What does this sentence from Star Trek: The Alternative Factor mean?
Jim, madness has no purpose ... or reason ... but it may have a goal.
As far as I know purpose and goal are synonyms. How about this case?
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A goal is a concrete eventuality you're trying to accomplish, while purpose implies a broader, more abstract teleological drive. The speaker is basically saying that crazy people may be trying to do something, they just aren't doing it for a reason. Which is ridiculous, but sounds portentous when you formulate it bombastically enough.
Goal is something considered worth achieving, as an 'object': «[...] but winning is an object (= a goal) [...]».
I think that in the following sentences the word 'goal' cannot be replaced with 'purpose'.
The Third Reich was a sui generis horror: a state resting on systematic mass murder as a central goal.
Define your goals before investing.
On the other hand, in the following sentences the word 'purpose' cannot be replaced with 'goal'.
For rhetorical purposes, logic is essential.
The preferred form for ordinary purpose [...].
Conclusively, the difference is actually a shade: the goal* gives the idea of something that have been set, something specific, say the "specific purpose" of a study of a mission, etc., but purpose have a little more general connotations.
* Useful mnemonic: Goal is SMART (S: Specific; M: Measurable; A: Attainable; R: Realistic; T: reached in a finite period of Time.)
I believe the goal was to say that madness may lead to actions meant to achieve something which a person cannot understand in a sane context. No purpose or reason - as in "something understandable to a sane person" - but a goal, as in Silence of the Lambs, to become a woman by making a woman suit out of skin flayed from murder victims.
To a sane person, this is obviously not going to work, so there's no (sane) purpose; there's no provable chain of logic that demonstrates it's effective: no (sane) reason; but the serial killer is trying to do it nonetheless: a goal.