Now it can certainly be said that the one that engages in adultery, whether through the actual and physical action or through the desire of which Jesus here speaks, would not be spoken of as being pure in heart. To that one would add that this does not really take an observer any further down the path towards seeing the Creator God, which is said to be the lot of those that are pure in heart. Again, Jesus is making some programmatic statements, which would imply that He has a program in mind. Likewise, Matthew presents Jesus programmatically, so it behooves the reader to allow the sermon to build on its statements internally, while also looking for the way in which the sermon works itself out in application to the entirety of the narrative that is on offer in the whole of Matthew.
Before moving on to the next “heart” statement, let it be noted that there are many uses of “heart” throughout Matthew’s Gospel, and all of them escape the lips of Jesus. However, it is reasonable to presume that the explanation of what it means to be “pure in heart” is to be found within the sermon, as Jesus goes on to define His own terms within this bracketed context. Here, one must also consider the possibility that Matthew has taken teachings of Jesus that were offered up in various times and places, and grouped them all together into this one “sermon,” especially if he was desirous of highlighting Jesus as a Moses-like figure, thus fulfilling the Deuteronomic insistence that another prophet would arise like Moses.
A reinforcement of such a notion, though one could also consider that Jesus spoke what is heard from Him in Matthew on numerous occasions, including this one, comes from the fact that Luke has Jesus saying much the same thing (though quite a bit less than Matthew) on a plain, rather than from a mountain. Along with that, if looking to the Gospel of Mark and again considering that Jesus can indeed say these things on more than one occasion (which is quite the reasonable and probable proposition), then one sees a fair number of Jesus’ pronouncements, mountain-related in Matthew, scattered throughout Mark’s narrative. So if it is the case that Matthew has purposely grouped together these words of instruction from Jesus, remembering that they, regardless of the format in which they are presented, present Jesus’ conception of the life of the citizens of the Creator God’s kingdom, then it is all the more important to allow for an internal consistency, with terms defined by the sermon itself. This is what is being attempted in regards to the term “pure in heart.”
Now, having mentioned Deuteronomy in the context of Matthew’s desire to present Jesus as a lawgiver Who is like Moses but, in fact, superior to Moses (“you have heard that it was said… but I say”), it is worth going there to review what it was that was reported to have been spoken by Moses. Now whether or not Moses actually said these things, and there is little reason to dispute this (though some do), such would not change the fact that Israel understood itself and defined itself according to its historical narrative (which included Deuteronomy), and especially that of the exodus and its attendant events (Sinai, the giving of the law, the wilderness wandering, entrance into the promised land, etc…).
Upon arrival there one finds “The Lord your God will raise up for you a prophet like me from among you---from your fellow Israelites; you must listen to him” (18:15). This is then confirmed by the voice of the Lord, Who says “I will raise up a prophet like you for them from among their fellow Israelites. I will put My words in his mouth and he will speak to them whatever I command” (18:18). In between the two insistences that such will take place, which Matthew must simply have in mind as he constructs his theologically-tinged biography of Jesus, Moses says “This accords with what happened at Horeb in the day of the assembly” (18:16a). So when Moses speaks about the prophet like himself, he actually connects it to what took place on a mountain. It is then unsurprising to hear Jesus speaking from a mountain, which makes the Moses-related point even more forcefully.