If you have a UNIQUE constraint on post_tags(post_ID,tag_ID), and you can verify that the elements of thisTags are unique, then you could do something like this:
SELECT post_ID FROM post_tags
WHERE tag_ID IN ($thisTags[0], $thisTags[1], $thisTags[2], $thisTags[3])
GROUP BY post_ID
HAVING COUNT(1) = 4
This approach REQUIRES that the elements in $thisTags
are unique. You can easily work around the uniqueness issue in the post_tags table (but the query above requires that to be unique as well.)
There are other SQL statements, other approaches, that can achieve an equivalent result, but the query above is the most concise. (Some of the other approaches are to use EXISTS predicates, or to use JOIN operations on the sets of post_ID returned for each tag.)