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By 'we' I mean human beings who have got intellect to reflect and analyse things and then to increase their 'knowledge' (not information) or by any other means. With the progress of time we are unlocking many mystries of past. If not then it can also be asked what are the limits of our 'ability to know', if there exists a limit? Yes Wittgenstein said,"the limits of my language mean the limits of my world", but the language is itself also progressing. So does there exist a final limit in our 'thought experiment'? If yes, then is it possible to know about that limit?

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    "the limits of my language mean the limits of my world". But then I can easily say, "those things that are beyond the limits of my language", or "those things that I have no words for". – Luís Henrique Mar 9 '17 at 12:19
  • I have trouble understanding what do you mean by "knowledge, not information". – erreka Mar 10 '17 at 20:56
  • @erreka Knowledge is based on reason and for information you just needs to have your 5 basic senses. For me information is first step towards knowledge. – Ather Cheema Mar 13 '17 at 7:30
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Arguably "yes", there's a limit, as follows, based on two pretty reasonable premises. First, every (written) language consists of finite sequences of symbols taken from a finite alphabet, so every language contains at most a countably infinite number of wff's. Second, and maybe a bit shakier, suppose your semantic domain of "all knowledge" (whatever that is) is uncountable. Then all semantic functions mapping language syntax to domain semantics will be "into", but none can be "onto". Indeed, countable subsets of an uncountable set have "measure zero", e.g., like the rationals comprise only an infinitesimally small "amount" of all reals. So Wittgenstein's limit is rigorously correct -- any language comprised of sequences of symbols is very limited in the domains of knowledge it can completely represent.

  • Please don't confuse mathematics "infinity" with philosophical infinity. Knowledge is unrelated with the number of symbols an alphabet consists of. – John Am Feb 7 '17 at 10:50
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    @JohnAm Number of symbols is a minor, minor, minor point -- it's obviously finite, and I was just stating all premises. Much more relevant is "limits of language". And then the Sapir-Whorf hypothesis, en.wikipedia.org/wiki/Linguistic_relativity , comes into play. And my construction (actually, a ubiquitous textbook construction) is based on that philosophical position. – John Forkosh Feb 7 '17 at 11:00
  • Knowledge takes the form of statements, treatises, disciplines, social processing etc. not mere words. Language is a social-historical construct under constant evolution and unlimited by its nature. The theory you mention is obsolete. Languages are equivalent depending on their historical evolution because these roughly fulfill the same social historical purposes and all societies are interrelated. – John Am Feb 7 '17 at 11:26
  • en.wikipedia.org/wiki/… – John Am Feb 7 '17 at 11:33
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    @JohnAm you're not getting the point of "countable infinite" number of expressions as opposed to "uncountable infinite" number of beliefs (or facts, or whatever). – erreka Mar 9 '17 at 18:14
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knowledge itself is static and human knowledge usually can grow regularly (through learning).

human learning trajectory (all, but not only a single human) is a dynamic, there is no such limitation on absorbing knowledge, however, due to the evolution and other side effect which can occur, human tends to forget or remove relatively useless knowledge naturally (that explained why history told us human always committed the same mistakes).

it means that human can absorb unlimited knowledge logically, but there is a threshold exists in their DNA. it is a typically machine learning tricks, when during with complicated issue, we tends to know the answer, instead of the procedures to solve the issues.

human learn "forget something they have learnt" and they will claim it is "a new thing which they haven't learnt".

it is a iteration of knowledge which could restrict the human learning process (it is the reason why human can find satisfactory in their mediocre life).

as the same situation prolonged to a single human life, human start not willing to learn new thing by choice (free-will). they tends to apply their experience to solve the existing problem.

as long as problem is able to be solved by the current knowledge foundation, human usually will not learn/know new thing.

thus, any stimulation(issues, problems, threats) can boost the knowledge base of human, for example world war 2 there is a lot of difference type of technology invented and researched.

human tends not to explore the universe, or their own bodies until the crisis of human population and serious disease.

a single human is a event driven object with some randomized pulse to force them to do creative things. but the entire human species are still event driven as the correlation activities of them (society).

  • "static" and "grow regularly" seems contradictory. – Mr. Kennedy Mar 11 '17 at 1:02
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Can we know about everything?

Yes.
Can we know everything all at once? No.
Can we state our knowledge about everything all at once. No.
Perhaps, the question is better answered if posed, "can we know about any thing?" or do you mean, "can all of humanity know everything every where all at once?"?

By 'we' I mean human beings who have got intellect to reflect and analyse things and then to increase their 'knowledge' (not information) or by any other means.

Why limit your consideration to we few homo sapien sapiens when we are certainly not the only conscious and intelligent animals in the world? I suspect the answer has to do with the commonality of language amongst us humans.

Otherwise, yes, one of the distinguishing features of modern and contemporary intellectual life is that knowledge grows.

Note however that we do not increase our knowledge by our intellect, we increase our knowledge by our senses.

With the progress of time we are unlocking many myst[e]ries of [the] past.

That is poetry.

If not[,] then it can also be asked what are the limits of our 'ability to know', if there exists a limit?

Yes there are epistemic limitations. A doctor cannot know their patients' pains, else diagnosis and prognosis would be a trivial endeavor.

"If not" which?

  1. "If with the progress of time we are not unlocking many mysteries of the past, then ..."
  2. "if human beings are not increasing their knowledge, then ...", or
  3. "if we can not know about everything, then ..."?

In the first case your meaning is ambiguous - do you mean unlocking past mysteries which remain unresolved, such as the location of Jimmy Hoffa's corpse, or, for example, our ability to conjecture falsifiable and verifiable hypotheses with more than abductive reasoning about such cosmological events as the formation of the Milky Way galaxy?

In the second case, at the very minimum with every passing day there are more humans and thus more knowledge.

Finally, in the third sense of your question, see below regarding epistemic limitations.

From here on out I will also take your meaning of "can we know everything" to be akin to "is there any thing in the world which can not be known?" and not an inquiry into the logistics of actually knowing each and every thing such as the highly mundane, restricted, classified or intentionally obscure such as the position of each grain of sand in the Sahara desert, launch codes for China's nuclear arsenal, redacted passages from the Warren Commission report, laundered monies, etc.

Note also my use of (each and) every thing from the term "everything" in the sense of a totality of things. If you are asking could one person or all people know everything all at once, the short answer is no. And this even in an extremely restricted sense of knowledge as empirical verification of what is (which I will describe later). At the very least we can imagine every wave-particle in the universe frozen for an instant in spacetime such that (each and) every thing from the thresholds of sub-atomic blinkering quantum decoherence to cosmological event horizons upon "black holes" (i.e. epistemically obscure whole objects) could be known, but - even if we had such power to pause such a contrived "universe" - in the time it would take to know each particle and its trajectory; every structure and their interactions once known and the universe set in motion again everything will have changed. Would we make a cinema of the world intermittently pausing in between each minimal unit of Planck time for the sake of record keeping? And where would this record be stored? In our memory? Bah. Who has the time or the space to devote to such fantasy except the young or idealistic? Such is the stuff of science fiction and in anycase, you might enjoy Isaac Asimov's short story, "The Last Question" if you have not already read it.

Yes Wittgenstein said,"the limits of my language mean the limits of my world", but the language is itself also progressing. So does there exist a final limit in our 'thought experiment'? If yes, then is it possible to know about that limit?

Consider some alternative translations to proposition 5.6 in Wittgensteins Tractatus Logico-Philosophicus:

  • The limits of my language stand for the limits of my world.
  • The limits of my language are the limits of my mind. All I know is what I have words for.
  • Original German: Die Grenzen meiner Sprache bedeuten die Grenzen meiner Welt.

Here's where the rubber meets the road:

Contrary to popular sentiments, knowledge is not justified and true belief.

  1. Knowledge is empirical verification of what is - else how do you KNOW what is??
  2. The (at most one) world which we live in is what is.
  3. The world (the case, states of affairs, the facts) is that which is empirically verified.

Therefore, if it is empirically verifiable, then we can know it.

It is, however, logically impossible to know the past for if we could empirically verify the past it would be present.

The world owes humanity no explanation and for all we know it is much weirder than we imagine, it could very well be infinite and without beginning or end. That we may be dreaming or deceived by some demonic agency with ill intent may wreak havoc with the outliers, but we land men on the moon, replace human hearts and build bridges across vast expanses with our imperfect empirical knowledge. So we do not know enough to adjudicate conclusively with any certainty regarding certain ponderable historical or cosmological mysteries - what is certainty except a mood?

Consider Wittgenstein's assessment of language's relationship between humanity and what is. From a collection of his aphorisms, "Culture and Value":

"People say again and again that philosophy doesn't really progress, that we are still occupied with the same philosophical problems as were the Greeks. But the people who say this don't understand why it has to be so. It is because our language has remained the same and keeps seducing us into asking the same questions. As long as there continues to be a verb 'to be' that looks as if it functions in the same way as 'to eat' and 'to drink', as long as we have the adjectives 'identical', 'true', 'false', 'possible', as long as we continue to talk of a river of time, of an expanse of space, etc. etc., people will keep stumbling over the same puzzling difficulties and find themselves staring at something which no explanation seems capable of clearing up. And what's more, this satisfies a longing for transcendence, because in so far as people think they see the 'limits of human understanding', they believe of course that they can see beyond these."

-Ludwig Wittgenstein
"Culture and Value"
pg. 15e
c.1931

So what then to make of our epistemic limitations when knowledge is empirical verification (and this whether knowledge you undergo - perception - or knowledge you undertake - verifying)? Note that there are there are three kinds of knowledge:

  1. Axiomatic or self-evident knowledge e.g. tautologies such as "2+2=4" or "a=b, therefore b=a" or, "dividends require financing."
  2. Empirical knowledge e.g. "brute" facts (pace Anscombe) such as "the Earth is an oblate spheroid" or, "the Earth is roughly 93 million miles from the sun" and also "institutional" facts (per Searle) such as, "Trump is President" or, "Brad and Angelina are divorced."
  3. Self-knowledge e.g. "I feel fine" or, "those Jenkem addicts crack me up!"

It might seem circular because it is so very basic, but knowledge is empirical verification of what is the case, the world, states of affairs, i.e. that which is empirically verified. In the case of expert or lay disagreement - is the disagreement over the case? the facts? the states of affairs? Is the disagreement of opinion regarding what is? Is there disagreement regarding interpretation of fact? Is there disagreement regarding implication of interpretation? In any instance, you have the tools of philosophy: logic, rhetoric and reason to guide your efforts such that knowledge may be obtained.

So, with this restricted formulation of knowledge, what then are the epistemic limitations:

  1. In the words of A.J. Ayer that axiom is only true because we do not allow it to be otherwise (from "Language, Truth and Logic," ch.4 "The A Priori" pg. 41).
  2. Outside of falsifiable and verifiable propositions, hypotheses can neither be confirmed nor advanced - only conjectured and either agreed or disagreed with.
  3. Self-knowledge can not be verified by any other than the self.

So, in short - can one person know about everything? No - there is an epistemic limit to what a doctor can know about a patient, a parent about a child, any self about any other, but in each instance the former and the latter may know their own self.

Can we literally know about each and every thing? Sure - inasmuch as every thing in this at most one world is actually empirically verifiable. Can we know about each and every thing all at once? No. Can we just know everything? No. Can we adequately explain everything? That depends upon the occasion of explanatory utterance.

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