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For similar reasons fragile natural states cannot support many, if any, private elite organizations.

As the two world wars and the Cold War of the twentieth century illustrate, external violence is a central if episodic aspect of the international environment.

What does if mean in this context?

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    If there means though, albeit, but. That's to say the writer thinks it's important to point out that the violence is only episodic, because otherwise his audience might assume that anything described as central would normally be ever-present, continuous. – FumbleFingers Nov 15 '15 at 16:20
  • @FumbleFingers, that's good for the second sentence, but the first is a different matter. The first sentence is quite baffling to me, but its usage of if is clear enough: the number of private elite organizations that such states can support is small and may well be zero. I can think of no possible substitute for if in that context, though. – Brian Donovan Nov 15 '15 at 16:26
  • @The meaning of "if any" is: "if there are any at all", or "(and there might not be any)". – Drew Nov 15 '15 at 16:34
  • @Brian: I obviously paid too much attention to this in the title, without even registering the fact that it was followed by plural sentences. Since the second example stood out more on the page, I just assumed it was this sentence. Looking at the first example now, I think you could replace if with or even [not]. It seems to me the conjunction with any is something of a "special case" of the commonplace "tentative negation" format in, say, ELL answers many if not most questions from non-native speakers better than ELU*. – FumbleFingers Nov 15 '15 at 17:54
  • In the first sentence "if any" is effectively a contraction of "if it can support any" and if is being used In the 2nd conditional sense. In the second sentence "albeit" is probably the best substitute. – Misneac Nov 15 '15 at 20:09
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If is a conjunction which should suggest possibility, but not absolute fact. Merriam Webster,com provides definitions, all of which relate to "possible".
Your first example:

For similar reasons fragile natural states cannot support many, if any, private elite organizations.

If any can be written possibly any

For similar reasons fragile natural states cannot support many, possibly any, private elite organizations.

The second example sentence:

As the two world wars and the Cold War of the twentieth century illustrate, external violence is a central if episodic aspect of the international environment.

may be abusive of the conjunction if.
The sentence probably should read:

As the two world wars and the Cold War of the twentieth century illustrate, external violence is a central, episodic aspect of the international environment.

In the first statement in the sentence

As the two world wars and the Cold War of the twentieth century illustrate,

the author establishes the episodic nature of 20th Century violence.
A conjunction might be used:

As the two world wars and the Cold War of the twentieth century illustrate, external violence is a central and episodic aspect of the international environment.

The use of if in this sentence probably should be classed as idiomatic. There may be other opinions on this matter; I'd prefer that if not confirm facts.

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