What are the main applications of large cardinals in ordinary mathematics, and what is the philosophy behind using them. In particular:

**Question 1.** What is the philosophy behind accepting large cardinals in mathematics?

**Question 2.** Who first introduced large cardinals, in which paper and for what reasons?

**Question 3.** Do large cardinals appear in finite or discrete mathematics? Would you please give examples if there are any. 
I think the work of Harvey Friedman is related to this question.

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> By large cardinal, I mean a cardinal which is at least strongly inaccessible.
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Thanks in advance.