Does it Make Sense to Ask Questions You Can't Answer?

[Duffy]

For your entity X example, you have created the form of a statement which looks like it creates the possibility for an infinite number of statements. At some point, the statement that you are trying to create will actually be larger than the universe itself, and thus it will not be possible to make this statement. Once again, there are only a finite number of statements.

[J.]

Duffy,

What if the universe is infinite?

[Duffy]

The observable universe is finite. Good luck making a statement out of stuff that is not observable. Moreover, either way, statements are finite. What you propose are statements that can't be expressed, that would go on forever. An unending statement is not a statement.

[J.]

Actually, I'm suggesting an infinite number of finite statements.

Currently astronomers around the world are working to determine the geometry of the universe. If it is curved then it must be finite, but if it is flat then it may be infinite. While their labors have yet to reach conclusive results, several methods have come back flat.

Thought Experiment:

Let us suppose that in the next few years they show that the universe is infinite, and that little gray aliens are doing strange things to rednecks. (I do have a reason for adding that last part, though I don't know if the little gray aliens do.)

So one night I set up a trap. I leave a broken down pick-up with a likely looking redneck on a lonely dirt road. When the little gray aliens show up, I kick their butts, and take their UFO.

I take my recently requisitioned UFO and head out into the universe. As I go I measure the spin of the particles that I meet along the way. If the universe is infinite, I will encounter an infinite number of particles. With each particle I will make the finite statement, "left" or, "right."

A bit silly, yes. But it does show the possibilty of making an infinite number of valid statements, without repeating yourself, while using a finite vocabulary.

[Mark]

The set of natural numbers is infinite. The statement "The one-armed undetectable deity created the universe" is a valid statement, and it is non-falsibiable. So is "The two-armed undetectable deity created the universe. Etc. The theoretically possible number of n-f statements is therefore infinite. If the physical size of the universe was a limit to the number of natural numbers (to pick just one set of numbers), we would have to rethink all of mathematics...

The key here, it seems to me, is to realise that these are non-falsifiable statements. This means these are statements that denote things I invent. The set of things they describe is therefore not "mapped" to the set of things that "exist" (whatever that means), and therefore its size is not limited by any "physical" constraints.

This dynamic exists in the set of natural numbers also: The number of natural numbers is infinite. But the number of natural numbers that mean something is finite. I believe (my knowledge on this is bit dated) Graham's number is the largest number that denotes something meaningful. There are infinitely many numbers larger than Graham's number, but they are not "assigned" to anything; no physical concept has yet been encountered that requires a number of this magnitude to be used.

In the same way, I think the set of n-f statements is therefore infinite, although the set of falsifiable statements if finite.

But Duffy's argument on the number of permutations of a set is intriguing. I would offer the following thought on this: The set that contains all possible symbols to express something is infinite. This can just be one symbol, uniquely identifiable by its anchoring to an initial position in the set, like the letter "z" in position 1, the letter "z" in position 2 etc. Call this the infinite set - this one would yield the number of n-f statements. The set that contains symbols to express something that "exists" (whatever that means) is finite. The infinite set yields an infinite number of finite statements (it's the binomial coefficient (S, k) with S=infinity. The finite set yields a finite number of finite statements.

I guess. Why are we talking about this again? :-)

[Mark]

J. wrote: "Actually, I'm suggesting an infinite number of finite statements.

Currently astronomers around the world are working to determine the geometry of the universe. If it is curved then it must be fini..."

I actually read this after i posted my comment. Seems we get to the same conclusion (hypothesis?) in different ways.

[Duffy]

You've raised another requirement that I would place on statements. Not only must they be capable of expression, but they must also have meaning. By your own admission, when we get to numbers large enough, they no longer have any meaning. Thus an expression using such a number would also be meaningless and hence not a statement. So, for very very large numbers, there are two objections: the first is that they cannot be expressed, and the second is that they have no meaning. Once again, the set of statements, meaning utterances which have meaning and can be expressed, is finite.

Also, infinity is not a number. Thus you can't express a binomial coefficient (S,K) with S=infinity. To give you a flip side example. We can do a thought experiment where a person flips a light on after a half second, off after another quarter, on after another eighth, off after a sixteenth and so on. The switch will flip an infinite number of times before a second has passed. We can do the thought experiment, but the switching itself is not possible. It won't take very long before the switch would have to move faster than the speed of light. There are other physical objections to this. What I'm saying about expressions being to large is simple the flip side of this. No matter how you express the natural numbers, using that system you will eventually reach a point where the number you are trying to express simply cannot physically be expressed.

Finally, I reject your idea of an alphanumeric system with an infinite number of characters to represent the natural numbers. Such a system would be useless, and beyond a very small set of characters, no one would be able to recognize any symbol. There would have to be one differentiating characteristic about every new number in this set of characters, and eventually, a single character would get so complex that it would also become impossible to express.

[J.]

Meaningfulness?

You realize that your new rule eliminates most if not everything that the human race has ever said or done. Your new meaning rule doesn't stand up to itself. I think you may have just created a new paradox.

[Duffy]

If you don't understand what my rule means, then you can't know whether it stands up to itself or not. If you do understand it, then I don't see your objection.

[Mark]

Duffy, you gotta chill... :-) We're having a friendly chat here, it's not a courtroom battle or a debating club final...

Just a few pointers as they come to mind: it is not the size of numbers that determine whether they are "in use", it is whether they are mapped to something that they meaningfully describe / numbers are not "meaningless" in themselves / infinity is a concept widely used in mathematics / your version of Zeno's paradox does not appear to add anything to the original / you state the result slightly incorrectly, it is correct to say that on the infinite-th (ha ha now infinity is a number) switch exactly one second has passed / the concept of "meaning" is a difficult one - the statement "Jesus Christ is the son of God" transports meaning for some, but not for others, and yet even those who are in the latter group surely have to concede that it is a statement.

[J.]

Duffy wrote: "If you don't understand what my rule means, then you can't know whether it stands up to itself or not. If you do understand it, then I don't see your objection."

My understanding of your new rule is psychological, so you may be right.

However for the sake of argument would you be kind enough to grace us with objective criteria for "meaning."

[Duffy]

I have no objective criteria for what makes an expression meaningful. I think th closest I could come up with is something that would act as an analogue to the idea of a string of symbols being "well formed" in logic.

Usually, when someone uses the light switch version of zeros paradox, the question posed is, after exactly one second is the light on or off. The only point I was trying to make is that we can conduct thought experiments which are impossible.

And that brings me back to the main point. For something to be a statement, it must be capable of expression. Whatever system you use for expression, there are actual, finite limits on what can be expressed. Whatever system you invent for the expression of large numbers, that system will involve some sort of iteration or recursion. Eventually, the recursion sequence will grow so large that it cannot be encompassed in the observable universe.

Maybe I want to say that ideas that lean to heavily on infinity tend to be precisely those kinds of thought experiments which are impossible.

[J.]

I disagree with your disdain for infinity. It is perhaps the most important concept with which we can wrestle.

Infinity is the ultimate logic buster. It cannot be multiplied, divided, added or subtracted. Everytime it shows up our logic is laid to waste. But heres the rub, infinity is either an artifact of our flawed logic or infinity is a reality and our logic is unable to handle it. Either way can their be any greater achievement of the mind than reconciling logic and the infinite?

[Duffy]

It can't be multiplied, divided, add or subtracted because its not a number. For the most part, self-reference has been much more problematic and interesting for logicians. For example, the Godel sentence relies on self-reference. Also, the barber paradox, which underlies the whole dispute about a theory of types for sets, also stems from a problem arising from self reference.

The infinitesimal probably causes more conceptual problems in math than infinity. I'm thinking of the basic contradiction at the heart of Euclidean geometry. A point takes up zero space. Add enough of them together and you get a line. That means that if you add zero to itself enough times it becomes first finitely, then infinitely large.

[Mark]

Duffy - many thanks for that clarification on your thought experiment with the light switch. The question whether the switch is on or off at the "end" is actually really amusing and got me thinking (again) about what exactly happens when we sum an infinite series.

But I was meaning to ask you a question: I am still not entirely sure whether i understand you correctly when you say that a statement needs to be "expressable". I entirely agree that it must be possible to express a statement, otherwise it would not be a statement. I just wonder why it should not be possible to express infinite quantities (forgive me if i misrepresent your point).

The very fact, for example, that i can sum an infinite series into a finite result bears testimony to the fact that the presence of infinity is not a limit to expressing a statement that "includes" it. As another example, the statement "the proportion of a circle's circumference to its diameter is constant" involves an infinity (as it is the number pi).

And yes, infinity is not a "number" as such, but so what? It is an important concept in maths, and we can use the concept quite easily in derivations etc (that does not mean the concept as such is banal, it just means that "maths does not abhor an infinity", so to speak.

[Duffy]

First, since infinity is not a number, there is no such thing as expressing an infinite quantity. If something is a quantity, that means it can be expressed in terms of some number.

Second, I'm not sure that I agree that numbers like pi or e or root2 have much to do with infinity. Yes, none of them can be expressed as a fraction, and any attempt to do so will lead to an endless calculation of the numerator, always yielding an approximation. But it's easy to express pi, in other ways. The word or symbol do quite nicely, and we can then say that it's simply the ratio of the circumference of a perfect circle to its diameter. (I'm not quite as sure about this point if we start talking about measuring the coast of England, but I will leave that aside for now.)

Here is what I'm trying to say about very large numbers. Suppose we have no rule for arithmetic, and instead we just have books of equations 1 + 1 = 2, 1 + 2 = 3, 1+ 3... And so on. At a some point, the second number in the series will become so large that it will take all of the resources of the observable universe to write it down. When that is so, actually long before that, the right hand of the equation will not be capable of expression.

Moreover, every system for the representation of whole numbers will involve some form of iteration or recursion. So adopting a more efficient way of expressing the numbers will only delay, and not resolve, the problem. Thus, when dealing with numbers, or other endlessly iterative things, there will necessarily come a point where things become so vast that it is no longer possible to express them in statements.

[Mark]

Thanks Duffy - understood. I believe this is exactly the point i was trying to make, though. As we agree, "pi" is expressed by defining it and assigning a Greek symbol to it - that was precisely my point. Fractal geometry (the coast of England) is another.

And Graham's number (you remember me talking about it) is a very good illustration of the concept: This number is rather large, really. It is represented as a series of "power towers", which generate increasing layers (64 in total) in G. Now, trying to write all this down in an ordinary way is bothersome - the mere number of power towers needed to calculate just the first of these 64 layers would be a number so large that the observable universe is too small to contain it (assuming you wish to give each digit of the number some physical representation within the space of a Planck volume).

So you are absolutely right. The observable universe is too small to contain even a minuscule fraction of G. And yet, here it is. I just expressed it: "G". The definition of G is clear, and the concept to which it relates is also clear (although a bit abstruse). And it is a number which by the constraint of your argument should not be expressable. And of course now I can start building power towers using G, expressing ever larger defined numbers.

The key, I believe, is to realise that you do not need to write everything down in an ordinary way to express things.

[Goetz]

All questions can be answered on one or the other way. Try Koans.

[Nobuyoshi]

I don't think it makes sense to answer questions you can't answer. For example, you can't answer a question such as "what will happen to you tomorrow?" because there are an infinite number of factors involved in it. And it doesn't make sense to try to figure out the infinite number of factors in order to answer the question. But there are also some questions you can answer. For example, you can answer "yes" to the question "Am I reading this?" You can also answer "infinite" to the question "How big is the universe?" because nothingness doesn't exist anywhere and there is always something around the universe, it depends on the definition of "the universe" though. And it makes sense to answer questions like them because you can.

[Will]

Yes

[Feliks]

In a sense, life itself--everyone's individual life, in progress and ongoing while we're each living it--is a 'question' to which none of us know the 'answer'.

like the infamous 'appointment in Samara'...

[[deleted user]]

Stano28 wrote: "I recently heard this quote: "It doesn't make sense to ask questions which you can't answer." Maybe there were used slightly different words, but it has same meaning. Where does this quote come fro..."

How can one know whether a question is unanswerable before one asks it?

There are algorithms for determining decidability, but from what I understand, they are far from comprehensive. Also, to ask whether something is decidable or not is a question to which one cannot have the answer to at the outset; therefore, there will always be at least one type of question to which we will not know the answer at the instance of its asking.

[Feliks]

Boradicus wrote: "How can one know whether a question is unanswerable before one asks it?..."

Nicely stated.

But maybe a better way to put all this, is: "Does it make sense to ask questions we can answer?"

The answer (for most people these days) is yes. But they're wrong.

Sure, it makes eminent sense for them to skip the whole thought process entirely, skip any kind of searching, probing, curiosity, or confusion. They want the fast question, the fast answer, and they don't want to form either of these these, on their own. That would require effort.

Really, no one is truly asking any kinds of questions at all anymore. Not since the arrival of the internet. All the questions one might possibly ask are now canned--with similarly canned answers--ready for spoon-feeding right into our slack-jacked, lolling open mouths.

We're intellectually and emotionally dead thanks to these "wonder-devices".

[L]

Asking questions is good, even if the answer isn't category or textbook. We should always wonder, explore and desire to know more, for the question may make others think and think about something else. You may be surprised at what you thought of or discover, even if the question doesn't have a ready answer that you can slot into a dictionary.

Keep dreaming big and asking those things that may not have been voiced as yet. That is the whole point of philosophy I think, to have that thought process and to delve into the small recesses of our minds that may have got a bit dusty.

[Mark]

Let me tell you a little story. It will put this discussion to rest and decisively answer the question at the top of this thread:

The Story
Some bloke found himself sitting next to Einstein on a long flight. Einstein was already bored before the flight started so he engaged the guy in a game. Here's what he said: "Ok I will pay you $500 if I cannot answer a question you ask me. And you have to pay me $5 if you cannot answer a question that I ask you."

Ok, thought the bloke. Dont look as I have much to lose here. So he was in, and Einstein asked him to explain to him how gravity warps time.

Huh. Without hesitating, the bloke reached inside his pocket and handed over a fiver. Then it was his turn. "What goes up the hill on three legs and comes down on four?"

Ahaaa! said Einstein. And..... after a noticeable pause "no - that's not it". For 5 minutes, he was circling through every possible answer he could think of. Then he gave up, and handed over a wad of 100 $5 bills.

It was Einstein's turn again. But his curiosity got the better of him. "Just to give me peace of mind, would you tell me what the answer is to that question you asked me?"

The bloke looked at Einstein for a second, then peeled off one bill from the wad of cash he got handed a minute ago, and handed it to Einstein.

The Answer
Yes. It absolutely does makes sense.
:-) :-) :-)

[[deleted user]]

It doesn't make sense to ask a question that you are unprepared to answer for yourself.

[Numi]

Stano28 wrote: "I recently heard this quote: "It doesn't make sense to ask questions which you can't answer." Maybe there were used slightly different words, but it has same meaning. Where does this quote come fro..."

The quote comes from a past clueless human (they are all still clueless). You should ask such questions in the context of survival - when you are peering into the unknown, looking for as-yet undiscovered potential threats (and benefits) to life in the universe, and then in finding solutions to them, and then in broadly implementing those solutions. This is all contained in the Philosophy of Broader Survival, which will be the philosophy of the future, since it offers humanity the ultimate sane mode of thinking.

[Mark]

"It doesn't make sense to ask questions which you can't answer."

What I'm thinking is I could interpret this statement two ways: 1. it doesn't make sense to ask unanswerable questions or 2. it doesn't make sense to ask questions that one doesn't know the answers to. I'm going to respond in reverse order. Interpretation two seems unreasonable, because the opposite conclusion would be, it only makes sense to ask questions that you know the answer to. If so, what's the point in asking questions, if it doesn't lead to discovery of something new. I think we can safely throw out the second interpretation of the statement as nonsense.

Interpretation one suggests there are unanswerable questions. I think we have to concede there are questions that likely are unanswerable. For instance, what actually is at the center of the Earth? Well, we can't physically access the Earth's center to ever know with complete certainty, so realistically we will never know what is at the center of the Earth. However, this implies that to "know" means to collect a sample and examine its contents. Yet, through reason, scientific principles, and some creative use of technology, we can develop a model of what we think is at the center of the Earth. https://www.popularmechanics.com/scie...

Thus, what is the value of asking questions that are unaswerable? We just might discover we were wrong! So, I reject interpretation one as well. I say, ask all the questions you can and seek for answers, but I think we will need a great deal of patience and persistence before we get answers to many of our difficult questions, but I say keep asking.

[Feliks]

Most of the aeons our mammalian species has inhabited this planet has proceeded along quite well enough without any questions being asked at all, and without any answers being offered by anyone. Information is fawned over these days, but remember the facts: we don't need it -- we never needed --it to survive on this earth. It's superfluous for the masses; humans always do 'whatever the heck they've always done' whether slaughter, slavery, famine.

Questioning and and answering though, are a boon for introspection. Self-examination. That's it's true value.

[Feliks]

Referring back to the OP of this thread. I'd like to pose a variation on what was originally asked.

Should all our human knowledge be knowledge which can be put into action?

Should all human knowledge be useful, practical, and leading towards some good end?

Are apparently "useless" things, still useful even if we don't recognize it?

Just wondering.

[Duffy]

Feliks wrote: "Referring back to the OP of this thread. I'd like to pose a variation on what was originally asked.

Should all our human knowledge be knowledge which can be put into action?

Should all human kn..."

I'm curious. If you knew the answer to this question, what use would it be?

[Feliks]

I see the humor in your reply.

But to answer soberly: it might change one's reading habits. Doesn't it seem to anyone else but me, that the internet promotes functionality rather than insightful or reflective knowledge?

[Walter]

Not according to Joni Mitchell.

[Skallagrimsen]

Doesn't it seem to anyone else but me, that the internet promotes functionality rather than insightful or reflective knowledge?

You're far from alone. See The Shallows: What the Internet Is Doing To Our Brains by Nicholas Carr.

[Georgia]

Skallagrimsen wrote: "Doesn't it seem to anyone else but me, that the internet promotes functionality rather than insightful or reflective knowledge?

You're far from alone. See The Shallows: What the Internet Is Doing ..."

Excellent book. Of course I'm on the internet now. But, when I'm off, I'm definitely off. We need to break away and think deeply, too.

[Feliks]

Positive replies. Thanks!

[Skallagrimsen]

Excellent book.

Agreed! It's on my re-read pile.