God is good.
Satan is bad.
Cancer is bad.
Cancer comes from Satan.
Syllogisms like this should never be the only way we do theology, or to use a less loaded term, the way we view life. I've heard this type of reasoning used when defining issues pertaining to how God knows and/or wills sickness like cancer--or just bad events in one's life. Now in using one lens via the Scriptures this is true, but not fully true or even mostly true. The problem with some who use reasonings like this to interpret Scripture and view life is that there is more to be said, and to only say this is most definitely not true. Some of the biggest lies in life come in kernels of truth and clever sentences.
Let me show you why viewing life this way doesn't work, using similar reasoning:
God is good.
Satan is bad.
Crucifying an innocent man is bad.
The crucifixion of Jesus comes from Satan.
Now, is that true? Well, in one sense you can say yes, but not in the fullest sense, in fact in the biblical sense the syllogism doesn't work at all and is proved untrustworthy in sufficiently dealing with theological matters (again, insert practical LIFE matters). Rather, here is one way the Bible uses syllogism particularly in this context:
God is good.
Satan is bad.
Killing Jesus is bad.
Killing Jesus pleased God.
This is a better syllogism, because Isaiah 53:10 states, speaking of Jesus the Messiah, "But the LORD was pleased to crush him, putting him to grief..." It pleased God to kill Jesus. The Father put His Son to grief. Yet to be fully biblical, we know Satan was involved in Christ's crucifixion, because he entered Judas; and sin was involved, because Jesus died for sinners. This shows that simple syllogisms don't always tell the full truth.
However, back to my first point on sickness, some may go further and say, "Well did not Jesus the Messiah pictured in this passage say that one of the reasons Jesus died was to cleanse those who trust Jesus from things like sickness since the same passage in context says, '...by his scourging we are healed'" (54:5). The answer is yes (sidenote: contextually the Gospel-writer interprets this verse to be used as a basis for Jesus physical healing, but Peter uses this verse to be used as a basis for spiritual healing from sin, which means both are true, and therefore not easily syllog-ized), but it's more then yes. Why: 1. Not all Christians experience physical healing in this life; 2. All Christians are promised that everything in there life works for good, and the everything includes every thing like sickness which happens in Christian's lives (Ro. 8:28).
Also, is not the "everything" in Ro. 8:28 the promise of God and secured by the atonement (see entire book of Romans on things secured by the atonement)? I believe it is, and because I believe the atonement "Is finished" and that God is good, every Christian who died from a sickness of _____ died in the favor of God and in Jesus' effective atonement that purchased them. They died in the promise that even that very sickness that was not healed was indeed part of the everything worked by a sovereign God for their good because the sickness they were given will not separate them from Christ's love and atoning work. Theological syllogisms aren't so simple, and God is always good, but not always in the way we might first think. Our syllogisms must always be in service to the Holy Spirit's breath, the entire Word of God, otherwise we easily drift toward half-truths and values that are conditioned by an over-emphasis of one thing (in this case physical healing) and and under-emphasis or God forbid, ignoring, of another (in this case God's sovereignty over all things). Let me put forth another syllogism:
God is good.
Satan is bad.
God is sovereign over all things.
Satan and sin and sickness are under God's sovereignty.
This is true, and this is good for us, even when it kills us, because nothing can kill those in Christ, those sons of God, without the Father's attentive sovereign eye and kind sovereign hand. Christian, you will never stand face to face with King Jesus until that which snatched you from life was sovereignly ordained to bring you into eternal life, because the hands of Jesus and the Father are greater then the hand of cancer and the hand of death and it is always His hands that hold you.