Let's try and separate the concepts of normative, positive, induction and deduction. First off, we need a distinction between the types of theories and the methods of proof that we use to test their validity.
Here's an analogy:
- Proof by INDUCTION and POSITIVE theories are kind of like ROAD and CAR
- Proof by DEDUCTION and NORMATIVE theories are kind of like RUNWAY and AIRCRAFT.
Roads and runways kind of look the same, they are black, hard, made of the same stuff, but they have very different designs and do very different things.
Cars and planes both get you places, but again, have very different uses. Which one is better? Well that depends on what you are doing. I can't just take a plane to Chadstone shopping center. Really a a car is only the best tool for this job.
Naturally a car matches the road, and runways are used by planes. But they can swap if they have to. Cars drive on runways all the time. There are MANY cases of planes landing on highways in emergency because it's better than crashing.
This what I mean by theories and their methods of proof crossing over. You simply use whatever theory is best able to do the job.
For illustration, have a look at this image below. Cars, roads, planes, and runways all in one image. It's one of the few places where the country's main highway also crosses their international airport. You'd make sure you don't mix up the differences between road and runways here otherwise there could be a very messy outcome. So too it is with your theories. Mixing your meaning often means your ideas will crash.
And this is 100% real. No Photoshop.
The point is, don't confuse the two. If I want to fly to Gibraltar, I wouldn't say "I'm going to take the runway to Gibraltar". Likewise, I wouldn't say my idea is deductive. Instead you would say "I have a normative idea and I will show you how it works using deductive methods".
I hope this makes the idea clearer for all!