you can usualy survive for a few days without water , a few more without food , a few minutes without air
assuming you can avoid dying of exposure , you can simply by sitting on youre butt , survive ... till you get rescued if rescue is coming that is .. no knife required
note tho , it is limited span of survival ... too long with nothing and doing nothing , and you fail to survive
having some basic gear .. water bottle , blanket food etc , and you extend the time you can sit on your butt waiting for "them" to come get ya and save ya butt
having some gear and some know how ... and you can probly turn it from being a lost hiker or standed motorist into a delay and there was no actual incident to survive really ...
is a knife one of the tools that would help ? hell yeah
just as people often begin talking to God when things get scary , I like to have a knife ... and talk
there is a lot of comfort in having it , it opens up a lot of options for a lot of stuff from fire lighting , making shelter , food prep , defence if it gets down to it even that are just not there without it
One of the guys I learned a lot of my bush craft from used to ask " what you do here with no white fella stuff " .. and Id have to think , get creative , give an answer .. learned a lot of ways to improvise a cutting tool among other stuff
Even he carried his own knife tho