What are ideas?

Plato is the first one known to have seriously pondered this question. He said that ideas are the ultimate reality and that what we mistakenly accept as reality is only an imperfect reflection of ideas. Plato got a little carried away, but what he said raises some good questions.

Are ideas real? Certainly not in the way a rock or an apple is real. I can’t build a device to detect an idea. Could ideas just be linguistic constructs? If so, then why do many of them have such practical applications? Do ideas exist apart from the minds that conceive them? If not, then ideas disappear whenever someone is not thinking of them, kind of like the joke about Descartes disappearing when answering a question by saying, “I think not.”

Some postmodernists have said that science and math are human constructs. Surely this can’t be right. We can’t arbitrarily construct the rules for science and math. Science is at least about things that are real. What about math? Are numbers real (including the complex ones)? Could there be a Universe where mathematics does not apply? There are some students who might be tempted to go there.

Okay, enough questions. My head is starting to hurt.