Is it ever correct to omit periods at the ends of paragraphs?

I encountered this claim from a user on cooking who seems to consistently remove periods at the ends of paragraphs:

Never use them. They have no place on electronic media, they are a legacy device?

And later:

End of paragraph periods were for bad typing/handwriting spacing. Computers format very cleanly, so no purpose, and they look weird on sentences that end in URL's or emoticons etc

Is there any broad or authoritative or "real" support for that idea?

Solution 1:

I don't think any authority supports it.

The idea has been discussed before; here's a Language Log post that talks about the issue: Aggressive periods and the popularity of linguistics. It links to this New Republic article: The Period Is Pissed, by Ben Crair, from which I took the following extracts:

In my text messages and online chats [...] people use the period not simply to conclude a sentence, but to announce “I am not happy about the sentence I just concluded.”

Near the end:

And these newfangled, emotional uses of terminal punctuation haven't crossed over into more traditional, thoughtful writing.

I think Stack Exchange posts are more like online newspaper articles or blog posts, and not so much like text or chat messages.

(Another Language Log article with some comments and links: Anticipatory confirmation)

(The practice of omitting a period specifically in paragraph-final position has also been discussed on the WordReference forums.)

Solution 2:

I don't think it is ever correct to omit a period (or full stop) at the end of a normal English sentence or indeed a paragraph. But that is not to say that I don't see it "in the wild", and indeed, am guilty of omitting correct punctuation in a few cases where the sense is clear even without it. I would omit a period at the end of a "sentence" that uses non-English words such as a fragment of code or a mathematical formula where any extraneous characters could lead to confusion or syntax problems. Example:

To fix the problem, use the switch /persistent:yes

Another example, in a presentation (ie projected on screen, PowerPoint, prezi, Keynote or whatever), I might use a series of bullet points without a closing period on any of them, not even the last. (I know! Heresy! Burn me as a witch!) The next bullet usually makes the sense clear enough. The fragmented nature of the bullets often means they don't properly parse as a sentence anyway. In a formal text such as software documentation or training manual I would more usually ensure grammatical completeness.

To demonstrate as a meta-example, there are four reasons for this:

• it is just as comprehensible
• the next bullet arguably serves the same purpose as a separator
• I find it easier to be consistent in omitting them than including them
• everyone else seems to get away with it

Solution 3:

The period signifies the end of a thought. The lack of a period at the end of a paragraph would tell me the thought, as a unit, is not complete.

The only acceptable omission of puncuation I've ever seen is the final quotation mark if the next paragraph is a continuation of the character's dialog.