Like "say," the word "speak" refers to thoughts and feelings moving from our more internal spiritual levels to our more external ones -- and ultimately from the Lord, who is in a sense the most internal spiritual level of all. This is generally called "influx" and "perception" in the Writings, meaning they are thoughts and feelings that flow in in a complete way from the Lord, rather than being things we have to think about and figure out. On a number of occasions "speak" and "say" are used together; in these cases "speak" refers more to intellectual instruction in matters of thought and "say" refers more to feelings and affections that flow in directly.

6520. 'As he made you swear on oath' means because he had it at heart. This is clear from the meaning of 'making to swear on oath' as having at heart, dealt with above in 6514.