Knowledge vs. belief

by Neil Rickert

[I seem to have taken a long vacation from blogging.  It’s time to get back into the swing.]

I’ve posted before about my dislike for the view that knowledge is justified true belief.  I have recently seen a couple of blog posts that are related, so I’ll comment about those.

Infinite worlds

The first is:

The author begins with:

In an infinite universe we would be absolutely ignorant, if my calculation is right.

The author does not give an argument to support that assertion.  He seems to take it as self-evident.  And I guess I’m not quite sure what he means by “absolute” here, as that qualifier does not seem to fit.  I presume him to be going by the assumption that knowledge is justified true belief.  And, with that assumption, presumably knowledge of an infinite world would require infinitely many beliefs.

My response is mathematics.  The world of  mathematics is an infinite world.  If the author’s assertion is correct, then mathematical knowledge would seem to be impossible.  Yet many knowledgeable mathematicians would disagree.

Education

My second example is a blog post on the conservative view of education:

In that post, the author writes:

If the central goal of education is the transmission of information, then the success of that education can be measured by a simple paper-n-pencil test. This is an idea that resonates with lots of people.

I don’t agree with that as the central goal, nor does the author of that post.  But “transmission of information” does fit with “justified true belief.”  As I commented on that blog post, if that were a correct account of education, then you would not need schools.  Books, or radio or television or the Internet would be sufficient.  Yet the evidence is that those are poor substitutes for what schools actually do.

Mathematical knowledge

Back to mathematics.

I have often heard mathematicians complain about students who “regurgitate” the lectures or the text book.  Yet, if knowledge is justified true belief, then regurgitation should be a clear demonstration of knowledge.  So there seems to be a widespread rejection of the idea of justified true belief among mathematicians, at least with respect to knowledge of mathematics.

The problem with justified true belief is that, while there is believing, the “knowing” could still be missing.  And it is that knowing that should matter for knowledge.

I don’t have any objection to philosophers studying justified true belief.  It’s just that I think something is missing in that account of knowledge.  And philosophy ought to be studying what it is that is missing.

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22 Responses to “Knowledge vs. belief”

  1. The problem is the confusion of ‘knowledge’ with ‘understanding,’ a problem long embedded in the debate s over ‘justified true belief,’ perhaps all the way back to Plato. There is a big difference between ‘knowing’ that squares are not circles, and ‘understanding’ why they never could be. In a different, yet related way, there’s a difference between ‘knowing’ that ‘Columbus discovered the Americas,’ and understanding that he did so only from the perspective of Europeans, and the implications of this.

    Yet for knowledge to be complete, it needs understanding. Information alone has no value without an explanatory framework given it value.

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  2. I was just dabbling with projective geometry, in the same way parallel lines intersect at the point of infinity and was trying to make a point to those that think we know a lot. But you are correct in that it can’t be proved and I’m assuming the universe is infinite (Big assumption). Put better would probably be “our the knowledge about what is around us can be considered infinitesimal in a universe with enormous scale and potential knowledge”

    I found the rest of the blog about knowledge very interesting. I would like to pose a question. If everyone agrees on something do that make it true?

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    • If everyone agrees on something do that make it true?

      I guess it would depend on what that “something” is. If you are asking question “Does everybody agree with P?” then the consensus might have some relevance to its truth.

      You connected that question with my posts on knowledge. So I’ll ask a different question: what does truth have to do with knowledge?

      Hmm, maybe I should make that the title of a future post.

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      • I guess it applies to most if not all things. To stay within the subject, If everyone agrees there is no difference between truth and knowledge, does that mean there is no difference. What if the dictionary shows a difference and everyone uses them the same and interchangeably, will people have to start using them correctly or will the dictionary change its meaning in the updated version, to make them the same.

        Just to make it a little more interesting, I’ve added another word and made 6 sentences. Is there any difference in the sentences below other than how people interpret them.

        the Knowledge of truth about reality,
        the Reality of truth about knowledge,
        the Truth of knowledge about reality,
        the Knowledge of reality about truth,
        the Reality of knowledge about truth,
        the Truth of reality about knowledge,

        I have a blog that talks about the limitation of language, which is relevant, linked below. Feel free to check it out.

        http://swarmverdict.com/2015/01/03/constraints-of-language/

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        • Just to make it a little more interesting, I’ve added another word and made 6 sentences. Is there any difference in the sentences below other than how people interpret them.

          Obviously, they are different permutations and combinations of the characters involved.

          If everyone agrees there is no difference between truth and knowledge, does that mean there is no difference.

          But everyone doesn’t agree. If everyone agreed, then you would not be asking this question.

          As asked, it is also ambiguous. If you had used “truth” and “knowledge” (i.e. quoted) you could be asking about the meanings of those words. But, without the quotes you seem to be asking about concepts, which already implies that you see them as different concepts.

          If asking only about meanings, then I go by Wittgenstein’s “meaning is use”. If everyone uses those words in equivalent ways, then they have the same meaning. But then there is not a truth issue, only a usage issue.

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  3. Neil,

    “My response is mathematics. The world of mathematics is an infinite world. If the author’s assertion is correct, then mathematical knowledge would seem to be impossible. Yet many knowledgeable mathematicians would disagree.”

    I would argue that mathematics doesn’t contain an infinite number of concepts, even though there may be an infinite number of examples of a particular concept. This may be a quibble over definitions here, so that’s all I’ll say about that.

    In any case, overall, I prefer the definition that knowledge is simply a set of recognized patterns in nature, that is, remembered instances of conditions that lead to some consequential result. Which is why I see human beings’ ability to possess knowledge, as basically our ability to recognize patterns with our sensual perception. When we are able to recall those patterns and use them to reach particular goals, we are effectively putting that knowledge to use. I would say that one could still apply this to the limited definition of justified true belief, by specifying that beliefs are ultimately patterns that we think exist, and they are justified beliefs more or less if we have empirical evidence to support them. In that sense, knowledge can be defined as justified true belief, but ultimately this comes down to recognized patterns, and how justified we are in believing that those patterns exist. If we can use those patterns to reach goals effectively and repeatedly, then every time they do so, gives us another inductive data point of justification for our reasoning. That’s my two cents on the issue…

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    • I would argue that mathematics doesn’t contain an infinite number of concepts, even though there may be an infinite number of examples of a particular concept.

      The place to look for concepts is in the mathematician, not in the mathematics.

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      • “The place to look for concepts is in the mathematician, not in the mathematics.”

        What I mean here is, for example, when we talk about addition, a mathematical concept, there may be an infinite number of examples of addition, each unique from the others, but that doesn’t mean that we need an infinite number of beliefs to implement or describe addition. We only need to know a finite number of rules and then we can apply it in an infinite number of ways (similar to the infinite productivity of language, despite only knowing some finite number of words and rules). That’s my main point here, regardless of the specific ontology of where those concepts lie (in math or the user of math).

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        • We only need to know a finite number of rules and then we can apply it in an infinite number of ways (similar to the infinite productivity of language, despite only knowing some finite number of words and rules).

          I’d say that’s consistent with my criticism of “justified true belief”. Our knowledge in this case is not the beliefs, but the procedures that we can use as needed in particular instances.

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          • Neil,

            “I’d say that’s consistent with my criticism of “justified true belief”. Our knowledge in this case is not the beliefs, but the procedures that we can use as needed in particular instances.”

            If we believe certain procedures to be effective in accomplishing our goals, and that’s why we use them (because we believe them to be effective at doing so), then we are in fact implementing our knowledge through beliefs that we have about those useful procedures. Without believing that they exist or that they are effective, unless they are unconsciously driving our behavior, they simply aren’t going to drive our behavior at all, and thus we can’t consciously use those procedures without believing that they exist in the first place. So I find it perfectly clear and coherent to simply define beliefs as the patterns of perception that we recognize and recall. If those patterns have a correlation with reality and can be used to accomplish particular goals, then not only are they useful, but they are also more likely to be true, and thus we are more justified in believing them as a result.

            To restate this, if we equate our beliefs with “causal patterns that we’ve recognized (even if erroneously) and stored into memory”, than the procedures used as needed in any particular instance to accomplish some goal will involve the recall and contextual implementation of those remembered causal patterns, that is, they will involve the recall and implementation of those remembered beliefs. One can quibble over how we define beliefs, but I think my basic definition “causal patterns that we’ve recognized (even if erroneously) and stored into memory” is reasonable and coherent and applies fairly well to our everyday usage of the term. We then determine the justification for those beliefs depending on the level of empirical evidence we have to support them. If they are unfalsifiable beliefs, then in my opinion, we’d have no justification whatsoever in believing them to be true (since no empirical evidence is available) and thus would fail to count as knowledge. If they have any empirical support for them, then one can quantify the justification for believing them just as we would with any claim made in science, with varying degrees of certainty. Over time, if our level of empirical support increases, we can be more confident that the patterns our brain has recognized do in fact correlate with reality, and thus that those beliefs are true.

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          • Without believing that they exist or that they are effective, unless they are unconsciously driving our behavior, they simply aren’t going to drive our behavior at all, and thus we can’t consciously use those procedures without believing that they exist in the first place.

            People use effective procedures that they have never expressed in a propositional form, and that they would not even know how to express in a propositional form. So, no, we do not need beliefs in order to have effective procedures.

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          • Neil,

            “People use effective procedures that they have never expressed in a propositional form, and that they would not even know how to express in a propositional form. So, no, we do not need beliefs in order to have effective procedures.”

            I never said that people need to express procedures in a propositional form per se prior to using them, but in any case, if they are following any kind of procedure, or set of steps to accomplish something, then they are really just recalling “causal patterns that they’ve previously recognized (even if erroneously) and stored into memory”, and thus they are just recalling and using beliefs. So, yes, people do need beliefs about procedures in order to consciously execute those procedures. They may do it unconsciously (and repeatedly effectively), but then those beliefs would have to be defined as constituting some form of implicit/unconscious knowledge.

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          • I never said that people need to express procedures in a propositional form per se prior to using them, but in any case, if they are following any kind of procedure, or set of steps to accomplish something, then they are really just recalling “causal patterns that they’ve previously recognized (even if erroneously) and stored into memory”, and thus they are just recalling and using beliefs.

            The odometer of my car increments every mile. So what pattern is it recalling? When did it previously recognize that pattern? What beliefs is it recalling and using?

            I agree my car is not a person. But if a car can follow a procedure without recalling/ recognizing/ believing, then why cannot we?

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          • “The odometer of my car increments every mile. So what pattern is it recalling? When did it previously recognize that pattern? What beliefs is it recalling and using?

            I agree my car is not a person. But if a car can follow a procedure without recalling/ recognizing/ believing, then why cannot we?”

            I never argued that a car odometer possesses any knowledge, so this is irrelevant. Furthermore, the car odometer isn’t following any procedure but rather is fixed mechanically (if an older odometer) to the transmission and merely a gear set. Thus, this is a poor analogy. Just because a car has some attribute or characteristic, doesn’t mean that we do too. We have brains with pattern recognition modules, where a car and odometer do not. We have knowledge, but the car and odometer do not. Perhaps I missed your point here…?

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          • Furthermore, the car odometer isn’t following any procedure but rather is fixed mechanically (if an older odometer) to the transmission and merely a gear set.

            That it is “fixed mechanically” does not make it not a procedure.

            It seems to me that we do sometimes have behavior that is “fixed mechanically”. We sometimes call those “habits”.

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          • Neil,

            “That it is “fixed mechanically” does not make it not a procedure. It seems to me that we do sometimes have behavior that is “fixed mechanically”. We sometimes call those “habits”.”

            Yes, however the odometer is mechanically linked to the transmission and thus it isn’t following any kind of procedure. It is only able to accomplish one directly mechanically linked function, and that is not the same as following a procedure. I think we can define a procedure as a series of actions conducted in a certain order or manner, or some plan of action to accomplish a particular goal. I don’t think most people would say that an odometer has a goal, nor follows a series of steps in order to accomplish something. You are getting off track here Neil. I suggest we stay on topic with regard to knowledge in conscious brains, and not steer off course thinking about non-conscious, brainless odometers…which though both are made of matter and have some overlapping characteristics (only a few), they do not pertain to this discussion — neither about knowledge nor about pattern recognition.

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          • Yes, however the odometer is mechanically linked to the transmission and thus it isn’t following any kind of procedure.

            You were wrong in your first response. Now you are splitting hairs with a bogus “No True Scotsman” (or “no true procedure”) argument.

            I’ve kept my responses to you as short as possible, so that you could easily choose to drop the whole off-topic line that you started. And now you accuse me of being off-topic?

            Just let it drop.

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          • “You were wrong in your first response. Now you are splitting hairs with a bogus “No True Scotsman” (or “no true procedure”) argument.”

            In what way was I wrong? Specify and quote me please.

            “I’ve kept my responses to you as short as possible, so that you could easily choose to drop the whole off-topic line that you started. And now you accuse me of being off-topic? Just let it drop.”

            What off-topic line did I start? I was talking about knowledge and you went off on a tangent about automobile odometers…Did I miss something here?

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          • Also, exactly when did I employ a “No True Scotsman” argument? Quote me please so we can see if what I said even qualifies…

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          • I’ll add that most people tend to think of beliefs as something that they are able to put into a propositional form, but my definition of belief given earlier expands on this erroneously assumed limitation, and encompasses both those that people can put into a propositional form, and those that can’t be put into such a form, especially given the limitations of language.

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