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The US constitution gives the reason explicitly as to "Promote the Progress of science and the useful Arts" thoughYeah, I agree. The entirety is:
To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;
That's the whole description in the constitution. At the time (1780s-1790s), other countries had patent systems, including the Empire from which the authors drew inspiration for at least other aspects of the constitution. A patent system wasn't a new idea. For that matter, the 1790 implementation of the patent system also looked very similar to the others of the time. My guess is they were thinking "hey, let's do that too".
