Are the phrases "He can play the guitar" and "he knows how to play guitar" interchangeable?

Yes.

Usually, yes. It depends on the context.

The ones in the title, yes. The ones in the post no, beside one of them has “not” in it and hence means the opposite of the other.

Yes, those have essentially the same meaning. It took me a moment to think of any case where I couldn't substitute one for the other. One possible example is this: let's say I'm forming a band, and someone suggests a friend to me because they play guitar, but I know they're not very good. I might say "Well, he *can* play the guitar...", emphasizing the "can", with the implication that yes, he technically can play, but he can't play *well*. By the way, in both sentences, either "guitar" or "the guitar" is acceptable. I think using "the" has a slightly more formal nuance, but the difference is very slight.

Yes. And to your edit, the first sentence is a specific tree. “He can climb that tree, but not the other one.” But climbing *a* tree is general.

no, "can" can be used for both ability and permission "knows how to" is used for knowledge. Some sentences where they might not be interchangeable "Can my son join the band?" "Sure, he can play the guitar" (he is allowed to join the band as a guitarist) We can also make a distinction between theoretical and practical knowledge "A music theorist may know how to write great songs, but that doesn't mean they can do it themselves" If Tom Morello lost his hands, then he'd know how to play the guitar and be a great teacher, but he can no longer play it himself. Otherwise they're very often interchangeable.

the phrases “He can play the guitar” and “He knows how to play guitar” are almost always interchangeable. The only distinction between the two lies in their context. For example, “He can play guitar” can be used when referring to his ability to play guitar, such as when asked, “Can he play guitar tonight?” You could respond with “He can play guitar tonight” or “He can’t play tonight,” but you couldn’t respond with “He knows how to play guitar tonight” because that doesn’t answer the question of whether he is available and capable of playing guitar tonight. I hope this explanation answers your question.

For a guitar, which usually requires some training, it seems the same. For tree climbing, I think "can" usually simply implies they have at least the normal able-bodied human baseline of tree-climbing abilities. However "knows how" seems to imply some decent practice or training. But it would all be context-sentive, like if someone says "I need a skilled tree climber." if you say "I can climb trees." then you're implying you're skilled at it, because you responded to this specific request. \--- For 'cannot' it depends, because by itself your example sentences it lacks a sense of time and context and so are *vague*. If you say "Alex cannot play the guitar." then depending on context, that could describe scenarios like these: * Alex doesn't know how to play guitar. * Alex is injured/disabled and that stops them from palying the guitar. * Alex is busy at the time that you care about, so cannot play the guitar at the relevant time (but can play it at other times). e.g.: * Alex can't play the guitar, because they never learned how. * Alex can't play the guitar, because their wrist is injured, and will need at least 3 weeks to heal. * Alex can't play the guitar, because we already have Alex playing the drums. Maybe if we put Barry on drums then we can put Alex on guitar instead. all sound natural enough to me. (They are a little forced to make my point, but they seem ok.)

As others have said, usually yes. However, there are contexts where someone *knows how* to do something but can’t physically do it. I use this distinction a lot because there’s a lot of things I know how to do but because of weight gain am unable to do. To use the example from your post, I *know how* to climb trees and was very good at it as a child, but I wouldn’t say I *can* climb trees because I’ve gained weight and lost muscle mass.

In this case they are, but to your edit, knowing how to climb a tree and saying he “can” are different. Knowing how means, knowing which branches would support weight best, how to move up the tree properly, maybe even how to climb a tree trunk without branches. But “can” is about capability. You can know how to something that you don’t have the physical strength to do (maybe due to age or fitness). That applies to other things as well. Maybe I know how to do something on my work computer, but I can’t do it because my access is restricted. Edit: I also realized that contextually if you said “he can play the guitar” in a situation where the question isn’t knowledge of how to play, but more *availability* to play, then they have a different meaning. “He knows how to play guitar, but he can’t play with the band this weekend”. Here, “can” is about capability in a way, but due to availability.

"He can play the \[musical instrument\]" is kind of unique, article-wise, because the point of comparison for "specific object" is the type of instrument, rather than the individual instrument. "He can play the piano, and he can play the tuba, but he cannot play the violin." Instruments of the same type are presumed to be interchangeable, and therefore, if he can play any piano at all, he can play this piano here. You can also skip the "can" entirely: He plays piano. He plays violin. He plays oboe. This construction doesn't need an article at all. Honestly, the other one doesn't either - "He can play guitar" is fine. "He can't play the guitar" would, lacking any specific context, suggest that he doesn't know how to play guitar. However, if you give it a time frame, like, "He can't play the guitar tonight," I would assume that he's injured his hand or has other time commitments. "He doesn't play the guitar" will generally mean that he just doesn't know how, and adding a time frame just sounds weird. "He won't play the guitar" sounds like he doesn't want to, but it could be that he's unable (I am imagining some mafia guy breaking the guitarist's fingers, then telling the boss: "He won't be playing his guitar tonight"). You would only say "he can climb the tree" if, for some reason, there's doubt about his ability to climb one specific tree. For example, if you were in a redwood forest looking at a tree that's 300ft tall, someone might question whether or not a person who is generally good at climbing trees is good enough to climb to the top of this tree in particular. Normally, it would just be, "he can climb a tree," or "he knows how to climb trees." I can see why you'd ask: Trees, like instruments, come in a lot of types, and theoretically one could be able to climb specific types but not others. However, the English language just doesn't really care. You can climb a maple or an aspen or a conifer. Maybe you don't know how to climb trees at all. It doesn't have the special consideration that instruments do.

1. Yes. 2. I think I get why it feels like they're not interchangeable. For instance, you could say "He knows how to climb a tree, but he can't climb *that* tree." (That is, that particular tree- it might be smooth or have nothing to hold onto at a height he could grab. Maybe it's unable to support his weight.) By contrast, if you know how to play a guitar, you can play pretty much any guitar. (There might be different kinds of guitar, but they're not so different that you can't figure it out.) 3) In that case, there's a few ways you could put it. The emphasis you might make is that the flaw isn't in him (He knows how to play a guitar), but in the guitar itself (it's warped, the strings are all broken, it's up a tree he can't climb, or whatever). Or he's injured, and can't put his knowledge to use.

Can means being physically able to do something. "He broke both his arms but he can still play the guitar". "He knows how to play the guitar" means he has the technical skills to play the instrument.

Yeah. Most of the time. But it'll be implied if there's any difference.