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What is the meaning of "we are not without ~"? e.g. Like a Goliath, the giant of evolution defies the living God day after day in the public arena. But we are not without our Davids. Our speaker is a David.

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  • It’s a double negation “not without”, the not cancels the out, leaving “N̵o̵t̵ witho̵u̵t̵”, aka “with”, aka “we have”. I believe the rhetorical device is known as litotes or meiosis or somesuch. But notice the implication of the double negative as opposed to asserting the positive is a diminuation: it’s a weaker statement of the case, or a statement of a weaker case. We have some Davids. Maybe not a lot, but we have some.
    – Dan Bron
    Commented Oct 28, 2018 at 17:12

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This is a case of litotes:

litotes
A figure of speech consisting of an understatement in which an affirmative is expressed by negating its opposite, as in:
This is no small problem.
American Heritage Dictionary

The above definition can be hard to get, but with examples it's very easy to understand.

"This is no small problem."

Means that the problem is not small. Logically speaking, when something isn't small, it doesn't mean that it's large. But in this style of speaking or writing (litotes), it actually implies the opposite. Here's an example from the Wikipedia article:

"He was not unfamiliar with the works of Dickens."

Logically if you're NOT unfamiliar with something, it doesn't mean you're necessarily knowledgeable. However this sentence means something like:

"He was quite familiar with the works of Dickens."

or if you want Wikipedia's version:

"He was acquainted with the works of Dickens."

In your example:

But we are not without our Davids.

In this particular form (litotes), means something like:

But we too have our Davids.

Sorry I can't go into more detail, as I don't have much context about this David and Goliath passage.

Here are a number of other examples, and an explanation of this style.

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