The file you included in your question is a custom page template, and would never be used by WordPress to render the single-post view of a blog post.
If you don’t have a single.php, then the template hierarchy will fall back to index.php to render the single-post view for blog posts.
Edit
From your comment below:
I’m sorry. I need my Posts to link to an individual [page]. I do not know how to do that. I thought WP automatically linked my posts to a page called single.php. I would like to know how to do that.
Please have a read through the Template Hierarchy Codex entry, which explains everything for you. I repeat my answer above: If your Theme doesn’t have a single.php, then the template hierarchy will fall back to index.php to render the single-post view for blog posts.
Those are the only two possible template files for WordPress to use to render the single-post view of a blog post.
Regarding this comment:
I don’t know how to make my Permalinks link to a single.php page, I don’t want them linked back to the index.php page.
I don’t think you fully grasp how WordPress uses its template files. The index.php file isn’t a “page”, but rather a template, used to output a given query. Your Theme could consist of no other template file than index.php, and the site will render perfectly fine, and as intended/expected. WordPress will simply use the template to define the markup used to render the data in the given query.
If that query is the blog posts index, then WordPress will use it to render all of the posts for the blog posts index. If that query is an archive index, then WordPress will use it to render all of the posts in the specified archive. If that query is a single blog post, then WordPress will use that template to render a single blog post.
So: is there any particular reason you don’t want your Theme to fall back to the index.php template file to render single blog posts?