Arguable ("susceptible to doubt") vs arguable ("susceptible to being supported")

Solution 1:

As always in such cases, you must rely on the context. In both of your examples the word clearly has its positive sense: a reasonable case can be made that Carl Lewis was the greatest Olympian ever, and the appellants can make a reasonable case that the minister’s decision exceeded his jurisdiction. In neither sentence would the negative sense of arguable make much sense. When the negative sense is intended, the sentence (or those immediately around it) generally make very clear that the speaker or writer has doubts.

Note that the two senses aren’t really contradictory: even something that is arguable in the positive sense is open to some doubt, or it would be certain or demonstrated, not just arguable.

Solution 2:

As others have noted, strictly speaking, arguable/arguably simply means "capable of being argued for or against (or indeed, about)". Context normally makes it clear if the speaker/writer wishes to emphasise either of the "value-laden" interpretations, and/or his own position (or no opinion).

I would add that I think if there's some proposition X which is normally held to be true, and a speaker wishes to oppose the consensus, he's likely to say "X is debatable". If X is normally held to be false, and a speaker opposes the consensus, he'll more likely say "Arguably X is true".

Say X is "God exists". If a devout speaker is addressing a heathen audience, he might say

• Arguably God exists

If the speaker is an atheist addressing a devout audience, he might say something like

• God's existence is debatable

TL;DR: Arguably normally implies support for a proposition denied by the audience/general consensus. Debatable implies disagreement with a proposition held by the audience.

Solution 3:

The two senses of 'arguable' that you have reproduced apply to the two parties on either side of the ideological fence. The meaning of 'arguable' is contextual & depends on which side of the argument you're predisposed towards. If someone presents a contentious point of view to you ("Carl Lewis is the greatest-ever Olympian", going by your example), and you agree, then arguable means convincing. Lets say your friend, who is also present when this opinion is presented, doesn't agree. To him, arguable applies in the sense of questionable/debatable.

In sum, it boils down to whether it's a case of yes, I agree, or no, I don't concur. In the former instance 'arguable' means justifitiable; in the latter case, it means questionable.

In your second example, the word 'arguable' also has a legal meaning not covered by your definitions:- cases are argued in court. Here, an arguable case is a shortened form of the formal legalese, 'a good arguable case', meaning, a case with enough scope within the legal/constitutional framework to be admitted for a hearing in court. The reporter might have verified with a legal expert that the appellants' case is arguable in the Appellate Court under the applicable/relevant laws, or gathered the story at a press conference called by a lawyer.