How to do undergrad summer research in philosophy, when there aren't any programs? I am a first year undergraduate student studying natural sciences at highly reputed university, and am pretty sure that in the future I would like to pursue studies in philosophical theoretical physics and mathematics, and philosophy of artificial intelligence, perhaps also dabbling in philosophy of mind. I wanted to explore this during the summer, however there aren't really any philosophy summer programs for undergraduates. I would be very interested to hear any suggestions that anyone has. I have come across the Summer School for Mathematical Philosophy for female students at the University of Munich, for example. However, it is only a one week long course and I have a 3 month long summer vacation! 

I was wondering if there are any other options? Perhaps I could email a professor at another university and I could spend the summer there? The problem is, I don't really know what this could entail, so I am not quite sure what to put in an email. If I were to spend, for example, 6 weeks in a department, what could I hope to achieve? Is it common for a humanities student to write a short paper during the summer while working under a department? I would rather not spend the summer at my university -- I think it would be good for me to spend some time in a different environment as well.
There are many options, a lot of research internships are offered across the globe, you should look what universities have relationships with yours, at national or international level, an then you can apply. However, for now just prepare writing short essays and get a partner so them can be reviewed, also, read a lot of philosophy; I tell you this because most of the research internships are for high-performance students, and you don't want to under-deliver, also, most of them only accept students with more than the 50% of the total credits finished.

So plan ahead and you'll do something really interesting, I was accepted in the Globalink program in Canada, and if I have no problem with mexican bureaucracy I'll be in Montreal this summer. Keep in mind that most of this stuff must be planned a year ahead, and always look for updates of many programs so you can have a variety to choose, there are also a lot of programs for practices and professional service if you university requires either of them. Greetings and good luck!