What is one piece of evidence that capitalism motivated exploration to and statement in the New World?
It would be naïve and narrow-minded for any student of history to believe that any one factor motivated the exploration and settlement of the New World by southern Europeans. The stated purpose of the first exploratory voyage by Christopher Columbus was to evangelize the sub-continent of India. The Spanish royalty had just concluded a worrisome war with the Moors--Muslims from North Africa--and were concerned that Islam would spread through India. Columbus, in his journal, notes about the King and Queen of Spain that,
"Your Highnesses, as Catholic Christians, and princes who love and promote the holy Christian faith, and are enemies of the doctrine of Mahomet, and of all idolatry and heresy, determined to send me, Christopher Columbus, to the above-mentioned countries of India, to see the said princes, people, and territories, and to learn their disposition and the proper method of converting them to our holy faith;"
Since this was the reason given, and there being no evidence to the contrary, one would indeed be a historical revisionist to say that missionary activity was not a--if not the--prime motivating factor in the discovery of the New World.
That being said, though, it is often instructive to pay attention to what people do rather than what they say. At least as far as the settlement of the New World is concerned. In an undated letter, but probably from two years after his discovery of several islands in the carribian, Christopher Columbus noted that around 2,000 potential colonists were ready to set up house on the island of Española (La Isla Española--modern day Haiti). He then made certain recommendations to their royal hignesses about what kind of laws should govern this new colony.
The first section is to allow the establishmnent of three separate towns or cities and the division of colonists to each. The third section deals with establishing civil authorities after the Spanish pattern and the fourth section deals with the establishment of a church in each town. The other ten sections deal with gold--who can look for it, what a person has to do should he find some, where he can take it, how he can transport it and to where and the penalties for not doing so properly. The final section deals with taxes, as in making it easier for people to establish new colonies in order to look for more gold.
So, while I do not doubt that Christopher Columbus and the King and Queen of Spain had other issues in mind when they went about discovering and overseeing settlement of the New World, in the first recorded communication after its discovery, a good eighty percent of the letter has to do with gold.
So, whether you want to call it capitalism or just plain greed, Christopher Columbus' Letter to the King and Queen of Spain (circa 1494) is a good document to help prove that this was the reason for the settlement of the New World, and where the 13th section states "In regard to the discovery of new countries, I think permission should be granted to all that wish to go, and more liberality used in the matter of the fifth, making the tax easier, in some fair way, in order that many may be disposed to go on voyages." I think we can include most, if not all, of the lands later discovered under this materialistic umbrella.