Advanced: Sub-Conclusions & Major Premises

Recall this argument.  Previously, this is how we labeled it:

Premise 1: All dogs are adorable.
Premise 2: Fluffers is a dog.
Conclusion: Therefore, Fluffers is adorable.

Let's add in two more statements to complicate matters a bit.

1. All dogs are adorable.
2. Fluffers is a dog.
3. Therefore, Fluffers is adorable.
4. All adorable things are cute.
5. Fluffers is cute.

Now, the argument continues from statement (3).  We know Fluffers is adorable.  But, now we also know that all adorable things are cute.  So, Fluffers is cute.

What’s happening is that statements (3) and (4) are supporting statement (5).  Why should I believe Fluffers is cute?  Because Fluffers is adorable and all adorable things are cute.

Statement (3) is no longer just a conclusion.  Sure, it still receives support from statements (1) and (2) but now it also gives support to statement (5).  We call a statement which receives and gives support a sub-conclusion/intermediate conclusion/major premise.  Along with statement (4), another major premise, the main conclusion/major conclusion/main point/statement (5) is supported.

That's all this is.  Fundamentally, we are still relying on the idea of support.  The only difference is how many layers down the support goes.