A Specific Question about Supporter Type Necessary Assumptions

[CharlesPasselius]

So, there are supporter type assumptions in which the stimulus speaker/writer makes an argument with multiple conditional statements and leaves a gap in the argument (a missing conditional premise) and the correct answer fills the gap. For example, in PT 5 S3 Q7, the Senator argues that P2/Subconclusion: "Government-funded artwork" --> /"Reflect the indepedent artistic conscience of the artist". Conclusion: "Government funding --> /creation of works of true artistic excellence." The assumption is "creation of works of true artistic excellence "--> "reflect the indepedent artistic conscience of the artist." (I'm ignoring the other premise that supports the subconclusion for simplicity.)

Or, more simply:
G --> /R
Therefore, G --> /E
Assumption: E --> R or /R --> /E (contrapositive that more readily shows the relationship)

Now, here is my question: would the assumption here be, properly speaking, BOTH a necessary AND a sufficient assumption for this particular argument? If it is both, does this apply to all supporter assumptions as a rule? I would be grateful if someone could help me clarify this issue. Thanks in advance.

[Dave Killoran]

Hey Charles,

Good question!

First, as you point out, it's good to establish that an assumption can simultaneously be both sufficient and necessary for an argument. The example you cite is a good one for that.

Second, the above does not mean that every Supporter Assumption is also a Sufficient Assumption. Certainly, they can be Sufficient, and I tend to think that happens in more simplified arguments where you have 3-4 central pieces and just a single "hole" or missing piece. There, a single statement fills the hole (the necessary supporter part) and justifies the conclusion (the sufficient part). But consider instead a more complex argument that had maybe 7-8 pieces. In an argument like that, you could have multiple gaps. And so, a Supporter Assumption there might fill one of the holes, but then not be enough to fully justify the conclusion because there's still another hole elsewhere that hasn't been filled.

That's abstract but hopefully it makes sense in context of your question!

[CharlesPasselius]

Thanks, Dave. That totally makes sense. So, to clarify, in the event that there is only one such gap, then the supporter assumption that fills the gap is both necessary and sufficient. But if there are two gaps or more, then it would be necessary but not sufficient. Is that an accurate understanding? Again, much appreciated.

[Dave Killoran]

Generally yes, but to be honest I was just trying to simplify the general scope of how it works, not provide or create a hard fast rule on what to do. The problem is you might only see one gap but there might be more that you didn't initially see, if that makes sense.

Thanks!

[CharlesPasselius]

Yes, that makes sense. I understood what you meant in an abstract sense. I was likewise asking for an abstract rule confirmation with the assumption that the one gap had been correctly identified and there were no others (hypothetically). Thanks as always. Super helpful.