What does the following phrase mean?
I can't go on, I'll go on.
It is not an idiom but a quotation from the end of the Samuel Beckett novel The Unnamable. It suggests a determination to overcome impossibility.
The meaning I take is "I cannot but I must". It describes an internal conflict or dilemma where the only possible course of action is one which is extremely objectionable or difficult. There may be a conflict of morals/ethics and duty, fatalism towards the outcome of an important action, or some other conflict.
I've never heard of this particular phrase as an idiom, however. I would think of "rock and a hard place", "between Scylla and Charybdis" or "irresistible force meeting an immovable object" or as more idiomatic.
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