Deterrence is seeing justice in action. All sentencing, like speeding and littering fines, are supposed to hurt _just enough_ to deter one from doing it, but not in excess. 8th Amendment "Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted." uses the word "excessive" twice.

All of this is opinionated since quantifying justice is often pretty difficult.

https://constitution.congress.gov/constitution/amendment-8