Logic of Omniscience

Originally posted by vistesd
[b] I'm not sure I understand. By agnosticism here, you are referring to agnosticism with respect to P or with respect to O?

O. The agnostic does not believe either O or ~O, but is committed to the possibility of O—as opposed to the atheist (assuming that O stands in for “god” of some sort), who is either weakly or strongly committed to ~O. (And I’m ...[text shortened]... g was in response to googlefudge’s claims about claiming knowledge with sufficient probability.)[/b]

I'm not sure I'm following, and I probably need to revisit this when I have a bit more time. But a couple things on first glance:

First, I do not understand why you would say that the atheist (or, the one who is weakly or strongly committed to ~O ) would not be committed to the possibility of O. That does not seem to follow at all, since the epistemic possibility of O is simply a matter of the evidence. Even if one is strongly committed to ~O, as long as his or her evidence is not sufficient to guarantee ~O, then there must be some epistemic possibility for him or her that O is true. So, even the proponent of ~O will generally be committed to the possibility that O.

Second, I'm not sure I'm following you about the disjunction (O or ~O). As long as O has determinate truth value, then this disjunction is basically a tautology which has to be true.

Originally posted by LemonJello
I'm not sure I'm following, and I probably need to revisit this when I have a bit more time. But a couple things on first glance:

First, I do not understand why you would say that the atheist (or, the one who is weakly or strongly committed to ~O ) would not be committed to the possibility of O. That does not seem to follow at all, since the epistemi ...[text shortened]... as determinate truth value, then this disjunction is basically a tautology which has to be true.

Well, I’m not being terribly clear.

First, I do not understand why you would say that the atheist (or, the one who is weakly or strongly committed to ~O ) would not be committed to the possibility of O. That does not seem to follow at all, since the epistemic possibility of O is simply a matter of the evidence. Even if one is strongly committed to ~O, as long as his or her evidence is not sufficient to guarantee ~O, then there must be some epistemic possibility for him or her that O is true. So, even the proponent of ~O will generally be committed to the possibility that O.

Okay, understood.

Second, I'm not sure I'm following you about the disjunction (O or ~O). As long as O has determinate truth value, then this disjunction is basically a tautology which has to be true.

Okay. (That actually dawned on me late last night.) One or the other option will be true. But, if neither term O or ~O is knowable, then that “more or less reduces to an implication that belief in [either one] is unjustifiable.”

So, evidentiary considerations only really come into play if O is knowable.

Is that all correct?

Originally posted by LemonJello
You claim to have provided a counterexample to the idea that propositions of the form “P and P is unknown“ represent an unknowable class. So you need to provide an example where a proposition of that form is known.

I did.

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 description of a forgetful creator God is an example where a proposition of that form is known. If it is not, then explain why it is not.

If there was anything else of interest in your post, do let me know as I will not be wading through pages of argument that I consider irrelevant. I specifically stated that I would not be interested in anything containing logic notation.

Either my forgetful creator God suffices as and example or it does not. Neither you nor DeepThought seem to be able to address that head on and instead go off on a tangent about how I must claim something else or prove something else which I have no obligation whatsoever to do.

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?

Originally posted by twhitehead
It is abundantly clear what I am disputing. I have quoted it directly several times .
Here it is again:

Suppose P is some proposition which is not known, then the proposition "P and P is unknown" is itself unknown.

Now it is entirely possible that I do not understand what that sentence means as it may have non-standard English meaning in ...[text shortened]... know does my forgetful God satisfy the condition that the above sentence claims is not possible?

You might have wanted to mention that you don't follow the symbolic logic earlier. Your argument fails to find a knowable Church proposition, as LJ more than adequately showed in his reply to your post. As an argument against the unknowability of there not being a omniscience it probably doesn't work either, I'm not absolutely certain about this as it could possibly be made to work at the level that LJ's "hairs on my head" argument does. You assume an agent who knows that no agent, including themselves, knows the truth of a particular proposition which has definite truth value. This begs the question as to whether there is an omniscience, and so begs the question about knowability of such a proposition as well.

Originally posted by twhitehead
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]

No, there are a pair of propositions, P and it's converse. Your argument produces the following proposition, the brackets are to illustrate the logical structure:

"It is known that [either (P is true and P is not known) or (not P is true and not P is not known)]."

You cannot get from that to:

"Either (it is known that [P is true and P is not known]) or (it is known that [not P is true and not P is not known])."

Which you need for your argument to work.

Originally posted by DeepThought
You might have wanted to mention that you don't follow the symbolic logic earlier.

I think I said several times that I had not followed through your whole OP but was only tackling the claim I quoted several times.

Your argument fails to find a knowable Church proposition, as LJ more than adequately showed in his reply to your post.
LJ went off on a tangent just as you keep doing. I notice you once again dodge the actual question and try to lay it on LJ. Merely stating that my argument fails is not good enough. Explain in detail why it fails. And once again, in case you have forgotten, I am only addressing the single claim I quoted and nothing else.

As an argument against the unknowability of there not being a omniscience it probably doesn't work either,
Again with the tangents. I never suggested anything of the sort.

You assume an agent who knows that no agent, including themselves, knows the truth of a particular proposition which has definite truth value.
Can such an agent exist or not? If it can, your claim is demonstrated to be false as you claim is that no such situation can occur.

This begs the question as to whether there is an omniscience,
No, it doesn't. It isn't necessary for my argument that a forgetful God exists. It is only necessary that you cannot think of a good reason why one couldn't exist.

Originally posted by DeepThought
No, there are a pair of propositions, P and it's converse. Your argument produces the following proposition, the brackets are to illustrate the logical structure:

"It is known that [either (P is true and P is not known) or (not P is true and not P is not known)]."

You cannot get from that to:

"Either (it is known that [P is true and P is not kn ...[text shortened]... nown that [not P is true and not P is not known])."

Which you need for your argument to work.

I don't follow. Why would I want to get to something else? Which of the two are you saying is your original claim in the OP?
You seem very good at using notation but terrible at explaining what you are referring to or why.

Lets break it down:

Suppose P is some proposition which is not known, then the proposition "P and P is unknown" is itself unknown.

Give me a simple example of what a proposition is.
Explain what it means for P to be unknown.
Explain what "P and P is unknown" would mean.
Explain whether or not a forgetful creator God could know "P and P is unknown".

Suppose P is some proposition which is not known, then the proposition "P and P is unknown" is itself unknown.

Tell me where I go wrong:
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?

Originally posted by twhitehead
I think I said several times that I had not followed through your whole OP but was only tackling the claim I quoted several times.

[b]Your argument fails to find a knowable Church proposition, as LJ more than adequately showed in his reply to your post.
LJ went off on a tangent just as you keep doing. I notice you once again dodge the actual quest ...[text shortened]... God exists. It is only necessary that you cannot think of a good reason why one couldn't exist.[/b]

LJ went off on a tangent just as you keep doing. I notice you once again dodge the actual question and try to lay it on LJ.

LJ went to considerable effort to reply to your post. You refused to read it. This is intensely discourteous. I have not dodged any question, it is simply that there is no point in me repeating what LJ said. The answer to your question is in his post. We did not merely state that your argument fails, we demonstrated quite precisely where it fails. If you want to know why then you need to read LJ's post. If you do not understand symbolic logic then I suggest reading the relevant pages on Wikipedia. If you do not know what a proposition is then I'm left wondering how you can form an opinion about this matter and what your purpose in posting is.

Originally posted by vistesd
Well, I’m not being terribly clear.

[b]First, I do not understand why you would say that the atheist (or, the one who is weakly or strongly committed to ~O ) would not be committed to the possibility of O. That does not seem to follow at all, since the epistemic possibility of O is simply a matter of the evidence. Even if one is strongly committed to ~O, ...[text shortened]... evidentiary considerations only really come into play if O is knowable.

Is that all correct?

Well, if O is not knowable then there cannot be any evidence.

Originally posted by DeepThought
Well, if O is not knowable then there cannot be any evidence.

Understood. It’s just that I’m at a point where, to steal from Niels Bohr, everything that I say should be seen as a question. Thank you for your patience.

____________________________________________

Let P = [E(O) or ~E(O)]: “there exists an omniscience or there does not exist an omniscience”. P is a tautology, and trivially true.

Let E(O) be unknown (by assumption).

—If E(O) is unknown then, trivially, ~E(O) is also unknown.

So, we have a P that is true, and is known to be true, though its constituent propositions are unknown. (What happens if you plug that P into the Church formulation?)

This seems to follow LJ’s point about the disjunction versus the individual disjuncts. However, this disjunction is clearly confined to “logical space”, with no need to talk about lotteries, etc. The tautology is (trivially) true for any x one plugs into it (one does not need to consider FF or TT).

{Now, Wittgenstein seems to argue in the Tractatus that all logical propositions can be reduced to tautology or contradiction. Wittgenstein also seems to use the word “mystical” to refer to things that cannot be known, and therefore about which no beliefs can be properly formed. W seems to consider that all metaphysical questions fall into this “mystical” category—once “bewitchments” based on confusions of language are removed (that is the “later W” ).

—These are impressions about W’s arguments: I have a long, long way to go. And even then, W is subject to multiple conflicting and contentious interpretations.}

This reminds me of a kind of Pyrrhonian Skepticism* with regard to belief—before one even gets to agnosticism per se. That is, judgment is withheld at the level of belief, not knowledge.

Now, how does one know if the existence of an omniscient entity can be known to a non-omniscient entity? [Singular or collective in either case.] Is the absence of logical contradiction in defining O sufficient for the claim that E(O) is in principle knowable?

And if it is not known if E(O) is knowable, then is not a Pyrrhonian suspension (epoche) of belief thereby justified?

Again, thanks for your patience.

_______________________________________________

* Apparently, some do not use the word “skeptic” with regard to the Pyrrhonians—though they did call themselves skeptics—because it has come to mean something other than what they meant (or a neo-Pyrrhonian would mean).

EDIT: I know this is afield of your original point; but the conversation had already gone afield by the time I arrived.

Originally posted by DeepThought
LJ went to considerable effort to reply to your post. You refused to read it. This is intensely discourteous.

It was not intended to be discourteous. I explicitly stated that I was not interested in going off and studying logic speak and then wading through miles of it just to discover that he didn't understand what I was saying. He clearly didn't understand what I was saying at the very start of his post in plain English.

I have not dodged any question, it is simply that there is no point in me repeating what LJ said. The answer to your question is in his post.
No, the answer is not in his post. I asked for an answer in English. He did not answer in English. I asked for one thing, he answered something else.

We did not merely state that your argument fails, we demonstrated quite precisely where it fails.
The problem is you are not listening. You are so confident in your symbolic language that you have forgotten how to speak English.
I wasn't making an argument as such, so if you have demonstrated quite precisely where 'my argument fails' then you have missed the point. I was providing a counter example. Either it is a counter example or it is not. If you need to make an argument, then you have missed the point.

If you want to know why then you need to read LJ's post. If you do not understand symbolic logic then I suggest reading the relevant pages on Wikipedia.
Why should I study symbolic logic just to find out whether or not my forgetful God matches the claim in the OP?
It is blatantly obvious that there is miscommunication between us, but why do you assume that it is all on my part. You have repeatedly suggested that I was making an argument that I did not make and repeatedly referred to numbered points that were not numbered. I could list a number of other cases where you clearly failed to understand my posts despite them being in plain English. I had to quote the same thing about 5 times before you would accept that I was referring to it. And even after that you attributed other arguments to me that I had never made.

If you do not know what a proposition is then I'm left wondering how you can form an opinion about this matter and what your purpose in posting is.
I do know what I think a proposition is. If you refuse to explain or correct me, but instead insist on acting superior, I am left wondering if you actually know what you are talking about.

I have repeatedly asked you to confirm whether or not my understanding of the sentence in question is accurate, you have repeatedly failed to do so but instead gone off on a tangent. Even now, after dissecting it for you to make it easier you still refuse to do so.

Originally posted by twhitehead
It was not intended to be discourteous. I explicitly stated that I was not interested in going off and studying logic speak and then wading through miles of it just to discover that he didn't understand what I was saying. He clearly didn't understand what I was saying at the very start of his post in plain English.

[b]I have not dodged any question, i ...[text shortened]... on a tangent. Even now, after dissecting it for you to make it easier you still refuse to do so.

A proposition is a statement, as opposed to a question or an order. Propositions can be built out of smaller propositions - for example we get to "Roses are red and violets are blue." by the conjugation of "Roses are red." and "Violets are blue". Now the sentence in question is P and P is unknown, would be something like: "There is intelligent life on more than one planet, but it is unknown that there is intelligent life on more than one planet.". This whole thing is a proposition, and it is perfectly plausible as we do not know of intelligent life elsewhere in the universe and it is quite likely due to the distances involved that aliens would not know either of us or each other. The claim is that the entire proposition is unknowable.

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.", then they know that:

"[Either (some snarks are boojums) or it is not the case that (some snarks are boojums)] and it is unknown that (some snarks are boojums) and it is unknown that (it is not the case that some snarks are boojums)."

This amounts to:

"Either (some snarks are boojums and it is unknown that some snarks are boojums) or (it is not the case that some snarks are boojums and it is unknown that some snarks are boojums)."

For your example to demonstrate the knowability of Church propositions you need to find a proposition which would be structured as follows:

It is known that (some snarks are boojums and it is not known that some snarks are boojums).

The problem is that knowledge doesn't distribute over disjunction - so knowing (the coin will come up heads or tails), is not the same as either (knowing the coin will come heads) or (knowing the coin will come up tails). This means that you cannot claim that one or the other is knowable.

Originally posted by vistesd
Understood. It’s just that I’m at a point where, to steal from Niels Bohr, everything that I say should be seen as a question. Thank you for your patience.

____________________________________________

Let P = [E(O) or ~E(O)]: “there exists an omniscience or there does not exist an omniscience”. P is a tautology, and trivially true.

Let E(O) be ...[text shortened]... eld of your original point; but the conversation had already gone afield by the time I arrived.

Don't worry, this stuff's confusing.

Your proposition P is known as it consists of an exhaustive disjunction over other propositions. So ¬K(P) is false because P is known, this means that P & ¬K(P) is false. So we have ¬K(P & ¬K(P)) = ¬K(false) which is fine as one cannot know things that aren't true.

Regarding a non-omniscient agent's ability to know if an omniscience exists; I'm not sure, I suppose if the omniscience were interrogatable one could ask it things like: "What am I thinking?" so a sequence of questions no normal agent would be able to answer. This might produce enough evidence to satisfy some fallible knowledge justification criterion.