Is it a copyright infringment if I my blog title has the same two words as someone else's blog tilte? Even if you had no Idea?

No. Titles aren't protected by copyright.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.

While copyright may not be an issue, you may want to be concerned with trademark rights that the blog owner may have in the title. With many blogs, the title is the brand name for the service/product of the blog and trademark rights can and do flow from it. So it is conceivable that the other blog owner may assert his/her trademark rights against you.

If your blog is a source of revenue, you may want to consult and IP/business attorney.

hope this helps.

Disclaimer: This answer is for informational purposes only and does not constitute general or specific legal advice, nor create an attorney client relationship.