Recently, I came across what is probably the first patent, issued to Fillipo Brunellesci, in 1421, in Florence, Italy. The preamble clearly states the purpose of the patent:
"Considering that the admirable Filippo Brunellesci, a man of the most perspicacious intellect, industry and invention, a citizen of Florence, has invented some machine or kind of ship, by means of which he thinks he can easily, at any time, bring in any merchandise and load on the river Arno and on any other river or water,for less money than usual, and with several other benefits to merchants and others; and that he refuses to make such machine available to the public; in order that the fruit of his genius and skill may not be reaped by another without his will and consent; and that, if he enjoyed some perogative concerning this, he would open up what he is hiding, and would disclose it to all; and desiring that this matter, so withheld and hidden without fruit, shall be brought to the light, to be profit to both to said Filippo and to our whole country and others; and that some privilege be created for said Filippo, as hereafter described, so that he may be animated more fervently to even higher pursuits, and stimulated to more subtle investigations..." (emphasis added)
Ideas are private things - as long as you keep them to yourself. Once divulged, they do indeed enter the public arena, the "domain" of the public. Of course, anyone can choose to keep their ideas private - through trade secrets, or through private, by invitation only displays or performances of works of art.
Patents and copyrights seek to induce artists and inventors to share their works with the public; in exchange, the government secures their interests for a limited time.
Yet the Founders viewed philosophy through a private property and inseperable individual rights lens, and their legalisms are best interpreted from that aspect, rather than considerations of the "public domain". In so doing one is likely to achieve deeper understandings of the law, and how the Framers came to it.