Modus Tollens and why Christianity is falsified if one rejects a subsidiary aspect of ontology from the Bible. The big idea is this. Issues of transgender, homosexuality, 6-day creation, how to defeat depression, and Jesus being the only savior of sins, are subcategories of Christian ontology; and if they are denied, they will falsify God Himself..
I will not go long into defending or outlining a Christian doctrine of logic. I would for now recommend Vincent Cheung, Ultimate Questions. I will quickly go over a modus tollens, which is a valid deduction. What makes this deduction SOUND is if the “if…then” connection is necessary, and the denied consequent is true. This is called in long hand, Denying the Consequent. As a reference, scientific experimentation uses Affirming the Consequent, which is a logical fallacy. Therefore, all science is false. In addition, a modus tollens argument used on science theories, because it is valid, is why science can only be shown to be false but never obtain knowledge. But that is for another essay.
Jesus Christ used a modus tollens argument (in a reductio ad absurdum) to falsify the Jewish leaders claim that He was the king of demons. Jesus starts with a premise the Jews started with. “(P) Jesus is Satan and is casting out his own demons.” This leads Jesus to the necessary first premise of the argument. “(Q) If Satan is casting out Satan, (R) then Satan is divided against himself.” And so, the argument is really a modus tollens chain argument. A normal syllogism is 3 preemies. But a chain argument (4 or more) works both in a categorical syllogism, or in propositional logic, or in other higher logics, which a truth table will demonstrate. Paul makes a 4-premise argument in Romans 8:30. At any rate, if it is a modus tollens form, then it does not matter how many premises (as long as they are true) are chained together. If the last is false, then the first is as well. Thus, the last denied antecedent in our passage would be, “It is false that Jesus is Satan casting out his own demons.”
Luke 11:18-20, “If Satan also is divided against himself, how will his kingdom stand? Because you say I cast out demons by Beelzebub.”
M.1. (R) “If Satan is divided against himself, (~T) then his kingdom does not stand.
M.2. ~(~T) The demonic kingdom is strong and active; and so, It is not the case that his kingdom does not stand.
M.3.~(R) Thus, Satan is not divided against himself.
There were many demon possessed people all around Jesus. Even Gentiles and foreigners are running to Jesus in public to get demons cast out. This is being done for all to see and witness. Thus, the demonic kingdom is not divided, unorganized and weak; rather, it is strong and active. Thus, the consequent of a divided demonic kingdom is false. Therefore, whatever antecedent would necessary lead this consequent is false.
Jesus’ use of logic is that the Jewish leaders are morons. In addition, for blaspheming the Holy Spirit they are ethically doomed.
Also note the importance of logic used here by Jesus. Jesus did not quote scripture. He only used a deductive logical maneuver to make His point. To use logic correctly is biblical; it bears the glorious image of the Logos, that is, of Jesus Christ. Reversely, it is human philosophy and speculation to be against logic.
Another example. What if my opponent says that, ‘“x” is a human.” Having blond hair or being exactly 6 feet tall is not a necessary category in order to be a human. However, for predicates that are necessary for the subject, if they are denied in the consequent, then the antecedent is denied.
G.1. “(P) If “x” is a human, (Q) then “x” is warm-blooded.
G.2. ~(Q) This “x” is not warm-blooded.
G.3. ~(P) Thus, “x” is not a human.”
Christianity ontology is God’s absolute and direct sovereignty over all reality. Thus, If God controls all things, then God controls x, y, and z.
Because subsidiary ontologies are a necessary result from the ultimate level of Christian ontology (God), then if you deny the subsidiary, it logical denies the ultimate.
I often avoid talking with fellow Christians about hot topics in politics, because if I try to bring in Scripture, they oddly become unable to think anymore. On top of this many so-called Christians do not know logic, even though it is a biblical doctrine they ought to be well practiced in.
The soteriology or the doctrine of salvation is ultimately a sub-category of Christian ontology. That is, salvation is how God is using His absolute sovereignty over all things toward two groups of people. These two groups are the reprobate and the elect. Therefore, the inevitable inference, (as a modus tollens) that happens when one rejects a subcategory of Christian ontology is that they falsify or kill the ultimate level of ontology. If you deny election, then you kill God. If you deny 6-day creation, then you kill God.
If you deny God’s creation of a man and woman in exchange for transgenderism, you falsity God.
H.1. (P) If God created man and women by His definition, (Q) then their sexes are fixed.
H.2. ~(Q) you can identify your sex by your feelings; and so, sexes are not fixed.
H.2. ~(P) Therefore, God did not create man and women by His definition.
This argument above should be another chain argument with the first premises being, “(P) If God is the only, ultimate ontology, (Q) then God created all things by His definition. (Q) If God created all things by His definition, (R) then God created man and women by His definition.” And so, the last antecedent to be denied is that God is not the ultimate ontology.
I have told this to others, and they seemed shocked that if I am required to affirm “x” I will kill my God. That is, if any person or the government forces me to do this, I am being asked to falsify my God. Without Christian ontology I have nothing left. Without God all is lost for me.
At any rate, the same goes for ethics. This time the modus tollens will be put into a chain argument, like how Paul did on in 1 Corinthians 15. A truth table will quickly show the logic to be valid.
J.1. (P) If God is the only God (the Bible says this), (Q) then God is the ultimate lawgiver (the Bible says He is).
J.2. (Q) If God is the ultimate lawgiver, (R) then murder is wrong because He commands it so (Bible says this).
J.3.~(R) Murdering babies is good because you can’t tell a woman what to do with her body; and so, It is not the case that murder is wrong because God commands it so.
J.4. ~(Q) And so, it is not the case that God is the ultimate lawgiver.
J.5. ~(P) Therefore, God is not the only God.
God’s direct and absolute sovereignty over all things is His nature itself. (P) If God’s direct and absolute sovereignty is His nature itself, (Q) then God is the metaphysical author and cause of all things. (Q) If God is metaphysical author of all things, (R) then God is the metaphysical author of all subsidiary categories of metaphysics such as creation, man, biological sex, sex, sin, redemption (etc.).
If any of the last is denied then the unavoidable inference is that one kills the top level of Christian ontology, and so God is gone. You cannot simply deny or let go a smaller issue of a Christian doctrine as if it is not so important. The logical implications are heaven and hell level. Jesus says if you deny Him before men, then He will in like manner deny you. If you deny subcategories in the consequent, then you deny God in the antecedent. The political implication is that Christians cannot deny subcategories of ontology or ethics. And if the government tries to make them deny subcategories of ontology, then the implication is that the government is forcing people to deny their entire Christianity.
Also, see Norman Geisler and Ronald Brooks, introduction to logic book, “Come Let Us Reason.”
 Or in a simple Natural Deduction format,
P ⸧ Q / Q ⸧ R / ~R ⸫ ~P
 This must be one of the dumbest arguments I have ever heard, especially if from co-called Christians. Every command in the Bible is about God telling you what you do or don’t do with our body and mind. Every law in government is about the government—under penalty—telling men and women what they should do or don’t do with their bodies. I am told by the government not use my body to pick up a hammer and hit a person with it, because it is a violent assault.