Justified degree of confidence doesn't align neatly with the presence or absence of knowledge, at least if we assume that it's true that I know where my car is parked (with 99.9% confidence) but false that I know that my lottery ticket will lose (despite 99.9999% confidence it will lose). (For puzzles about such cases, see Hawthorne 2004 and subsequent discussion.) My question for this post is, how far can this go? In particular, can I know something about which I'm less than 50% confident?
"I know that my car is parked in Lot 30; I'm 99.9% confident it's there." -- although that might sound a little jarring to some ears (if I'm only 99.9% confident, maybe I don't really know?), it sounds fine to me, perhaps partly because I've soaked so long in fallibilist epistemology. "I know that my car is parked in Lot 30; I'm 80% confident it's there." -- this sounds a bit odder, though perhaps not intolerably peculiar. Maybe "I'm pretty sure" would be better than "I know"? But "I know that my car is parked in Lot 30; I'm 40% confident it's there." -- that just sounds like a bizarre mistake.
On the other hand, Blake Myers-Schulz and I have argued that we can know things that we don't believe (or about which we are in an indeterminate state between believing and failing to believe). Maybe some of our cases constitute knowledge of some proposition simultaneously with < 50% confidence in that proposition?
I see at least three types of cases that might fit: self-deception cases, temporary doubt cases, and mistaken dogma cases.
Self-deception. Gernot knows that 250 pounds is an unhealthy weight for him. He's unhappy about his weight; he starts half-hearted programs to lose weight; he is disposed to agree when the doctor tells him that he's too heavy. He has seen and regretted the effects of excessive weight on his health. Nonetheless he is disposed, in most circumstances, to say to himself that he's approximately on the fence about whether 250 pounds is too heavy, that he's 60% confident that 250 is a healthy weight for him and 40% confident he's too heavy.
Temporary doubt. Kate studied hard for her test. She knows that Queen Elizabeth died in 1603, and that's what she writes on her exam. But in the moment of writing, due to anxiety, she feels like she's only guessing, and she thinks it's probably false that Elizabeth died in 1603. 1603 is just her best guess -- a guess about which she feels only 40% confident (more confident than about any other year).
Mistaken dogma. Kaipeng knows (as do we all) that death is bad. But he has read some Stoic works arguing that death is not bad. He feels somewhat convinced by the Stoic arguments. He'd (right now, if asked) sincerely say that he has only a 40% credence that death is bad; and yet he'd (right now, if transported) tremble on the battlefield, regret a friend's death, etc. Alternatively: Karen was raised a religious geocentrist. She takes an astronomy class in college and learns that the Earth goes around the sun, answering correctly (and in detail) when tested about the material. She now knows that the Earth goes around the sun, though she feels only 40% confident that it does and retains 60% confidence in her religious geocentrism.
The examples -- mostly adapted from Schwitzgebel 2010, Myers-Schulz and Schwitzgebel 2013, and Murray, Sytsma, and Livengood 2013 -- require fleshing out and perhaps also a bit of theory to be convincing. I offer a variety because I suspect different examples will resonate with different readers. I aim only for an existence claim: As long as there is a way of fleshing out one of these examples so that the subject knows a proposition toward which she has only 40% confidence, I'll consider it success.
As I just said, it might help to have a bit of theory here. So consider this model of knowledge and confidence:
You know some proposition P if you have it -- metaphorically! -- stored in your memory and available for retrieval in such a way that we can rightly hold you responsible for acting or not acting on account of it (and P is true, justified, etc.).
You're confident about some proposition P just in case you'd wager on it, and endorse it, and have a certain feeling of confidence in doing so. (If the wagering, expressing, and feeling come apart, it's a non-canonical, in-between case.)
There will be cases where a known proposition -- because it is unpleasant, or momentarily doubted, or in conflict with something else one wants to endorse -- does not effectively guide how you would wager or govern how you feel. But we can accuse you. We can say, "You know that! Come on!"
So why won't you say "I know that P but I'm only 40% confident in P"? Because such utterances, as explicit endorsements, reflect one's feelings of confidence -- exactly what comes apart from knowledge in these types of cases.