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Knowing

by Bill Meacham on September 26th, 2025
Daedalus flying

In ancient Greek mythology Daedalus was quite an accomplished craftsman, inventor, artist, and architect.[1] He is said to have designed and built the labyrinth on Crete and is best known for constructing wings made of beeswax and feathers that allowed him and his son Icarus to escape imprisonment from that very labyrinth by flying away. Unfortunately, Icarus ignored his father’s advice, flew too close to the sun thereby melting the wax that held his wings together, and fell to his death. The story cautions us to take the advice of people who know more than we do.

Daedalus was also famous for creating statues that were so lifelike that they could move. Plato uses the idea of these statues to make a point about what knowledge is. His Meno contains a brief discussion of how knowledge differs from beliefs that happen to be true. Both knowledge and true beliefs can be equally useful. If you live in Austin and have been to San Antonio you can tell someone how to get there, and so can someone who has never been there. Both will tell you to head south on I-35, and both pieces of advice will work. But there is a crucial difference between them, and it has to do with knowledge. Only the first person really knows; the other one merely has true belief. Meno asks Socrates why knowledge is valued more than true belief and what makes them different. Socrates replies by referring to the statues of Daedalus:

They too run away and escape if one does not tie them down but remain in place if tied down. … To acquire an untied work of Daedalus is not worth much, like acquiring a runaway slave, for it does not remain, but it is worth much if tied down, for his works are very beautiful. What am I thinking of when I say this? True opinions. For true opinions, as long as they remain, are a fine thing and all they do is good, but they are not willing to remain long, and they escape from a man’s mind, so that they are not worth much until one ties them down by (giving) an account of the reason why. … After they are tied down, in the first place they become knowledge, and then they remain in place. That is why knowledge is prized higher than correct opinion, and knowledge differs from correct opinion in being tied down.[2]

The tying down of the errant statue is equivalent to having good reasons for your beliefs, reasons you can return to if in doubt. (Plato says that one good reason is remembering certain truths that you learned before birth, but that’s beside the point for present purposes.)

Here’s an example. Suppose you read on a website somewhere that intermittent fasting is good for you because it helps you lose weight. Even though you don’t practice it yourself you recommend it to your obese friends. But suppose you find another website that says it could be very dangerous for you and lead to eating disorders.[3] Then you’ll change your mind and quit recommending it. In neither case do you have any real knowledge, only beliefs that might or might not be true. And your beliefs waver; they are not settled.

But then suppose you actually try it for yourself for a while and observe the effects. You’ll find out for sure whether it is beneficial or harmful (or has no effect), at least for you yourself. No random website will make you change your mind, because when tempted to do so you can remember what happened when you tried it. You have a good reason for your belief.

Ever since then, at least until recently, philosophers have defined knowledge as justified true belief. To count as knowledge, your belief has to be true, obviously. You can’t know that the earth is flat no matter how fervently you believe that it is because it’s not. But you also need to have some justification for what you believe. Most likely you believe that the earth is not flat but round. If you believe that because everybody says so, it’s not really knowledge, according to this definition. But if you watch a ship sailing away from you on the ocean and you notice that in addition to getting smaller it seems to sink down gradually into the water until it finally disappears, then you have good reason to believe that the earth is round. You have even better reason if you are an astronaut orbiting it and you see its roundness with your own eyes.

In 1963 Edmund Gettier poked a big hole in this definition. There are cases in which a person’s belief happens to be true and the person has good reasons for their belief, but the belief is true only by chance. His examples are a bit far-fetched, as can be expected of edge cases, but sound. Here’s one:

Two people, Smith and Jones, are up for promotion. Smith has heard the boss say that Jones will get the job, and Smith knows that Jones has ten coins in his pocket because he saw Jones put them there. So, Smith has good reason to believe that the person who will get the job has ten coins in his pocket. But the boss is actually going to choose Smith. And, although he doesn’t know it, Smith also has ten coins in his pocket. In this case it’s true that the person who will get the job has ten coins in his pocket, but we would not say that Smith knows it, even though his belief is true and he has good reasons for believing it.[4]

Here’s another, from well before Gettier and halfway around the world. In 632 CE the Buddhist monk Xuanzang in China sees what looks like a body of water as he hikes through the desert, so he believes that there is water ahead. In this desert there are numerous mirages that look like water. By chance Xuanzang sees an actual body of water, not a mirage. Does he really know that there is water ahead? His belief is true, and his belief is justified because he sees the water. But it’s just a matter of luck that he sees the real body of water and not a mirage.[5]

In both these cases your belief is true only because you got lucky. But it’s no good having epistemic luck be part of how you justify your belief because if it is, your belief doesn’t count as knowledge. Each of these cases—and there are many more in the literature—shows that being true and having good reasons are not enough to ensure that a belief is knowledge. These factors are necessary but not sufficient. Something else is needed to banish epistemic luck.

There many suggestions about what that something else is.[6] The true belief must not be deduced from a false belief. Your chain of reasoning must contain no “defeaters,” propositions that, were they known, would lead you to disbelieve what you are otherwise convinced of. There must be a connection, for instance a reliable process for forming true beliefs, between some state of affairs in the world and your belief. Or there must be a causal connection between some state of affairs in the world and the belief. Such a connection might be direct perception, memory, your own agency, or inference, each step of which is warranted. There are other suggestions, and each has its proponents and opponents. As is usual in philosophical debates, there is no clear answer and certainly none that convinces everyone.

The author’s own preference is for the reliable process option, just because it seems to make the most sense. How do you ensure that your justification is sound? By adopting it according to a process that reliably produces true beliefs. C.S. Peirce, to whom we will turn shortly, has things to say about the reliability of various processes for acquiring beliefs.

And at least one of the objections to reliabilism is ridiculously implausible: that an evil demon might cause a person to think something is true. Even if that belief turns out to be in fact true and even though a reliable process would yield the same result, it would not count as justified because it’s caused by an evil demon rather than the process.[7] But in the real world we have no truck with evil demons. As Daniel Dennett says, the utility of a thought experiment is inversely proportional to the size of its departure from reality.[8] Such arguments lead us into the weeds of philosophical debates that can be great fun but have little practical effect.

Considerations such as these and the fact that the correct answer, if there is one, is so hard to find are clues that something may be amiss in the original question.

What’s amiss is that we think that knowledge must have some sort of essence that we can discover by careful inquiry, something unchanging that is found in all instances of knowledge. We reify it (from the Latin res), meaning we treat it as a real thing. But most likely there is no such essence, and we can get a better handle on the issue by following Ludwig Wittgenstein’s advice to look at it in terms of usage.

Wittgenstein says “For a large class of cases … the meaning of a word is its use in the language.”[9] Let’s look at how we use the word “knowledge” and related words such as “know” and “knowing.” Let’s look at what the concept of knowledge is used for and what role it plays in the structured social interactions that Wittgenstein calls “language games.”[10]

There are lots and lots of language games and thus lots of roles. To begin with, there are two types of knowledge, which Bertrand Russell calls “knowledge by acquaintance” and “knowledge about.”[11] (There is a third type, knowing how to do something, colloquially known as “know-how.” Since it combines aspects of them both, I discuss only the two.) The former is how we know a person or a place (or many other things). If I say “I know Alice” or “I know Pease Park,” I merely assert familiarity with the person or place. The latter is how we know a proposition or theory. If I say “I know that modus ponens is a valid form of inference,” I assert that I can explain the concept and use it correctly. If I say “I know epistemology,” I assert that I can speak with confidence about the various ideas and arguments in that field. This essay concerns only the latter, knowledge-about.

There are numerous contexts in which the words “knowledge” or “know” are used to indicate some kind of knowledge-about. If you say that you know something, you signal to others that you think they should believe you. If others think that you know something, they are likely to take your word for what you say rather than investigating further. If you think you know something, you are unlikely to seek further evidence for it. In many social arenas, if people think you have knowledge about something, you have high status, especially if what you know about is a specialized field of inquiry. In other social arenas claiming to know something might cause you to be mocked as a know-it-all. (This list is not intended to be exhaustive, just illustrative.)

Claiming knowledge about a class of people can be a way to exert social control over them, especially if your way of speaking about and defining them dominates the discussion. The field of study called Sociology of Knowledge deals with knowledge as a social production, asserting that knowledge and knowing are contextual, shaped by interaction among people. In this view, what a person believes to be true is fundamentally shaped by their social position in society—their race, class, gender, sexuality, nationality, culture, religion, etc.—and by the dominant ideologies that frame their understanding of that position.[12]

Given such disparate uses of the term “knowledge,” it seems unwise to try to find a singular essence of its referent. Instead, the various uses form what Wittgenstein calls “family resemblances.”[13] They are all similar in some ways, but different in others. You don’t know the Pythagorean theorem in the same way that you know that the sun will come up tomorrow, nor in the same way that you “know” (i.e., that you believe firmly) that certain people who are different from you are inferior and not to be trusted. But despite differences, they are all similar enough that we all know what the term means—meaning we all know how to employ it—in diverse situations. Accordingly, despite quibbles about edge cases, the definition of knowledge as justified true belief is good enough in most contexts.

In practical terms, however, the problem remains of how to justify our beliefs. If reliability of process is the add-on needed to counteract Gettier-type objections, we need to determine what counts as a reliable process.

A process is a series of actions or steps taken to achieve a goal. A reliable process is one that it is repeatable and gives consistent results. A simple cookie recipe is an example, as is the complex industrial process that converts crude oil into gasoline. In our case the goal is true belief. We want a way to make our beliefs stand firm against doubt, just as we would want a way to tie down a statue of Daedalus.

The American Pragmatist C. S. Peirce (pronounced “purse”) addresses the issue. His influential paper “The Fixation of Belief” describes four different methods to fix (i.e. to establish, not to repair) a belief. Only one of them is reliable enough to turn a belief into knowledge.

First, he defines belief. Knowledge is a form of belief, obviously, one that is true and reliably justified, so this is a good place to start. Belief, he says, is that upon which a person will act. This is Peirce’s original and influential contribution to philosophy and the foundation of Pragmatism as a philosophical movement. He says,

Our beliefs guide our desires and shape our actions. … The feeling of believing is a more or less sure indication of there being established in our nature some habit which will determine our actions. … Belief does not make us act at once, but puts us into such a condition that we shall behave in some certain way, when the occasion arises.[14]

Peirce comes to this view by observing how belief and its opposite, doubt, actually function in ourselves and in the world. He says that doubt and belief differ in three ways:[15]

  1. They feel different. The sensation of doubting is a kind of irritation. The sensation of belief is calm and satisfactory.
  2. They have different effects on our actions in the world. In a state of doubt we do not act with confidence. Doubt gives us no guidance; we do not know what to do, so we act hesitantly if at all. In a state of belief we do act with confidence. We are sure of what we believe and act on it quite readily.
  3. They have different effects on our actions toward themselves. “Doubt is an uneasy and dissatisfied state from which we struggle to free ourselves and pass into the state of belief; while the latter is a calm and satisfactory state which we do not wish to avoid, or to change to a belief in anything else.”[16]

Peirce’s method is scientific; he observes reality and learns from it. He advocates this method over three others that people use to quell doubt and settle on something to believe. The four ways to fix belief are as follows:[17]

  1. Tenacity. The tenacious person simply holds on to their belief, constantly reiterates it and refuses to entertain doubts. This method works until you encounter people who don’t believe as you do. Then you have doubt, which is exactly what you don’t want. You might just double down on your belief and refuse to listen, but eventually, because humans are social animals and can’t help but influence each other, you suspect that other ideas may have some merit. Your belief wavers.
  2. Authority. A person with excessive respect for authorities such as the state or the church or even their peer group simply believes what they are told to believe. A bumper sticker sums it up: “God said it. I believe it. That settles it.” (There is a certain amount of tenacity in this one as well.) This method works until you start to notice the atrocities committed by people with great power and consideration only for their own welfare, especially if the atrocities affect you or your loved ones. Then you start questioning authority and again need to find another way to determine what to believe.
  3. A priori method. This method consists in basing your beliefs on something that seems indubitably true. A great many philosophical systems employ this method, reasoning from a first premise to a whole system. Descartes’ famous Cogito is an example. Peirce says “Systems of this sort have not usually rested upon any observed facts…. They have been chiefly adopted because their fundamental propositions seemed ‘agreeable to reason.’ This is an apt expression; it does not mean that which agrees with experience, but that which we find ourselves inclined to believe.”[18] The issue here is that different people start with different premises without a way to choose between them, and there is no agreement on which one is proper or best.
  4. Scientific method. This method is the only one that works reliably. It assumes that a real world exists independently of what we may think about it and that by carefully examining it we can find out things about it. We come up with beliefs that are not subject to the deficiencies of the other three methods. And it is the only one that is self-correcting.

The scientific method is the only one that ensures that your beliefs will be true, that they will “coincide with the fact,” as Peirce says.[19] The others have their uses. Tenacity buys you peace of mind. Respect for authority stabilizes a community against willful disobedience. The a priori method can be quite pleasing to the intellect. But they are unreliable. Only a method that starts with and returns to careful observation of reality will do.

You don’t have to be a scientist in a laboratory to practice this method. The scientific method is just a formalized approach to everyday problem solving. Suppose your car won’t start. You hypothesize that it’s out of gas. You test your hypothesis by putting gas in it. If it starts, you know you were right (your belief is true); and if it doesn’t, you hypothesize something else. Carefully elaborate that procedure, put in stringent safeguards to isolate the variables so you are sure that you are measuring just what you want, and you have the scientific method. 

Someone might object that knowledge is supposed to be something unassailable, something final, but scientists keep changing their minds. People used to “know” that the earth is flat, but now we know that it is (approximately) round. Science used to tell us that when things burned, they released a substance called phlogiston, but now we know that burning is a process of chemical combination with oxygen. Scientists used to believe that Newtonian physics governed the whole of physical reality, but now they know (or at least believe with good evidence) that on very tiny scales quantum mechanics gives a better explanation and at very large scales the theory of relativity does. But quantum mechanics doesn’t quite jibe with relativity, so maybe we don’t really know anything.

The way out of this skepticism is to note that from an individual point of view what we call knowledge is basically the same as firm belief. One effect of knowing is that you act with confidence; you don’t hesitate. But the same is true of firmly believing. Another effect is that you think others should agree with you and perhaps you try to persuade them, but again the same is true of firmly believing. For clarity, we need to distinguish between an objective view of knowing, that we believe on good evidence something that’s true, and a subjective view, that we are firmly convinced. On the latter view it is no contradiction at all to say that people used to know that the world is flat, but now we know that it’s round.

Instead of saying we know something, we could merely say that we are convinced of it because we have good evidence. Pragmatist Richard Rorty agrees, saying that the term “knowledge” is only “a compliment paid to the beliefs we think so well justified that, for the moment, further justification is not needed.”[20] “Knowledge” and “reliably justified true belief” work equally well to denote the same thing. But of course “knowledge” is shorter and easier to say.

Regardless of what you call them, what we are really after is beliefs we can count on to help us navigate around our world and act in it successfully. The important thing is not what we call our beliefs but to know how to justify them. For that, close observation of reality is key.

###

References

AFPA (American Fitness Professionals & Associates). “Food and Nutrition Debates That You Need to Pay Attention to as a Health Professional.” Online publication https://www.afpafitness.com/blog/8-controversial-nutrition-topics#h-intermittent-fasting as of 18 September 2025.

Cole, Nicki Lisa. “Introduction to the Sociology of Knowledge.” ThoughtCo, May 7, 2025. Online publication https://www.thoughtco.com/sociology-of-knowledge-3026294 as of 22 September 2025.

Dennett, Daniel. Intuition Pumps and Other Tools for Thinking. NY: W. W. Norton and Company, 2013.

Engel, Mylan, Jr. (Internet Encyclopedia of Philosophy). “Epistemic Luck.” Online publication https://iep.utm.edu/epi-luck as of 19 September 2025.

Gettier, Edmund. “Is Justified True Belief Knowledge?” Analysis, Vol. 23, No. 6 (Jun., 1963), pp. 121-123. Online publication http://www.jstor.org/stable/3326922 as of 25 August 2009.

Koka, Maya. “Xuanzang & the Gettier Problem.” Philosophy Now, Issue 169, August/September 2025. Online publication https://philosophynow.org/issues/169/Xuanzang_and_the_Gettier_Problem as of 16 September 2025.

Littlejohn, Clayton (Internet Encyclopedia of Philosophy). “The New Evil Demon Problem.” Online publication https://iep.utm.edu/evil-new as of 23 September 2025.

Peirce, Charles Saunders. “The Fixation of Belief.” Popular Science Monthly, Vol. 12, pp. 1-15 (November 1877). In Charles S. Peirce: Collected Writings (Values in a Universe of Chance), pp. 91-112. Ed. Philip P. Wiener. New York: Dover Publications, 1958. Online publication http://www.bmeacham.com/whatswhat/OP/Peirce_FixationOfBelief.htm.

Plato. Meno. Tr. G.M.A. Grube. Online publication https://commons.princeton.edu/eng574-s23/wp-content/uploads/sites/348/2023/02/Plato-Meno.pdf as of 17 September 2025.

Rorty, Richard. “Solidarity or Objectivity?” In Relativism: Interpretation and Confrontation ed. Michael Krausz, pp. 167-183. Notre Dame: University of Notre Dame Press, 1989. Available online at https://sites.pitt.edu/~rbrandom/Courses/Antirepresentationalism%20(2020)/Texts/Rorty%20solidarity-or-objectivity.pdf as of 22 September 2025.

Russell, Bertrand. “On Denoting.” Mind, new series, 14 (October 1905), pp. 479-493. Online publication http://www.jstor.org/stable/2248381 as of 3 July 2014.

Wikipedia. “Daedalus.” Online publication https://en.wikipedia.org/wiki/Daedalus as of 17 September 2025.

Wikipedia. “Language game (philosophy).” Online publication https://en.wikipedia.org/wiki/Language_game_(philosophy) as of 22 September 2025.

Wittgenstein, Ludwig. Philosophical Investigations. Tr. G. E. M. Anscombe, P. M. S. Hacker and Joachim Schulte, fourth edition tr. Hacker and Schulte. Oxford: Blackwell Publishing Ltd., 2009.

Notes


[1] Wikipedia, “Daedalus.”

[2] Meno, 97d-98a

[3] AFPA, “Food and Nutrition Debates.”

[4] Gettier, “Is Justified True Belief Knowledge?”, p. 122.

[5] Koka, “Xuanzang & the Gettier Problem.”

[6] Engel, “Epistemic Luck.”

[7] Littlejohn, “The New Evil Demon Problem.”

[8] Dennett, Intuition Pumps, p. 183.

[9] Wittgenstein, Philosophical Investigations, remark 43.

[10] Wittgenstein, Philosophical Investigations, remark 7. See also Wikipedia, “Language game.”

[11] Russell, “On Denoting.”

[12] Cole, “Introduction to the Sociology of Knowledge.”

[13] Wittgenstein, Philosophical Investigations, remark 67.

[14] Peirce, ed. Weiner, “The Fixation of Belief,” pp. 98-99.

[15] Ibid., pp. 98-99.

[16] Ibid., p. 99.

[17] Ibid., pp. 101-108.

[18] Ibid., pp. 105-106

[19] Ibid., p. 111.

[20] Rorty, “Solidarity or Objectivity?”, p.171.

From → Philosophy

7 Comments
  1. Nice example distinguishing knowledge (justified true belief) from true belief (“true opinion” per Socrates).

    You introduced Daniel Dennett’s advice: the utility of a thought experiment is inversely proportional to the size of its departure from reality. This may be useful in handling some extreme or borderline cases (such as evil demons). Unfortunately, this advice may introduce error by causing an unwitting observer to disregard the possibility that what looks like water could be a mirage.

    You introduce the “scientific method” as the most reliable method saying “Scientific method. This method is the only one that works reliably. It assumes that a real world exists independently of what we may think about it and that by carefully examining it we can find out things about it.”

    The key word is “examining”. There are two kinds of causal science:
    * hard science or ideal science. Experiments where a treatment is applied to the subject.
    * soft science: Observational studies where things are passively observed at different times or in different circumstances at the same time.

    Thinking the earth was flat was based on soft science. “Objects fall at the same rate regardless of their weight” was based on hard science (researcher varied the weights).

    You concluded that “The way out of this skepticism is to note that from an individual point of view what we call knowledge is basically the same as firm belief.”

    Are you redefining knowledge from being absolute (what is known by some one with omniscience) to being contextual (what is justified belief by those having the broadest context in a given area of study)?

    Some may criticize the contextual definition noting that quantum mechanics and general relativity ‘overturned’ Newtonian mechanics. This claim is ambiguous. If they are claiming that none of Newtonian physics is true, then their claim is false. Newtonian physics is still valid in a given context.

    It seems that you are dealing with the problem of induction. Yet the word induction produced no match with anything you posted on your website.

    • Thanks for your insightful comments. I have a thought regarding this one:

      > Are you redefining knowledge from being absolute (what is known by someone with omniscience) to being contextual (what is justified belief by those having the broadest context in a given area of study)?

      I hadn’t thought of it that way, but it seems reasonable. We don’t know any omniscient people, and if we did we might not know what they believe. My point was to examine how people use the terms “know” and “knowledge,” not to define the essence of knowledge. Words are tools. It’s helpful to use them in sensible ways.

  2. Ralph permalink

    Nice synopsis to instigate thought, Bill. Since I do a lot of thinking about epistemology with no one with which to speak, so pardon me while I’ll make a comment here.

    Sensation is the basis of knowledge (ignoring inherited biological instincts for the moment). In addition to the primary sensory cognitive activities of cataloging experience, i.e. entering experience into memory, I understand there to be 2 more modes in the human activity of knowing, next: Identification, where organizational relations are made and object naming takes place. Lastly, the Know-how or skill or mastery level in knowledge commonly referred to as wisdom or skill in a matter or topic. This is slightly different than Russell’s 2 types or your own 3 types. I think there is overlap but to not belabor points various points of overlap, there is 1 commonality in all the models I am not too aware of being a focal point in epistemological discussions, that of knowledge being a cognitive event in human consciousness as opposed to being a collected factoid.

    This is important because it views knowing as a human activity as opposed to knowing being collected and symbolized expressions recorded in various media. It also suggests that the binary propositional approach to knowledge as being ‘justified true belief’ may be inadequate (but not wrong) for the complex ways in which objects of belief are identified. Experientially we deal with degrees of truth with which we are usually wholly incapable of providing cognitive justifications for, even though we may have (or not have) such justifications buried in our understanding. This is where self-knowledge acquired from self-reflection comes in handy. We, as ourselves are both subject and object, that is, we are the inspector and the abstracted object of our own inspections upon which we are making judgments.

    In support of most all basic information being sensory related, I’ll refer to Peirce’s cognitive pleasure and irritation occurring in the act of cognitive judgment as also being “sensory”. From the article:
    /* Peirce comes to this view by observing how belief and its opposite, doubt, actually function in ourselves and in the world. He says that doubt and belief differ in three ways:[15]

    They feel different. The sensation of doubting is a kind of irritation. The sensation of belief is calm and satisfactory.
    */
    Perhaps this is also what the medieval scholastics called “synderesis”, excluding the individual’s ability to always correctly recognize these judgment sensations within one’s mind. This sensation of the ability to judge is very important because of the societal accountability we ascribe to individuals for their actions.

    The a priori method ought not to be discarded, at a minimum because it delivers hypotheses from which to conduct experiments. However, identifying it’s limited supported for propositional truth is important. I suppose I view it as similar to the strengths of deductive and inductive arguments.

    The Scientific method also ought not to be wholly accepted because the limitations of human awareness and understanding supplying the premises may not fully cover the problem arena in question. But I think this was covered in the article. The previous comment by Milo covers some of the weaknesses uncovered with the hard and soft approaches to method. Of course, dealing with universals and abstract objects as objects of truth evaluation should prove to be an article on its own.

    • Thanks for your comments. Here are just a few responses to some of your points.

      > … knowledge being a cognitive event in human consciousness ….

      Yes, I agree except I would say “knowing” instead of “knowledge” because it has more of a connotation of activity, which is your point. Also the term “consciousness” is problematic. See my paper “How to Talk About Subjectivity (Don’t Say ‘Consciousness’)” at https://bmeacham.com/whatswhat/TalkAboutSubjectivity_v4.html.

      > The a priori method ought not to be discarded, at a minimum because it delivers hypotheses from which to conduct experiments.

      Peirce has an account of how to form hypotheses. Look up “abduction.” That method, unlike the a priori method, does start with observation of reality.

      > self-knowledge acquired from self-reflection ….

      The ability to reflect upon oneself is extremely important. I call it the distinctive human virtue in my book How To Be An Excellent Human, chapter 20. It’s available on Amazon and on my site at https://bmeacham.com/ExcellentHumanDownload.htm.

      Thanks again for your comments.

  3. Parmenides permalink

    Excellent essay, thanks. You don’t touch on mathematical knowledge, which is a very interesting and illustrative special case. Gödel demonstrated that “justified true belief” (in the sense of provability from universally accepted axioms) can never encompass all true statements!

    There is an interesting real-world example: the problem known as “P = NP”, which says that certain problems cannot be solved quickly, even though a solution, once found, can be quickly checked. For example, no known fast method exists to factor a hundred-digit integer, but if someone tells you the factors, you can multiply them to check the factorization. Now, codes based on this idea power the security of every credit-card transaction, and they control access to the nuclear-Armageddon codes, etc., etc. So people have a VERY firm belief that these “NP-hard” problems cannot be solved quickly. But nobody can “justify” this belief except by the empirical fact that nobody has yet found a way to solve them quickly. So in a way that’s the “scientific-method” justification, I guess.

    • Thanks for the reminder about mathematical knowledge. It’s clear from the rest of the Meno that Plato thought logical deduction was the paradigm case of being able to “tie down,” i.e. justify, your belief. I suppose I should have mentioned that. Good point about P-NP scenarios as well.

  4. Excellent overview on the history of epistemology and the most important philosophical arguments about knowledge and kinds of knowledge. I really appreciate your discussion of Pierce. I don’t think that there is any one thing called “the scientific method” I agree that observation is key to science, but only because it confirms and refutes theory. I don’t think that there is any reliable way to distinguish between pure induction and confirmation bias. You need theory to explain what is there and observation to correct your mistakes, which are inevitable. You have to start with conjectures about how things work, because observations don’t contain enough connections to everything else. For that you need an explanation. And almost every explanation is going to contain errors, which observations are used to correct. I think that our experience of knowing may not be closely related to scientific knowledge, since our experience is not mind-independent. Pragmatism is based on practice, which is not mind-independent. This fits our everyday beliefs, but not theoretical explanations which are designed to convey objective facts about the world.

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