God has spoken

All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness (2 Tim 3:16).

1. This is the locus classicus for the inspiration of Scripture, although that's misleading since the database for biblical inspiration is far broader than one traditional prooftext.  

2. I've discussed "God-breathed" before. I think that's Paul's way of saying Scripture is equivalent to divine speech–the spoken word of God committed to writing. And that dovetails with OT exemplars of inspiration (i.e. "The word of the Lord came to X").

"Breath" is associated with speech, speaking, the spoken word. So what's breathed out by God is divine speech. That stresses the immediacy of Scripture as the very word of the living God. 

So it could be paraphrased: "All Scripture is the word of God". 

3. Syntactically, the statement can be rendered two different ways:

i) All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness.

ii) Every Scripture which is breathed out by God is profitable for teaching, for reproof, for correction, and for training in righteousness.

According to (ii), Scripture falls into two different classes: inspired Scripture and uninspired Scripture. And only inspired Scripture is profitable for those things.

But it's inexplicable to suppose Paul is dichotomizing Scripture into two divergent subsets, inspired and uninspired, only one of which is profitable. On that view, what's the purpose of the uninspired Scripture? And what's the distinction between uninspired Scripture and uninspired writings generally? 

Rather, Paul must mean that inspiration is a necessary condition for what makes a writing Scripture. Not a sufficient condition since not all inspired speech is committed to writing or preserved for posterity. 

Put another way, Scripture has its source of origin in the process and product of inspiration. Not all inspired speech becomes Scripture, but all Scripture must be inspired. And that dovetails with OT models, which Paul undoubtedly has in mind. 

4. Finally, there's the scope of Scripture. Minimally, Paul is alluding to the OT. However, some NT writings by then in circulation might also be in view. 

And whether or not Paul has any NT writings in mind, they are implicitly covered by Paul's statement. The principle is the causal and logical relationship between inspiration and Scripture. If NT writings meet that condition, then they too are Scripture–just like the OT writings.