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I've been thinking about the nature of questions and answers to questions. Can I ask people opinions on whether they think it is possible to ask an infinite amount of questions or do we as human beings have a finite limit to how many questions we can ask?

If it turns out we can only ask a finite amount of questions what would happen when we reach the stage when we could answer every question that we can ask?

Does this lead to the conclusion that we human beings could be nothing put sophisticated computer programmes?

Additionally if reality is a construct of human knowledge and each society to come into existence is based on the disposable knowledge at that given moment in time then if knowledge is finite and we reach the last stage of human knowledge potential what would happen to that society?

closed as unclear what you're asking by Conifold, Eliran, Frank Hubeny, Dave B, Mr. Kennedy Oct 17 '18 at 19:42

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    even discounting the finite rate of speech a human has, we have a finite rate of thinking thoughts (somewhere in the ballpark of 1 Hz to 10 Hz) and we have a finite lifespan (maybe 2 or 3 billion seconds, let's assume we don't sleep). a finite rate times a finite time is equal to a finite number.\ – robert bristow-johnson Oct 15 '18 at 22:24
  • A finite amount can get very large. I am trying to understand what this has to do with being a computer program. Perhaps you have a reference that would help provide context. Regardless, welcome to this SE! – Frank Hubeny Oct 15 '18 at 23:11
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    How do you get from finite amount of questions to reaching the stage when we could answer every question that we can ask? There may well be questions we will never answer. How this leads, or even connects, to "human beings could be nothing put sophisticated computer programmes"? The last paragraph question is off-topic here because we do not allow opinion based speculations, but I am not sure that the question, like the previous ones, even makes sense. Please clarify your reasoning and what you are asking (it can not be asking for speculations). – Conifold Oct 16 '18 at 0:03
  • There are more questions than a human can ask in his/her lifetime but they are not infinite. – Fuel Oct 16 '18 at 1:37
  • If someone has no more questions to ask, he will be a God. Therefore, there id no limit of questions. There's always something else to know. – RodolfoAP Oct 16 '18 at 15:35
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If I am correct, you asked if, as humans, we can always find a new question for which we do not know the answer. This means that there will never be a human that knows the answer to any question he/she can ask.

I think that the answer is yes. For example, you can always ask, what is the next prime number?

If your question is about the number of question that it is possible to ask in this universe, given that there is a finite number of particles with a finite number of states and a finite number of possible transitions, you cannot have an infinite number of questions in a finite interval of time. This means that humans cannot ask or have asked at any given time an infinite number of questions.

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One simple way to generate infinitely many questions is as follows:

"Does Alice know X?"

"Does Bob know whether Alice knows X?"

"Does Alice know whether Bob knows whether Alice knows X?"

etc. But it is not clear that this implies much about your other questions.

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Suppose there is a finite maximal length L for questions to be readable and answerable. Denote, in addition, the number of symbols in all known human languages (including punctuation, spaces, mathematical symbols, etc.) by M.

Then the number of possible questions is bounded by (i.e. <) M^{L}, that is finite (but quite large). This is a strict upper bound since there are semantic and grammatical constraints in constructing sentences that are not taken into account here. Correspondingly, the number of possible answers of maximal length L' would be bounded by M^{L'}.

The only way to have an infinite number of questions and answers is to allow for questions and answers of infinite length (perhaps recursively as in another answer is suggested). However, any such question of infinite length would be impossible to read or write for any finite number of humans, and since with the utmost probability humanity will be present only for a finite timespan (bounded by the sun's lifespan as an active star), it will then be impossible to read or write even by mankind as a whole.

As a side note, this type of question reminds me of J. L. Borges story "La Bilblioteca de Babel", where he imagines a library containing all possible books (with a standardized format, and written only with latin characters). The main character of the novel at some point argues that the library is infinite, however it is not, by the same reasoning as above (nonetheless, for the purpose of the story, it is much more poignant that the library is actually infinite - and it could be, provided there are (infinitely many) duplicate books).

  • You may also include the possibility that part of the question is not composed of a symbol that varies discreetly, but instead continuously - For instance pointing somehwere and asking 'what is there'? then you do not need infinite question-length to produce infinite variability. – bukwyrm Oct 16 '18 at 14:10
  • Interesting point, however allowing for sensory aids in posing questions would make the number of such questions rather difficult to quantify. In fact, it is not completely clear (at least to me) that a finite number of humans are potentially able to produce an infinite number of "sensory question parts", each with distinct and universally unambiguous meaning. – yuggib Oct 16 '18 at 14:23
  • the 'distinct and universally unambiguous' might be too ambitious even for questions asked with discreet symbols; As questions would also be concerning real objects (as opposed to pure logic and math), the issue gets muddied again: Is a question about a hurtling stone the same question as it's clone regarding the same stone, but 5 seconds later (different velocity, position, lighting,...) ? – bukwyrm Oct 17 '18 at 12:38
  • There are an infinite number of natural numbers, but no natural number is infinite. We can have an infinite number of question with questions of finite (but arbitrarily large) length. If we're not using physical limitations on the number of questions asked (and if we're asking if it's infinite we can't be), it doesn't seem fair to put it on the size of a given question. – David Thornley Oct 17 '18 at 17:43
  • @DavidThornley What is the meaning of a question that is impossible to read, because it would take one thousand lifetimes to read it (still being of finite length)? It is true that there are an infinite number of questions of arbitrary length, but it is true as well that already the finite number of questions with fixed maximal length is, by all practical purposes, impossible to manage and thus essentially "infinite-like". – yuggib Oct 17 '18 at 21:08
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If you are asking whether the human species can get to a point in its development where it runs out of questions to ask, the answer would unfortunately depend strongly on the philosophical school that answers. Reason being the very different metaphysical positions available. https://en.wikipedia.org/wiki/Metaphysics

Certainly from a Materialist view, and specifically from the Scientific establishment, the answer would be plainly "Yes". Science is built on the assumption that the "laws of nature" can be discovered, that eventually we will know everything. But what a small universe would that be in comparison to worlds that we have and will imagine. So then if you allow imaginary objects to be valid subjects of inquiry... Only your imagination could answer then.

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As others noted in the comments, on the assumptions that (1) the amount of time it takes to utter a question is bounded below by a positive real number; and that (2) the lifetime of a person contains at most finitely many time intervals no smaller than that lower bound; then a human utter at most finitely many questions in their lifetime.

Now if the number of humans who ever live -- or more generally the number of entities of any type that are capable of uttering questions -- is finite, then only finitely many questions may be uttered. To utter a question means by definition to express it in the physical world, or to think it as a conscious thought. Instantiating the question as a physical process that inputs energy and outputs heat plus an utterance.

How could the number of question-asking entities be infinite? First, the universe would need to be temporally infinite. And questioners would have to keep on existing for the duration. That's the only way you could physically utter infinitely many questions. For example if the human race never goes extinct. Or if the last thing we do is build a self-replicating, question-asking computer.

Of course as @present already noted, if instead of physically instantiating each question we are allowed to merely conceive it abstractly; then the set of questions "Is n equal to n?", one question for each natural number n, is already a countably infinite set of questions.

If we assume that a question must be framed as a finite-length string over an at most countably infinite alphabet, there can only be countably many questions. If we allow infinite-length questions, we can have uncountably many of them. Clearly we can conceptualize or encode finite-length questions as natural numbers; and infinite-length questions as real numbers.

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No, because it’s impossible to do anything for an infinite amount of times. The largest “meaningful” number in the universe is called a googolplex, and according to the article:

If you filled the entire volume of the observable universe with fine dust particles roughly 1.5 micrometers in size, then the number of different combinations in which you could arrange and number these particles would be about one googolplex.

Even if you took a googolplex of a googolplex of questions, it still wouldn’t be any closer to reaching infinity than one question. If mankind lives forever, there will still never be an infinite amount of questions because there’s no such thing as an “infinite amount”.

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There are two things one can distinguish here:

  1. How large is the set of questions that can be asked?
  2. How many questions do we have the time and space to formulate?

The trivial recursive example given by @present suggests (1) is infinite. However, present a series to a mathematician and they'll try to come up with an nth term, so maybe not definitive proof.

However, thinking mathematically, one can ask:

  1. Is mathematics finite? Are there a finite number of questions in mathematics?

I am not sure this has been shown, but I am fairly sure most expect that mathematics is not finite; i.e. for each problem we solve, we always create new questions.

This suggests to me that the answer to (1) is that there is an infinite number of real questions.

(2) depends on how much space and time we use to formulate our questions. This is a physics and engineering question. I would suggest that physics does not provide a bound. The finite size of the 'observable universe' right now does not imply a bound of the size of the space that can be accessed over arbitrarily long time. From an engineering perspective, clearly we always have bounds on the resources we can control and hence on the size of the questions we can ask and hence the total number we can ask.

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There is an infinite amount of numbers, dates, amount of virtual money toename a few. One could ask: Does two follow one? Yes Does three follow two? Yes And so on

Or

Does this cost 1 cent? Yes Does this cost 2 cents? No And so on

Or

Is 11 oktober 1582 an existing date? No Is 11 oktober 1682 an existing date? Yes And so on

We could be asking an infinitely amount of questions, but ‘we’ is not specified, so asking is limited to the ability of ‘us’ to ask on.

It is like having three wishes come true and the last is wishing all your wishes come true. The whole point of a finite set of wishes or questions is irrelevant in an infinite universe. There is an infinite amount of questions and answers possible.

  • Welcome Ajagar. There is substance in your answer but it would help if you would expand it. The question is, I think, about whether in principle there is a limited number of questions. I am not sure what precise philosophical issue lies back of the question but I don't think the Q involves a hypothesis to be tested. Think about how you might elaborate your point. Best : GT – Geoffrey Thomas Oct 17 '18 at 9:28

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