For some proposition, p, using standard notation
Kp = I know that p (is true)

And let's define the following proposition
ω = I'm omniscient

Then, by definition of omniscience, we must have that
ω ⇒ Kω
and by contraposition
¬Kω ⇒ ¬ω

I can safely say that I don't know if I'm omniscient or not, I don't know either way
¬Kω ∧ ¬K¬ω
so, both of these hold
¬Kω
¬K¬ω

From not knowing, i.e.
¬Kω
I find that I'm not omniscient
¬ω
which I then know, since I deduced it, i.e.
K¬ω
but this is contrary to ¬K¬ω above, thus a contradiction

I just think ¬K¬ω is false. The premise "I don't know that I'm not omniscient" is a contradiction. You do know that you're not omniscient.

More proof. If you were omniscient, you would have known that you would want to delete all this. You would just not have posted it in the first place. Does an omniscient being even need to actually do anything? if you know x is going to happen, then x must happen, otherwise you are not omniscient. Does being omniscient make you the acting agent that makes things happen?

Isn't this taking the metaphysical concept of omniscience and treating it as a logical concept? A category error.

More proof. If you were omniscient, you would have known that you would want to delete all this. You would just not have posted it in the first place. — Bitter Crank

I did know, but I also knew that posting anyways and asking for it to be deleted was better than not posting it in the first place in order to elicit your insightful response. :)

Michael, so this snippet is the wrong part (or translated incorrectly to the logic stuff)?

I, for one, can safely say that I don't know if I'm omniscient or not, as a matter of certainty I mean. — jorndoe

Isn't this taking the metaphysical concept of omniscience and treating it as a logical concept? A category error. — Cavacava

This seems to be a well formed proposition, yes?

ω = I'm omniscient — jorndoe

That issue is avoided by the condition of omniscience. If I know everything, then I would know I was omniscient. Assuming I'm interested in being truthful, then I would identify myself as omniscient.

A possible issue for omniscience, in practice, is limited window of any instance of knowledge. Since each instance of understanding is a specific instance, which can be found nowhere else, the experience of knowledge is always limited. If I'm thinking about a tree, then I'm not thinking about yesterday's game of cricket. One cannot think of everything all at once, even if they were to have a consciousness which held all the ideas "at once (each idea is still a separate moment of their existence)."

Though, it's fair to say that our notion of knowledge probably accounts for this issue anyway. When we think of knowledge as a sum, we aren't talking about what someone knows in an immediate moment, but rather to information they have stored, which they can recall when prompted. In this sense, there is no logical barrier to omniscience. For someone to be able to recall any information is logically coherent.

If you're omniscient, then you must also know that you are. — jorndoe

Per the link provided:

Fitch's paradox asserts that the existence of an unknown truth is unknowable. — Wikipedia entry for Fitch's paradox of knowability

A limiting condition of omniscience is knowing all that is knowable. If one's own state of omniscience is unknowable, then one can be omniscient and not know one is by virtue of the unknown truth of one's own omniscience being unknowable.

I'm curious: if omniscience is knowing all the members in the set of knowable propositions, can the set of knowable propositions be an empty set? Can a being be omniscient by virtue of not knowing anything? It seems that the set of knowable propositions must at least contain tautologies. Is there anything we can put in the set, or remove from the set?

I, for one, can safely say that I don't know if I'm omniscient or not, as a matter of certainty I mean.
So, I guess I'm not, I can't be, as per above.
But then I actually know that I'm not, with certainty, since I just found that out deductively. — jorndoe

Why aren't you certain that you're not omniscient? You could claim that this is because you, as a human, can't be certain of anything... But where do you derive that? Because, if you derive the premise that you can't be certain of anything from your own non-omniscience, then the argument is circular.

Additionally, I think there may be a problem with the certitude of the conclusion. The fact that something was arrived at deductively isn't a guarantor of certainty. The conclusion of a deductive argument is only as certain as the premise. If my car is red, then "My car is in the parking lot outside" implies "There is a red car in the parking lot outside," and this is deductively valid. But my premise - that my car is in the parking lot outside - is not certain, since someone may have stolen my car before I wrote that sentence. Thus, my conclusion is not certain either, even though the argument is deductively valid, because deductive validity is a necessary but not sufficient condition for certainty of a conclusion. The other necessary condition is the certainty of the premise.

I'm more into auto-omniscience (temet nosce) than allo-omniscience (knowing the other); it feels doable and what's amazing is that they might be the same thing in an Atman-Brahman/fractal sense.

Would omniscience transcend identity or would it give potential access to all identities/perspectives, including hypothetical/imaginary ones? If so, how would such information access be managed, stored, sorted, retrieved.

Knowing everything would include everything that is not worth knowing. There must be a value assumption built in to the concept omniscience, that assumes only useful knowledge but that isn't all knowledge and is relative to a kind of temporal/spatial identity. But maybe I don't even know what it means to know something.

Omniscience is an impossibility. Omniscience excludes the science of that which or who who possesses the science. Postulating that even that is contained in the knowledge is delegating the knowledge away from the knower to a heavenly domain of knowledge. If it is God having this knowledge then He can't intervene in that what his omniscience is about. If He did, then He would be not omniscient about the universe anymore, as he cannot possibly know everything about the universe when he interacts with it. His knowing about the universe cannot be part of the knowledge, and since He interacts with the universe, His knowledge about the universe must be incomplete.

If you want to know everything about a part of the world you have to isolate it and impose precise initial conditions. You will know how the process develops. Any further interaction will arrest the development and invalidates the knowledge. If God knew our moves in detail, and he chooses to intervene, the knowledg he had before that moment is invalidated. If God takes His intervention into consideration, then the knowledge of the new situation contradicts his former knowledge. Intervening will result in a continuously changing omniscience, meaning He's not omniscient at all.

Fitch's paradox asserts that the existence of an unknown truth is unknowable. — Wikipedia entry for Fitch's paradox of knowability

I would say the argument establishes only that the assertion "p is an unknown truth" results in a contradiction. To assert the truth of p is to claim knowledge that p. To assert that the truth of p is unknown is to disavow knowledge that p. So "p is an unknown truth" is simultaneously to claim and to disavow knowledge.

I cannot think of an example of anyone claiming "p is an unknown truth". There are many claims of the form "If p is true, it is not known that p; and if p is false, it is not known that not-p". Or "The truth of the supposition that p is not known." That is why a more usual form of words would be: "We don't know whether p or not."

Example. We don't know whether there is a highest pair of twin primes. It would be odd to claim that there is a highest pair of twin primes (i.e. it is true that there is) and also to claim that we don't know that there is a highest pair (i.e. it is an unknown truth). That latter claim would be of the form "p is an unknown truth" but it is not a claim that anyone makes.

I think the paradox shows that a kind of claim that nobody ever makes would result in a contradiction. Not a great discovery but worth something.

It is sensible to claim "Either p is an unknown truth or not-p is an unknown truth" With this amendment the conclusion of the argument is that we know p v not-p. That'll do nicely.

Anti-realism holds that stuff is dependent in some way on us, that thinking makes it so. That is, some statement p is true only if it is believed or known to be true.

For anti-realism, something's being true is the same as it's being known to be true.

Now a direct implication of this is that if something is true, then it is known - that we know everything.

Anti-realism is apparently committed to omniscience.

The problem does not occur in realism, which happily admits to there being unknown truths. — Banno

Notice that "p is an unknown truth" uses a proper name - p - for the unknown truth. It is quite different to the everyday "there are things we do not know".

:heart:

I can safely say that I don't know if I'm omniscient or not, — jorndoe

Then you can't be omniscient. :chin:

Whether the concept is coherent depends on how it is used. Just like any concept it can be misused, and as a consequent it can be incoherent.

Whether the concept is coherent depends on how it is used. — Sam26

Can you show us how?

Well, it seems to me that if I make the claim that I'm omniscient, most people would say the claim is false. However, how could you say it's false if it was incoherent? How are you able to have this discussion if the word was incoherent? Are you saying that the concept omniscience is the same as "xfisdia?" And, what are you saying when you say it's incoherent?

If I say that I know everything, i.e., there are no facts hidden from me, is this incoherent? I don't see how it's incoherent. So, it depends on how you are using the concept. You might argue that no one has access to all the facts. Okay, if no one has access to all the facts, then no one is omniscient, which would make my claim to be omniscient, false. But, again, I don't see where the conversation about omniscience is incoherent.

Notice that "p is an unknown truth" uses a proper name - p - for the unknown truth. It is quite different to the everyday "there are things we do not know". — Banno

I find the phrase "unknown truth" to be problematic, to say the least. If X is known to be true, which is what this statement seems to imply, then how can it be unknown? It's like saying, "I both know, and don't know, that X is true, which is contradictory. If truth in this statement is just a claim without justification, then you can't say it's true, you can believe it's true, but that's not the same as being true. Claims don't equate to truth, so I'm not sure the statement "P is an unknown truth" even makes sense. This reminds me of the Gettier problems, they say things that seem to make sense, but in reality don't make sense. People tie themselves up in linguistic nonsense.

"There are things we don't know" seems to imply that "there is at least one truth that we do not know is true", or "there are unknown truths".

Someone give me an unknown truth! Saying we don't know X, Y, or Z, is one thing, it makes sense. And, saying there are unknowns, makes sense, but the rest of this is senseless to me. There are states of affairs that are unknown, viz., facts that we haven't discovered. There are claims that are potential truths, but they are potentially false too. A claim is about propositions, and the only way to know if a proposition is true, is if we can justify it in some way. However, if we justify it, it then becomes knowledge. This, I believe is just a confused way of talking. Where am I going wrong?

Also, we apply the word truth to actual claims, not some invisible claim existing in the ether.

We can say "I don't know algebra," or "I don't know if I remembered his name correctly." But do we ever say, "I don't know that it's true (i.e., I'm affirming the truth, not doubting the truth), that Paris is the capital of France." So, it's true, but I don't know it. What!?This is essentially what you're doing by affirming an unknown truth. I can say, "I don't know if Paris is the capital of France," which expresses a doubt about one's knowledge.

Again, linguistic knots.

As far as I know,

Words, that includes "omniscience" and "coherence"

1. Can have meaning in the usual sense (as referents). Which meanings of this strain makes omniscience coherent?

2. Can have meaning in a Wittgensteinian sense (use). How could we use these words (unlimited options) to make omniscience coherent?

To tell you the truth, I haven't a good grasp of Wittgenstein.

It's like saying, "I both know, and don't know, that X is true, which is contradictory. — Sam26

To assert the truth of p is to claim knowledge that p. To assert that the truth of p is unknown is to disavow knowledge that p. So "p is an unknown truth" is simultaneously to claim and to disavow knowledge. — Cuthbert

Notice that "p is an unknown truth" uses a proper name - p - for the unknown truth. — Banno

So, it's true, but I don't know it. What!?This is essentially what you're doing by affirming an unknown truth. — Sam26

Agreement seems to be breaking out wildly on this thread. So how did it get to be a paradox? It's actually pretty clever and not so simple to pinpoint the exact place where the problem or fallacy occurs. I think it might be the premiss p -> LKp. That is because Kp -> ~ ( ~ Kp). So K(p & ~Kp) entails a contradiction. But can we buy the proposition that there are true propositions that cannot be known? And can we know that proposition to be true?

If you're omniscient, then you must also know that you are. Kind of comes with the territory.
By contraposition, if you don't know that you're omniscient, then you're not. Makes sense.

I, for one, can safely say that I don't know if I'm omniscient or not, as a matter of certainty I mean.
So, I guess I'm not, I can't be, as per above.
But then I actually know that I'm not, with certainty, since I just found that out deductively.
I know there are things unknown to me.
Which is contrary to me safely not knowing in the first place.

Contradiction, it seems? What went wrong?

As an aside, of course I'm not omniscient, that would be a rather bold assertion.
Also, there are a few ways in which omniscience leads to an infinite regress. — jorndoe

In my humble opinion, in order to be omniscient one not only must know about everything but even more importantly they most also know about all events that have taken place and the consequences of every action take either by humans or nature. In other words they are kind of a "super computer" that can perfectly predict any data science question or problem that is thrown their way. Also it is pretty much a given that they can read every person's thoughts since they are completely aware of the circumstances that led them to be they are at any given moment and can predict every action whether it be a physical one or merely a mental one.

Of course it would be a non-trivial problem to both build or even to correctly hypothesize how to create such a machine (or how a sentient being could process such information). All that we can do is create some semblance of a system that can handle it by either a machine or be calculate through some analytical means by a person. How a real computer system could cope with real omniscient like problems or how a sentient being could deal with such issues (other than through committees or groups of scientist, politicians, etc. which we do in real life) is a bit beyond the scope of either today's science or technology is capable of. In fact we are hardly aware of what it would be like to be omniscient of any given circumstances. The only two academic fields that deal with problems relating to such issues are critical thinking (which philosophy is merely an discipline of) and perhaps critical thinking. There is also data science but that is a field that deals with how to make machines solve such issues.

I believe the only hint at what it might feel like to be omniscient is that it would be like being a character in a movie yet they would already know what was going to happen in the coming hours or days in the movie so they could change their actions based on what they already know what was going to happen. Perhaps if taken a step even further, such a character would know not only every action that was most likely going to happen (ie how the events would normally play out), but also what would happen if other actions were taken instead, such as with Bill Murray in the movie ground hog day. Of course real omniscience would take knowledge of what would happen in close to an infinite number of possible situations and would also require knowledge of again close to an infinite number of subjects as well as all the details contained in such subjects, but the ability to have the power to nearly perfectly predict what would happen in any given circumstances is as close as to what we can understand what it would be like to be omniscient.

But can we buy the proposition that there are true propositions that cannot be known? And can we know that proposition to be true? — Cuthbert

My view, is that it's largely a misunderstanding of the concepts involved. You also see this in the Gettier problem. But to answer your question, and I think you're leaning this way too, is that there is a serious problem with the phrase, "unknown truths." One can say "unknown facts," facts being states of affairs, but "unknown truths" is a misunderstanding. Again, it seems this phrase, as has been pointed out, is saying "unknown knowns." If we have an X that is true, then how can we say it's true, if it's not known to be true? Otherwise you just have a proposition that's either true or false, a claim that's not known to be true, an opinion.

As to your second question, what proposition? There is no proposition that corresponds to this supposed "true proposition." It's an illusion. Language again confounds us. Can we call an imaginary claim true or false?

In The Open Universe Karl Popper has some interesting arguments about the theoretical limitations of omniscience within known physical constraints. Worth a read.

1. Can have meaning in the usual sense (as referents). Which meanings of this strain makes omniscience coherent? — Agent Smith

The idea that meaning is generally derived from referents has been debunked. There are exceptions, but meaning should be seen, primarily, as a function of use. There are no referents for words like, time, nothing, the, free will, etc. Freeing yourself from this idea is very helpful in philosophy.

I gave you an example of a coherent use of omniscience. Read my other post to you above. Remember you can always create examples where a particular concept doesn't make sense, or is incoherent. The problem is that people want to give some precise definition to the word, and there may not be one. I like the general definition of omniscience as, knowing all that's possible to be known. There maybe things that are impossible to know, for anyone, including a god. And, because people don't like the concept, because it has religious overtones, they go a bit overboard in their analysis.