Category Archives: Christian Logic

Christianity Is False, If a Subcategory of Ontology Is Denied

Modus Tollens and why Christianity is falsified if one rejects a subcategory 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, 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.[1] 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 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. 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, “Jesus is not 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.”

Modus Tollens

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[2], (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 then the world and all things are lost to me. It would all be pointless to 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.[3]

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[4], 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. One of the biggest Christian tricks have occurred, in that some theologians say we must unite on the core gospel issues, but be open handed on non-core issues. They are more like Loki, the god of mischief, than the God of truth.  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.[5] Because of denying the consequent is a valid deduction you cannot have non-core issues in theology and doctrine. If one says otherwise they are both intellectually broken and spiritually malfunctioned.

I could give countless examples in Scripture to show this, but for brevity consider how Paul quotes a little passage about “do not muzzle an Ox as it treads,” (1 corin. 9:9). Because all Scripture is truth, cannot be broken and is useful for godliness, it is ALL a core issue of life and godliness. Jesus when leaving this world said to the apostles, Matthew 28:20 (NLT), “Teach these new disciples to obey ALL the commands I have given you.”[6] Jesus, as with the rest of Scripture, do not divide “core issues with non-core issues,” but says “all,” that I have commanded. One of the things Jesus commanded, over and over, in John chapter 14-16, is that we pray for whatever we wish and get it in His Name. How many teachers obey Jesus on this point? Are they not disqualified by Jesus’ requirement? These Loki theologians of mischief love the idea of core and non-core issues of unity, precisely because the Scripture does not make this divide; and thus, they (man) gets to be the ones to decide this outcome. They get to play God, but the only god they are playing is one of mischief and rebellion. It is a man-centered view in what it means to be God-centered. It is a theology of man.

Leave the mischief and rebellion to the theologians, but you believe and observe all of God’s definitions.



[1]  *for clarification, I do quote Vincent often, but I am not officially with him or represent him.
Also, see Norman Geisler and Ronald Brooks, introduction to logic book, “Come Let Us Reason.”

[2]  Vincent Cheung will use “definition” or precepts for ethics, and “decree” for ontology. However, I am using “definition” in a broader sense: definitions about all metaphysic given by epistemology.

[3] Or in a simple Natural Deduction format,
P ⸧ Q / Q ⸧ R / ~R  ⸫  ~P

[4] 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.

[5] 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.

[6] Emphasis added by author.

Be Good Stewards of Pain, Or God’s Promises?

I read this irritating quote from Jerry bridges the other day.


“….We usually think of Christian stewardship in terms of money. Some churches have ‘stewardship campaigns’ during which they seek to get their membership to pledge toward the annual church budget. Then the concept of stewardship was broadened to include our time and talents—or as one slogan puts it, ‘Be a good steward of your time, talents, and treasure.’ The idea behind these concepts is that whatever resources God has given us, He has entrusted them to us as stewards to use for His glory.
“Now apply that idea to pain, either physical or emotional. If we believe God is sovereignly in control of all circumstances of our lives, then our pain is something He has given to us just as much as our time or talents or treasure. He has entrusted the pain to us as stewards to be used for His glory.
“How can we be good stewards of the pain God gives us? One way … is to trust Him even though we don’t understand the purpose of the pain…… ”
“Joy of Fearing God.” Pg. 225 Jerry Bridges.

Ontology Is Not Ethics

There are a few problems with this. The first main “if…then,” argument only in essence says, “ If God CAUSES all things, then God CAUSES this thing.” It is a broad but correct deduction. So far, so good. This category is only dealing with ontology. Yet, the conclusion he makes that pain is like stewardship, is an implied “ought.” So that we ought to obey God by using pain in such and such a way. This is now a category or ethics—a different category. Ethics is what God commands. However, Jerry provides no command from God (in what I read) clearly showing we “ought” to treat pain the way he seems to imply. It is made up human superstition and disobedience.

Informal Fallacy

This is an inductive argument in the form of arguing from analogy, which is invalid. [ That is, X, R, T, and F all have characteristic 1, 2, and 3. Also, X, R and T have characteristic 4. Thus, F has characteristic 4 as well. ]
The problem with an invalid argument from analogy is when one takes it further. If we see where it leads it would imply that pain is not merely something to “steward,” but even a “gift.” I surely take my “talent” to play music for God as a gift – and money, and time. Some theologies treat pain like a sick religious fetish. The Kingdom of self rules them. The kingdom of human superstitions (induction) and human starting points of knowledge is their idol and god.


We do in fact know –broadly speaking—what to do with suffering that GOD CAUSES in us. Everything in reality is explained by God directly causing it. So What? This gives us no command to know what we “ought to do,” when God causes something. Hannah knew what to do when she dealt with the pain of not having a child, she asked for a miracle and received one – a gift. She did not like the pain and wanted it to go away. God gave her a son, as a gift. The pain stopped. God has commanded us to believe in His promises. Christian ethics is not an inductive conclusion taken from some nebulous notion of what one thinks God’s causality is doing at a given moment.

Hannah, therefore, was a hero of faith and ethics. After speaking of God’s sovereignty (“God kills and makes alive”) she proclaims that for the humble who believe in Him, (1 Sam. 2:9,8) “For the foundations of the earth are the LORD’s; on them he has set the world. He will guard the feet of his faithful servants, but the wicked will be silenced in the place of darkness. It is not by strength that one prevails. He raises the poor from the dust and lifts the needy from the ash heap; he seats them with princes and has them inherit a throne of honor.”
Hannah, therefore, was a faithful steward of the promises of God by believing in them – and giving glory to God as a “GOOD” Father by receiving the very thing she asked from Him (a fish for a fish, bread for bread, an egg for an egg, and a son for a son).


God’s Will, Made Me Unwise


First a clarification of Christian categories.

Vincent Cheung has been helpful on this topic to me, and he gives some good examples from Scripture on this distinction of Metaphysics/decree versus the different category of Ethics/God’s Precepts. Notice the “will of God,” in Mark 3 and 1 Peter 3 are used differently.

1 Samuel 2:25

His sons, however, did not listen to their father’s rebuke, [precept] for it was the LORD’s will to put them to death. [decree]…

Mark 3:35, For whoever does the will of God, he is my brother and sister and mother. [precept]

1 Peter 3:17, For it is better to suffer for doing good, if that should be God’s will, than for doing evil. [decree [1]

Paraphrasing Mark and Peter with a more direct meaning of the term “will of God.”

Mark, “Whoever obeys God’s commandments is my brother.”
Peter, “It is better if God causes you to suffer for doing good rather than evil.”

Second. So the advice is if God sovereignly gives you something you accept it? How stupid can you get. God sovereignly gives and causes all things, even all sin. In this metaphysis sense, God is the metaphysical author of sin.[2] So what? This has nothing to do with human ethics, or that is, what we ought to do.

By God’s sovereign will, He make all of us born as unbelievers and sinners. How are we to “steward” this? The question is an “ought” question (not metaphysics); therefore, we need to know what God commands, and not what He has caused. God commands for us to repent and be saved through faith in Jesus Christ. Thus, this is how we steward being born sinners by God’s sovereign will.

If you have a “lack of wisdom,” then God sovereignly caused you to have it. How does one steward this lack of wisdom? This again is asking an ethics question; that is, “what ought I do?” Christian ontology—God sovereignly making you have a lack of wisdom—is not a category of ethics; thus, to conclude from this descriptive premise of ontology into ethics is invalid. Pragmatically speaking it is voodoo and witchcraft.

As for ordinary life difficulties, it is God’s will for victory. James says if you face the common difficulty of lacking wisdom you are to ask in faith, and then God will give it to you. Think about it! It is not God’s will for you to stay in a lack of wisdom. What you “ought” to do is have faith and be victorious over this hardship of confusion by getting wisdom from God. This is not a self-help tip. It is a precept from your Master. The command is that BY YOUR FAITH, YOU are to obtain it.

Give it some thought.

If God directly controls all reality, then everyone who lacks wisdom is due to God’s Will.

(P) If it is God’s will [decree] for me to lack wisdom, (Q) then what I ought to do is accept God’s Will [ethic] and be unwise.

You realize how incredibly moronic this is, right? You realize how disobedient and disrespectful that is toward God, right? What God causes you to experience is not the same category of what you ought to do about it. If you want to know what you should to do, then ask what are God’s commands about this. Obey God. Get some wisdom by your faith. If you do not get wisdom because of your lake of faith, then you are in direct disobedience of God.

James command about healing, since we started about “pain,” is that we not merely pray about it, but that “by your faith” you actually get healed and get forgiven.




[1] Vincent Cheung’s essay, “Ezekiel 18:23 and 33:11.” ( It is also found in his book, “Sermonettes Vol. 8, chapter 4.” 2015. Pg, 22-32.

[2] I got this phrase, “metaphysical author of sin,” from Vincent Cheung. See, Systematic Theology, And Commentary on Colossians and Reflections on Second Timothy.



Valid Logical Sequence is Not Devised, But Only Observed by Man

This is a short quote from St. Augustine talking about the nature of logic (i.e. deductive valid logic, not irrational induction). Ultimately, he says, it’s origin is with God. I would say that Logic is man pointing out particular common or rudimentary structures of God’s thinking, and then giving them names. Some of these structures are so foundational to God’s own thoughts, such as the law of contradiction, that if man does not follow them, man ceases to think at all. The Logos doctrine in John 1 includes this doctrine of logic, so that to translate “Logos” as “Logic” is as good a translation as “Word.”
Also, Augustine focuses on the fact that Logic is observed, not made up by man. Logic is what makes math work. Thus, think about this from the perspective of math. Man does not make up the idea that 1 plus 1 equals 2; rather, man discovers a truth of God and can be smart by affirming this or be dumb and wicked by denying it. I have 1 and 1 arms; and so do most people. There is a reason why you do not find shirts at the store with 170 sleeves stitched in. The reason is that 1 and 1 equals 2 sleeves, and not 170.
St. Augustine
Valid Logical Sequence is Not Devised But Only Observed by Man.
50. And yet the validity of logical sequences is not a thing devised by men, but is observed and noted by them that they may be able to learn and teach it; for it exists eternally in the reason of things, and has its origin with God. For as the man who narrates the order of events does not himself create that order; and as he who describes the situations of places, or the natures of animals, or roots, or minerals, does not describe arrangements of man; and as he who points out the stars and their movements does not point out anything that he himself or any other man has ordained;—in the same way, he who says, “When the consequent is false, the antecedent must also be false,” says what is most true; but he does not himself make it so, he only points out that it is so. And it is upon this rule that the reasoning I have quoted from the Apostle Paul proceeds. For the antecedent is, “There is no resurrection of the dead,”—the position taken up by those whose error the apostle wished to overthrow. Next, from this antecedent, the assertion, namely that, there is no resurrection of the dead, the necessary consequence is, “Then Christ is not risen.” But this consequence is false, for Christ has risen; therefore the antecedent is also false. But the antecedent is, that there is no resurrection of the dead. We conclude, therefore, that there is a resurrection of the dead. Now all this is briefly expressed thus: If there is no resurrection of the dead, then is Christ not risen; but Christ is risen, therefore there is a resurrection of the dead. This rule, then, that when the consequent is removed, the antecedent must also be removed, is not made by man, but only pointed out by him. And this rule has reference to the validity of the reasoning, not to the truth of the statements.” [St. Augustine, Christian Doctrine. ch.32]

Logic & Jesus Christ: The Law of Non-Contradiction


These are the most basic for 2 reasons. One, they are the most fundamental to the motion of God’s mind itself. God’s knowledge is the content of His mind logic is the motion of God’s mind.  If we do not follow these most basic motions, then we no longer think. Second, they form the foundation for all other logics and mathematics.

The best advice I can give for being better at logic, and thinking more like God is practice. Particularly, to practice in the basics of logic, such as the three basic laws, defining terms, having precise and truthful premises, avoiding informal follicles and lastly to make valid inferences.  It is not good enough to just read a book on logic, but one must practice over and over until it becomes second nature. This lesson is to practice the most basic, the Law of non-contradiction. For this reason I will post several people teaching on this for your practice of it.


FIRST. The law of contradiction.

Jesus appeals to it in,

Mark 12:37, “Therefore David himself calls Him ‘Lord’; how is He then his Son?” And the common people heard Him gladly.”

If the LoC is not an immutable motion of thinking, then Jesus’ appeal to it would mean David’s son(Jesus) is not David’s Lord and is David’s Lord. They would cancel each other out. There would be no doctrine to affirm or deny. There would be no knowldge, no thinking.  Jesus’ point was the David’s promised Son is not merely human, for if so, then he could not be David’s Lord. But since this promised son is the God-man, then it is possible for Him to be both David’s son, physically, but also David’s Lord because He is the eternal Son of God.  This means the laws of identity (thus, no category fallacies) and non-contradiction are not violated. Subjects and predicates are put together in proper categories and affirmed in understanding.

Also, in 1 Corinthians 14:7, “Even things without life, whether flute or harp, when they make a sound, unless they make a distinction in the sounds, how will it be known what is piped or played?

For a word or sound to have intellectual meaning it must not only mean something, it must also not mean something: it must have definite meaning; it must make a distinction from other meanings.  Aristotle’s explanation will open up what this means more.

Below is Clark to talk about the meaning behind the Law of noncontradiction. I could just give a symbolic notation for the Law such as ( A is B” and “A is not B”) are exclusive of each other, or give it in Natural Deduction, but on this matter a more in-depth explanation seems to be better to due to the importance of the subject.  I prefer to see circle diagrams in my mind for a visual help.

If Oshea is predicated in the category of “man,” then there is no way for the category of non-man to be predicated to Oshea because of the immediate deduction of (obversion)[1], “Oshea is a man,” is “No Oshea is non-man.” That is, to destroy the LoC would be to fail the rest of logic/Logos, it would kill God in essence. God could not affirm, “Jesus is My only Son,” because it could men “Jesus is not My only Son.” Jesus could not affirm that He is the truth, because it could be that Jesus is not the truth. See diagram.

For Doctrine: There are many verses which directly teach or use logic in the Bible. Jesus is the Logos. Jesus appeals the law of non-contradiction. Jesus at times would not quote the O.T. but only use logic to refute His opponents. We are made in His image.  Thus, within the doctrine of Systematic Theology, there is a Doctrine of Logic. Christians ought to know this better.

Man - NON-man LoC

Cannot Deny It!

I deny the Law of non-Contradiction.” I must use the LoC to say this premise, otherwise, my denying of the LoC would men, “I affirm the Law of -non-Contradiction.”

Words are not important.” If that is the case, then the words I used to say words are not important are not important.

Anyone who says anything absolutely is arrogant.” If this is not said absolutely, then it does not apply to me, and so I do not care. But if the person who said it, does say it absolutely(as a dogmatic), then they by definition, are arrogant.

These statements, in order for them to be true, must be false at the same time. But the world I live in is not false. My existence is not false; that is, I must us my existence to deny it, and thus, I prove it.

St. Augustine had a way to show the stupidity of skepticism with the self-authenticating aspect of the LoC, by asking his opponent, “would you please deny your own existence (hint: without using it)?”

This is an important aspect ( must use the LoC to deny it) to remember, because Romans 1 says that the non-Christian is a moron because they cannot rationally deny God’s innate knowledge He put in them.

Romans 1:20-22, 2:14-15 (NLT)

20 For ever since the world was created, people have seen the earth and sky. Through everything God made, they can clearly see his invisible qualities—his eternal power and divine nature. So they have no [rational denese]* for not knowing God.

21 Yes, they knew God, but they wouldn’t worship him as God or even give him thanks. And they began to think up foolish ideas of what God was like. As a result, their minds became dark and confused. 22 Claiming to be wise, they instead became utter fools [Morons].

 Even Gentiles, who do not have God’s written law, show that they know his law when they instinctively obey it, even without having heard it. 15 They demonstrate that God’s law is written in their hearts

*Strongs Greek. “ἀναπολόγητος [anapologetos /an·ap·ol·og·ay·tos/] adj. From 1 (as a negative particle) and a presumed derivative of 626; GK 406; Two occurrences; AV translates as “without excuse” once, and “inexcusable” once.
1 without defense or excuse. 2 that which cannot be defended, inexcusable.”

This is where we get the word Apologetics. It is like a lawyer in court giving an objective rational defence for something.  In context of God writing His laws on our minds–then  when we see the world it stimulates this innate knowldge of God to our thoughts– is the logical reason why it is impossible to give a rational defence for suppressing God’s truth.  To do so, one must use God’s innately written truths to deny it; thus, they prove it.  This is not the Law of contradiction itself,  but a method using it to show its undeniablity.  Vincent Cheung has do a good job explaining this “method” (don’t confuse this for the apologetic itself, which is the Bible) for Christian apologetics. See his book, Ultimate Questions.  Also, Gordon Clark,  A Christian View of Men and Things.

Because the Bible speaks about this in context of Christian apologetics then it a doctrine Christian ought to know and practice.


It is an amazing coincidence of history that Plato and Aristotle (384-323 B.C.) lived in the same century and that the latter was the pupil of the former. No other century can boast of such an amount of genius; no other pupil had such a teacher, and no other teacher had such a pupil. Extreme enthusiasm for Kant or Hegel might place the one or the other nearly on a level with Plato or Aristotle, but sober judgment fails to find an equal combination anywhere. Coincidences of history, however, may be of little significance. It is the clash of ideas that is important.

In the last chapter, in the section on the Parmenides, it was stated that Aristotle accepted the objections which Plato raised against his own theory. And there are others also. Accordingly, Aristotle considered the world of Ideas as a useless duplication of this world: useless, quite aside from the apparently intolerable difficulties involved in Platonism, because skepticism and all the troubles inherited from the Presocratics can be satisfactorily removed without its dubious aid. The student should be forewarned that Aristotle is not building on unaltered Platonic foundations; but precisely what Aristotle accepts from Plato and what he rejects, and how he combines and modifies the several factors, is a long and intricate story which makes Aristotle one of the hardest philosophers to understand. Then, too, his dull and methodical style does not cheer the flagging spirit. Plato was a vigorous and stimulating writer; he could combine the subtleties of epistemology, the excitement of politics, and the mathematical awe of astronomy all in one dialogue. The interrelations of the subjects, he constantly keeps before our eyes. Aristotle, on the contrary, carefully devotes one book to Logic, another to Physics, another to Psychology, and so on. This method undoubtedly has advantages, but the interrelations, which still exist, are hidden from view and must be sought out.

The Law of Contradiction

It is most appropriate to begin an account of Aristotle with some reference to his views on logic because the books on logic are logically put first in the corpus, and because his discussion of the fundamental laws of logic – the law of contradiction and the law of excluded middle – though taken from the Metaphysics, Book Gamma, forms a firm connection between earlier philosophy and the body of Aristotelian thought. For if Aristotle rejects the essential principles of Platonism, we should see at once how he will avoid the skepticism of Protagoras. Also it is at this point that the connection between logic and natural philosophy in general can be most clearly seen. For although logic aims to discover the principles on which all true judgment depends, it is not a merely formal science of thinking; but rather, since truth requires a relation to reality, the laws of logic must be not only the laws of thought, but the laws of reality as well.

Logic and Reality

Aristotle introduces the topic by questioning whether logic and reality are the objects of the same science or of two different sciences. In view of the fact that the truths of logic and the principles of reality apply universally and are not restricted to any special field of study, Aristotle concludes that they belong to the same science. The truths of botany or of geometry, on the other hand, do not apply universally: Geometry concerns being in so far as it occupies space, and botany is limited to being as it exhibits nutrition and growth. Yet all the special sciences make common use of the laws of logic because these laws hold for all reality, and not merely for that part of reality that the special science studies. But the special sciences use logic without discussing it. It would be incongruous for a botanist or an astronomer to discuss the nature of truth and the law of contradiction. No doubt some of the Presocratics did so, and their inclusion of this material is perhaps defensible on the ground that they thought they were discussing the whole of reality. But in this they were mistaken; for nature is only one genus of reality, and physics, while it is a kind of wisdom, is not the first kind. Therefore there must be a still more universal science that deals with primary being, and to this science Aristotle sometimes gives the name of First Philosophy. As the botanist or physicist is responsible for the most general principles within his special sphere, principles applying to the particular kind of being that forms the subject matter of that science, so the philosopher must state and explain the principles that apply to being without qualification, to all being without exception, to being qua being – principles that are absolutely universal without any restriction at all. It is therefore the prerogative of philosophy, and not of botany or any other special science, to study the most general principles of all existence.

The most certain of all principles is the law of contradiction, for it is impossible to be mistaken about it. It is not an hypothesis, a tentative by which to rise to something more general, for a principle which everyone must have who knows anything about being cannot be so characterized. The principle is this: The same attribute cannot attach and not attach to the same thing in the same respect. Or, otherwise, contrary attributes cannot belong to the same subject at the same time. This principle, be it noted again, is stated not merely as a law of thought, but primarily as a law of being. The ontological form is basic; the purely logical is derivative: It becomes a law of thought because it is first a law of being. If anyone should object to the law of contradiction and should assert, as Heraclitus is supposed to have done, that contrary attributes attach to the same thing, it would be necessary to conclude that he cannot believe what he says. For if we have shown that the number three cannot be both odd and even, and that a stone cannot be both heavy and light, and so on, then it follows that no one can think that three is both odd and even, even though he verbally makes such an assertion. Anyone who pretended to believe that contrary attributes attach to the same subject would be affirming two contrary opinions at the same time; and these two opinions would be, as it were, two contrary attributes attaching to him as a subject. But this is what the law of contradiction makes impossible.

Indemonstrable Axioms[3]

Not only has the Heraclitean coexistence of contraries been maintained, but there are some writers who, thinking that the above derivation of psychological from ontological impossibility is circular, demand that the law of contradiction be formally demonstrated [deduced]. This demand, however, evinces their ignorance. The demonstration [deduction] of a proposition, such as any theorem in geometry, is completed only when it is referred to the axioms. If the axioms in turn required demonstration [deduction], the demonstration [deduction] of the proposition with which we began would remain incomplete, at least until the axioms could be demonstrated [deduced]. But if the axioms rest on prior principles, and if these too must be demonstrated [deduced] – on the assumption that every proposition requires demonstration – the proof of our original theorem would never be finished. This means that it would be impossible to demonstrate [deduce] anything, for all demonstration [deduction] depends on indemonstrable [non-deducible] first principles. Every type of philosophy must make some original assumptions. And if the law of contradiction is not satisfactory, at least these Heracliteans fail to state what principle they regard as more so. Nonetheless, though the law of contradiction is immediately evident and is not subject to demonstration, there is a negative or elenctic[indirect] argument that will reduce the opposition to silence.

Significant Speech

The negative method avoids the charge of begging the question, for it is the opponent and not oneself who makes the assertion. Of course, this depends on the opponent’s willingness to say something. The proof aims to show the opponent who attacks the law of contradiction that so soon as he says anything at all, he is recognizing the principle. If he should say nothing, we have neither an opponent nor an objection to face. Nor need we insist that he make some tricky admission that plays into our hands. All that is required is that he say something significant for himself and for us, for this is the presupposition of every understanding between two persons, or even of one person’s understanding himself. Let the opponent then say something: that three is an odd number or that Socrates is a man. It will always be of the form, x is y. Now, in the first place, the word is has a definite meaning and does not mean is not. Therefore, Protagoras was mistaken when he said that everything is and is not.1 But perhaps the argument will be clearer if we consider the x and the y.

In any sentence the predicate, the y, must have a single, definite meaning; and when we say that x is y, or that Socrates is a man, we are asserting of Socrates the meaning of man, whatever it may be – two-footed animal, perhaps. Thus we assert something definite. The remark that words have several meanings will not damage this contention, provided the meanings are limited in number. Suppose the word man had ten different meanings: It would be possible to invent ten different terms so that each term would stand for a single meaning; and once more the predicate and the assertion as a whole would be definite. If, however, terms had an infinite number of meanings, then all reasoning would come to an end. For if a word is to convey a significance, it must not only mean something, it must also not mean something. If it had all the meanings of all the terms in the dictionary, it would be useless in speech. Therefore, if terms had an infinite number of meanings, no term would have one meaning; and not to have one meaning is to have no meaning; but if words have no meaning, it is impossible to argue with other people or even to reason privately within oneself. If we do not think one thing, we think nothing; but if we can think of one thing, then we can assign to it a single unambiguous term. On this basis it is impossible that being a man should mean precisely not being a man, or that perception should be non-perception, or that a wind should be both y and not-y. And this is in reality a justification of the law of contradiction.

The Sophists, both of antiquity and of the present, ignoring the ontological basis of this argument, attempt the reply that what one person calls a man, another may call a mouse and not a man. Hence the same thing would be both man and not-man. But this is elementary ambiguity. The question is not whether a subject can be man and not-man in name, but whether it can be so actually or ontologically. If man and not-man mean two different things, as was indicated above, and if man means two-footed animal, it follows that anything that is a man must be a biped. But if this must be so, i.e., if this is necessary, the contrary is impossible: It is impossible that the subject should not be a two-footed animal, and hence the same subject cannot possibly be both man and not-man.

Denial of Substance

Further to refute his opponents, Aristotle plunges into logical and ontological complexities that will try the most ambitious student. Those who argue against the law of contradiction must also deny substance and reality. To explain how this is so and why it is absurd requires reference to the theory of categories, later to be explained. To anticipate, however, it may be briefly stated that a category is a predicate; or, more precisely, the ten categories are the ten types of possible predicates. For example, of Socrates it may be said that he is a man, he is ugly, he is wise, he is short, he is heavy, and perchance he is a musician. But of these, the predicate man holds a favored position. Heavy and musical are accidental predicates; that is, it is not necessary or essential to being a man that one should be heavy or musical: There are men who are frail and unmusical. These predicates and other accidental predicates fall under the categories of quality, quantity, relation, or others. But the predicate man, when one says that Socrates is a man, is no accident: Man is what Socrates essentially is. The predicate man falls under the category of substance or reality. And the category of substance is basic because there can be no quality or quantity unless there is a substance that it is the quality of.

The Sophistic opponents of logic, however, do away with substance, for they must say that all attributes are accidents, and that no subject is essentially man. The line of reasoning behind this is as follows. To be essentially and substantially man is incompatible with being not-man or not being man, for when we say that Socrates is essentially man, we are designating his substance; and to designate a thing’s substance, essence, or reality is to deny that it is essentially or really something else. The skeptical relativists must say, therefore, that nothing can be defined, and that all attributes are accidental. But if all predication is accidental, there will be no reality of which the predication is made, and predication would be endless. This, however, is impossible, because, far from being endless, not more than two terms can be joined in accidental predication. We may say that the musician is blond or even that the blond is musical; but the accidental conjunction of blond and musical is possible only because they are both accidents of the same reality – Socrates perhaps. In the absence of an underlying subject of which both are predicates, blond could not be predicated of musical nor musical of blond. Now, when we say that Socrates is musical or that Socrates is blond, the predicate is not related to its subject as in the previous predications, for, while blond and musical were equally accidents of an underlying reality, Socrates and musical are not thus on the same level as accidents of some third subject. Socrates is not a predicate at all, and hence there cannot be an infinite series of predicates: Every series must end with a reality.

As this section of Aristotle is somewhat subtle, and as its importance has been seen in Plato’s refutation of Protagoras, it will be well to elaborate a little. Aristotle may be willing to admit that the law of contradiction as stated does not hold for accidental predication. The musician can be white; yet since white is “not-musical,” the musician can be “not-musical.” But with substantial predication, the case is different. Suppose we ask the opponent if A is a man. He could answer, Yes, but he is also white and musical, and these are not-man; hence, A is man and not-man. This answer is correct to the extent that a subject may have an indefinite number of accidents; but so understood the answer is beside the point. Our original question was, Is A essentially a man? If the opponent ignores the “essentially,” as he did in the answer just given, he should list all the accidents – all, and that includes the negative as well as the positive ones. He should therefore say A is man, musical, white, not-green and therefore blue, not-ship and therefore house. For, if it is true that man is not-man, as the opponent claimed just above, it is all the more true that man is not-ship; but since house is not-ship and since on this theory contrary accidents attach, the man must be both a house and also a ship. Such a list of accidents would be infinite. Yet, if the opponent begins to list these accidents, he ought to continue with them. Let him give all or none. There is no reason for specifying only three or four. From which it follows that if he begins and continues, he will take so long that we shall be spared the trouble of answering him. In other words, if the opponent depends on accidental predication, if he repudiates the distinction between substantial and accidental predication, discussion ends. On this theory no predicate is definitive, and the metaphysical implication is that reality does not exist.

Now, to repeat a thought previously stated near the beginning of this analysis of the law of contradiction: This analysis or “proof” is a negative or elenctic one. It is not a demonstration based on more original principles. A careless reading might conclude that the law is demonstrated from the principle that every word must have a single meaning. But the truth of the matter is quite the reverse. Aristotle is saying rather that every word must have a single meaning because the principle of contradiction holds. He is applying the law to this particular case. And the particular case is chosen for the purpose of showing that an opponent cannot carry through his own theory. He becomes tangled in an infinite regress and must drop out of the argument. Therefore, if anyone, including the opponent, wishes to argue, reason, discuss, or say anything meaningful, he must presuppose the law of contradiction. Hence, this law is not demonstrated from some higher principle, but Aristotle shows that it must be presupposed by anyone who wishes to speak intelligibly.

The inanity of skeptical relativism was hinted at in the remark above that the musician must be a not-ship and therefore a house. This has a further ontological implication. If contradictory statements are true of the same subject at the same time, evidently all things will be the same thing. Socrates will be a ship, a house, as well as a man; but then Crito too will be a ship, a house, and a man. But if precisely the same attributes attach to Crito that attach to Socrates, it follows that Socrates is Crito. Not only so, but the ship in the harbor, since it has the same list of attributes too, will be identified with this Socrates-Crito person. In fact, everything will be everything. Therefore, everything will be the same thing. All differences among things will vanish and all will be one. Such is the metaphysical nonsense to be derived from Protagoras or anyone else who denies the law of contradiction.[4]

As a Christian deductionalist it is important to consider logic and theology proper.  Thus, here is Clark to talk about John 1:1.  Clark’s board focus is, “the Logic was God,” but particularly he focuses on the law of non-contradiction and the motion of God’s thinking.

Gordon Clark. He explains how the LOGOS is the Divine Nature itself. Thus, not only is logic a doctrine taught from the Bible, it is a Ultimate Question of life for man.

Logic Is God

It is to be hoped that these remarks on the relation between God and truth will be seen as pertinent to the discussion of logic. In any case, the subject of logic can be more clearly introduced by one more Scriptural reference. The well-known prologue to John’s Gospel may be paraphrased, “In the beginning was Logic, and Logic was with God, and Logic was God…. In logic was life and the life was the light of men.”

This paraphrase-in fact, this translation-may not only sound strange to devout ears, it may even sound obnoxious and offensive. But the shock only measures the devout person’s distance from the language and thought of the Greek New Testament. Why it is offensive to call Christ Logic, when it does not offend to call him a word, is hard to explain. But such is often the case. Even Augustine, because he insisted that God is truth, has been subjected to the anti-intellectualistic accusation of “reducing” God to a proposition. At any rate, the strong intellectualism of the word Logos is seen in its several possible translations: to wit, computation, (financial) accounts, esteem, proportion and (mathematical) ratio, explanation, theory or argument, principle or law, reason, formula, debate, narrative, speech, deliberation, discussion, oracle, sentence, and wisdom.

Any translation of John 1:1 that obscures this emphasis on mind or reason is a bad translation. And if anyone complains that the idea of ratio or debate obscures the personality of the second person of the Trinity, he should alter his concept of personality. In the beginning, then, was Logic.

That Logic is the light of men is a proposition that could well introduce the section after next on the relation of logic to man. But the thought that Logic is God will bring us to the conclusion of the present section. Not only do the followers of Bernard entertain suspicions about logic, but also even more systematic theologians are wary of any proposal that would make an abstract principle superior to God. The present argument, in consonance with both Philo and Charnock, does not do so. The law of contradiction is not to betaken as an axiom prior to or independent of God. The law is God thinking.

For this reason also the law of contradiction is not subsequent to God. If one should say that logic is dependent on God’s thinking, it is dependent only in the sense that it is the characteristic of God’s thinking. It is not subsequent temporally, for God is eternal and there was never a time when God existed without thinking logically. One must not suppose that God’s will existed as an inert substance before he willed to think.

As there is no temporal priority, so also there is no logical or analytical priority. Not only was Logic the beginning, but Logic was God. If this unusual translation of John’s Prologue still disturbs someone, he might yet allow that God is his thinking. God is not a passive or potential substratum; he is actuality or activity. This is the philosophical terminology to express the Biblical idea that God is a living God. Hence logic is to be considered as the activity of God’s willing.

Although Aristotle’s theology is no better (and perhaps worse) than his epistemology, he used a phrase to describe God, which, with a slight change, may prove helpful. He defined God as “thought-thinking-thought.” Aristotle developed the meaning of this phrase so as to deny divine omniscience. But if we are clear that the thought which thought thinks includes thought about a world to be created-in Aristotle God has no knowledge of things inferior to him-the Aristotelian definition of God as “thought-thinking-thought” may help us to understand that logic, the law of contradiction, is neither prior to nor subsequent to God’s activity.

This conclusion may disturb some analytical thinkers. They may wish to separate logic and God. Doing so, they would complain that the present construction merges two axioms into one. And if two, one of them must be prior; in which case we would have to accept God without logic, or logic without God; and the other one afterward. But this is not the presupposition here proposed. God and logic are one and the same first principle, for John wrote that Logic was God. At the moment this much must suffice to indicate the relation of God to logic. [5]


H.W.B. Joseph gives a short summary of the Three Laws of Logic.

The Three Laws of Thought.

The connection between questions about our thinking, and what we must think things to be, is excellently shown in the so-called Laws of Thought. These are certain very general principles exemplified in all thinking, and some have supposed the task of Logic to consist merely in developing their implications. They are known as the Law of Identity, the Law of Contradiction, and the Law of Excluded Middle. The Law of Identity may be formulated by saying that whatever is, is ‘ : or symbolically, that A is A’ ; the Law of Contradiction, that ‘ a thing cannot both be and not be so and so ‘ that ‘ contradictory propositions cannot both be true ‘, or that A cannot be B and not be B ; the Law of Excluded Middle, that is a thing either is or is not so and so ‘, that contradictory propositions cannot both be false ‘, or that ‘ A either is or is not B ‘. In other words, if we think about anything, then (1) we must think that it is what it is; (2) we cannot think that it at once has a character and has it not; (3) We must think that it either has it or has it not.
Now though these are called laws of thought, and in fact, we cannot think except in accordance with them, yet they are really statements which we cannot but hold true about things. We cannot think contradictory propositions, because we see that a thing cannot have at once and not have the same character; and the so-called necessity of thought is really the apprehension of a necessity in the being of things. This we may see if we ask what would follow, were it a necessity of thought only; for then, while e.g. I could not think at once that this page is and is not white, the page itself might at once be white and not be white. But to admit this is to admit that I can think the page to have and not have the same character, in the very act of saying that I cannot think it; and this is self-contradictory. The Law of Contradiction then is metaphysical or Ontological.

So also, is the Law of Identity. It is because what is must be determinately what it is, that I must so think. That is why we find a difficulty in admitting the reality of absolute change, change when nothing remains the same; for then we cannot say what it is which changes.

The Law of Excluded Middle is so far different as a disjunctive proposition expresses doubt, and doubt belongs to the mind, not to things. But to deny that this page need either be or not be white is to deny that it need be anything definite; determinateness involves the mutual exclusiveness of determinate characters, which is the ground of negation; and that is a statement about things. In other words, unless the primary Laws of Thought were Laws of Things, our thought would be doomed by its very nature to misapprehend the nature of things.[6]

Vincent Cheung explains the concept of how a contradiction cancels the two propositions out. Thus, in theology would be there would be no doctrine to affirm or deny. There would be no salvation, no God or no man to affirm or deny.

For any proposition that affirms X, the proposition that contradicts it is one that affirms not-X. This is what a contradiction means. Any proposition that affirms one thing is by necessity also a denial of its opposite. To affirm X is to deny not-X, and to affirm not-X is to deny X. To keep this simple, let us assume that Y = not-X, so that the opposite of X is Y. Thus to affirm X is to deny Y, and to affirm Y is to deny X. Or, X = not-Y, and Y = not-X. Then, since to affirm a proposition is to deny its opposite, to affirm X and Y at the same time is the equivalent of affirming not-Y and not-X. Thus to affirm two contradictory propositions is in reality to deny both. But to affirm both not-Y and not-X is also to affirm X and Y, which again means to deny Y and X. And so the whole operation becomes meaningless. The upshot is that it is impossible to affirm two contradictory propositions at the same time.

To affirm the proposition, “Adam is a man” (X), is to deny the contradictory proposition, “Adam is not a man” (Y, or not-X). Likewise, to affirm the proposition, “Adam is not a man” (Y), is to deny the contradictory proposition, “Adam is a man” (X). Now, to affirm both “Adam is a man” (X) and “Adam is not a man” (Y) is only to deny both propositions in reverse order. That is, it is equivalent to denying “Adam is not a man” (Y) and “Adam is a man” (X). But then we are back to affirming the two propositions in reverse order again. When we affirm both, we deny both; when we deny both, we affirm both. Therefore, there is no intelligible meaning in affirming two contradictory propositions. It is to say nothing and to believe nothing.

To illustrate, it is clear that divine sovereignty and human freedom contradict each other.[7]If God controls everything, including man’s thoughts, then man is not free from God. If man is free from God in any sense or to any degree, then God does not control everything.[8] Yet some theologians claim that the Bible teaches both divine sovereignty and human freedom, and so they insist that we must affirm both. However, since to affirm divine sovereignty is to deny human freedom, and to affirm human freedom is to deny divine sovereignty, then to affirm both only means to reject both divine sovereignty (in the form of an affirmation of human freedom) and human freedom (in the form of an affirmation of divine sovereignty). But to deny both means to affirm both in reverse order, and to affirm both means to deny both in reverse order again.

The necessary result is that the person who claims to believe both divine sovereignty and human freedom believes neither. In claiming to believe all of the Bible, he in fact believes none of it. In this example, since the Bible affirms divine sovereignty and denies human freedom, there is no contradiction – not even an apparent one. On the other hand, when non-Christians allege that the incarnation of Christ entails a contradiction, the Christian does not have the option to deny either the divinity or the humanity of Christ. Rather, he must formulate the doctrine as the Bible teaches it, and show that there is no contradiction. The same applies for the doctrine of the Trinity. In any case, if a person claims that he sees contradictions in the Bible, this means that he does not – he cannot – believe the Bible.

A popular response is that these are only apparent contradictions; that is, the doctrines only seem like contradictions to the mind of men, but they are in perfect harmony in the mind of God. This answer is futile. There is no difference between an apparent contradiction and an actual contradiction when it comes to affirming it. It remains that to affirm one thing is to deny the other at the same time, so that to affirm both is to deny both, and that to deny both is to affirm both again. Thus the person who affirms an apparent contradiction really affirms nothing and denies nothing. Whether the contradiction is only an apparent one is irrelevant. As long as it appears real to the person, it is real enough.

Moreover, how can a person distinguish between an apparent contradiction from an actual contradiction? He can never know that a contradiction is only an apparent one.

Unless he knows how to resolve the apparent contradiction, it will appear the same to him as an actual contradiction. And if he knows that a contradiction is only an apparent one, then he has already resolved it, and the term contradiction no longer applies. If we must tolerate apparent contradictions, then we must tolerate all contradictions. We often challenge non-Christian views on the basis that they contradict themselves. But if we tolerate apparent contradictions, then there is nothing to prevent non-Christians from claiming that the contradictions in their worldviews are only apparent ones.[9]



[1] Obversion works because of the Law of Noncontradiction and excluded middle.

[2] Clark will be giving Aristotle’s explanation for the law of noncontradiction with his own commentary woven throughout. In General it seems Clark agreed with Aristotle’s indirect defense of the LoC because Clark used some similar remarks about the LoC and in defending the coherence of the Scripture against non-Christian worldviews in, “A Christian View of Men and Things,” see last chapter. And in his essay, “God and Logic.”

[3] Gordon is using the term “indemonstrable” as “non-deducible.” He states there are indirect arguments for logical tautologies. These are more like indrect methods to show. Similar to how a reductio ad adsurdum argument is an indirect use of denying the consequent.

[4] Gordon Clark. Thales To Dewey – A History of Philosophy. The Trinity Foundation. 2000. Pg.86-92. Chapter on Aristotle.

[] – Added by Author. Emphasis added by author.

[5] Gordon Clark, God and Logic.  Copyright © The Trinity Foundation, Post Office 68, Unicoi, Tennessee 37692
Phone: 423.743.0199 Fax: 423.743.2005

[6] H.W.B. Joseph. 1906. An introduction to LOGIC. Pg.13

Read the book here.

[7] The doctrine of divine sovereignty will be discussed and applied throughout this book. Also see Vincent Cheung, Commentary on Ephesians and The Author of Sin.

[8] The doctrine of compatibilism teaches that man is not free from God, but that man is still free in a sense. However, unless the kind of freedom under consideration is freedom from God, it is irrelevant, since the topic concerns God’s control over man. See Vincent Cheung, The Author of Sin.

[9] Vincent Cheung. Systematic Theology. 2010. Chapter, Scripture, sub-section, The Unity of Scripture.

Logic Lesson – Categorical vs. Hypothetical. James Creighton

By: James Creighton
§ 41. Relation of Categorical and Hypothetical Arguments.
— It is evident that the form of the hypothetical syllogism is very different from that of the categorical. But, although this is the case, it must not be supposed that with the former we have passed to a new and wholly distinct type of reasoning. In hypothetical reasoning, as in categorical, it is the presence of a universal principle which enables us to bring into relation two facts which formerly stood apart. Indeed, in many cases, it is a matter of indifference in which form the argument is stated. Thus, we may argue in hypothetical form: —
If a man is industrious, he will be successful,
A is an industrious man,
Therefore A will be successful.
The same argument may, however, be expressed equally well in categorical form: —
All industrious men will be successful,
A is an industrious man,
Therefore A will be successful.
It is clear that, in spite of the different forms in which the argument is expressed, the reasoning is essentially the same in both cases. The middle term, or general principle which makes it possible to unite the subject and predicate of the conclusion, in the hypothetical as well as in the categorical syllogism, is ‘ industrious.’ A will be successful, we argue, because he is industrious, and it is a rule that industrious men are successful.
Moreover, if an argument is fallacious in one form, it will also be fallacious when expressed in the other. The defects of an argument cannot be cured simply by a change in its form. When an hypothetical argument, in which the antecedent is denied, is expressed categorically, we have the fallacy of the illicit major term. Thus, to state the example of denying the antecedent given on page 146, we get: —
The case of his being well is a case of his writing,
The present is not a case of his being well,
Therefore the present is not a case of his writing.
Similarly, when an argument in which the consequent is affirmed is changed to the categorical form, the defect in the reasoning appears as the fallacy of undistributed middle —
If this tree is an oak, it will have rough bark and acorns,
This tree has rough bark and acorns,
Therefore it is an oak.
When this argument is expressed in categorical form, it is at once clear that the middle term is not distributed in either the major or minor premise: —
All oak trees are trees having rough bark and acorns,
This tree is a tree having rough bark and acorns,
Therefore this tree is an oak.
The change from the categorical to the hypothetical form of argument, then, does not imply any essential change in the nature of the reasoning process itself. Nevertheless, it is important to note that hypothetical propositions and hypothetical arguments emphasize one aspect of thinking, which is entirely neglected by the theory of the categorical syllogism. When dealing with the extension of terms (§ 16), we pointed out that every term, as actually used in a proposition, has both an extensive and an intensive function. That is, the terms of a proposition are employed both to name certain objects or groups of objects, and to connote or imply certain attributes or qualities. In the proposition, ‘ these are oak trees,’ the main purpose is to identify the trees given in perception with the class of oak trees. When, on the other hand, we say,’ ignorant people are superstitious,’ the proposition does not refer directly to any particular individuals, but states the necessary connection between ignorance and superstition. Although the existence of ignorant persons who are also superstitious is presupposed in the proposition, its most prominent function is to assert a connection of attributes which is wholly impersonal. We may perhaps say that, in spite of the categorical form, the proposition is essentially hypothetical in character. Its meaning might very well be expressed by the statement,’ if a man is ignorant, he is also superstitious.’ What is here emphasized is not the fact that ignorant persons exist, and are included in the class of superstitious persons, but rather the general law of the necessary connection of ignorance and superstition. The existence of individuals to whom the law applies is, of course, presupposed by the proposition. It is not, however, its main purpose to directly affirm their existence.

Creighton, James Edwin, 1861-1924

An Introductory Logic.

Martin Luther- The Bondage of the Will – Commentary

Martin Luther. The Bondage of the Will.

Quotes from, unless noted are from, Martin Luther, The Bondage of the Will; translated by J. I. Packer and O. R. Johnston; Fleming H. Revell ,1957


Martin’s argument in a quick summary. It seems to me it is constructed like a large fortiori argument. He defends the lesser in greater length, (relative level) to say you ought to accept the greater(ultimate), since the same conclusion is in both, which is, there is no free-will. But if you do, then how much more is the point made?

 God is the ultimate cause of all things directly and absolutely. That is, in philosophy verbiage, Christian ontology is God’s direct causality over all things, even evil. And so God is the author—on the ontological level—of all things including good and evil. God directly causes Satan to will evil, as directly as He causes a Saint to will to do good. However, if this seems too much for you right now, then consider it on the relative level. Man, relative to Satan’ power and their own inward evil heart is not free to will contrary to these masters. Also, the Saints in heaven, are not free to will to do evil. They are under the motion and master of God’s Spirit to do good. Their wills are non-effective to resist the Spirit’s control.  Thus, man’s will is non-effective against relative things such as Satan control, their sin nature’s control, and for saints, the Spirit’s control. Thus, for man’s will to be effective it must be free, but it is non-effective against its masters. Non-effective effective is nonsense. Thus, a non-freewill freewill is nonsense. However, since this is true, then why resist the Scripture’s teaching on the Ultimate level? For it would result in the same conclusion, that man will is non-effective.

Yet, for the God’s chosen they will be saved, sanctified and glorified. They will enjoy happiness without end, for God’s will is indeed very effective toward His chosen ones.

The end result then? Argumentum a fortiori. If man on the lesser “relative level” is not-free to sin and Satan, or to the Spirit of Life, then how much more is man not free on the “ultimate level,” when God is the only direct cause of all things? If man’s will is non-effective on the lesser, then how much more is it non-effective to the greater! Also, if God’s will is so effective when considered on the lesser relative level, and not from His position, then how much more is God’s will effective over all things when considered on the Ultimate level where He alone directly controls all things?


“So that which we call the remnant of nature in the ungodly and in Satan, as being a creature and a work of God, is no less subject to Divine omnipotence and action than all the rest of God’s creatures and works. Since God moves and works all in all, He moves and works of necessity even in Satan and the ungodly (204). [i.e. on the ultimate level God directly works evil in creatures as he does good in creatures.]

Here you see that when God works in and by evil men, evil deeds result; yet God, though He does evil by means of evil men, cannot act evilly Himself, for He is good, and cannot do evil; but He uses evil instruments, which cannot escape the impulse and movement of His power. The fault which accounts for evil being done when God moves to action lies in these instruments, which God does not allow to be idle. In the same way a carpenter would cut badly with a saw-toothed axe. Hence it is that the ungodly man cannot but errand sin always, because under the impulse of Divine power he is not allowed to be idle, but wills, desires and acts according to his nature (204).” [i.e. God created man—after Adam—with an evil nature. So on the relative level man wants evil, but the on ultimate ontology level God picks up this defective hammer, and by direct causality this defective hammer is moved and cannot but move when God moves it. Because it is defective and damaged it hammers badly, and so it is judge and defined as bad by God’s command.]

“So God’s hardening of Pharaoh is wrought thus: God presents from without to his villainous heart that which by nature he hates; at the same time, He continues by omnipotent action to move within him the evil will which He finds there. Pharaoh, by reason of the villainy of his will, cannot but hate what opposes him, and trust to his own strength; and he grows so obstinate that he will not listen nor reflect, but is swept along in the grip of Satan like a raging madman (207) [i.e. on the relative level Pharaoh wants to be bad. On the ultimate level, Pharaoh cannot resist God’s direct causality upon him and upon Satan.]

[Pharaoh’s] evil will would not have been moved or hardened of itself, but as the omnipotent Agent makes it act by means of his own inescapable movement.(207)” [.i.e. Ultimately, God is the author of evil, by direct causation]

“Had there been in Pharaoh any power to turn, or freedom of will that might have gone either way, God could not with such certainty have foretold his hardening” (211). [i.e. God foreknew because God predestined first. ]

“It is true that Judas acted willingly, and not under compulsion, but his willing was the work of God, brought into being by His omnipotence, like everything else.(213)” [i.e. God the author of evil, by direct causation]

“Paul teaches that faith and unbelief comes to us by no work of our own, but through the love and hatred of God (228).” [God the author of all good and evil, of all things by direct causation]

“What I assert and maintain is this: that where God works apart from the grace of His Spirit, He works all things in all men, even in the ungodly; for He alone moves, makes to act, and impels by the motion of His omnipotence, all those things which He alone created; they can neither avoid nor alter this movement, but necessarily follow and obey it, each thing according to the measure of its God-given power. Thus all things, even the ungodly, cooperate with God(267).” [God the author of all good and evil, of all things by direct causation]

“The king’s will cannot escape the action of the omnipotent God by which all men’s wills, good and bad, are moved to will and to act (259).” [God the author of all good and evil, of all things by direct causation]

“I answer: Whether God permit, or whether He incline, that permitting or inclining does not take place without the will and operation of God: because, the will of the king cannot avoid the action of the omnipotent God: seeing that, the will of all is carried along just as He wills and acts, whether that will be good or evil (10c Discussion: Second Part (Sections 114 – 130).” [God the author of all good and evil, of all things by direct causation]

It would certainly be a hard question, I allow-indeed, an insoluble one-if you sought to establish both the foreknowledge of God and the freedom of man together; for what is harder, yea, more impossible, than maintaining that contraries and contradictories do not clash? (215) [ free-will and God’s sovereignty are contradictions]

The apostle, therefore, is bridling the ungodly who take offense at his plain speaking, telling them they should realize that the Divine will is fulfilled by what to us is necessity, and that it is definitely established that no freedom or “free-will” is left them, but all things depend on the will of God alone (215).

What God wills is not right because he ought, or was bound, so to will; on the contrary, what takes place must be right, because he so wills it” (209). [There is no law over God. God’s Ethic is His ‘Choice’ or ‘Decree’ itself]

What does Luther say to Erasmus about this issue of God’s absolute and direct sovereign control, over man’s will and yes, even evil?

I give you hearty praise and commendation on this further account-that you alone, in contrast with others, have attacked the real thing, that is, the essential issue. You have not wearied me with those extraneous issues about the Papacy, purgatory, indulgences and such like trifles. . . . You, and you alone, have seen the hinge on which all turns, and aimed for the vital spot (319).


” Heap together, therefore, out of the large Concordances all the imperative words into one chaos, provided that, they be not words of the promise but of the requirement of the law only, and I will immediately declare, that by them is always shown what men ought to do, not what they can do, or do do. And even common grammarians and every little school-boy in the street knows, that by verbs of the imperative mood, nothing else is signified than that which ought to be done, and that, what is done or can be done, is expressed by verbs of the indicative mood.

Thus, therefore, it comes to pass, that you theologians, are so senseless and so many degrees below even school-boys, that when you have caught hold of one imperative verb you infer an indicative sense, as though what was commanded were immediately and even necessarily done, or possible to be done.[1]

[i.e. God’s command imposes responsibility, not freedom to do. “Ought to do,” is Ethics, and “can do,” or necessarily done,” is ontology.  So that God’s command/ethics does not include the power in man to do it.  These are different categories of systematic theology/philosophy. This phrase, “necessarily done,” is like the sophist’s saying, “necessary immutability,” i.e. ultimate ontology. Thus, Martin did include in this category contrast, Ethics versus ultimate ontology.]


“But what do they effect by this playing upon words” This is no more than saying, the act is not God Himself. This remains certain, that if the action of God is necessary, or if there is a necessity of the consequence, everything takes place of necessity, [then] how much [more] the act be not God Himself. But what need was there to tell us this? As though there was any fear of our asserting the things done were God Himself….” [2] [i.e. God is not what He causes. If God creates a river and directly causes it to move north, then God Himself is not a north flowing river. The same with men and their good and evil choices that God directly causes. Or if God causes a man to choose evil, then God is not that.]

“And what is the design of the apostles in proving their preaching by the Scriptures? Is it that they may obscure their own darkness by still greater darkness? What was the intention of Christ, in teaching the Jews to “search the Scriptures” (John v. 39,) as testifying of Him? Was it that He might render them doubtful concerning faith in Him? What was their intention, who having heard Paul, searched the Scriptures night and day, “to see if these things were so?” (Acts xvii. 11.) Do not all these things prove that the Apostles, as well as Christ Himself, appealed to the Scriptures as the most clear testimonies of the truth of their discourses? With what face then do we make them ‘obscure?’  [.i.e. The Scripture interrupted themselves and are revealed to be clear and precise to man about knowledge of God.]

Are these words of the Scripture, I pray you, obscure or ambiguous: “God created the heavens and the earth” (Gen. i. 1). “The Word was made flesh.” (John i. 14,) and all those other words which the whole world receives as articles of faith? Whence then, did they receive them? Was it not from the Scriptures? And what do those who at this day preach? Do they not expound and declare the Scriptures? But if the Scripture which they declare, be obscure, who shall certify us that their declaration is to be depended on? Shall it be certified by another new declaration? But who shall make that declaration?— And so we may go on ad infinitum.

In a word, if the Scripture be obscure or ambiguous, what need was there for its being sent down from heaven? Are we not obscure and ambiguous enough in ourselves, without an increase of it by obscurity, ambiguity, and darkness being sent down unto us from heaven? And if this be the case, what will become of that of the apostle, “All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction?” (2 Tim. iii. 16.) Nay, Paul, thou art altogether useless, and all those things which thou ascribest unto the Scripture, are to be sought for out of the fathers approved by a long course of ages, and from the Roman see! Wherefore, thy sentiment must be revoked, where thou writest to Titus, (chap. i. 9) ‘that a bishop ought to be powerful in doctrine, to exhort and to convince the gainsayers, and to stop the mouths of vain talkers, and deceivers of minds.’ For how shall he be powerful, when thou leavest him the Scriptures in obscurity—that is, as arms of tow and feeble straws, instead of a sword? And Christ must also, of necessity, revoke His word where He falsely promises us, saying, “I will give you a mouth and wisdom which all your adversaries shall not be able to resist,” (Luke xxi. 15.) For how shall they not resist when we fight against them with obscurities and uncertainties? And why do you also, Erasmus, prescribe to us a form of  Christianity, if the Scriptures be obscure to you![3]  [ i.e. Erasmus, You contradicted yourself. LOL. This is like saying all propositions are uncertain. If that is the case, then that proposition is uncertain]

“ [Erasmus correctly quotes Martin saying], “That whatever is done by us, is not done by Free-will, but from mere necessity. And that of Augustine also—that God works in us both good and evil: that He rewards His good works in us, and punishes His evil works in us.”[4] [i.e. God ultimately is the only cause, and judges us by His commands, from the causality He worked in us]

“But, by necessity, I do not mean compulsion; but (as they term it) the necessity of immutability, not of compulsion; that is, a man void of the Spirit of God, does not evil against his will as by violence, or as if he were taken by the neck and forced to it, in the same way as a thief or cut-throat is dragged to punishment against his will; but he does it spontaneously, and with a desirous willingness.”[5] [i.e. “necessity of immutability” is saying Ontology on the ultimate level is God’s direct causality over all things. And “not of compulsion,” is saying on the relative level man does what he wants to do from his own soul.]

“Therefore, to say, that the will is FREE, and that it has indeed power, but that it is ineffective, is what the sophists call ‘a direct contrariety.’ As if one should say, “Free-will” is that which is not free. Or as if one should term fire cold, and earth hot. For if fire had the power of heat, yea of the heat of hell, yet, if it did not burn or scorch, but were cold and produced cold, I should not call it fire, much less should I term it hot; unless, indeed, you were to mean an imaginary fire, or a fire represented in a picture.—But if we call the power of “Free-will” that, by which a man is fitted to be caught by the Spirit, or to be touched by the grace of God, as one created unto eternal life or eternal death, may be said to be; this power, that is, fitness, or, (as the Sophists term it) ‘disposition-quality,’ and ‘passive aptitude,’ this I also confess. And who does not know, that this is not in trees or beasts? For, (as they say) Heaven was not made for geese.

Therefore, it stands confirmed, even by your own testimony, that we do all things from necessity, not from “Free-will:” seeing that, the power of “Free-will” is nothing, and neither does, nor can do good, without grace.”[6] [i.e. A contrariety is that the truth of one means the falsity of the other, thus, a non-effective effective will is nothing and nonsense. Like a contradiction they cancel each other out, so that there is no knowledge; there is nothing to affirm or deny, nothing.  Also, if the man’s will is non-effective on the relative level against the sin-nature and Satan, then how much more on the (necessity of immutability) ultimate level where God directly controls man’s mind, directly controls the sin-nature and directly controls Satan’s will?]

“And thus, as soon as he presented to it outwardly, that which naturally irritated and offended it, then it was, that Pharaoh could not avoid becoming hardened; even as he could not avoid the action of the Divine Omnipotence, and the aversion or enmity of his own will.” [7] [ i.e. Martin speaks both of the Ultimate and Relative level regarding man’s will. Man’s will is not free on the ultimate level of God’s directly causality, “could not avoid the action of the Divine Omnipotence.” And man’s will even on the lesser relative level, cannot avoid the “aversion of their own enmity, or if saved, the Spirit’s law of life.” Again, if man on the lesser relative level is not-free to sin and death, or to the Spirit of Life, then how much more is man not free on the ultimate level when God is the only direct cause of all things. That is, if man’s will is non-effective on the lesser, then how much more to the greater!]



[1] Martin Luther. Bondage of the Will. Translated by Henry Cole. 2009 kindle eBook.

[2] Martin Luther. Bondage of the Will. Translated by Henry Cole. 2009 kindle eBook.

[3]   Martin Luther. Bondage of the Will. Translated by Henry Cole. 2009 kindle eBook.

[4] Martin Luther. Bondage of the Will. Translated by Henry Cole. 2009 kindle eBook

[5] Martin Luther. Bondage of the Will. Translated by Henry Cole. 2009 kindle eBook

[6] Martin Luther. Bondage of the Will. Translated by Henry Cole. 2009 kindle eBook

[7] Martin Luther. Bondage of the Will. Translated by Henry Cole. 2009 kindle eBook

Romans 8:28-30 – Logical Chain Argument

Romans 8:28-30

A logical chain argument, or, a Categorical Sorites.

Rom. 8:28-30 LEB

  1. And we know that all things work together for good for those who love God, for those who are called according to his purpose,
  2. because those whom he foreknew [i.e. Foreloved], he also predestined to be conformed to the image of his Son, so that he should be the firstborn among many brothers.
  3. And those whom he predestined, these he also called, and those whom he called, these he also justified, and those whom he justified, these he also glorified.[1]


The logical deduction Paul uses here is called a Sorites. This is simply a normal bullseye syllogism (i.e. A.A.A, where A is a proposition that = All Subject is in the Predicate),  but it continues to add additional categories, where the previous category is placed inside the next one.  (All A is inside of B, and all B is inside of C; Thus, all A is inside the category of C.)  What needs to happen is that the predicate of the previous proposition needs to be the subject of the next with affirmative propositions. This will create a circle diagram where one circle will be placed in the next. The circles do not lie; they give a visual demonstration of the deduction; to show if it is invalid or not. In this case, it is valid. Because this is a normal AAA bullseye type syllogism but only longer (i.e. A.A.A.A.A.), one is able (if the sorites is done correctly) to take any two premises and form an independent AAA syllogism.

There are exceptions for a particular premise, for a negative one, and when it is stated in the form of a hypothetical (If P, then Q) but that is for another time.  Also, this type of syllogism may be stated in a reverse format. [2]

The form looks like this with a 6 premise sorites.


All A is inside the category of B

All B is inside the category of C

All C is inside the category of D

All D is inside the category of E

All E is inside the category of F

Thus, All A is inside the category of F.

A to F Sorites


I see examples of other people mentioning this sorites in Romans 8:30, however, they are prone to leave out verse 29, and thus only make this a 4-premise syllogism. This is a mistake, because the first premise comes from verse 29; and thus, the syllogism is in fact 5 premises.

At any rate, the first premise starts with, Those whom God foreloved are those He predestined.” The rest of the verse gives us extra insight as to what this predestination results in for both Jesus and for the ones predestined; however, this is not relevant for the immediate syllogism being made by Paul,  because the next verse simply picks up at the category of,  “whom He predestined … .” The predicate of premise is the subject of the starting premise in verse 30.  Paul does not give the conclusion of this syllogism.  However, in my experience of reading Paul he normally does gives the conclusion. I suspect that he does not here simply because he so exactly spells out the rest of this enthymeme sorites that the conclusion it is not needed, for it is obvious.

In summary, we are told all things work for our good who are called by God in verse 28. Paul then gives a sorites to show the undeniability of this reality. We are told from the initial love of God to glorification the saints are directed by God’s decree to love them, and that this decreeing leads to a good end, without any falling through the cracks or mishaps. Whom God foreloves He glorifies.  God direct and absolute sovereignty is the totality of all Christian metaphysics and ontology.  Soteriology is in fact a sub-category under metaphysics. That is, it is how God uses existence and causality toward this particular group of elect persons.

Also, it is in this syllogism that Paul shows the reality of verse 28’s category of “the called.” Paul shows us that this category needs to be seen in the larger logical and metaphysical reality of God’s decrees.  He desires for them to see it all put together in a chain argument. Here we find being “Called” is in the middle of the decreeing, and that the decree starts with being foreloved first, and then finally ends –without fail—being glorified with Christ.

See my book or article called, The Order of the Divine decrees to see how this fits together in an even larger view of the Divine Decrees.  Foreloved would be in decree 2. Predestination would be decree 3. Called would be 8. Justification would be 9. And Glorification would be point 10.


(A) Those whom God foreloved are (B) those whom God predestined.

(B) Those whom God predestined are (C) those whom God called.

(C) Those whom God called are (D) those whom God justified.

(D) Those whom God justified are (E) those whom God glorified.

Therefore, (A) those whom God foreloved are (E) those whom God glorified.



Predicate Logic.

Chain syllogism Rule for Natrual Deduction


 HCS = Hypothetical Chain Syllogism rule for Natural Deduction. (see pic)


L = Foreloved. g = God. P=predestined. C = Called. J = Justified. G = glorified. s = Sally.

For every x, if x is fore-loved by God, then x is predestined by God; and, if x is predestined by God, then x is called by God; and if x is called by God, then x is Justified by God; and if x is Justified by God, then x is glorified by God.

1. Ɐx (Lgx ⸧ Pgx) • Ɐx(Pgx ⸧ Cgx ) • Ɐx (Cgx ⸧ Jgx) • Ɐx (Jgx ⸧ Ggx )
2. Lgs         ⸫ Ggs
3. (Lgs ⸧ Pgs) • (Pgs ⸧ Cgs ) • (Cgs ⸧ Jgs) • (Jgs ⸧ Ggs )       1,2 UI
4. Ggs         3. HCS



[1] [] added by author.

[2] All A is B,  All C is A, All D is C,  All E is D, Thus, All E is B.