One's belief may be false, not so one's knowledge. — Banno
Introduction
The truth of the statement "One's belief may be false, not so one's knowledge" depends on the meaning of "knowledge". The nature of knowledge has been discussed since at least Plato, so I don't think I will be able to resolve the matter in this post.
Knowing and believing
I am trying to keep my use of the words "knowledge" and "belief" within a framework, whereby a sentient being pre-language knows internal consciousness , knows external observations and believes external possibilities. A sentient being with language knows internal consciousness, believes external observations and believes external possibilities.
One advantage of a sentient being with language only believing in external observations rather than knowing them is possibly an answer to Russell's problem of how to think about non-existent things - a problem approached by Wittgenstein in his
Tractatus regarding possible worlds.
Different theories of knowledge
Whether knowledge can be false depends on the definition of knowledge, as there are different defintions as to what knowledge is.
For example, there is internal knowledge. There is knowledge of a skill or ability, such as "I know how to play football". There is knowledge of one's own consciousness, such as "I know pain"
There is external knowledge. There is knowledge by acquaintance, such as "I know there is a tree in the garden". There is knowledge by proposition, such as "I know the Eiffel Tower is in Paris".
I cannot doubt internal knowledge, but I can doubt external knowledge.
It is possible to have different types of knowledge at the same time. For example, when looking at a post-box, I know the proposition "red light has a wavelength of between 620nm and 750nm", I know that I am looking at a post-box and I know my conscious experience of a particular colour
Wittgenstein and knowing
Wittgenstein in
On Certainty was concerned with excluding doubt in his refutation of scepticism - OC 341. "That is to say, the questions that we raise and our doubts depend on the fact that some propositions are exempt from doubt, are as it were like hinges on which those turn."
However, in order to exclue doubt, one must also exclude knowing - OC354 "Doubting and non-doubting behaviour. There is the first only if there is the second"
As Grayling wrote - i) "The well-known, and persuasive, central tenet of OC is its view that claims to knowledge only make sense where the possibility of doubt exists." - ii) "His contribution is to insist on the internal connection between the concepts of knowing and doubting. "
For this reason, Wittgenstein argued against Moore when Moore said "Here is one hand", "How absurd it would be to suggest that I did not know it, but only believed it, and that perhaps it was not the case!"
For Wittgenstein, the word "know" is only an assurance - OC21. Moore's view really comes down to this: the concept 'know' is analogous to the concepts 'believe', 'surmise', 'doubt', 'be convinced' in that the statement "I know..." can't be a mistake.
For Wittgenstein, Moore should have argued from "here is one hand" rather than "I know that here is one hand"
IE, For Wittgenstein, it is not the case that knowledge cannot be doubted, but that knowledge is only an assurance, and as such can be doubted.
Justified true belief
Since Plato, knowledge has been defined as justified true belief. If the three conditions of justification, truth and belief are met for a given claim, then we have knowledge of that claim.
However, in 1963 Gettier argued that, by giving counter-examples, whilst an individual can have a JTB, the individual may still fail to know it because the reasons for the belief, whilst justified, turn out to be false.
There are different solutions to the Gettier problem. Some look for a fourth condition, others look to replace "justification" with something else. As yet, no definitive solution has been agreed upon.
Summary
As some kinds of knowledge may be doubted, there remains an overlap between knowledge and belief, in that the statement "I know that the post-box is red" overlaps with the statement "I believe that the post-box is red"