Can ideas be property? Sure, but not because the state says so. Only because you can control them.
First, you can keep your ideas secret. So you have control until you disclose them.
You can disclose them contractually, and try to keep control that way. That works a fair bit of the time if you're dealing with fair minded people, which is generally a good idea.
Suppose you invent free energy. It converts sand into energy without any pollution. This has huge value! You can donate your idea humanity if you want, or you can try to keep control of your idea. If you donate the idea to humanity, terrorists also get it.
If you manufacturer your device, or work with a trusted partners to manufacture your free energy device, then you can try to keep control. You can only sell it with contractual restrictions against disclosure. Still, a bad guy would be highly motivated to steal your idea, since for very little work, he would get free energy.
You can increase the cost of stealing the idea by protecting the idea with physical restrictions such that stealing the idea for the formula involves breaking and entering and possibly destruction of physical property. That will give you an excuse to go after him. Still, say he passes it to a third party before you catch him, and the cat is out of the bag. Well, that's pretty much going to happen eventually, but ideally, by applying your entrepreneurial spirit, you're already cashing in.
If I figure out how to light the first candle ever, that has huge value, even though other candles can be lit from mine without lessening my candle. Does that mean you can light your candle from mine without permission? No, it does not - that would involve force. And I can contractually restrict you from lighting other people's candles with the fire that originated with mine. And I can even make it economically to your advantage to send them to me, by sharing some of my income from my candle lighting business. Or you can steal the light from my candle, sell it, and cash in, but in so doing you have labeled yourself a thief, so you better decide if it is worth it, since as word spreads, no one will trust you again. And if your candle burns out, and you don't understand how to restart it except by stealing the light from someone else, you're screwed.
It's really not fair to talk about ideas as property in a solely abstract way, just as it is not fair to talk about physical property in a totally abstract way. "Property is theft", say the Marxists, but that doesn't mean anything. "Ideas can be copied without harming anyone" also doesn't mean anything. It strips away authorship and credit which are hugely valuable to people, and people who appreciate that, respect it. Other's don't, but they are uncivilized.
That's my $0.02 on intellectual property. Patents are crap, but that doesn't mean there is no such thing as intellectual property.