Can "fall out" mean "fall into place"?

Question

See the following passage.

For example, Locke thought that the claim 'Where there is no property, there is no injustice' was a proposition as certain as any demonstration in Euclid'. If you can't immediately see why, this could be a sign that the ideas that come to mind when you read the words 'property' and 'injustice' are not quite the same as Locke's. Locke himself defines property as a right to any thing' and injustice as the invasion or violation of that right'. His 'no injustice without property' line falls out pretty easily if you start with these ways of defining the key terms. — Knowledge: A Very Short Introduction

Longman Dictionary says there are three meanings of "fall out".

1. To have a quarrel
2. If a tooth or your hair falls out, it is then no longer attached to your body
3. If soldiers fall out, they stop standing in a line and move away to different places

I think that all of these meanings aren't appropriate for the attached. Given the context, Maybe It means something similar to "fall into place" rather.

What exactly does "fall out" mean in the context?

Answer 1

This usage doesn't seem to match that found in the online dictionaries. It would seem to be a figurative use. When something "falls out" (literally) it becomes loose and falls without any effort. Compare "His hair fell out" with "His hair was pulled out."

Metaphorically a mathematical problem, or proof, can be "stuck", but if you use the right algebraic trick, it becomes simple (or "loose") and then is solved without any effort. The problem metaphorically "falls out".

I can't remember seeing this use before, but from the context, this must be the intended image.