Ghost installation won't update - "Unexpected identifier" error

I am trying to update my Ghost installation through the console. I’ve signed in, changed directory to var/www/ghost, and updated the Ghost CLI to the most recent version (1.31.1 as of this writing). But then when I type ghost update I get this:

/usr/lib/node_modules/ghost-cli/lib/command.js:108
    static async _run(commandName, argv = {}, extensions) {
                 ^^^^

SyntaxError: Unexpected identifier
    at createScript (vm.js:56:10)
    at Object.runInThisContext (vm.js:97:10)
    at Module._compile (module.js:549:28)
    at Object.Module._extensions..js (module.js:586:10)
    at Module.load (module.js:494:32)
    at tryModuleLoad (module.js:453:12)
    at Function.Module._load (module.js:445:3)
    at Module.require (module.js:504:17)
    at require (internal/module.js:20:19)
    at Object.<anonymous> (/usr/lib/node_modules/ghost-cli/lib/bootstrap.js:6:17)

I get the same result if I also switch to the Ghost manager first.

Any help would be much appreciated.