Hey van.
I'm guessing this was meant for me, but I'm not sure. My definition of ordain doesn't fit your description of my definition. That's why I'm not sure who this was directed towards. The term ordain allows for both predestine (positively cause) and positively allowing, a permissive will, as they call it, but not bare permission. Ordain encompasses God's complete sovereignty. So, predestine can be ordained, but ordained is not necessarily always predestine. You can probably find a verse that says that people were ordained to hell, but you'll never find one that says that God predestined anyone to hell. You'll find that both the terms ordained and predestined are used to describe the elect.
Using Scripture as my boundaries, this is the best sense that I can make out it. It holds true to Scripture as far as I know. There are some bad translations, and theologians, like Calvin, who used the terms outside of these boundaries, and you can see the confusion that it causes. People claiming that Calvin believed in double predestination. When in fact, theologically speaking, he did not. As Spurgeon once said, in disgust I suppose, that these discussions are usually more about the terms and there definition of those terms than anything else. It's easy to read something into what someone said without clear ideas of what the terms mean Biblically.
I know we can get technical and pose questions 'Does God do a thing because it is good or is the thing good because God does it? I really didn't want to get into all that. Again, based on the boundaries from Scripture, God never creates evil, or sin. Sometimes all the context is not made available to us, but He seems to have gone out of His way to make sure that there is no misunderstanding in this matter. All that He created was good. Even today, every child born, while born with a sinful nature, is innocent due to their ignorance, just like Adam and Eve. I don't believe that this common theme with God's creation is just a coincidence.
But there is context to consider. First, this is not a random hardening but a judicial one. Secondly, this hardening doesn't specify the details. Many times Scripture says that God did something, when in fact, He simply allowed it to happen, allowed Satan to rob, bling, harden, etc.
Also, that hardening was to provoke the Jews, but it was not a complete hardening. God can harden by simply moving away from them. Consider vs. 35-36 in that same chapter of John 12. And in Romans...
23 And they also, if they do not continue in unbelief, will be grafted in, for God is able to graft them in again.