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The statement "Lions live in Africa" is true. Therefore, believing it qualifies as knowledge, but not believing it is does not.

The statement "Lions live in Norway" is false. Therefore, neither believing it nor disbelieving it qualify as knowledge.

However, if you do not believe that statement, then you're effectively saying that lions do NOT live in Norway, which is true. Therefore, not believing this false statement implies that you know lions don't live in Norway. Wouldn't this option therefore qualify as knowledge?

Similarly, consider the statement "Lions do not live in Africa."

It's another false statement. So wouldn't NOT BELIEVING it qualify as knowledge?

EDIT

On top of the answers given, I discovered another problem: Accepting negated beliefs as indicative of the opposite is simply a sloppy process that opens the doors to a variety of problems. If you don't believe polar bears do not live in Greenland, then we might surmise that you believe they DO live in Greenland (a true statement).

But consider this statement:

Pam dyed her hair purple in the morning.

If you don't believe that statement, then what DO you believe - that she dyed her hair orange? She dyed in the evening, or she didn't dye it at all?

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    Not believing a statement does not amount to believing its negation, even "effectively", as debates between atheists and agnostics illustrate. Not believing that lions live in Norway and believing that they do not live there are two different things, ~B(p) vs B(~p). If one accepts Plato's formula of knowledge as justified true belief lack of belief either way entails lack of knowledge on the matter. – Conifold Dec 14 '19 at 6:47
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    Lions do live in Norway. Just not in the wild. – Sean Dec 14 '19 at 23:36
  • Yes, I should have qualified my statement: WILD lions do not live in Norway. – David Blomstrom Dec 14 '19 at 23:39
  • @DavidBlomstrom On the contrary, wild lions could live in Norway - you do not know whether the lions were bred in captivity or not. :) – brightlySalty Jan 22 at 21:21
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I might know that the sun is more than 100,000 miles from the earth, and the statement 'The sun is more than 100,000 miles from the earth' is true. It is not itself knowledge, however. Knowledge is a state of the knower; a statement is not a state of anything.

I am not foreclosing on the nature of a knower; a knower might be a person, an individual mind, an 'extended' mind, an AI machine and other things besides. Also I am flexible about the kind of state that knowledge is. It could be e.g. dispositional or occurrent.

In the first case, if you believe the (true) statement, 'Lions live in Africa', then you have merely a true belief: more needs to be added to a true belief for it to qualify as knowledge. There has to be a justificatory or evidential ground for the belief (internalism) or a certain causal explanation for your having the belief (externalism). Mere true belief does not suffice for knowledge.

In the second case, 'Lions live in Norway' may be false (but what of lions in zoos?), yet if you neither believe or disbelieve it either - to take the most obvious possibilities - you are ignorant of the statement or though aware of it you are ignorant whether it is true or not. In neither case do you have knowledge about lions in Norway. Mere lack of false belief does not suffice for knowledge.

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  • What you're saying is that a true belief could just be a good guess, right? Each time you buy a lottery ticket you might believe that it will win something; occasionally you'll be right, but you never actually "know" until after the drawing. – Barmar Dec 14 '19 at 21:06
  • Yes, that's a fair way of puttng. Thanks for reading answer and seeking clarification. Appreciated: GLT. – Geoffrey Thomas Dec 14 '19 at 21:08
  • And can't false beliefs also be considered knowledge? The Sun going around the Earth was "common knowledge" in the ancient world. – Barmar Dec 14 '19 at 21:17
  • Ref: Bertrand Russell's definition of "belief": "That for which there is no evidence". But "the sun goes around the earth" is a bad example, because even with Galilean relativity (ignoring Einstein) it is just as true as the statement that the earth goes around the sun. And before radio navigation and GPS, every ship and aircraft navigator did their work starting from the assertion that the sun did go round the earth. – alephzero Dec 14 '19 at 23:35
  • @alephzero I'd say those navigators did their work starting from the assertion that the sunlight comes from a direction going around the Earth. As soon as you introduce the sun as an actual physical object, the view that it goes around the Earth becomes very hard to defend. Relativity does not allow this, because the sun wouldn't be in an inertial system then. The Earth meanwhile does go around the sun in a very tangible sense, namely that the barycenter around which both orbit in their inertial systems lies within the sun. – leftaroundabout Dec 15 '19 at 1:31
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PLACEBO EFFECT: "improvement in the condition of a patient that occurs in response to treatment but cannot be considered due to the specific treatment used" (Webster).

The statement is clearly false because it is self-contradictory. - occurs in response to a treatment - but cannot be considered due to the specific treatment used

Is Webster's definition of cancer "knowledge"? Yes. Even though it is clearly false.

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