Deuteronomy 13:3
Does God tempt people?
There is a semantic difference between 'test' and 'tempt'. An examination of a complete English dictionary will verify this. Note that some of the meanings carry positive connotations, while some carry negative connotations.
In Genesis 22:1 the root of the Hebrew verb rendered 'tempted' in the KJV (and the more idiomatically-true-to-the-meaning 'tested' in the NIV) is nasah. Hebrew lexicons show that both 'test' and 'tempt' are appropriate renderings of this verb. As with any mode of human communication, context determines the shading being used. To build an argument for error on an English translation instead of referencing the Hebrew fails to account for this nuance.
In James 1:13 the verb peirazo is used. Greek lexicons show that there is a wide range of semantical meanings, both positive and negative, attached to this word. Again, context determines the meaning. It is perfectly appropriate to let context determine usage and to let the text interpret itself. A robust historical methodology avoids pressing a wooden and literalistic meaning onto ancient documents, which can create artificial tensions.
The mention of Matthew 6:13 as refuting the claim of St. James that God does not tempt men introduces an interesting point. There is a difference between God acting as the author of sin and God permitting situations where our faith is tested or where our fallen nature might struggle. What James is stating is that God is not the direct agent in a man's temptations; He will not cause one's favorite vice to appear before one's eyes so as to induce sin in the man. On the other hand, as God is omniscient and ruler over all, everything that happens in the universe is known and seen by Him.
When a man sins, surely God could step in and prevent it, couldn't He? In essence, every sin is 'allowed' by God in the fashion just described. The petition in the Lord's Prayer can be understood in a passive sense -- in His divine mercy may He not allow us to fall into situations where our weak nature will succumb to sin. To press it against James 1:13 is to make various texts clash when there is a reasonable solution which makes the texts harmonize.
When Deuteronomy 4:34 is cited as being problematic, it relies on the particulars of the KJV translation, which here translates the Hebrew noun root massah as temptation. However, we must analyze texts by the original language, not a particular translation. It is a fact that massah has a variety of semantic shadings: testing(s), trial(s), and it is debatable about whether or not temptation(s) is a shading of the word. In fact, the Brown-Driver-Briggs lexicon does not allow 'temptation' as a proper shading of the word. The NIV is more idiomatically faithful to the Hebrew by its replacement of the KJV's 'temptation' by 'testing'.
James 1:13 brings up a secondary issue. It says God cannot be tempted; but what about the Temptation of Jesus? God cannot be tempted with evil. The word behind 'evil' means sickness or depravity. Satan made some offers, but none of them were depraved or perverse. And again, the word used here has varying shades of meaning that must be determined by context and subject. Furthermore, it is helpful to differentiate between the external offering of temptation and the internal yielding to it. While one might attempt to 'tempt' God, the divine nature cannot be corrupted. James' comment indicates that God cannot be lured by evil, whereas the Gospels speak of Christ enduring the external presentation of temptation without inner capitulation.
Regarding the objection that since God asked Abraham to sacrifice Isaac, it follows that 'tempt' should be understood in the negative sense: Abraham had obtained a promise of a nation through Isaac. Abraham himself was confronted with an apparent contradiction. Would God be true to his promise regarding Isaac? If so, then Abraham could proceed to honor the divine command in confidence that God did not intend that Isaac should die.