Let's start by saying I'm not talking about a specific god or religion. I'm actually going to be exploring an interesting train of thought in a story setting where some unfortunate person's existence becomes infinite. My question simply is this:

If a Being was in all areas, all dimensions, at all space and time, that would cause omniscience (specifically, all-knowledge, all-intelligence). Let's assume a limited capacity of mind; so while that Being has a giant 'working area' of an entire universe to scribble ideas on and view live scenarios, and access to all areas/times effortlessly, they don't retain all things in their mind. It's the Google effect on a mass scale; you know where the pertaining knowledge is, but you haven't memorised the knowledge itself. Like being a librarian with a Candy Crush addiction.

If a someone were to ask the Omnipresent Being a question about any property of any thing in their universe in any point of time, they would be able to respond instantly with complete accuracy.

Does omnipresence, however, imply you are all-wise?

If given a physical scenario where Captain Omnipresent were not present (gasp!), but it would occur within the same physical constraints and physical logic (same laws of nature, e.g. a parallel universe), would the good Captain be capable of answering omnisciently - without all-knowledge, but with all-wisdom?

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    Just because I'm at the corner of First and Main, doesn't mean I know everything that's going on at First and Main. I might not be paying attention. To clarify my understanding, why does omnipresence imply omniscience? A being could be omnipresent yet omni-oblivious. What do you think?
    – user4894
    Mar 29 '16 at 2:51
  • @user4894 In this scenario, the being has infinite time to think on the problem, and infinite case studies. They can access all the information in the universe at any time on any level they wish. They know where the information is, as well; if they wanted to investigate the physics of a star, they could - for each star, on any level, at any part of the star's lifetime. Hence, it's implied omniscience. Perhaps omnipresence is the wrong term?
    – Phi
    Mar 29 '16 at 3:05
  • I don't know the official philosophical definition. If I heard the word omnipresent I would think it means what it literally says: Being everywhere at once. I don't see why anything else should be implied other than mere presence. If you want your being to be attentive as well, I think you should have to say that. After all gravity is omnipresent in the universe. There is no corner or region of space immune from gravitational fields. But gravity doesn't know anything.
    – user4894
    Mar 29 '16 at 3:33
  • @Phi you seem to be hiding some work in how you are using omnipresent at least in your comment. Moreover, you are also deciding in favor of what is called B-theory time -- in implying omnipresence means not only places but also times. You also need to give us a definition of "wise." Is wise equivalent to knowledgeable?
    – virmaior
    Mar 29 '16 at 6:30
  • Also in the clearest simplest terms what is your question about philosophy?
    – virmaior
    Mar 29 '16 at 6:30

I will make a couple of assumptions that are necessary to answer your question:

  • We are assuming the computational theory of mind, all thinking and reasoning can be represented as some form of computation achievable by a Turing machine. If we allow for a mind with super-Turing capabilities (for example in Penrose's theory that human minds are more powerful than Turing-machines), then all bets are off on what a such mind can do and cannot do, and your question becomes unanswerable.

  • Wisdom here implies an increased capacity to compute: There is no standard philosophical definition of wisdom (or for intelligence for that matter). Using colloquially there term wisdom to mean the ability to make properly understand situations and to make good decisions (that is to accurately model relationships between data, and predict the outcome of events based on new inputs), Wisdom implies a certain capacity to solve computational problems. Again, if we include other possible factors in the definition of wisdom (i.e. emotional responses, empathy, moral and ethical judgements,...) your question becomes unanswerable.

Now for the answer: simply put, No.

Your being, being in all space, is equivalent to saying that a Turing machine has infinite tape.

Being in "all time" would be hard to define, but I am going to take as either meaning that the Turing machine is non-deterministic, or it is an Oracle machine.

Either way, there will always be problems a given Turing machine cannot solve.

Increasing the amount of tape available or allowing for non-deterministic processing allows for greater speed in solving problems, but doesn't increase the scope of which problems a given Turing machine can solve.

Even assuming for a magical Oracle that can retrieve an answer with perfect accuracy, there will still be problems a Turing machine can't solve.

This a result of the halting problem and the limits of Turing machines: For any given Turing machine, there will always be undecidable problems. Even If you take a Turing machine (deterministic or not) and add an Oracle to it to allow for it to answer questions immediately using that Oracle (for example by providing it with an Oracle for the halting problem), there will still be a class of problems that it cannot solve. If you add a super-Oracle for solving those problems as well, you will face a new set of problems that the new system (Turing machine + Oracle + Super-Oracle) problem cannot solve. This leads to a hierarchy of problems called the arithmetical hierarchy.

There are those that argue that super-Turing computation might be possible, but that stance is not accepted by most computer scientists and mathematicians (see here and here). You will find many philosophers who might argue for the possibility of hyper-computation, but that usually leads to metaphysical proportions, which I said at the beginning of my answer make your question unanswerable.

To summarize: a being with infinite computational resources (in terms of space and time) will still face questions it cannot answer. This is due to a fundamental limit on what a Turing machine, even one equipped with an Oracle can and cannot solve.

After reading your comments and the discussion you're having with Virmaoir, I will add the following relevant information. If by wisdom, you mean an ability to correctly predict outcomes, than another way of seeing why omniscience doesn't lead to "omni-wisdom" is Woplert's theorem.

Mathematician David Woplert proved in 2008 that no intelligent agent can fully predict the evolution of a system that it is part of. In the context of your question, an being within a universe can never completely predict the future state of that universe. The only way to do that would be from outside the universe, i.e. the being has to have all the information contained in that universe, and more (i.e. be able to observe it from the outside). Wolpert's result was published as a refutation of the idea of Laplace's demon: Laplace proposed that a demonic being with absolute knowledge of every particle's current position and current speed in the universe, should be able to infer all the past states and all of the future states of the universe from that information. Wolpert arrived at his results using a method similar to Turing's result with regards to undecidability and the limits of Turing machines. So the two results are ultimately variations on the same principle.

See here for Wolpert's original paper and for an article on his result.

  • Okay, so the problem is either that it hasn't seen that type of scenario before, or that it will may never stop working it out? Even if the scenario is finite, and in a setting where it's well familiar with?
    – Phi
    Mar 29 '16 at 3:44
  • The easiest way of looking at it is the following (this is a simplification of the reason why undecidable problems exist no matter what you try): Even when allowing for an arbitrary number of oracles, the total number of possible Turing machines is countable, the total number of possible problems is uncountable, ergo there will always be strictly more problems than there are Turing machines. Mar 29 '16 at 4:15
  • So while knowledge relates to existing problems answered, thus being all-knowing is possible, the potential amount of nonexistent problems will make being all-wise impossible?
    – Phi
    Mar 29 '16 at 7:37
  • @Phi see my additional edits. Mar 29 '16 at 20:44
  • I guess this would answer the question! If a full prediction is not possible even with the entirety of information of the present available, then it's not possible to predict with full accuracy (although very good accuracy is doable). I suspected someone investigated this idea, I just didn't have the fancy paper names.
    – Phi
    Mar 31 '16 at 3:41

You will find every philosophical question involving the prefix "omni-" to run into strange behaviors. The English language is notoriously good at generating paradoxical behaviors that look legitimate, using the "omni-" prefix.

The first key question is defining the difference between knowledge and wisdom. Typically one can assume that your listener understands the difference, but when you start playing with "omni-" the fine lines between words start to matter. An exacting definition of "wisdom" is particularly difficult to construct.

The second issue you'll need to deal with is the inherent paradoxes that arise with self-reference if Captain Omnipresent is fully present in spacetime. If so, he can have all knowledge about himself. This creates all sorts of wonky effects which are played out in other questions ("Can God create a rock so heavy even He cannot lift it?), but it may give an answer. If he can know enough about himself to know what he doesn't know, perhaps that is wisdom? It's all in the definition, after all.

The other question may be how much this Omnipresent Being interacts with the universe. You may find the answer is that this being can coax the universe into a state where the entity is all-wise, depending on many variables which are not mentioned in the quesiton.

  • Ah, I'm presuming where they are not omnipotent. The omnipresence is more omniaccess, I suppose, they can observe things on a minute or grandiose level as they wish, but they are not capable of physically altering as they wish. I understand if they can alter things to far greater simplicity, wisdom is much easier to obtain, but that's not the case here. Although, would such a creature be all-wise?
    – Phi
    Mar 29 '16 at 2:58
  • @Phi I'm not talking about needing omnipotence, just some limited potence. A omnipresent being with a great deal of free time on their hand can use their limited potence to shape the universe in a way that permits them to be more wise. That being said, the yes or no answer you are looking for is still hidden behind the monumental challenge of defining wisdom well enough to permit yes or no answers involving "all-wise"
    – Cort Ammon
    Mar 29 '16 at 3:00
  • In essence, the question is, given every case study in the entire universe, can one be accurate to the point of perfect foreknowledge of the end, when given a new scenario they can only see the setup of? And yes, I guess, the definition of wisdom needs clarification. I'm assuming prediction abilities and relatability of scenarios to previous ones is wisdom.
    – Phi
    Mar 29 '16 at 3:07
  • I think the answer would be "yes, if he is self aware." As an example trivial solution, if the entity is part of the universe, he can simply observe himself, at the end of the universe, and observe the answer to the question through his own [future] eyes.
    – Cort Ammon
    Mar 29 '16 at 3:52
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    @phi that's a very different question than you asked, actually. You specified a very specific scenario regarding random access to a great amount of physical state information about the universe. In that case, a related question would be "how much wisdom does the internet (especially Wikipedia) grant you today?" Given the behavior of many on the internet, I'd say access to all areas of experiences doesn't make you wise at all.
    – Cort Ammon
    Mar 29 '16 at 6:26

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