Jake Arrieta doesn't need to be "talked into" a 4-year deal. It's an auction market; it doesn't matter if he "wants" a 7-year contract. If nobody offers him that, he'll either accept a shorter-term contract, or go into a different line of work.
If there really is collusion, Arrieta will get the same offer from several teams - and none of those teams will be willing to deal around the edges to make their offer more attractive, to get an edge over other bidders.
If, on the other hand, all the clubs have concluded (based on evidence) that signing a pitcher to a contract that assumes he'll be effective into his late 30s doesn't make sense (because pitchers tend to implode by their mid-30s - see Roy Halladay; see Cliff Lee).
For Arrieta, four years looks about right - maybe five (that would be his age 36 season). But seven? Err..no thanks. Yes, he might remain effective that long - but odds are he won't. If some club is willing to wager against the odds, more power to them.
So, make him a fair offer, for a number of years that makes sense given his most probable future performance. Maybe use excess dollars (which the Phils have in abundance right now) to sweeten things up front (signing bonus). Maybe a vesting option (or series of same), but only if those vesting options are dependent on performance (and I don't mean innings pitched, given the tendency in the industry to kowtow to veterans' desires for playing time notwithstanding marginal performance). But no guarantees past age 35 or maybe 36. If somebody else is prepared to go there...fine. Somebody else can deal with a millstone contract down the road.