Ah, the dreaded comma splice. That's what happens when you have two independent clauses, no coordinating conjunction, and a comma—the weakling of punctuation marks—trying to separate them.
The Chicago Manual of Style notes:
Some readers will be distracted by it; some will consider it
incorrect; a few will take it as one more sign that civilization is
coming to an end. However, as Bryan Garner writes in Garner's Modern
American Usage: "Most usage authorities accept comma splices when (1)
the clauses are short and closely related, (2) there is no danger of a
miscue, and (3) the context is informal."
Professor Tina Blue elaborates:
If the independent clauses are very short, especially if the subject
is the same for both clauses, then a comma splice is probably
acceptable. . . . When fairly short independent clauses express
contrast, a comma splice is often the most effective way to punctuate
the sentence. This is especially true if the first clause makes a
negative statement, the second an affirmative one, or if the first
clause is affirmative, and the second is negative (as in one form of
question).
.
Your clauses certainly qualify as short, closely related, informal, same-subject, and contrasty:
Shoot first, ask questions later.
And Julius Caesar's been getting away with this since forever:
I came, I saw, I conquered.
But if you're worried that your usage authority will take this as a sign that civilization is coming to an end, you have many other options:
Shoot first—ask questions later.
Shoot first (ask questions later).
Shoot first; ask questions later.
Shoot first, and ask questions later.
Shoot first. Ask questions later.
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Further reading:
Comma Splices and Run-On Sentences
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