The Penal-Substitution Theory of the atonement maintains that Christ died on the cross as a substitute for sinners. God imputed the guilt of our sins to Christ, and he, in our place, bore the punishment that we deserve. This was a full payment for sins, which satisfied both the wrath and the righteousness of God, so that He could forgive sinners without compromising His own holy standard.
The Penal-Substitution Theory of the atonement was formulated by the 16th century Reformers as an extension of Anselm's Satisfaction theory. Anselm's theory was correct in introducing the satisfaction aspect of Christ's work and its necessity, however the Reformers saw it as insufficient because it was referenced to God's honor rather than his justice and holiness and was couched more in terms of a commercial transaction than a penal substitution. This Reformed view says simply that Christ died for man, in man's place, taking his sins and bearing them for him. The bearing of man's sins takes the punishment for them and sets the believer free from the penal demands of the law: The righteousness of the law and the holiness of God are satisfied by this substitution.
- Isaiah 53:6 - "the LORD has laid on him the iniquity of us all."
- Isaiah 53:12 - "yet he bore the sin of many, and makes intercession for the transgressors."
- Romans 3:25
- 2 Corinthians 5:21 - "For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God."
- Galatians 3:13 - "Christ redeemed us from the curse of the law by becoming a curse for us -- for it is written, Cursed is everyone who is hanged on a tree."
- Hebrews 10:1-4
The penal aspect of the the atonement is often a stumbling block to modern theology, yet some would say "it is the dominant Atonement imagery used in the Bible."  By way of contrast, the Arminian Governmental theory of atonement not only denies the penal aspect of the atonement but also substitution in the normal sense of the word. To the Arminian, Christ died not as a substitute for sinners but as a substitute for punishment.
"The language of propitiation specifically implies God's hatred of sin and emphasizes the gracious work of Christ as sin-bearer (Rom. 3:25). The Bible further includes the forensic, legal language of justification (Rom. 3:20-26, 4:25, 5:16-18). These images make clear the reality of our guilt and the required penalty." Dever
See main article on Propitiation.
Relation to other doctrines
The principle of penal substitution is held, by many of its proponents, to be the control through which all other views of the accomplishments of Christ on the cross are to be seen and the mechanic by which all other accomplishments work. Some examples of this are given below.
The cross as ransom. Jesus is described as having paid our ransom on the cross; but this image only works because Jesus was paying our penalty in our stead.
The cross as example. Christians truly should be inspired by Christ's work on the cross to self-sacrifice; but this only happens because before our identification with Christ in his sufferings, Christ identified with us in our sin, bearing the punishment due in place of us.
The cross as victory. Christ's death and resurrection were real victories over sin and death and hell; but once again, we only take part in the victory of the Son of God by virtue of our union with him, we can only be united with him if our sin is dealt with, that can only happen by the punishment for our sin being borne, and that punishment was borne by Christ our substitute.
The cross as reconciliation. "God was reconciling the world to himself in Christ, not counting men's sins against them." (2 Cor. 5:19, NIV) The exchange being contemplated here is that our sins are taken away by Christ's death and thus, we are made acceptable to God.
For further explanation and clarification, Stott's The Cross of Christ deals with this controlling imagery in some detail (pp. 168–203, 217–224, 231–239).
It is worth noting that a great number of the "critiques" of Penal Substitution come from those who embrace it: major proponents of Penal Substitution such as John Stott, J.I. Packer, James Denney, all have sharply criticized various aspects of Penal Substitution. Stott critiques the idea that God can be appeased. Packer critiques any attempt to found it on human models of retributive justice and that suggests that it be seen not as a mechanical explanation (how it works) but rather than kerygmatically (what it means to us). Denney critiques the idea that it is forensic and judicial, saying that these are impersonal cold terms. All of these critiques do not function to debunk the theory, but rather to rescue it from its "cruder" forms.
It is not representative of the Early Church
Gustav Aulen in his book Christus Victor argues that Penal Substitution is not rooted in a biblical understanding but instead in the Catholic idea of penance (which the Reformers rejected). He further argues that the early church father's primary model of the atonement was the dramatic image of Christ overcoming sin, death, and the devil which as come to be known as the "Christ Victor" view of the atonement.
Some Evangelical theologians while still affirming Penal Substitution have come to view the Christus Victor view of the atonement as more central because it goes beyond dealing only with man's sin and speaking of God's victory over the whole cosmos. One example of this is Gregory Boyd in his book "God at War". Beyond this a great number have called for Penal Substitution to be seen as one of many views arguing that Scripture has a number of ways of speaking of the atonement, of which Penal Substitution is but one. Some prominent examples here include John Stott in his classic "The Cross of Christ" and P.T. Forsyth in "The Work of Christ".
"What I want to say is not that this theory is wrong... I want to say is that the atonement is so much more than this. And, if it is so much more than this, then it follows that using “penal substitution” as our guiding term is inadequate and misleads others. At the least, it does not provide enough information to explain what one really believes occurs in the atonement" --Scot McKnight
See main article on Christus Victor.
It is unjust
Penal Substitution is based on the concept of a criminal justice system which demands punishment for transgression. But no criminal justice system in the world (except possibly tyrannical states) would ever say that it is just to punish the innocent in place of the guilty. That would in fact be a travesty of justice. Some of the most prominent critics of penal substitutionary theory who advanced arguments such as these include Peter Abelard who criticized what he saw as the inherit injustice of Anselm's theory, and Faustus Socinus in his polemic De Jesu Christo Servatore (Of Jesus Christ the Saviour).
"What Socinus did was to arraign this idea as irrational, incoherent, immoral and impossible. Giving pardon, he argued, does not square with taking satisfaction, nor does the transferring of punishment from the guilty to the innocent square with justice" J. I. Packer
It is based on Natural Theology
J.I. Packer argues that Penal Substitution was formulated during a period when "Protestant exegesis of Scripture was colored by an uncriticized and indeed unrecognized natural theology of law. . . drawn from the world of contemporary legal and political thought" . Natural theology refers to knowledge of God drawn from our world around us (in this case from their own judicial concepts) as opposed to knowledge of God contained in the revelation of Scripture. Although Packer rejects basing Penal Substitution on the Natural theology of law and limiting the concept to retributive language, he argues for the "substantial rightness of the Reformed view of the atonement."
It necessarily implies universalism
"It seems logical that if the death of Yeshua satisfied God's need for justice, and if humans made no contribution to the process, then salvation and atonement should be granted to everyone -- to Christian believers and unbelievers alike. It is unclear why only those individuals who trust Yeshua as Lord and Savior will attains salvation, atonement, and Heaven." 
See main article on universalism.
"It is a form of cosmic Child Abuse"
In the UK, prominent member of the Evangelical Alliance Steve Chalke has popularised an attack on penal substitution which argues it portrays God as vengeful and unable to have a loving relationship with his son Jesus. This has given rise to a significant backlash, an example of which can be found on Adrian Warnock's Blog. Steve Chalke has said that penal substitution is "a theory rooted in violence and retributive notions of justice" and is incompatible "at least as currently taught and understood, with any authentically Christian understanding of the character of God." Banner of Truth
It necessarily implies definite atonement
See main article on definite atonement.
Some tend to reject the penal-substitutionary aspect of the atonement because it seems to imply a limited or definite design in the atonement. However, it is worth noting that some scholars holding to penal substitution maintain that definite atonement is not a corollary of the position (see for instance, I. Howard Marshall's paper linked below, footnote 68).
- Robert Reymond, A New Systematic Theology of the Christian Faith (Nashville: Thomas Nelson, 1998) Chap. 17 The Character of the Cross Work of Christ.
- J. I. Packer, Celebrating the Saving Work of God (Carlisle, UK: Paternoster, 1998) chap. 8 "What Did the Cross Achieve?" Chap. 9 Sacrifice and Satisfaction.
- J. I. Packer, Knowing God (Downer’s Grove: Inter Varsity Press, 1973) chap.15 "The Wrath of God"; chap. 18 "The Heart of the Gospel".
- Leon Morris, The Cross in the New Testament (Grand Rapids: Eerdmans, 1965) Chap. 8 The Cross in the Epistle to the Hebrews.
- Leon Morris, The Apostolic Preaching of the Cross, 3rd ed. (Grand Rapids: Eerdmans, 1998).
- John Stott, The Cross of Christ (Downers Grove: IV Press, 1986).
- Stephen Finlan, Problems With Atonement: The Origins Of, And Controversy About, The Atonement Doctrine, ISBN 0814652204
- "If Christ by his death actually propitiated God’s wrath, reconciled God, and paid the penalty for sin (which is what I mean by an atonement of infinite intrinsic value), and if he sacrificially subsituted himself for, on behalf of, for the sake of, and in the stead and place of sinners, then it follows that for all those for whom he substitutionally did his cross work he did all that was necessary to procure their salvation and thus guarantee that they will be saved." Robert L. Reymond, A New Systematic Theology Of The Christian Faith, p. 478
- A spillover from Calvinism into Arminianism has occurred in recent decades. Thus many Arminians whose theology is not very precise say that Christ paid the penalty for our sins. Yet such a view is foreign to Arminianism, which teaches instead that Christ suffered for us. Arminians teach what Christ did he did for every person; therefore what he did could not have been to pay the penalty, since no one would then ever go into eternal perdition. Arminianism teaches that Christ suffered for everyone so that the Father could forgive the ones who repent and believe; his death is such that all will see that forgiveness is costly and will strive to cease from anarchy in the world God governs. This view is called the Governmental theory of atonement. . . They also feel that God the Father would not be forgiving us at all if his justice was satisfied by the real thing that justice needs: punishment. They understand that there can be only punishment or forgiveness, not both, realizing, e.g., that a child is either punished or forgiven, not forgiven after the punishment has been meted out. J. Kenneth Grider, Arminianism in the Evangelical Dictionary of Theology 
- Penal Substitution, by Dr. Greg Bahnsen
- Christ Our Penal Substitute, by R. L. Dabney
- Revisiting Penal Substitution (pdf), by Kevin D. Kennedy
- The Theology of the Atonement (pdf), by I. Howard Marshall
- The Logic of Penal Substitution, by J. I. Packer
- Nothing But the Blood, by Mark Dever - More and more evangelicals believe Christ's atoning death is merely a grotesque creation of the medieval imagination. Really?
- A Scandalous Attack on The Cross, by Martin Downes
- Penal Substitution Refuted by John Miley
- Rethinking Penal Substitution, by Paul Owen
- Penal Substitution vs. Christus Victor
- Ten propositions on penal substitution, by Kim Fabricius
- The Meaning of the Atonement by Mark M. Mattison
- Did Christ Pay for Our Sins?, by R. Dennis Potter (Mormon): tinyurl.com/dqcyh
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