*

Solving this derived set of propositions gives complete information about the position on P.

This chain of derived statements should hold all the way down to the axioms if the system is to be consistent

**disagreeing with TheRumpus**

+TheRumpus Account has claimed that statements like not-accept are illegal because they lead to contradiction.

I disagree. Statements that

*are contradictions*are illegal, but statements that are not contradictions are fine-just-fine (but might be

*incomplete*).

The way in which this becomes crystal clear for me is to see it from an outsiders perspective trying to find out what some person's position is

So lets write the legal positions.

**The set where I agree with TheRumpus**

PAA ⇒ PBB ∧ PCB

*position is known: the person Accepts P (e.g., Theism)*

PBA ⇒ PAB ∧ PCB

*position is known: the person Rejects P (e.g., Hard Atheism)*

PCA ⇒ PAB ∧ PBB

*position is known: the person Abstains on P (e.g., Agnosticism)*

Since the position is known, any of these sufficiently answers the question:

“What position does the person hold on P?”

**The set TheRumpus calls illegal**

¬PAA ⇒ (PBA ∨ PCA)

*position is unknown: the person either Rejects or Abstains on P (e.g. non-theism)*

Along with PAA, sufficiently answers the question “Does the person Accept P?”

Technically the full form is: ¬PAA ⇒ (PBA ∨ PCA) ∨ (PBC ∧ PCC) but it can be reduced with no loss.

¬PBA ⇒ (PAA ∨ PCA)

*position is unknown: the person either Accepts or Abstains on P*

Along with PBA, sufficiently answers the question “Does the person Reject P?”

Technically the full form is: ¬PBA ⇒ (PAA ∨ PCA) ∨ (PAC ∧ PCC) but can be reduced with no loss.

¬PCA ⇒ (PAA ∨ PBA)

*position is unknown: the person either Accepts or Rejects P*

Along with PCA, sufficiently answers the question “Does the person Abstain on P?”

The long form would contain a contradiction in the second part of the statement so that part must be excluded (giving a consistent reduction)

And there are other non-contradictory values in the derivations such as

PAC ∧ PBC ∧ PCC which would reduce to PC but I would argue that it a possible answer in case the person doesn’t know of P (literally, doesn’t know of the proposition itself)

Contrast this with ternary values (T - true, F - false, U - undefined).

A negation of ternary values would work something like:

¬T=F

¬F=T

¬U=U

And applying that to the examples in which this ternary system is proposed, you could get the following exchange:

"Are you an Agnostic?" - "No!" - "Oh, so you're an Agnostic then."

**Conclusion**

All of this violates the excluded middle rule but maps much better to how people actually think (since ignorance is a major component of cognition) and converse.

It could be interesting to derive the mathematical properties and rules of the system and construct truth tables (or rather the

*position*tables) to see how the positions interact and sum up to see which form of ternary logic would fit best.

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- I will try and give you a fulsome answer tomorrow, I have been up to my eyeballs today and I haven't been able to give this thread my full attention.Oct 25, 2017
- +TheRumpus thank you.

Also, what I call "Abstain" you call "Neither Accept nor Reject"

Does that mean that you'd also accept the answer "Neither Reject nor Abstain" for "Accept"

And if that works, again it would point to "Not Accept" being equivalent to "Either Reject Or Abstain"

why can you offer a composite statement to get a single value but don't accept that its reasonable to get a composite value when going the other way.

But you already know that.. sorry.~~-~~

Another perspective:

A superposition of two values is a value. It is a legal value. You cannot measure it. when you measure it you only ever get one of the two values. Does that work for you?Oct 25, 2017 - +barney tearspell
**1)**

I haven't read all of your posts but I have just fully read the last one in which you say about me*"Then you appealed to set theory insisting that {A, B} is A AND B and cannot be A OR B. I've checked, it can.**Now we're down to it's ambiguous. and "we demand"**"You must give an unambiguous answer" triggers my agnostic past :**AA: "the proposition is god exists, what is your position on that proposition"**Me: "I don't know"**AA: "you must say true or false, nothing else"**Me: "I must nothing"**You did this thing because defining labels and positions is not truth values and the logic for covering all of them is unclear and convoluted.**I know you know that those values are meaningful and useful because you've stated that you started out trying to define them. You claimed at that point you've found all the contradictions and had to abandon that pursuit.**Here, we've resolved the contradictions."*

How on earth did you come to the conclusion that I was demanding that you "you must say true or false, nothing else" ????????? ( What is AA? in this dialogue, I presume it is me )

So I am going to have to repeat myself, which is depressing.

When someone is asked to respond to a proposition it is generally accepted that they must give an unambiguous answer and a non-contradictory answer.

So for instance it would not be acceptable for the response that they

"Accept OR Reject"

the proposition. That would be a response without value.

So it is perfectly reasonable that the response to a proposition is constrained to be non-ambiguous, non-contradictory responses, irrespective of the ternary system.**2)**

You said in a post above that*"When you define your ternary system you say**Given a proposition X, there are only three possible responses that can be given:**1 - Accept**2 - Reject**3 - Neither Accept nor Reject"**in other words**X is either 1 OR 2 OR 3**If that is an illegal statement in your system then how do you define the system?"*

Yes the response can be ONE of that set, but NOT the SET!

SO YOU HAVE TO PICK ONE!**3)**

I have just read the first post and......... it is insane! It is making the same mistake that Nesslig was making.

You are deriving propositions from propositions!!!!!!!!! Which is invalid.

When someone gives a response to a proposition, THEY ARE NOT GIVING ANOTHER PROPOSITION! THEY ARE DECLARING THEIR POSITION ON THE PROPOSITION. That is NOT the same as making a new claim.

Layers of derived claims is not the issue here.**4)**

I still haven't read all of the posts but going back to the point about ternary logic and that

"Contrast this with ternary values (T - true, F - false, U - undefined).

A negation of ternary values would work something like:

¬T=F

¬F=T

¬U=U

"

I was yesterday going to make a point about this and NOT Accept.

If as the logic of the above quote indicates, and is compatible with my own reading of the subject, one can use NOT operators to give unambiguous and single results.

And I did say in the hangout and in the text of my diagram that NOT Accept was illegal because it leads to contradictions, but IF the person who declared the "NOT Accept" was KNOWN to USE and understand ternary logic then one could presume that he knew that

NOT Accept = Reject

and not as I implied ( which is what someone using Boolean logic would have done that

NOT Accept = Reject AND ( NOT Reject AND NOT Accept )

But if such a person who was known to understand Ternary logic had said NOT Accept, then they would have known that that is the same as Reject, SO THERE WOULD HAVE BEEN NO POINT IN CLOUDING THE ISSUE BY SAYING "NOT Accept" rather than "Reject".

By using NOT Accept, SUGGESTS the respondent is NOT using Ternary logic, but BOOLEAN logic, and therefore WAS making a contradictory statement.

So I maintain that the use of NOT Accept is contradictory because someone who understood ternary logic would realise that was = Reject and for clarity's sake would have just said Reject.

Someone who uses NOT Accept is clearly using BOOLEAN logic and not understanding the logical implications of what they are saying.

I still haven't read all of your posts but that should cover most of it I think.

If there are is still stuff unresolved, perhaps we ought to have another hangout, ( in which I might have further some comments about +Ozymandias Ramses II II's claims ) to clarify further and I can also highlight that +Steve McRae was suggesting here that giving a response as a set of options was an acceptable response to a proposition, which it is NOT.

Phew!Oct 28, 2017 - +TheRumpus I'd love to have a hangout with you on this topic iff we can agree not to talk over eachother and adress one point at a time.

AA example was an analogy and not directly adressing this or you. I was just saying that our current impasse reminds me of atheist activists (AA) deny the answer 'True OR False' (agnosticism)

I would say that that answer is valid and agree with you that it's not valuable (it offers no information in respect to the proposition).

In our ternary system the answer (Not Accept) is not only valid but it DOES provide some information in respect to the proposition.Oct 28, 2017 - +barney tearspell

Well I don't usually talk over other people in hangouts, but in the one on claims I had to deal with +MP and +Steve McRae being very keen to speak, and there were some key points that had to be made. I don't think one could claim I actually prevented points being made, though there were some time constraints which meant we were all fighting for time, that presumably would not be the case in a hangout we had.

On consideration I don't think ternary logic is relevant to any of this. I think the NOT operation is a set complement operation, a binary operation which splits members of a set of options into two. I have updated the diagram to reflect this.Oct 31, 2017 - +TheRumpus on ternary logic.. that's exactly the point that I was trying to make (that's why I gave the T-F-U example, to show it doesn't fit).

And the complement is a set that you get by difference. So agreed again.

And I'm (to be clear) not faulting your logic or your reasoning. As stated before, I think it's a great system and it works (as you've described it).

And I even understand that getting an ambiguous answer is an undesired outcome. I'd much prefer it if everyone would answer every question in a clear and unambiguous way.

But saying that that is "illegal", or "forbidden" or "not allowed" is taking it too far IMHO.

I see that there is at least some value in the answer (ambiguous as it is) and I see that you could perform further operations on it (both logically and cognitively) to derive and infer further information even from an ambiguous answer.

That is all I'm saying.

You're right, just don't be so stringent.Oct 31, 2017