Sorry, I wasn't trying to offend. A major component of my day job is problem solving. I would never tell someone to tear it down and start over. There's almost always a solution. However, since I don't know the particulars, it's difficult to give a suggestion. What are you using for joists? How far apart are they? What are the spans in each direction you are working with? What is the purpose of the space (its intended use)?
To meet code for live load using dimensional lumber I had to use 2x10s and I had to keep spans in both directions to 12' or less. The "suggestion" I was trying to get across in my last post was that, if you used something less than that, you will need more support. Plywood in the flat is not the answer.
Not having any of the particulars, here are some suggestions:
1) Is it possible to run a beam (or beams) under the existing floor joists to increase stability prior to laying down the 1/2" ply? Here's a link to a span calculator: https://courses.cit.cornell.edu/arch264/calculators/example8.1/index.html. You can cut and paste it into your browser. It will give you an idea of where you need to be at so you have a starting reference point.
2) Another way to beef up the joist is to take aspenite (or some of your existing 1/2" if you have enough), rip it into strips (wider than your existing joists) glue it to your joists and sandwich another 2x (on edge) (and glued) along the bottom portion of the plywood. The objective here is to increase the depth of the existing joist.
3) Is it possible to sister wider 2x's to the existing joists to add depth?
4) Do you have a center beam that could be supported with jack posts or some type of pillars?
Those are some thoughts. I know you're probably looking for a less expensive and easier option and if you decide I'm nuts that's OK but make sure, prior to laying the plywood, that you use construction adhesive. That will add strength. Having said that I must again point out that, if the joist are bouncy with nothing on them, the concern is what happens as you add load? As you increase the load on the joists (that includes the weight of the 1/2" or 3/4" plywood, flooring, furniture, kids, wife, dog.... it all adds up) at some point down the road, depending on the intended use for the space, the under engineered structure will fail. That's why they have building codes. I'm not saying that to insult you. I'm not much of a diplomat but I am trying to help. My final "suggestion": Take the opportunity to beef it up now before you move on to the next phase of construction.