Do you have a particular area of the world in mind? Also, do you have a particular gender, race, and/or ethnicity in mind?

This response to a similar question can shed light on the experiences of a woman looking for specialized studies in early America.

Making the decision to study just philosophy and political science would make you atypical for the era, as specific courses of study were not as common as they are today. There was also a different approach to formal education in the Colonial era versus after The Civil War. But assuming we're talking before 1850 or so, It's more likely your father wanted you to become an educated man. Although it's not a perfect analogy, it's helpful to think the sentiment around formal education of the era akin to how we think of going to the gym today - the goal wasn't to get good at a particular thing, the goal was to build your thinking muscles so that you could do anything asked of a gentleman. The mark of an educated man was one who could read and write Greek and Latin and recite passages on demand. One who was familiar with Euclidean geometry, and knew the basics of natural sciences, but most importantly had social connections. If you were born on American soil, you would likely attend one of the Colonial colleges (from a related previous question.)

If you were wealthy, you were most likely white. It's possible you were the son of a land-owning white man and a Black or African enslaved woman, but if your father was encouraging you to pursue formal education or a particular trade, you could likely pass as white. (The story of Thomas Jefferson's and Sally Hemings' children provides interesting insight into what that conversation may have looked like. Annette Gordon-Reed's book, The Hemingses of Monticello: An American Family is a fascinating read.)

It's also possible your father hired a private tutor - one who had a reputation of being well-versed in philosophy and political sciences. This would most likely be the case were you unable to pass as white or had a physical disability that made attending formal education difficult. Such a tutor wouldn't be uncommon and may have supplemented your general studies. The tutor likely worked with sons in your social class and had established himself as knowing his stuff, as it were. Your wealth would give you access to a library that stayed at your home (odds are good your father had an extensive library of his own) as opposed to relying on the texts your tutor carried with him.

All of that said, it's possible your father could have sent you abroad for your studies (though less likely as again, an important trait of an education man was his social connection to other educated men and those bonds were formed at Harvard, Yale, etc.) I'll defer to those more familiar with European colleges and universities for what that experience may have been like.