You speak of "The Arminian view", but I am not arguing from this. I have never read any of this guys works, and the greater majority of my theological books, are by men like, Machen, Bottener, Calvin, Dabney, A & C Hodge, etc, etc.
I have yet to meet a single Reformed/Calvinist in almost 40 years of being saved, who has ever explained from John 3:15-18, that Jesus Christ only died for a limited number, and not for the entire human race. Every single Greek lexicon that I have consulted, have said that the Greek "kosmos", which is always translated "world" here, in this passage, ,means, "the human race". It is only when one uses their "theology" to understand this passage, and not let it say what God intends, is when they force its meaning to teach a "limited atonement", etc. Even John Calvin, who is supposed to be the man behind the so called "Five Points of Calvinism", in his commentary on this verse, is very clear that it does not refer to other than the human race. In fact, he uses the term, "everyone without exception", which is very much non-Calvinstic! Another strong Calvinist, Robert Dabney, honestly says on John 3:16, "In Jno. iii; 16, make 'the world' which Christ loved, to mean 'the elect world'; and we reach the absurdity, that some of the elect may not believe, and perish".