QUESTION: What is meant by a "saint"?
ANSWER: The word saint is used in the New Testament to refer to all Christians from the moment they trust Christ as Saviour. It does not single out special ones who have exceptional holiness or more saintly conduct.
Sainthood is not based on human achievement, but is a state into which God graciously calls us. It reflects our position in God's sight, not our condition in daily experience (though we are certainly called to live holy lives as well, I Pet. 1:15). The Greek word, also translated holy in the Bible, is hagios, meaning separated or set apart. The saints of God (believers) are ones God has set apart for Himself.
Here are some texts that indicate the inclusive nature of the word "saints."
Romans 1:7: Paul writes his letter to "To all who are in Rome, beloved of God, called to be saints. The words "to be" are in italics in the King James Version, to indicate they have been added by the translations. More literally, the phrase reads simply "called saints." However, even leaving "to be" in there leads us in the same direction. The believers are called to be saints (set apart ones), not by the apostles or the church, but by God Himself, by whom they are "beloved."
First Corinthians 1:2: Paul writes "to the church of God which is at Corinth, to those who are sanctified in Christ Jesus, called to be saints, with all who in every place call on the name of Jesus Christ our Lord." "Sanctified" translates another form of the Greek word hagios, and indicates Christians are set apart in Christ Jesus–our standing before God. And again the words "to be" can be omitted. The Christians in view are merely called saints.
Second Corinthians 1:1: Paul addresses, " the church of God which is at Corinth, with all the saints who are in all Achaia." Ephesians is addressed "to the saints who are in Ephesus, and faithful in Christ Jesus" (Eph. 1:1). Philippians was sent "to all the saints in Christ Jesus who are in Philippi" (Phil. 1:1). Colossians is addressed "to the saints and faithful brethren in Christ who are in Colosse" (Col. 1:2).
Second Thessalonians 1:10: Speaks of the day of Christ's return when He will be "glorified in His saints and to be admired among all those who believe." The word "and" (kai in Greek) can have the force of "that is," or "in other words." If that is the sense here, the first and second clause are both speaking of the same people.
While it's true that, in their behaviour, some people are more pious and holy than others, yet as to their position before God, in Christ, all Christians are saints, set apart and specially blessed by God as His own, beloved of God, and called saints by Him (Rom. 1:7). Our standing is based fully on Christ's perfect righteousness, not our own.
QUESTION: Does John 3:16 actually mean that anyone can be saved if they believe in/call upon Him?
ANSWER: I'm not sure why you would question the word "whoever" in John 3:16. As the old Bible expositors used to say, "If the plain sense makes good sense, seek no other sense." In passage after passage, the gospel invitation is extended to all–though the Bible is equally clear that not all will be saved.
Christ paid the debt for all the sin of all men for all time. But the payment has to be accepted, by faith. We understand that in daily life. Someone rich and generous person can say, "Here's a cheque to cover the cost of your new car." And we can either accept the gift or reject it.
But let's check out a few passages that indicate all are potentially included in the work of salvation, and the payment of our debt (italics mine, for emphasis).
"The Lord has laid on Him [Christ] the iniquity of us all" (Isa. 53:6). He is "the Lamb of God who takes away the sin of the world" (Jn. 1:29). Eternal life is granted to "whoever believes in Him" (Jn. 3:16). The Father's desire is "that the world through Him might be saved" (vs. 17).
With the Samaritan woman at the well, "living water" is used as a picture of the life-giving work of the Holy Spirit. And "whoever drinks of the water" will have everlasting life (Jn. 4:14). And "If anyone thirsts, let him come to Me and drink" (Jn. 7:37-39). "Whoever desires, let him take the water of life freely" (Rev. 22:17).
"Whoever calls on the name of the Lord [i.e. in faith] shall be saved" (Acts 2:21, and Rom. 10:13). "Whoever believes in Him will receive remission [forgiveness] of sins" (Acts 10:13). "All that believe are justified from all things, from which ye could not be justified by the law of Moses" (Acts 13:39).
Christ Jesus...gave Himself a ransom for all" (I Tim. 2:5-6). "That He, by the grace of God, might taste death for everyone" (Heb. 2:9). "The Lord...is not willing that any should perish but that all should come to repentance" (II Pet. 3:9). "He Himself [Christ] is the propitiation for our sins [the full satisfaction of God's justice], and not for ours only but also for the whole world" (I Jn. 2:2). "The Father has sent the Son as Saviour of the world" (I Jn. 4:14).
Seems pretty clear to me! It is an open invitation to all who are willing to receive it.