Spirituality
28 Jan 16
Originally posted by DeepThoughtThat is what I thought. Why did you suggest that I had it wrong?
A proposition is a statement, as opposed to a question or an order.
Your proposition is that an agent knows that some proposition has a definite truth value and knows no one else knows either it or its negation. Suppose the basic proposition is that "Some snarks are boojums.",
Why couldn't you stick with what I already proposed with Jimmy and a cow on Jupiter?
For your example to demonstrate the knowability of Church propositions you need to find a proposition which would be structured as follows:
Why do you always change the words? Now I don't know whether or not you are addressing what I actually said, or again arguing at a tangent about something I didn't say. I know for a fact that I never claimed to have 'demonstrated the knowability of Church propositions'. I may have tried to give an example of one Church proposition that is knowable, but since you have changed the language and refused to address it head on, I do not know whether you agree or disagree or what.
This means that you cannot claim that one or the other is knowable.
Why can't you answer direct questions? Here it is again:
There is nothing in existence except the forgetful creator God. His name is Jimmy.
He creates a universe similar to our own but with no entities in it.
There is a cow on Jupiter.
Jimmy knows the truth of the proposition "There is a cow on Jupiter".
Jimmy decides to forget whether or not there is a cow on Jupiter.
Does Jimmy now know a proposition P such that "P and P is unknown"?
If not, then what does "P and P is unknown" mean in plain English and not whatever code it is in?
Please stop telling me what I 'need to do', and tell me whether or not what I did actually do meets the requirement and if not, why not.
08 Feb 16
Originally posted by twhiteheadYou don't seem to appreciate how long it takes to write some of these posts. I've spent several hours writing posts in this thread and have already answered your point more than once. LJ gave a more than adequate answer. If you don't understand then there isn't much more I can do to explain. I'm sorry but I'm not prepared to put more effort in, especially since you give me every impression that you're just going to complain about whatever I say.
That is what I thought. Why did you suggest that I had it wrong?
[b]Your proposition is that an agent knows that some proposition has a definite truth value and knows no one else knows either it or its negation. Suppose the basic proposition is that "Some snarks are boojums.",
Why couldn't you stick with what I already proposed with Jimmy and a ...[text shortened]... o', and tell me whether or not what I did actually do meets the requirement and if not, why not.[/b]
08 Feb 16
Originally posted by DeepThoughtI don't think you appreciate how annoying it is when I ask the same question over and over and only get what appears to be avoidance. What you call a 'more than adequate answer' did not answer the question asked. Instead I keep being told that I must prove something or do something suggesting neither of you actually understand what my stance is at all.
You don't seem to appreciate how long it takes to write some of these posts. I've spent several hours writing posts in this thread and have already answered your point more than once. LJ gave a more than adequate answer. If you don't understand then there isn't much more I can do to explain. I'm sorry but I'm not prepared to put more effort in, espec ...[text shortened]... ally since you give me every impression that you're just going to complain about whatever I say.
If you go back a few posts you will see that I even suggested making it simpler and broke it down into parts so you can tackle them one by one, but instead you decided to completely ignore that and went off on a tangent again and told me I had to "find a proposition which would be structured as follows: "
Huh?
I have stated that I believe I have found an example that proves your opening claim false.
Either I have found such an example or I have not.
If I were to 'find a proposition which would be structured' as you dictate, it would not tell me whether or not I have found such an example. For you to tell me that I need to do so suggests you still don't understand what I am saying at all.
Lets try for the third time:
There is nothing in existence except the forgetful creator God. His name is Jimmy.
He creates a universe similar to our own but with no entities in it.
There is a cow on Jupiter.
Jimmy knows the truth of the proposition "There is a cow on Jupiter".
Jimmy decides to forget whether or not there is a cow on Jupiter.
1. Does Jimmy now know a proposition P such that "P and P is unknown"?
2. If not, then what does "P and P is unknown" mean in plain English and not whatever code it is in?
Answer the questions in order with numbers and answer only the questions asked not what has not been asked. If you did so from the beginning you could have saved us both hours of writing.
Originally posted by twhiteheadOkay, let us try again.
I did.
[b]Your argument, again, is that one can know that a proposition has a determinate truth value and that this truth value is unknown.
My argument was that a forgetful creator God could, yes.
Fine, let’s go through it in steps.
No. I am uninterested in your steps. They are irrelevant. All that matters is whether or not my descripti ...[text shortened]... cular proposition has a determinate truth value and that this truth value is unknown. Yes or no?[/b]
Here is the claim that you explicitly stated you are arguing against: “Suppose P is some proposition which is not known, then the proposition "P and P is unknown" is itself unknown.” You claim to have a counterexample to this. Then, clearly enough, your counterexample should be a case wherein a proposition of the form “P and P is unknown” is known. That much, at least, should be very clear.
Now, your offering is a case where it is known that a particular proposition has a determinate truth value and that this truth value is unknown. Fine, let us fully agree that your forgetful creator God case does indeed exemplify this. I repeat: I am fully conceding that your forgetful creator God example satisfies such a case. Regardless, the problem for you is this: such a case does not actually constitute a counterexample of the type outline above.
Again, what you need to provide is an example wherein a proposition of the form “P and P is unknown” is known. Now, a proposition of the form “P and P is unknown” is a compound proposition using ‘and’ of two simpler propositions. So it breaks down as:
“P is true” AND “P is unknown”. (1)
Now, let us consider how your example breaks down by comparison. What you claim is known is also a compound proposition using ‘and’ of two simpler propositions. The first of these simpler propositions is that P has a determinate truth value; the second is that the truth value of P is unknown. The former of these (that P has a determinate truth value) means that either P is true or P is false. The second means that P is unknown. So, the proposition that your example shows is known breaks down as:
“Either P is true or P is false” AND “P is unknown”. (2)
Now, compare (1) and (2). They are clearly different, since the first simpler proposition of each is clearly different. One can see that they are different because, for example, (1) entails that P is true, whereas (2) does not. For another example, (2) does not entail (1).
So, you were supposed to show that a proposition of the form (1) is known. Instead, you showed that a proposition of the form (2) is known. Now, what I tried to explain in my earlier post that you poo-pooed is that not only does knowledge of a proposition like (2) not qualify as an instance of knowledge of a proposition like (1); but there is also simply no valid way to get from knowledge of (2) to knowledge of (1). So, your argument fails: you have not provided a counterexample wherein a proposition of the form “P and P is unknown” is known. If you follow the logic through, your example only provides a case wherein a proposition of the form “P and P is unknown” is true.
Does my forgetful creator God know that a particular proposition has a determinate truth value and that this truth value is unknown. Yes or no?
Yes. But does that suffice to show that a proposition of the form “P and P is unknown” is known? No.
08 Feb 16
Originally posted by LemonJelloYes.
Here is the claim that you explicitly stated you are arguing against: “Suppose P is some proposition which is not known, then the proposition "P and P is unknown" is itself unknown.” You claim to have a counterexample to this. Then, clearly enough, your counterexample should be a case wherein a proposition of the form “P and P is unknown” is known. That much, at least, should be very clear.?
Regardless, the problem for you is this: such a case does not actually constitute a counterexample of the type outline above.
OK, at least a definitive answer.
Again, what you need to provide is an example wherein a proposition of the form “P and P is unknown” is known. Now, a proposition of the form “P and P is unknown” is a compound proposition using ‘and’ of two simpler propositions. So it breaks down as:
“P is true” AND “P is unknown”. (1)
So then, I did not understand what P means. I took it to mean 'a proposition exists'. Not that it has to be true.
Now, let us consider how your example breaks down by comparison. What you claim is known is also a compound proposition using ‘and’ of two simpler propositions. The first of these simpler propositions is that P has a determinate truth value; the second is that the truth value of P is unknown. The former of these (that P has a determinate truth value) means that either P is true or P is false. The second means that P is unknown. So, the proposition that your example shows is known breaks down as:
“Either P is true or P is false” AND “P is unknown”. (2)
No, actually, it doesn't. My example, in the version with a cow on Jupiter, actually has "P is true."
Now, compare (1) and (2). They are clearly different, since the first simpler proposition of each is clearly different. One can see that they are different because, for example, (1) entails that P is true, whereas (2) does not. For another example, (2) does not entail (1).
But it is trivial to simply take a case where P is true as I did with the cow on Jupiter example.
So, you were supposed to show that a proposition of the form (1) is known.
That would make no sense. You are saying it is known that P is true and it is known that P is unknown. That is self contradictory.
Now, what I tried to explain in my earlier post that you poo-pooed
I did not mean to poo-poo it.
I still do not follow.
How can one possibly know that P is true and P is unknown?
Use my Jimmy and cow on Jupiter example and tell me what would constitute such a situation. What would Jimmy need to know in order to satisfy the statement?
Or is the original statement self contradictory?
Originally posted by twhitehead
Yes.
[b]Regardless, the problem for you is this: such a case does not actually constitute a counterexample of the type outline above.
OK, at least a definitive answer.
Again, what you need to provide is an example wherein a proposition of the form “P and P is unknown” is known. Now, a proposition of the form “P and P is unknown” is a compou ...[text shortened]... eed to know in order to satisfy the statement?
Or is the original statement self contradictory?
So, you were supposed to show that a proposition of the form (1) is known.
That would make no sense. You are saying it is known that P is true and it is known that P is unknown. That is self contradictory.
Right. That follows more or less immediately from axioms B and T. And that's exactly what DT showed in the very first post of this thread. And the original claim you quoted and explicitly said you are arguing against was just reporting this fact (it was in fact the very lead-in to DT's subsequent proof). So, now, the only thing that is confusing is to wonder why you claimed you were arguing against it. Obviously, the confusion here lies in how you interpreted that claim versus how DT intended it.
How can one possibly know that P is true and P is unknown?
Use my Jimmy and cow on Jupiter example and tell me what would constitute such a situation. What would Jimmy need to know in order to satisfy the statement?
Or is the original statement self contradictory?
One cannot know that, unless somehow we jettison axiom B or T. That's the point.
Your Jimmy case is a case where it is true that P is true and P is unknown. It's not a case where it is known that P is true and P is unknown; nor could it be.
08 Feb 16
Originally posted by LemonJelloSo you mean all this time, over 50 posts or so, you and DeepThought have known that the statement in the OP is trivially self contradictory and neither of you thought to just come out and say so?
Right. That follows more or less immediately from axioms B and T.
So, now, the only thing that is confusing is to wonder why you claimed you were arguing against it.
No. The confusing thing is this:
1. The statement, when read by someone who understands the subject and logic notation, is trivially self contradictory.
2. I clearly did not think so.
3. You assumed that I would understand its exact meaning and logic notation etc and chose to explain it all to me in that language.
4. You got annoyed when I apparently didn't understand what you were on about.
That is what is confusing.
Obviously, the confusion here lies in how you interpreted that claim versus how DT intended it.
Obviously. Yet nobody thought to point that out despite numerous attempts on my part to get to the bottom of it and requests for exact explanations.
How can one possibly know that P is true and P is unknown?
Use my Jimmy and cow on Jupiter example and tell me what would constitute such a situation. What would Jimmy need to know in order to satisfy the statement?
Or is the original statement self contradictory?
One cannot know that,
Once cannot know what?
unless somehow we jettison axiom B or T. That's the point.
Seems a little silly to start a thread which says:
This is true.
I will now prove it.
Axiom 1.
Axiom 2.
My claim follows trivially from Axiom 1 and 2.
Meanwhile anyone who knows what the original statement actually means would know it is obvious from the outset.
Your Jimmy case is a case where it is true that P is true and P is unknown. It's not a case where it is known that P is true and P is unknown; nor could it be.
Well that's kind of obvious. To say that you have found such a case would be incoherent. As you would be saying you know something that is unknown. It is irrelevant whether or not it is true.
"You can't know something that is unknown. Therefore you cannot prove that an omniscience doesn't exist."
Is that an accurate summary of the OP?
08 Feb 16
Originally posted by twhiteheadRegarding your last line. Propositions that are false are not knowable on trivial grounds, to be knowledge it must be true. So the unknowability claim refers to a proposition that is constructed from a true proposition which is unknown. Sadly the proof in the OP fails for reasons outlined by LJ on the first page, but I was hoping to use such a proposition to show a contradiction regarding the claim that it is knowable that an omniscience does not exist.
So you mean all this time, over 50 posts or so, you and DeepThought have known that the statement in the OP is trivially self contradictory and neither of you thought to just come out and say so?
[b]So, now, the only thing that is confusing is to wonder why you claimed you were arguing against it.
No. The confusing thing is this:
1. The statemen ...[text shortened]... ore you cannot prove that an omniscience doesn't exist."
Is that an accurate summary of the OP?[/b]
As an aside I satisfied myself that it is not possible to derive a contradiction from the statement that "It is known that there is an omniscience.". So we're left with empirical evidence, which isn't going to satisfy anyone. Since all absence of evidence ever is is absence of evidence.
08 Feb 16
Originally posted by DeepThoughtSo again, it is not plain English, but a special code that you omitted to explain despite numerous requests to do so.
Regarding your last line. Propositions that are false are not knowable on trivial grounds, to be knowledge it must be true.
So a 'proposition' is 'known' only when the knower thinks it is true and it is true. If it is false and the knower thinks it is false, then the knower knows a different proposition not P.
Is that right?
So the unknowability claim refers to a proposition that is constructed from a true proposition which is unknown.
I still don't see how the claim is anything more than a tautology.
Sadly the proof in the OP fails for reasons outlined by LJ on the first page,
That would appear to contradict what LJ just said about it being a trivial observation based on two axioms.
So we're left with empirical evidence, which isn't going to satisfy anyone.
Actually I put forward a number of other arguments.
08 Feb 16
Originally posted by twhiteheadKnowledge is justified belief that is true. I believe I said that in the OP. If the proposition is false and the agent has a justified belief that it is false, then they know not P. That the basic proposition P is unknown is contingent, it depends on what is known. The conclusion that (P and P is not known) is not known is unconditionally true, it is not only not known but unknowable. The proof in the OP of the unknowability of there not being an omniscience was the one that failed.
So again, it is not plain English, but a special code that you omitted to explain despite numerous requests to do so.
So a 'proposition' is 'known' only when the knower thinks it is true and it is true. If it is false and the knower thinks it is false, then the knower knows a different proposition not P.
Is that right?
[b]So the unknowability claim ...[text shortened]... , which isn't going to satisfy anyone.
Actually I put forward a number of other arguments.[/b]
Originally posted by twhitehead
So you mean all this time, over 50 posts or so, you and DeepThought have known that the statement in the OP is trivially self contradictory and neither of you thought to just come out and say so?
[b]So, now, the only thing that is confusing is to wonder why you claimed you were arguing against it.
No. The confusing thing is this:
1. The statemen ...[text shortened]... ore you cannot prove that an omniscience doesn't exist."
Is that an accurate summary of the OP?[/b]
So you mean all this time, over 50 posts or so, you and DeepThought have known that the statement in the OP is trivially self contradictory and neither of you thought to just come out and say so?
The statement in the OP that DT put forth (Suppose P is some proposition which is not known, then the proposition "P and P is unknown" is itself unknown) is not a self-contradictory statement. It is a true statement. And DT even took the time right there in OP to demonstrate its truth by way of proof by contradiction. That is all right there in the very first part of the very first post of this thread.
Later on, it was not very clear what exactly you were arguing with respect to the statement; I know that I asked you directly for clarification somewhere around page 3. But when you did clarify (for example on page 4), you explicitly quoted that statement and explicitly stated that you were arguing against it. So, understandably, DT tried explaining in more detail his opening proof for the statement (which after all, demonstrates that the statement is true); but you curiously responded that you have no need to understand such a proof.
Seems a little silly to start a thread which says:
This is true.
I will now prove it.
Axiom 1.
Axiom 2.
My claim follows trivially from Axiom 1 and 2.
Meanwhile anyone who knows what the original statement actually means would know it is obvious from the outset.
I would recommend simply re-reading DT’s opening post with a fresh perspective. It basically has two sections. The first section contains the opening statement above and the proof for it, thereby establishing that propositions of the form (P & ~K(P)) are unknowable. Yes, that part is a bit trivial in a sense (although it sure had you confused), but that is really not DT’s main argument. He is just setting the stage for the actual argument to come in the second section. The argument he makes in the second section is very interesting but, I think, unsuccessful. It’s a very clever failure though, if that makes sense. At least, it is a good exercise to think about why it does not work. It is also interesting to think if it could be modified a little to be successful, but I do not see a way to accomplish that.
"You can't know something that is unknown. Therefore you cannot prove that an omniscience doesn't exist."
Is that an accurate summary of the OP?
No.
09 Feb 16
Originally posted by LemonJelloYes, I misspoke. We have been going round and round in circles so long its getting more confusing not less. What I meant to say is that any counter example will be trivially self contradictory.
The statement in the OP that DT put forth (Suppose P is some proposition which is not known, then the proposition "P and P is unknown" is itself unknown) is not a self-contradictory statement. It is a true statement.
And DT even took the time right there in OP to demonstrate its truth by way of proof by contradiction.
Which seems unnecessary given that you earlier stated that it was obvious from the first two axioms, and I think it is obvious from the statement itself.
Correct me if I am wrong but translated into English it appears to say nothing more than:
You cannot know what is not known.
Seems a little trivial to me to be basing any vast claims about the cosmos on.
I would recommend simply re-reading DT’s opening post with a fresh perspective.
OK, fair enough, I will do so when I have time to sit down and really look at it and look up a few definitions.
10 Feb 16
OK, here goes another attempt at a different sentence from the OP.
"In other words it is unknowable that there is not an omniscience."
Now I bet that that is not plain English and doesn't mean what it says but here is a proof that the plain English version is false:
Jimmy the forgetful God is alone in reality. He creates a universe and knows that he has not created a single entity in it capable of knowledge. His is omniscient.
He chooses to forget one single fact.
He is no longer omniscient.
He now knows that there are no omnisciences in existence.
10 Feb 16
Originally posted by DeepThoughtOne thing we can take as an absolute: If there is an omniscient being AND it does not want it's presence known, it will remain unknowable till it decides otherwise.
I know the coin toss will come up heads or tails, but not I know that it will come up heads or I know it will come up tails.
I'm not sure about the conjunction part. I'm relying on K(A&B) <-> K(A)&K(B) (the necessity part assumes there is only one agent doing the knowing) and it is a fairly well accepted axiom of epistemic logic. Your example seems ...[text shortened]... don't see how knowledge can distribute over conjunction of propositions if justification cannot.
In that sense, if an omni does not wish to be known, we can act as if there were no omni and it would make zero difference in the outcome of any philosophic or religious argument or any morality issue. So we clearly have that as reality, with the exception we see no display of deities or a deity and to me that signals we can do whatever we bloody want.
If we off ourselves in the process, Earth will recover just fine and in another couple million years maybe something better than human will evolve.
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Originally posted by DeepThoughtUm, again, no.
Since all absence of evidence ever is is absence of evidence.
Absence of evidence IS evidence of absence.
How strong that evidence is will depend on the particular circumstances involved in any
given case.
EDIT:
http://lesswrong.com/lw/ih/absence_of_evidence_is_evidence_of_absence/