Deduction simply applies the knowledge

Helped a friend work out a syllogism yesterday, regarding God’s absolute sovereignty or causality. The important thing to remember here is that deduction is an application of knowldge, or that is, deduction does not manufacture new information and then add it to the conclusion, which is what induction does. For this reason all induction is a non-sequitur, that is, all inductive conclusion are, “it does not logically follow.” By importing new information not from your source premises, you just ruined all validity.
Deduction simply applies the knowledge already stated to particular instances. If the bible says, all men have sinned, then to say this to the particularly man Oshea (Oshea has sinned), is simply “applying” the knowledge. It does not makeup or manufacture new information to shove into the conclusion like induction does. Thus, when the Scripture shows a doctrine that God is the ulitmaite sovereign and absolutely controls all things, then to “apply” this knowledge one would need to affirmed it on every particular instance.
G.1: All [things that happened/ens] are [ caused by God].
G.2.: All [Adam’s fall] is [a thing that happened].
G.3. Thus, [Adam’s fall] is [caused by God].
Or since this is about causality, or ontology, I personally put such into propositional arguments. Here, I would put an extra conjunction in the antecedent, and so it would technically be a Natural Deduction format, but for simplicity, we will look at it as a basic Modus Ponens.
H.1. If (P) God caused/s all things to happen, and (Q) Adam’s fall is a thing that happened, then (R) God caused Adam’s fall.
H.2. P and Q.
H.3. Thus, R