• Self Referential Undecidability Construed as Incorrect Questions
    I hope not, and that I've misunderstood, because (this sentence is not true) cannot be false. — Banno

    "This sentence is not true." is not a truth bearer and thus cannot be true
    or false. "What time is it?" is also not a truth bearer.

    Self-reference itself is not problematic. So, for instance the following sentence is true and self-referential. This sentence contains five words. Hence, further, "This statement is not provable in F" may be self-referential but true. — Banno

    Yes that is the same example that I use of self-reference that is not problematic.
    If you understand the basics about how mathematical proofs work then you know
    that a proof is a sequence of inference steps that ends in a conclusion.

    When an expression of language G asserts that it is not provable in F
    G := (F ⊬ G) then to be proven in F requires a sequence of inference
    steps in F.

    Everything that is provable in F always requires some sequence of
    inference steps in F that reach a conclusion.

    Since we are proving that G is unprovable in F then these steps must
    prove that they themselves do not exist. It may be intially difficult
    to understand. It took me quite a few years to explain how this
    is self-contradictory.

    The most important aspect of Gödel's 1931 Incompleteness theorem
    are these plain English direct quotes of Gödel from his paper
    ...there is also a close relationship with the “liar” antinomy,14 ...
    ...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
    ...We are therefore confronted with a proposition which asserts its own unprovability. 15 ...
    (Gödel 1931:43-44)

    Gödel, Kurt 1931.
    On Formally Undecidable Propositions of Principia Mathematica And Related Systems

    https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

    Antinomy It is a term often used in logic and epistemology, when describing a
    paradox or unresolvable contradiction
    https://www.newworldencyclopedia.org/entry/Antinomy

    Quoted from above indicates that Gödel knews that he relied on self-contradiction
    ...14 Every epistemological antinomy can likewise be used for a similar
    undecidability proof...
  • Self Referential Undecidability Construed as Incorrect Questions
    ↪PL Olcott Sure, nice. So whereabouts in such a coding are we going to see the equivalent of (p & ~p)? Where's the demonstration? — Banno

    I never said anything like that. That is merely contradictory and thus not at all self-contradictory.
    "This sentence is not true." is self contradictory. If it is true that it is not true that makes it true.

    My unique take on Gödel 1931 Incompleteness (also self-referential)
    Any expression of the language of formal system F that asserts its
    own unprovability in F to be proven in F requires a sequence of
    inference steps in F that prove they themselves do not exist.

    It is not at all that F is in any way incomplete.
    It is simply that self-contradictory statements cannot be proven
    because they are erroneous.
  • Self Referential Undecidability Construed as Incorrect Questions
    ↪PL Olcott perhaps that is not as clear as you seem to think. My guess is that a much more formal account is needed. The problem is that “self” is ambiguous. — Banno

    A more formal account is probably beyond the technical capability of most here.
    This D is defined to do the opposite of whatever Boolean value that H returns.
    // The following is written in C
//
01 typedef int (*ptr)(); // pointer to int function
02
03 int D(ptr x)
04 {
05   int Halt_Status = H(x, x);
06   if (Halt_Status)
07     HERE: goto HERE;
08   return Halt_Status;
09 }
  • Self Referential Undecidability Construed as Incorrect Questions
    Carol answers no without this being a paradox because there is no possibility of being "correct". As in: can she [answer correctly]? no, she cannot. — Antony Nickles

    When Carol says "no" indicating that "no" is an incorrect answer
    this makes "no" the correct answer thus not incorrect thus Carol is wrong.

    The exact same thing equally applies to input D to decider H
    where D does the opposite of whatever Boolean value that H returns.

    The halting problem specification is a self-contradictory thus an
    incorrect question for some decider/input pairs.

    The HP proofs do not limit what can be computed any more than the
    fact that CAD systems cannot draw square circles limits computation.
  • Self Referential Undecidability Construed as Incorrect Questions
    So presumably you mean something else by”self contradiction”, but it is unclear to me what that might be. — Banno

    When input D is defined to do the opposite of whatever value that decider
    H returns then "Does your input halt on its input?" becomes a self-contradictory
    question for this decider/input pair.
  • Self Referential Undecidability Construed as Incorrect Questions
    ↪PL Olcott Sure. What's unclear to me is what it is you think this tells us about the halting problem. — Banno

    As I and Professor Hehner have said the halting problem specification is essentially
    a self-contradictory thus incorrect question for some decider/input pairs, thus places
    no actual limit on computation. It is the same as the inability of CAD systems to correctly
    draw square circles.
  • Self Referential Undecidability Construed as Incorrect Questions
    The supposed outcome is that no computer program A can say what another computer program B will do when B does the opposite of whatever A says

    But what if A just prints "B will do the opposite of whatever I say it will do"?

    So I'm unconvinced.     — Banno

    Yes that is the article that I am basing this on. Professor Hehner
    totally agrees with my understanding of his work. We discussed
    it as recently as yesterday and many other times.

    There was a nearly identical version of Carol's question that was
    addressed directly to me in 2004 long before Professor Hehner
    wrote about these things. This one was called Jack's question.

    Hehner's version corrected some loopholes. Then someone else
    pointed out another loop hole recently. Carol could correctly answer
    the Hehner version with a word that is synonymous with "no".
    Thus I added a restriction on the solution set.

    Can Carol correctly answer “no” to this [yes/no] question?

    Most people familiar with the theorem of computation halting
    problem proofs understand that the halt decider is only allowed
    to answer with something equivalent to yes or no.
  • Self Referential Undecidability Construed as Incorrect Questions
    When the solution set is restricted to {yes, no} and no element of this solution set is a correct answer from Carol then the question posed to Carol is incorrect.
    — PL Olcott
    Well, depending on the question-statement, I would rather say ambiguous or circular or self-contradictory or --if it refers to an argument-- a fallacious argument.
    I think that the attributes "correct" and "incorrect" are too general and/or ambiguous themselves.     — Alkis Piskas

    An incorrect question is any question that lacks a corresponding correct answer
    because there is something wrong with the question. © 2015 PL Olcott

    A self-contradictory question is a type of incorrect question that lacks a correct
    answer because the question contradicts both elements of the solution set: {yes, no}

    Can Carol correctly answer “no” to this [yes/no] question?
    Is a self-contradictory (thus incorrect) question when posed to Carol.

    When Carol says "no" indicating that "no" is an incorrect answer
    this makes "no" the correct answer thus not incorrect thus Carol is wrong.

    When Carol says "yes" indicating that "no" is a correct answer this makes
    "yes" the wrong answer.
  • Self Referential Undecidability Construed as Incorrect Questions
    OK. But why is the question being asked to Carol if it will end up in an incorrect answer? — javi2541997

    Because is has the exact same form as the halting problem: decider/input
    pair it proves that the most important computer science theorem that exists
    is incorrect.

    Simplified as this:
    No computer program H can correctly say what another computer program
    D will do when D does the opposite of whatever H says.

    As long as it is understood that Carol's question is self-contradictory for Carol and
    it is also understood that input D for program H is self-contradictory for H then
    it can be understood that the only reason that the halting problem proofs can
    show that the halting problem cannot be solved is that the input D to H derives
    a self-contradictory thus incorrect question.

    When presented with a self-contradictory thus incorrect question the blame
    for not answering this question must go to the question and not the answerer.
  • Self Referential Undecidability Construed as Incorrect Questions
    OK. I don't get this. I thought we were debating about Carol — javi2541997

    Carol's question was written by a PhD computer science professor as
    a simple analogy to the halting problem proofs. It was written to provide
    a rebuttal to these proofs.
  • Self Referential Undecidability Construed as Incorrect Questions
    What I disagree with, is that an omission from Carol is not necessarily an incorrect answer — javi2541997

    It <is> the lack of a correct answer thus
    Can Carol correctly answer “no” to this [yes/no] question?
    has (a) yes (b) no (c) anything else as not a correct answer to Carol's question
    thus proving that anything that Carol can say or fail to say is not a correct answer
    when posed to Carol.
  • Self Referential Undecidability Construed as Incorrect Questions
    Unless synonyms or omissions are allowed, yes, Carol will always fail to answer this stipulated question set — javi2541997

    So Carol's question when posed to Carol meets the definition of an incorrect question
    in that both answers from the solution set of {yes, no} are the wrong answer.

    Simplified Halting Problem Proof
    Likewise no computer program H can say what another computer program D will do
    when D does the opposite of whatever H says.
  • Self Referential Undecidability Construed as Incorrect Questions
    Well, after having a reasoning with myself, I came to the conclusion that omission cannot be an incorrect answer from Carol. — javi2541997

    Someone did find a loophole in Carol's question, it is corrected below:
    (Carol could answer with a word that is synonymous with no)

    Can Carol correctly answer “no” to this [yes/no] question?
    is proven to be "no" on the basis that anything that Carol can say or fail to say cannot possibly provide a correct answer to that question from the stipulated solution set of {yes, no}.
  • Self Referential Undecidability Construed as Incorrect Questions
    PL Olcott is simply confused. Besides being rude. — Alkis Piskas

    No, it is wrong to say that a question has a correct answer. — Alkis Piskas

    I honestly can't see how your above statement can possibly be correct and you have not provided a correct version of my statement to contrast with. You must be using some obscure idiomatic (term of the art) meaning that 99% of the population never heard of.

    Well, depending on the question-statement, I would rather say ambiguous or circular or self-contradictory or --if it refers to an argument-- a fallacious argument.
    I think that the attributes "correct" and "incorrect" are too general and/or ambiguous themselves.     — Alkis Piskas

    That statement indicates that you have a very good understanding of what I am saying.
    I use the term "incorrect question" so that the question gets the blame for the lack of a
    correct answer. Conventionally the question is always considered correct and the decider
    gets the blame.
  • Self Referential Undecidability Construed as Incorrect Questions
    Let me think about this deeply. Maybe I can come back with more substantive comments, and see other possibilities. I appreciate how you considered each feasible scenario of Carol's behaviour. I still believe that there can be a possible correct answer. — javi2541997

    That is great.
    (a) Carol answers "no" and she is wrong.
    (b) Carol answers "yes" and she is wrong.
    (c) Carol does anything else and she has not provided an answer within the solution set of {yes,no}.
  • Self Referential Undecidability Construed as Incorrect Questions
    Well, depending on the question-statement, I would rather say ambiguous or circular or self-contradictory or --if it refers to an argument-- a fallacious argument. — Alkis Piskas

    It is clear that self-contradictory expressions are untrue and unfalse because they are self-contradictory. Analogous reasoning applies to self-contradictory questions.

    It the same way that the Liar Paradox: "This sentence is not true" is an incorrect statement self-contradictory questions are incorrect questions.

    Is this sentence true or false: "This sentence is not true" is an incorrect question because zero elements of the entire solution set of {true, false} are a correct answer.

    Then we apply this same reasoning to self-contradictory decision problem instances.
    When neither return value of {true, false} is correct for a decider/input pair then this
    decider/input pair is essentially an incorrect question.
  • Self Referential Undecidability Construed as Incorrect Questions
    "Is the living mammal of an elephant any type of fifteen story office building?"
    has the correct answer of "no".
    — PL Olcott
    No, it is wrong to say that a question has a correct answer.     — Alkis Piskas

    That seems to be a ridiculous statement on your part. It is like you are saying
    that it is impossible to determine whether or not an elephant is a fifteen story
    office building. How would you phrase the exact same idea that I am referring to?

    When a decision problem decider/input pair lacks a correct Boolean return value from this decider then this decision problem instance is semantically unsound.
    — PL Olcott
    I wouldn't state it like that myself, but I agree. :smile:     — Alkis Piskas

    Most people call this an undecidable instance, yet it is not at all any
    matter of the decider not being able to figure out which of true/false
    is the correct return value. It is a matter of both true and false are
    incorrect return values.
  • Self Referential Undecidability Construed as Incorrect Questions
    By extension, all this applies and is an answer to your topic itself: If the context in which a question is asked is mission or not clear, of course this question might receive not incorrect, but inappropriate answers, i.e. answers "out of context" or "off-topic", as we use to say. A classic example is an ambiguous question that can be answered with both "Yes" and "No", about which you talked in your description. — Alkis Piskas

    When the solution set is restricted to {yes, no} and no element of this solution set is a correct answer from Carol then the question posed to Carol is incorrect.
  • Self Referential Undecidability Construed as Incorrect Questions
    Yet again, I claim that the 'incorrect' question doesn't depend whether is posed on Carol or not. — javi2541997

    The PhD computer science professor that has been published in several highly esteemed computer science journals disagrees.
    (a) Yes is not a correct answer from Carol.
    (b) No is not a correct answer from Carol.
    (c) No answer is not a correct answer from Carol.
    We have exhaustively examined every possibility and thus proven every action taken by Carol does not result in a correct answer.
  • Self Referential Undecidability Construed as Incorrect Questions
    1) A question cannot have a correct answer. — Alkis Piskas

    "Is the living mammal of an elephant any type of fifteen story office building?"
    has the correct answer of "no".

    Is the following sentence true or false: "This sentence is not true."
    has no correct answer from the set of {true, false}.

    My intention is not to criticize you, but to pinpoint important elements in a philosophical discussion. And I'm addressed to the general public, because I see the phenomenon of lack of clarity and misuse of terms only too often. — Alkis Piskas

    My purpose of being here is to get feedback so that I can make my words clear enough so that they can be understood as correct.

    When a decision problem decider/input pair lacks a correct Boolean return value from this decider then this decision problem instance is semantically unsound.
  • Self Referential Undecidability Construed as Incorrect Questions
    Correct/incorrect are not related to the truth or false in your question to Carol. — javi2541997

    Is this sentence true or false? "This sentence is not true" is an incorrect question because the Liar Paradox is neither true nor false and the solution set is limited to {true, false}.

    The same thing applies to Carol's question when posed to Carol:
    Can Carol correctly answer “no” to this question?

    Since both yes and no are an incorrect answer from Carol this conclusively proves that Carol's question meets the stipulated definition of an incorrect question when posed to Carol.

    An incorrect question is defined as the case whenever a yes/no question posed to a person has no correct yes/no answer from this person then this question is incorrect when posed to this person.
  • Self Referential Undecidability Construed as Incorrect Questions
    I still do not see the correlation between 'yes/no' - or 'correct/incorrect' - and true and false. — javi2541997

    Carol's question is incorrect for Carol, thus it is the fault of the question and not the falt of Carol for the lack of correct answer from Carol.

    There no is element in the entire solution set of {yes, no} that Carol can use as her answer thus making the question incorrect on the basis of the definition of incorrect question.

    An incorrect yes/no (technically polar) question is any yes/no question lacking a correct answer from the set of {yes, no} or {true, false}.

    A self-contradictory (thus incorrect) question is the analog to a self-contradictory statement such as:
    "This sentence is not true".
  • Self Referential Undecidability Construed as Incorrect Questions
    What I do not understand is why you consider the question as 'wrong' when we are debating whether Carol is capable of answering the question correctly. — javi2541997

    One thing that I found in my 20 year long quest is that self-contradictory expressions are not true. As a corollary to this self-contradictory questions are incorrect.

    When we add one more step that the context of who is asked a question is a mandatory aspect of the full meaning of this question then Carol's question is incorrect for Carol.
  • Self Referential Undecidability Construed as Incorrect Questions
    What I do not understand is why you consider the question as 'wrong' when we are debating whether Carol is capable of answering the question correctly. — javi2541997

    Some (if not all) undecidable decision problems are only "undecidable" because there is something wrong with the problem. When zero elements of the entire solution set provide the correct answer then this indicates that there is something wrong with the problem.

    If I ask you how many feet long is the color of your car? no one can provide a correct answer because the question itself is incorrect. The same thing happens when a self-contradictory question is asked.
  • Self Referential Undecidability Construed as Incorrect Questions
    Can Carol correctly answer 'no' to this question? There is a true possibility that Carol could do so. — javi2541997

    This is very tricky like the Liar Paradox: "This sentence is not true" <is> not true yet does not make it true because if it was true then it would not be not true.

    We have the exact same issue with Carol's question.
    Carol cannot correctly answer her question yet when she says "no" then she has correctly answered her question making "no" the wrong answer.

    When Carol says "yes" this means that she can correctly answer her question with "no" yet we just proved that is incorrect.
  • Self Referential Undecidability Construed as Incorrect Questions
    ↪javi2541997


    We must not change Carol's question because it is the exact same form as
    the most important theorem in computer science the halting theorem.
    A PhD computer science professor wrote Carol's question with this in mind.

    Once we understand that any yes/no question that lacks a correct answer
    (within the linguistically required context of who is asked) is an incorrect
    question then

    We understand that Carol's question and the halting theorem decider/input
    pair are also merely incorrect questions.

    The halting theorem proves that a halt decider cannot possibly return a
    correct true/false value when its input does the opposite of whatever Boolean
    value that it returns. https://simple.wikipedia.org/wiki/Halting_problem

    Since this turns out to merely be an incorrect question it does not place
    any actual limit on computation. The fact that a baker cannot bake an
    angel food cake using only house bricks for ingredients place no limit
    on the baker's baking skill.
  • Self Referential Undecidability Construed as Incorrect Questions
    ↪javi2541997

    I changed the words to the better words of the PhD computer science professor.
  • Self Referential Undecidability Construed as Incorrect Questions
    ↪unenlightened

    I changed the words to the better words of the PhD computer science professor.
  • Self Referential Undecidability Construed as Incorrect Questions
    ---
  • A very basic take on Godel's Incompleteness Theorem
    ↪TheMadFool
    G=This sentence is not provable in T — TheMadFool

    If G was provable in T then this requires a sequence of inference steps in T
    that prove that they themselves do not exist.

    Copyright 2023 PL Olcott
  • Witnesses in mathematics
    ↪alcontali
    S = "S is not provable in T"
    A proof of S in T requires a sequence of inference steps in T
    that prove that they themselves do not exist.

    Copyright 2023 PL Olcott
  • Solution to the Gettier problem
    I would say that direct observations of the empirical world, such as "it is raining, right here right now, can be all but absolutely certain, provided our thinking doesn't slip into radical skepticism, wherein we might think the rain we see is a simulation, illusion or elaborate hoax. — Janus

    It may be best to keep the radical skepticism in the back of our mind just to force a little more humility so that we don't excessively trust the merit of our own opinion.
  • Solution to the Gettier problem
    So, your point relies on radical skepticism, and I think we can rule that out just by accepting the phenomenal world as it appears and making and thinking of the truth or falsity of knowledge claims only within that context. — Janus

    Was your response meant to address—that is agree or disagree—with what I had said, or is it more of an aside? — Janus

    After reading this again I agree.
    I was also trying to show why knowing the limits of logically justified certainty is important.
  • Solution to the Gettier problem
    No one cares about the Tarski Undefinability Theorem for practical purposes. If you're going to go that in depth, then you're going to have to be in depth in your analysis. Ok, that's likely the last response now. Good luck in your work! — Philosophim

    I think that your criticism of my view has lots of merit. You do seem to be describing
    more accurately how people actually use knowledge. When I cut out the stochastic
    aspects of this it makes it a less accurate model of knowledge.
  • Solution to the Gettier problem
    The system seems to have crashed for a little while...

    So, your point relies on radical skepticism, and I think we can rule that out just by accepting the phenomenal world as it appears and making and thinking of the truth or falsity of knowledge claims only within that context. — Janus

    Only when one fully comprehends the actual limits of logically justified certainty is one's mind forced open enough to see reality for what it truly is as opposed to and contrast with the brainwashing of conditioning of the socialization process. (This is Eastern religion stuff).

    All that said, I'd be happy enough to stop talking about knowledge altogether and instead talk about more or less justified belief, while acknowledging that we have no absolutely precise measure of justification. — Janus

    I have been studying and pondering the mathematical foundation of the notion of analytical truth for many years. I just recently discovered that this is anchored in truthmaker theory.
  • Solution to the Gettier problem
    If you're just concerned about knowledge for practical purposes, nothing needs to be written or done. — Philosophim

    Back to pure epistemology
    The Tarski Undefinability Theorem "proves" that True(L, x) can never be computed on the basis that Tarski did not understand that the Liar Paradox must simply be rejected as not a truth bearer. https://liarparadox.org/Tarski_275_276.pdf
  • Solution to the Gettier problem
    This is another major problem. By the way, my paper has an answer to the problem of induction. Its the last section. Induction cannot be used to ascertain truth. — Philosophim

    Although the problem of induction seems to prove that the very next time you drop your coffee cup it might just hang there in the air levitating, I dismiss this as unreasonably implausible.

    Again, this does not answer the question of, "How do I know that what I know is true?" — Philosophim

    It answers it well enough for all practical purposes. Since we cannot even know that five seconds ago actually existed we can't even know that we have ever met our own mother, even if she just left the room. https://en.wikipedia.org/wiki/Omphalos_hypothesis#Five-minute_hypothesis I dismiss this as unreasonably implausible.

    Such as system that I propose can compute that claims of election fraud in the 2020 presidential election really are nothing more that copying Hitler's own "big lie" for the purpose of overturning a valid election.

    It can also compute that drastic climate change by humans is real and must be mitigated very soon to prevent horrific future consequences.

    https://www.researchgate.net/publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
  • Solution to the Gettier problem
    This is a fine desire, but your current trajectory will destroy this. Also, your desire may not be real. That is something we also have to accept as philosophers. "I want to define knowledge that includes truth," cannot logically be done. Or, if it can, you must ignore everything else and answer the one question, "How do I know that what I claim I know is true?" in the synthetic sense. Ambitions are fine, but without this core pillar established, the whole roof will collapse around you. — Philosophim

    I am taking all of the things known through induction, (ignoring the problem of induction) and converting them into axioms in the verbal model of the actual world. These are all construed as knowledge that is known to be true. This same model also includes all analytical truth.

    Empirical knowledge now becomes only the mapping of sets of physical sensations to their corresponding elements in this model of the world. This system allows people and machines to correctly compute True(L, x) as pure deductions within this model of the actual world.
  • Solution to the Gettier problem
    I would read my paper first to understand where I'm coming from, but consider instead that knowledge is simply a tool humanity uses in an attempt to get as close to the truth as logically possible. What would be wrong with that? If we have concluded one thing is impossible, then the next step is to determine what is possible within our goals. — Philosophim

    I haven't fully read it yet. It seems that you and I have two different goals. You are trying to define knowledge accurately within the common terminology of epistemology. I am estimating that you have significantly achieved this. I will try and sum up your view here: Because knowledge does include things that have less than logically justified certainty this entails that knowledge must include some untruth. That makes perfect sense to me.

    My goal is to define truthmaker theory and epistemology is such a way that ordinary people learn correct reasoning in common terms that they already understand. When they are jurors in court cases they really need to know all of the details of how interpreting sensory perceptions can diverge from truth. By calling even these distortions "knowledge" makes it too easy for them to get away with less than due dilligence.

    We must also overcome the egoistic bias of overconfidence in one's own subjective opinions. In this case we can have some very bad outcomes if we allow knowledge to be false: I know that X murdered Y and X was put to death for this even though X did not murder Y. For this reason it is best to construe "knowledge" that turns out to be false as presumption and not any kind of actual knowledge at all.

    The additional goal of defining a True(L,x) that can compute what is true and what is not true is much easier in that it only relies on an axiomatic correct model of the actual world. In other words all of its computations are pure deductions.
  • Solution to the Gettier problem
    I would read my paper first to understand where I'm coming from, but consider instead that knowledge is simply a tool humanity uses in an attempt to get as close to the truth as logically possible. What would be wrong with that? If we have concluded one thing is impossible, then the next step is to determine what is possible within our goals. — Philosophim

    I saved the whole thing as a 33 page PDF. Only the first 12 pages are your paper.
    With the free PDF readers of recent years I can highlight key sections as needed.

    Dictionaries seem to agree with your view in that they seem to be saying something like
    knowledge is a very coherent set of ideas that tend to have very practical application.
    I think that when it refers to facts that these expressions of language must be true.

    (1) acquaintance with facts, truths, or principles, as from study or investigation; general erudition:
    knowledge of many things.

    (2) familiarity or conversance, as with a particular subject or branch of learning:
    A knowledge of accounting was necessary for the job.
    https://www.dictionary.com/browse/knowledge

    When analytical knowledge is defined as a justified true belief such that the justification necessitates the truth of the belief then the Gettier problem is no longer possible.

    Empirical knowledge is defined as a justified true belief such that the justification makes every possible attempt to correctly match a set of physical sensations to their corresponding elements in a correct verbal model of the actual world.

    Unless you actually see the five coins that you believe that your friend has and made a best possible attempt to verify that they are not counterfeit you have no knowledge that your friend has these five coins.

    If we don't make the definition of knowledge as tight as possible something mistaken for knowledge could make humanity extinct. Because of the human ego many people take their own wrong headed opinions as exactly one-and-the-same thing as verified facts.

    Since the cost of making a mistake could make humanity extinct (or worse) it might be better to err on the safe side and say that empirical knowledge is impossible. This view tends to keep reinforcing humility.

    Studies have shown that mistaken eyewitness testimony accounts for about half of all wrongful convictions. Researchers at Ohio State University examined hundreds of wrongful convictions and determined that roughly 52 percent of the errors resulted from eyewitness mistakes.
    https://www.crf-usa.org/bill-of-rights-in-action/bria-13-3-c-how-reliable-are-eyewitnesses

    Eyewitness testimony is mistaken to be very reliable and this causes grave errors.
    https://www.simplypsychology.org/eyewitness-testimony.html

    A person could be put to death because jurors were unaware of the divergence of empirical knowledge from truth. Because of this it might be best to refer to {empirical knowledge} as a {reasonable guess} and never call it any kind of knowledge at all.
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