In the August 1998 issue of Creation Ex Nihilo Technical Journal (subsequently re-named Journal of Creation -- CMI's pseudoscientific rag, a so-called " peer reviewed science journal"), the famous chess-player Jonathan Sarfati tried his hand at writing a primer on the subject of logic, entitled Loving God with All Your Mind: Logic and Creation.
In keeping with the general observation that creationists cannot tell a proposition from a logical connective, let alone make a cohesive argument, this primer, um, leaves some things wanting.
In this side-by-side, we comment on the article in its entirety.
|Logic and reason are far from being incompatible with biblical Christianity. Rather, they are essential. Without them it is impossible to deduce anything from the true propositions of the 66 books of Scripture, the Christian’s final authority. This applies to Creation, one of the foundational doctrines of Christianity. Examples of valid and fallacious reasoning are discussed, with emphasis on showing how logical reasoning can support the truth of biblical creation, and demonstrate the fallacies in many evolutionists’ arguments.||One suspects from the introduction that the "logical reasoning" used is highly fallacious. One will not be disappointed.|
|Logic is the science of the relations between propositions.||Zero for three: logic is not science, not about relations, and does not concern only "propositions."
Logic is not science due to its entirely a priori nature. Depending on how it is studied it can be a part of philosophy or of mathematics.
Logic is not generally about relations on propositions, as propositional logic concerns only Boolean functions, a specific sort of relation.
Logic is not all about propositions, as propositional logic is not the only sort of logic. The aspiring logician should at least be familiar with first-order logic, which instead of propositions makes use of sentences or predicates; the well-known "Socrates is mortal" syllogism cannot be expressed in propositional logic.
|Logic can tell us what can be inferred from a given proposition, but it cannot tell us whether the given proposition is true in the first place. All philosophical systems rely on logical deductions from starting assumptions—axioms—which, by definition, cannot be proven from prior assumption. For our axioms, it is rational to accept the propositions revealed by the infallible God in the 66 books of the Bible.||Hint, fellows: if you are to accept a literal interpretation of the Bible as your set of axioms, then the only law of logic you need to know is the principle of explosion.|
|Martin Luther correctly distinguished between the magisterial and ministerial use of reason.
The magisterial use of reason occurs when reason stands over Scripture like a magistrate and judges it. Such "reasoning" is bound to be flawed, because it starts with axioms invented by fallible humans and not revealed by the infallible God. But this is the chief characteristic of liberal ‘Christianity’.||On the contrary, St. Augustine distinguished between what the Bible actually says and how it is interpreted, stating that while the former is not subject to reason, the latter is, and warning against the tendency "to affirm rashly some one meaning to the prejudice of another and perhaps better explanation." He also said of those who do this, "For then, to defend their utterly foolish and obviously untrue statements, they will try to call upon Holy Scripture for proof and even recite from memory many passages which they think support their position, although they understand neither what they say nor the things about which they make assertion."|
|It is refuted by Scriptural passages such as Isaiah 55:8–9:
8. "For my thoughts are not your thoughts, neither are your ways my ways,’ declares the Lord.
9. ‘As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts.’
Note that this does not say ‘My logic is higher than your logic’. If so, then if we believed 2+2=4, God could believe 2+2=5. What it does mean is that God knows every true proposition, while we know only a part. Another passage is Romans 9:19–21:
19. One of you will say to me: ‘Then why does God still blame us? For who resists his will?’
20. But who are you, O man, to talk back to God? Shall what is formed say to him who formed it, ‘Why did you make me like this?’
21. Does not the potter have the right to make out of the same lump of clay some pottery for noble purposes and some for common use?
|Dr. Sarfati, along with the other people at CMI, should mark St. Augustine's statement above concerning quote-mines of the Bible. And in this case he has picked up verses that have nothing to do with logic, instead dealing on morals and the problem of evil, respectively. In the process illustrating the doctrine of alternative facts.|
|The ministerial use of reason occurs when reason submits to Scripture. This means that all things necessary for our faith and life are either expressly set down in Scripture or may be deduced by good and necessary consequence from Scripture.||How, after all this, CMI lackeys can still call themselves "scientists" is beyond comprehension.|
|Many Scriptural passages show that Christians are not supposed to check in their brains at the church door, but to use their God-given minds in subjection to God’s Word, e.g. Isaiah 1:18
“”‘Come now, let us reason together,’ says the Lord. ‘Though your sins are like scarlet, they shall be as white as snow; though they are red as crimson, they shall be like wool.’
|Obviously Dr. Sarfati ran out of even remotely relevant Bible quotes and is now just grepping the Bible for occurrences of the word "reason."|
36 ‘Teacher, which is the greatest commandment in the Law?’
37 Jesus replied: ‘Love the Lord your God with all your heart and with all your soul and with all your mind.’
38 This is the first and greatest commandment.’
|Now they stray even further, into complete irrelevance.|
“”Do not conform any longer to the pattern of this world, but be transformed by the renewing of your mind. Then you will be able to test and approve what God’s will is—his good, pleasing and perfect will.
|1 Corinthians 2:16
Note—mind of Christ, not feelings or emotions of Christ.
“”‘For who has known the mind of the Lord that he may instruct him?’ But we have the mind of Christ.
|In other words, "True Christians are infallible because they've been lent all of God's brain-power." It would follow that God is somewhat dim.|
|Much confusion arises when some people disparage ‘head knowledge’. For example, Geoff Smith, who was Pastor of the large Auckland Bible Church (New Zealand), has pointed out that in some churches, anything that has to do with rational thinking is suspect and strongly discouraged.||Psychological projection meters are overloading.|
|Rational thinking is branded as something coming from the flesh. People of the Spirit won’t try to understand what’s happening—they will simply accept the ‘blessing’. The catch words are unmistakable: ‘Don’t try to understand this’, ‘Don’t try to analyse this’, ‘Don’t try to figure this out with your mind’, etc.
In such thinking there is no real understanding that faith is always built on knowledge. The prophet Isaiah asks repeatedly ‘Do you not know, have you not heard?’ (Isaiah 40:21,28).
Jesus repeatedly asks: ‘Have you not read …?’ and tells the Sadducees that they are in error because they ‘do not know the Scriptures or the power of God’ (Matt. 22:29).
In his letters Paul constantly shows that true, functional faith is always built on knowledge. Conversely, deficient faith is traced back to its unmistakable cause—deficient knowledge. Paul repeatedly asks the question ‘Don’t you know …?’ (Rom. 6:3, 16; 11:2; 1 Cor. 3:16; 1 Cor. 5:6; 1 Cor. 6:2, 3, 9, 15, 16, 19; 1 Cor. 9:13, 27). Notice also the same question being asked by James (James 4:4). Philip asked the Ethiopian eunuch: ‘Do you understand what you are reading?’ (Acts 8:30).
Part of the confusion lies in the misunderstanding of the word ‘heart’ in the Bible. Some people make a false contrast between ‘head-knowledge’ and ‘heart-trust’. When interpreting Scripture, it is important to work out what the authors meant by the term. In this case, one should work out what ‘heart’ meant to ancient Semites, not what it means in Hollywood pop-psychology. In the Bible, the word ‘heart’ is used 75% of the time to mean the mind or intellect. However, the Bible frequently contrasts the heart and the lips—sincerity vs. hypocrisy, for example:
“”The Lord saw how great man’s wickedness on the earth had become, and that every inclination of the thoughts of his heart was only evil all the time.
The New Testament concept of faith is compatible with reason. The Greek word for ‘faith’ is πίστις (pistis) which is related to the verb πιστεύω (pisteuo) meaning ‘believe’, and πείθω (pietho) meaning ‘to convince by argument.’ It never has the connotation of ‘believing six impossible things before breakfast’, but ‘is being sure of what we hope for and certain of what we do not see.’ (Heb. 11:1).
“”The fool says in his heart, ‘There is no God.’ They are corrupt, their deeds are vile; there is no one who does good.
|On the contrary, Jesus said that believers ought to think like newborn children with regard to doctrine (Luke 18:17).|
|Many non-Christians have a misconception of biblical faith, and unfortunately some Christians have accepted this.||Now if Dr. Sarfati will just grasp that many Christians, including himself, also have said misconception of their own accord, he will be sitting pretty.|
Logic in Biblical preaching and witnessing
|Christ’s chief apostle, Peter, commanded us (1 Peter 3:15):
“”But in your hearts set apart Christ as Lord. Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have. But do this with gentleness and respect.
The Greek word translated ‘answer’ in 1 Peter 3:15 is in fact ἀπολογία (apologia). This term is derived from the Greek words ἀπὸ (apo) = away from and λόγος (logos) = logic/reason, so means ‘out of logic/reason’, so refers to a reasoned defence that would be given in a court of law. The classic example is Plato’s Apology, Socrates’ defence against the charges of atheism and corrupting the youth. The word also appears in the negative in Rom. 1:20: unbelievers are ἀναπολογήτους (anapologētous) (without excuse / defence / apology) for rejecting the revelation of God in creation.
The word for ‘reason’ above is λόγος (logos), in this context meaning evidence that provides rational justification for one’s belief.
|The First Epistle of Peter was written to persecuted churches in Asia Minor; 1 Peter 3:15 occurs in the context of a paragraph on "suffering for doing what is right." In 1 Peter 3:15, Peter is saying that Christians should not be afraid to proclaim their belief in the resurrection of Jesus -- not that they need to give reasons for said belief.|
|Christ’s half-brother, Jude, commanded in verse 3 of his epistle:
“”‘… earnestly contend for the faith which was once delivered unto the saints.’
This implies a real intellectual battle to convince people of something righteous and true. Paul elaborated on this in 2 Corinthians 10:4–5:
“”4 The weapons we fight with are not the weapons of the world. On the contrary, they have divine power to demolish strongholds.
5 We demolish arguments and every pretension that sets itself up against the knowledge of God, and we take captive every thought to make it obedient to Christ.
|Of course, evolution is the major anti-God pretension of our age, so we must make great efforts to demolish it.||Not only is evolution not the "major anti-God pretension of the modern age" (that distinction has to go to Marxism-Leninism) but it is not even anti-Christian, let alone "anti-God."|
Accurate Definitions of Words
|It is impossible to have a logical discussion with people if there is no agreement on meanings of words, or with those who are dishonest with their terminology. Socrates, in Plato’s Phaedo, stated succinctly, ‘To use words wrongly and indefinitely is not merely an error in itself, it also creates evil in the soul.’
Many cults, including liberal ‘Christianity’, often use biblical terminology, but invest the words with entirely new meanings. They resemble Humpty-Dumpty who replied scornfully to Alice’s ignorance of what he meant, ‘When I use a word, it means just what I choose it to mean—neither more nor less.’||The ongoing psychological projection here has us in stitches. Also, note the scare-quotes around "Christianity" in reference to theological liberalism; those people disagree with the CMI party line, hence cannot be correct in the slightest.|
|Some prize examples of semantic gymnastics can be found in the ramblings of liberal ‘Christians’. Since they are being paid to defend doctrines they don’t believe, they redefine them instead. That way, they can pretend they are not violating their ordination vows. For them, God is not the Creator, but the ‘ultimate concern’; ‘Jesus is Risen’ means that His influence continued after His death; ‘Christian faith’ need not consist of holding any doctrines, although the NT states that those who forsake orthodox Christian doctrine have departed from the faith (1 Tim. 4:1, 5:8, 2 Tim. 3:8; cf Eph. 4:5).||Getting a little hot under the collar, are we? If all theological liberals are insincere about it, as is claimed here, whyever should they not pretend to be "orthodox" instead, as was previously done?|
|These are all examples of stipulative definitions. This fallacy is common among evolutionists who contrast ‘scientists’ and ‘creationists’. A creationist would respond by producing evidence that there are thousands of practising scientists who believe in biblical creation. But some evolutionists respond that such people cannot be true scientists because no true scientist can accept a creationist explanation, regardless of his qualifications or research experience.8 This becomes essentially a circular argument: all who are qualified in science and practice science and reject creation are opposed to creation.||This is of course making a straw man out of that terminology. We along with other evolution supporters contrast creationists and scientists, not because there are no reputable scientists who are creationists (which is true), but because creationism, having integral supernatural components to it, is categorically not science. Hence, with regard to the creation/evolution controversy, creationists approach it as creationists (no matter if they also work in science) and evolutionary biologists approach it as scientists.|
|The worst example of intellectual dishonesty is equivocation, that is, switching the meaning of a single word part-way through an argument. This deceitful practice is used by many evolutionary propagandists when defining the word ‘evolution’.|
|The theory of evolution really means the development of all living things from a single cell, which itself came from non-living chemicals.||Ironic that a section about moving the goalposts should start with a straw man. They are actually describing a combination of abiogenesis, common descent, and evolution. Although "evolution" is used as shorthand for this combination by both sides, evolution supporters were not the ones who started using it that way.|
|But many propagandists define evolution as ‘change in gene frequency with time’ or ‘descent with modification’ and use Darwin’s finches and industrial melanism in the peppered moths as clinching proof of ‘evolution’ and disproof of creationism!||A simple mistake to make, as it has taken a long time, plus barrelsful of evidence that only a person with Velveeta for brains could attempt to controvert, for creationists to accept even intra-baramin evolution.|
|An example is the atheist Eugenie Scott, Executive Director of the pretentiously named National Center for Science Education, the leading US organisation devoted entirely to evolution-pushing. She approvingly cited a teacher whose pupils said after her ‘definition’: ‘Of course species change with time! You mean that’s evolution?!’||And the lady spoke true.|
|Of course no creationist disputes that changes occur through time, but creationists disagree that the type of change required for molecules-to-man evolution occurs, i.e. changes that increase information content.||The CMI people are not very educated in the area of information theory and have made the above distinction into a pseudoscientific one that masks the true line of demarcation, viz., mutations that contradict a literal reading of the Bible did not happen.|
Truth and Falsity
|A simple definition of truth and falsity goes back at least as far as Aristotle (384–322 BC): ‘If I say of what is that it is, I speak the truth. If I say of what is not that it is, I speak falsely.’ That is, a statement is true if it corresponds to the facts, and false otherwise.||Quoting pagan philosophers! Get ready for the bullshit whammy in the next paragraph...|
|This should be obvious, but the atheistic anti-creationist Ian Plimer wrote:
Of the many crass blunders he makes in logic, mathematics, science and exegesis, which are well documented on this website, this is the worst.
“”‘In my view, the Bible is not true. However, it is the Truth.’
|The "atheistic" Prof. Plimer is no doubt being quote mined here. For starters, note that "true" has a lower-case T, while "Truth" has an upper-case T; he is speaking of two different kinds of truth.|
|In logic, an argument is defined as a sequence of statements comprising premises that are claimed to support a conclusion. As shown above, Scripture teaches that Christians are to argue in this sense. This is not the same as being argumentative, or arguing just for the sake of arguing.||It is not within the purview of logic to make assumptions as to why people are arguing; this is approaching the territory of the ad hominem fallacy. One can easily make a well-formed argument just to be argumentative, or just for its own sake.|
|Arguments can be either deductive or inductive. Deductive reasoning is reasoning from the general to the particular. Inductive arguments reason from a finite set of examples to a general rule.|
|Deductive arguments are the most important, so I will concentrate on them below.||In science, inductive arguments are far more important. Unless perhaps CMI gets all its "science" via extrapolation from the Bible, in which case the confusion is understandable.|
|A syllogism is a common type of deductive argument with two premises and a conclusion.|
|A valid argument is one where it is impossible for the premises to be true and the conclusion false, i.e. the conclusion follows from the premises. Note that validity does not depend on the truth of the premises, but on the form of the argument.
One example of a valid argument with true premises is:
1) All whales have backbones;
2) Moby Dick is a whale;
∴ Moby Dick has a backbone.
An example of a valid argument with a false premise and false conclusion is:
1) All dogs are reptiles;
2) All reptiles have scales;
∴ All dogs have scales.
|An invalid argument with a true premise and true conclusion is:
This is invalid because the conclusion contains terms not contained in the premise. It is important to recognise valid forms of argument, and use them.
The sun is larger than the earth;
∴ polytheism contradicts the Bible.
|This sort of logical fallacy is called a non sequitur. For countless examples of said fallacy, see CMI's website.|
|Many invalid arguments can be found in the works of politicians. On the astute British television political satire, Yes, Minister (episode ‘Party Games’), two head civil servants (Sir Arnold Robinson and Sir Humphrey Appleby) illustrated ‘politician’s logic’:
1) Something must be done;
2) This is something;
∴ We must do it.
As pointed out in the program, this is just as invalid as:
1) All cats have four legs;
2) My dog has four legs;
∴ My dog is a cat.
|A sound argument is a valid argument with true premises. The conclusion of a sound argument must be true. So, to prove the conclusion of a valid argument, it is sufficient to prove all premises are true. For example:
The form of the argument is valid, premises (1) and (3) are true by the normal definitions of words, (2) can be proven by science and Scripture (Gen. 25:22 and Lk. 1:41 use the same words for unborn and born children), (4) is proven by Gen. 9:6, Ex. 20:13, Rom. 13:9, so the argument is sound.
1) Abortion is intentional killing of a fetus;
2) A fetus is an innocent human being;
3) Intentionally killing an innocent human being is murder;
4) Murder is forbidden by God;
∴ Abortion is forbidden by God.
|Whyever not use the old "Socrates is mortal" argument instead of a politically loaded one whose soundness is hotly disputed?
Many people would dispute the second premise, that a fetus truly counts as a human being. The third premise is also debatable, such as with regards to euthanasia. It goes without saying that the fourth convinces nobody who doesn't share the same specific beliefs.
|A contradiction is defined as the conjunction of the affirmation and denial of a premise, in the same time, place, and sense (i.e. p and not-p, or in symbolic form, p.~p). For any pair of contradictory premises, one must be true and the other false. The Law of Non-Contradiction prevents both premises being true, while the Law of Excluded Middle points out that a pair of contradictory premises exhausts all possibilities. Another way of putting it is: a proposition must be either true or false—not both true and false, nor in some limbo state in between truth and falsity. This can be useful in listing all possible alternatives and refuting all of them but the correct one.|
|C.S. Lewis’s famous Trilemma argument is a good example.
- Jesus Christ is reported to have claimed to be God. The reports are either true or false.
- 1) If the reports are false, the reporters either knew they were false or they did not.
- 1a) If they knew they were false, they were liars—but who would die for what they know is a lie?
- 1b) If they did not know, then it is a big problem to explain how legends could accumulate around a historical figure in such a short time.
- 2) If the reports are true, then Jesus was either speaking falsely or truly.
- 2a) If Jesus spoke falsely He either knew it or he did not.
- 2ai) If He knew, He was a liar.
- 2aii) If He knew not, then He was a lunatic, since a claim to be God is the most absurd claim a mere creature can make.
- 2b) If Jesus spoke truly, then He really is God.
|This point is actually an expansion of the original Lewis trilemma ("Mad, Bad, or God"). One can easily tell the difference between what Prof. Lewis wrote (contained in point 2) and what Dr. Sarfati wrote, the reason being that Prof. Lewis possessed a brain, and furthermore actually used it when producing his argument.
The questions in both points (1a) and (1b) may be easily answered.
For (1a), Seneca the Younger is reported to have written, “Religion is regarded by the common people as true, by the wise as false, and by the rulers as useful.” It follows that a wise political activist would see reports of Jesus claiming divinity as false on their face, but also as a useful catalyst to rally the common people to a political movement. If this movement could be furthered by their becoming martyrs, it is entirely possible that they would do that.
For (1b), some people will accumulate legends really fast if there is a fast buck in it for them. And, as Acts 2:44 attests, many fast bucks awaited the apostles of the new religion.
Sarfati provides no explanation for why (2ai) and (2aii) must be false.
|Anti-Christians often charge the Bible with contradicting itself, as they realise that if the charge were proven, it would show that it affirms at least one false statement, thus disproving divine authorship. But most of these sceptics are ignorant of the above definition of a contradiction.||No, they are not. The "anti-Christians" may not know much about Biblical exegesis, but the average creationist is far more likely to be ignorant of the basic rules of inference.
And the Bible, or at least CMI's preferred literal reading of it, does contradict itself; see our article on problems with biblical inerrancy.|
|For example, Mt. 20:29 ff. which states that Christ healed two blind men does not contradict Mk. 10:46 ff. which states that Bartimaeus was healed, as the latter does not say only Bartimaeus was healed.||This passes the strictest logical muster, but muddies the much-touted "clarity" and "simplicity" of the Bible.
Alternatively, one can argue that this non-contradiction is something of a given, since the Gospel of Matthew used the Gospel of Mark as a source.|
|Some other alleged contradictions can be resolved by showing that words are being used in different senses, e.g.:
John 1:18 vs Exodus 24:9–10: in the former, Jesus states, ‘No man has seen God [in His full glory as Sovereign of the Universe] at any time; the only begotten God [Jesus] … has explained Him.’ In the latter, Moses was clearly beholding a veiled presence of God, metaphorically referred to as ‘under His feet’. In Exodus 33:18–23, a distinction is also made between beholding God’s full glory (‘face’) and His veiled presence (‘back’).||Given this interpretation, why CMI insists that the word yom in Genesis refers to 24-hour days is pretty much beyond comprehension.|
|Although many cults claim that the biblical doctrine of the Trinity is self-contradictory, it is not. The oneness and threeness of God refer to different aspects. The three eternal and co-equal Persons of the Godhead—Father, Son and Holy Spirit—are the same in essence but distinct in role—three Persons (or three centres of consciousness) and one Being.||It took entire legions of very smart people several centuries and a good deal of ancient Greek philosophy to hammer out the doctrine of the Trinity in such a way as not to be contradictory. They really had to stretch things to accomplish the task.|
|An important aspect of contradiction is self-refutation. Many statements by anti-Christians might appear reasonable on the surface, but when the statement is turned on itself, it refutes itself.||"Anti-Christians" are not the only ones making these statements. See, for example, the old refutation to the argument from design, "If everything needs a designer, then who designed God?"|
|Some common examples are:
- ‘There is no truth’—this would mean that this sentence itself is not true.
- ‘We can never know anything for certain’—so how could we know that for certain?
- ‘A statement is only meaningful if it is either a necessary truth of logic or can be tested empirically’ (the once popular verification criterion for meaning of the ‘Logical Positivists’)—this statement itself is neither a necessary truth of logic nor can it be tested empirically, so it is meaningless by its own criteria.
- ‘There are no moral absolutes, so we ought to be tolerant of other people’s morals’—but ‘ought’ implies a moral absolute that toleration is good.
|Most of these are legitimate examples of self-refuting ideas, but the one about logical positivism is not. The statement can be tested empirically to some degree, and thus it took many centuries for Gödel to come along with his incompleteness theorems, which refuted it.|
4) Conditional Statements and Implications
|These are of the form: ‘if p then q’ (if p is true, then q is true). Another way of putting it is ‘p implies q’, or in symbolic form p ⊃ q (or p → q). Yet another way is saying that p is a sufficient condition for q, while q is a necessary condition for p. P is called the antecedent; and q is called the consequent.|
|Asserting the truth of the implication (p ⊃ q) does not in itself imply that the antecedent (p) is true—only that if p were true, q must logically follow from it.||No, it is that if p is true, q is true. The truth of the implication means that q follows from p no matter if p be true or false.|
|For an example of a misunderstanding of this point, some use the following passage to ‘prove’ that it is possible to speak with ‘angelic tongues’—1 Cor. 13:1–3:
Paul makes several conditional statements showing that without love, no matter what other wonders he might hypothetically be able to perform, he would be nothing. He is no more asserting that there are special angelic tongues than that he moved mountains or gave his body to the fire. There may be passages to support a common Pentecostal practice, but this is not one of them (at Creation Ministries International, we take no position on this issue).
1 If I speak in the tongues of men and of angels, but have not love, I am only a resounding gong or a clanging cymbal.
2 If I have the gift of prophecy and can fathom all mysteries and all knowledge, and if I have a faith that can move mountains, but have not love, I am nothing.
3 If I give all I possess to the poor and surrender my body to the flames, but have not love, I gain nothing.
|Another good example is Jesus’ statement in Matthew 12:27:
27 And if I drive out demons by Beelzebub, by whom do your people drive them out? So then, they will be your judges.||That is not a well-formed conditional, but a question.|
|I doubt that any Christian would claim that Jesus was asserting that He drove out demons by Beelzebub! He was showing that if His opponents were right in their accusation, then the accusation would equally apply to their own people. Jesus’ argument is an example of reductio ad absurdum (see below).|
Table 1: Affirming the Antecedent
| p implies q
| p is true
| therefore q is true
| Affirming the Antecedent
|| Modus ponens
Table 2: Denying the Consequent
| p implies q
| q is false
| therefore p is false
| Denying the Consequent
|| Modus tollens
|From a conditional statement, one can construct two types of valid inference: modus ponens (Table 1) and modus tollens (Table 2). Modus ponens is Latin for ‘method of constructing’. The reason it is called ‘affirming the antecedent’ is that the argument proves that the consequent must be true if the antecedent is affirmed. Modus tollens is Latin for ‘method of destroying’. This type of argument proves that the antecedent must be false if the consequent is denied.
There are two types of invalid inference: the fallacies of affirming the consequent (Table 3) and denying the antecedent (Table 4).|
Table 3: Fallacy of Affirming the Consequent
| p implies q
| q is true
| therefore p is true
|| ∴ p
Table 4: Fallacy of Denying the Antecedent
| p implies q
| p is false
| therefore q is false
|| ∴ ~q
|To illustrate: starting with the implication: If Jesus rose from the dead (p), then His bones cannot be found (q); and combining this with four possible premises as follows:
1) Jesus rose from the dead (p is true)
∴ His bones cannot be found (q is true)
- - valid.
2) Jesus’ bones cannot be found (q is true)
∴ He rose from the dead (p is true)
- - invalid.
|A reminder: validity is independent of the truth or falsity of the premises or conclusion. We accept that Jesus rose, but not that every dead person whose bones are missing also rose.|
3) Jesus did not rise from the dead (p is false)
∴ His bones can be found (q is false)
- - invalid.
The conclusion does not follow; many people who did not rise were cremated.
4) Jesus’ bones can be found (q is false)
∴ He did not rise from the dead (p is false)
- - valid (despite the fact that both premises are false).
|The founders of many counterfeit religions still have skeletons mouldering away, which is proof that they are not risen.||Many of those "counterfeit religions" do not claim that their founder rose. Also, note the implied use of the fallacious syllogism (2) above: that since Jesus's bones have not been found, Jesus has risen, unlike the counterfeiters. (Which is not to mention that Jesus's bones just may have been found, in an ossuary in the Talpiot Tomb.)|
|One use of modus tollens is the reductio ad absurdum argument, i.e. showing that a premise is false by demonstrating that it implies an absurd conclusion.|
|An example is the effort by Bishop John Shelby Spong to show that homosexual acts are OK because some animals practise them. As it stands, the argument is invalid. To make it valid, another premise is needed that states: whatever animals do is OK.
1) Animals practise homosexual acts;
2) Whatever animals practise is OK;
∴ Homosexual acts are OK.
|Another straw man. The argument from animal homosexuality actually works like this: (1) Homosexuality is said to be wrong because it is "unnatural;" (2) animals are quintessentially natural, hence do not practice any unnatural acts; (3) animals practice homosexual acts; (4) therefore, homosexuality is not unnatural; (5) therefore, barring another argument that homosexuality is wrong, we should not regard it thus.|
|To prove the argument to be sound, that premise must be proved to be true. Conversely, to prove the argument to be unsound, the premise must be shown to be false. This can be done by showing that it leads to a ridiculous conclusion:
Now if one does not accept the conclusion, if one is logical one must reject one or more of the premises. As (1) is empirically true, (2) must be the false premise. So Spong’s argument contains a false premise and is thus unsound.
1) Animals practise rape and cannibalism;
2) What animals do is OK;
∴ Rape and cannibalism are OK.
|Rule of thumb: When calling person A out on some unstated premise or presupposition, try to pick one that A could reasonably hold; the argument looks better that way.|
|Another example: pro-abortionists often claim that the unborn child is merely a disposable part of the woman’s body. However, see what happens if this premise is combined with other indisputable premises in the following argument:
As the conclusion is false (feminists would detest it especially), at least one of the premises must be as well. All premises are indisputably true except the pro-abortionists’ (3), which was the disputed issue. So this argument proves it false.
1) If a is part of b and b is part of c, then a is part of c (This is called a transitive relation—an example is: if a brick is part of a wall and a wall is part of a house, then the brick is part of the house);
2) A male unborn baby has a penis (that is, a penis is part of him);
3) This baby is part of the pregnant woman;
∴ A woman pregnant with a male baby has a penis.
|This one is a veritable Gordian knot of absurdity, which we will untie as best we know how.
Many useful relations are intransitive; the relation, for example. The particular relation in premise (1) is not strictly transitive, if we consider the Christian doctrine of the hypostatic union, which would require the human body of Jesus to be part of God.
Not all aborted fetuses with XY-chromosomes to them have a penis, and none have the fully-formed penis that is supposed to make the conclusion absurd.
When trying to make precise logical arguments in this way, one should never be too vague about one's terms, and in this case Dr. Sarfati has tripped over a semantic issue: what makes the conclusion appear to be absurd is the image it conjures up of the scene in The Crying Game of the woman with the dangler, which clearly does not cover all cases in which a penis is part of a woman.
|An example of a fallacious reductio ad absurdum is the argument that the Sadducees used against the Resurrection—Matthew 22:23–34
23 That same day the Sadducees, who say there is no resurrection, came to him with a question.
24 ‘Teacher,‘ they said, ‘Moses told us that if a man dies without having children, his brother must marry the widow and have children for him.
25 Now there were seven brothers among us. The first one married and died, and since he had no children, he left his wife to his brother.
26 The same thing happened to the second and third brother, right on down to the seventh.
27 Finally, the woman died.
28 Now then, at the resurrection, whose wife will she be of the seven, since all of them were married to her?‘
|Note that they tried to refute the Resurrection by showing that it leads to the absurd conclusion that in this hypothetical situation the woman would not know whose wife she is. Jesus’ answer shows the masterful logic of the Logos of God.
“”29 Jesus replied, ‘You are in error because you do not know the Scriptures or the power of God.
First, Jesus points out that the starting presuppositions are wrong—the Sadducees only accepted the Pentateuch as Scripture, while Jesus, like the Pharisees, accepted the same books as the Protestant Old Testament. If they had not been ignorant of what the Scriptures were, they would have realised that Scriptures like Dan. 12:2 clearly teach the Resurrection.
Then He notes that if a conclusion of a valid argument is false, then it is enough for only one of the premises to be false. The false premise in the Sadducees’ argument was not the resurrection, but that people would be married in heaven:
“”30 At the resurrection people will neither marry nor be given in marriage; they will be like the angels in heaven.
|More likely it shows the skill of St. Matthew in conjuring up straw men.|
|However, refuting any number of arguments against a position does not in itself prove that position. So Jesus proved His own position, on the Sadducees’ own terms, using Scripture they accepted:
Even the Scriptures accepted by the Sadducees taught the resurrection: Christ demonstrated this with an argument showing that the Pentateuch taught that God was the God of the patriarchs and the God of the living. Therefore the patriarchs were living in a sense in Moses’ day, centuries after they had died physically. Note also that the argument depends on the present tense of the verb ‘to be’ implied in the Hebrew verbless clause of the passage (Ex. 3:6) Jesus cited. His argument makes no sense if He did not believe in verbal plenary inspiration of Scripture.
31 But about the resurrection of the dead—have you not read what God said to you,
32 ‘I am the God of Abraham, the God of Isaac, and the God of Jacob’? He is not the God of the dead but of the living.‘
33 When the crowds heard this, they were astonished at his teaching.
34 Hearing that Jesus had silenced the Sadducees, the Pharisees got together.
|"Humph! These arguments sound very well, but I can't help thinking that, if they were reduced to syllogistic form, they wouldn't hold water." -- W.S. Gilbert|
|The fallacy of denying the antecedent is committed by some groups that teach the error of baptismal regeneration by citing the following statement of Christ according to the Majority Text of Mark 16:16:
“”16 Whoever believes and is baptized will be saved, but whoever does not believe will be condemned.
The first part of the verse is an implication: if a person believes and is baptized then he will be saved. It is invalid to argue from this that anyone who is not baptized will not be saved. The second part is an explicit statement that unbelief results in condemnation.
To demonstrate the fallacy, examine the following statement which is in the same logical form: ‘Whatever has feathers and flies is a bird, but whatever does not have feathers is not a bird.’ This statement does not teach that there are no flightless birds.
|The logic here is good enough; the theology, not so much. By calling baptismal regeneration a doctrinal error, CMI is alienating the vast majority of Christians and theologians, going against Catholic, Orthodox, Lutheran, and traditional Calvinist positions on the subject.|
|Another example of the fallacy of denying the antecedent is when some people are upset because we can no longer use a stock creationist argument (e.g. the depth of meteoritic dust on the moon to prove a young moon). But the argument in schematic form is as follows, and the fallacy should be clear:
1) If the moon dust argument works, then the moon must be young;
2) The moon dust argument doesn’t work;
∴ The moon cannot be young.
|This should be a lesson that our primary evidence should always be the infallible written testimony of One who was there and never errs, not the evidence of fallible scientists who weren’t there and often err.||A more open statement than usual of the formal principle of CMI's so-called "science."|
|To see why this does not follow, consider:
But I could feel very full for many different reasons.
1) If I had just eaten a whole pizza, I would feel very full;
2) I feel very full;
∴ I have just eaten a whole pizza.
|True; however, the inductive reasoning of science is based on more observations than that. One would at least have to feel full and see an empty pizza-box nearby.|
|On the other hand, the famous falsification criterion for a scientific theory devised by the late Sir Karl Popper is based on the valid denying the consequent:
1) Theory T predicts O will not be observed;
2) O is observed;
∴ T is false.
|Good so far. But, any creationist citing Popper is probably going to chase the cite with a copious wad of bullshit...|
|We can apply this analysis to a major evolutionary argument:
This demonstrates that it is an example of the fallacy of affirming the consequent. The conclusion is not proven—the homologous structures could be due to a common designer, leaving a ‘biotic message’ that there is a single designer of life rather than many.
1) If organisms X and Y have a common ancestor, they will have homologous structures;
2) X and Y have homologous structures;
∴ X and Y have a common ancestor.
|This ignores that there are many such homologous structures, which make it a valid inductive argument.|
|On the other hand, ornithologists like Alan Feduccia argue against dinosaur-to-bird evolution for many good reasons, including a recent discovery that dinosaur embryos have an embryonic thumb that birds lack (I–II–III and II–III–IV digit patterns respectively). The argument is:
1) If birds evolved from theropods, they will have homologous digits;
2) Bird and theropods do not have homologous digits;
∴ Birds did not evolve from theropods.
This is valid (denying the consequent), so creationists have rightly publicised this evidence.
|However, philosophers like Imre Lakatos point out that core theories are not tested in isolation, but are ‘protected’ by auxiliary hypotheses. Denying the consequent only shows that one of the premises needs to be false, and it need not be the core theory. So the auxiliary hypotheses are modified instead. In schematic form, the valid argument is as follows:
For example, Newton’s theory predicted certain motions of Saturn, provided there were no other massive objects interfering. When Saturn didn’t move as predicted, either Newton’s theory was falsified, or there was another massive object perturbing the orbit—this turned out to be the planet Uranus.
1) Theory T and auxiliary hypothesis A predict that O will not be observed;
2) O is observed;
∴ Either T or A is false.
|Quite an astounding discovery, that theories can >gasp!< be split into several distinct parts! Now if we can just get creationists to accept this fact in earnest, and quit insisting that a few dodgy rocks or a fraudulent fossil disprove all current theories of geology and evolutionary biology...|
|The above was explaining the logic of the falsification criterion. This was not necessarily to endorse it—a coherent definition of science is hard to come by.||Of course they are not endorsing it; it removes the essential Goddidit escape-hatch!
This is another one of those statements that makes a person wonder how CMI's people can still call themselves scientists while completely ignoring the formal principle and limitations of science.|
|In the hands of evolutionists, ‘unscientific’ becomes a swear-word with which to attack creation. But it is more important whether creation or evolution are true or false, than whether one is more ‘scientific’ than another. Sometimes evolutionists are so keen to attack creationists that they don’t realise their self-contradictions. For example, the philosopher P. Quinn (an anti-creationist himself) demonstrates the illogicality of the Marxist evolutionist Stephen Jay Gould:
“”‘… Gould claims that “‘Scientific creationism’ is a self-contradictory phrase precisely because it cannot be falsified”…Ironically, in the next sentence Gould goes on to contradict himself by asserting that “the individual claims are easy enough to refute with a bit of research.” Indeed, some of them are! But since they are so easily refuted by research, they are after all falsifiable and, hence, testable. This glaring inconsistency is the tip-off to the fact that talk about testability and falsifiability functions as verbal abuse and not as a serious objection in Gould’s anti-creationist polemics.’
|When creationists resort to Goddidit, it is valid at that time to call their arguments unfalsifiable, but they do not usually do this until they are backed against the wall. The rest of the time, however, they are still violating another foundational principle of science, methodological naturalism, by making the supernatural an integral part of creationism.|
5) Disjunctive Syllogism
|The disjunctive syllogism is a valid form of argument familiar to those who have sat multiple choice examinations. Sometimes, a process of elimination can rule out all possibilities but one, which must therefore be true. An example is: Fred is flying either on QANTAS or Air New Zealand; he is not flying QANTAS; therefore he is flying Air New Zealand (see Table 5).|
Table 5: Disjunctive Syllogism
| Either p or q
|| p v q
| p is false
| therefore q is true
|| ∴ q
|To be sure that the conclusion is true, one must be sure that all possible alternatives are listed. The surest way is to apply the Law of Excluded Middle and have the disjunctive (either/or) premise contain a pair of contradictories (p or ~p).|
|An important example is that there are only two real explanations for the origin of different kinds of life—creation or evolution. For example, Professor D.M.S. Watson wrote:
I.e.: C v E; ~C; ∴ E.
“”‘evolution [is] a theory universally accepted not because it can be proven by logically coherent evidence to be true, but because the only alternative, special creation, is clearly incredible.’
|False dilemma, of course. There are any number of alternatives; for starters, a bushel-full of pagan mythologies and theistic evolution. Not all these are empirically viable, but they are logical possibilities.|
|As this is a disjunctive syllogism, it is a valid argument. But it cannot be over-emphasised that validity and truth are not the same—this argument is not sound! Many evolutionists starting with Darwin have used this reasoning. This also demonstrates the atheistic bigotry behind much evolutionist thinking. Of course, creationists can use the equally valid argument:
C v E; ~E; ∴ C.
I.e. evidence against evolution is automatically evidence for creation. This is both valid and sound.
Many evolutionary propagandists dispute this reasoning when creationists use it, on the grounds that creation and evolution are not the only alternatives. Creationists are thus accused of the fallacy of false alternatives, that is, the disjunctive premise leaves out a possible alternative. But as shown, many evolutionists agree there are only two, so there are double standards at work.
|If indeed there are evolution supporters who use this logic against creationists, we say that they are incorrect in doing that.|
|This can be shown by the Law of Excluded Middle: either things were made (creation) or they weren’t (evolution). It is true that biblical creation is not the only alternative, so it is not proven by disproof of evolution. Biblical creation is certainly consistent with disproof of evolution, unlike atheism.||Atheism is hardly incompatible with evolution being disproved; a little green man could have done the design work as easily as a big magic one.|
|A genuine example of the fallacy of false alternatives is the following ‘proof’ of the punctuated equilibria version of evolution:
This is basically the form of argument used by Niles Eldredge and Stephen Jay Gould in their seminal paper, as pointed out by creationists.
1) Life must have evolved either gradualistically or via punctuated equilibria;
2) There are major problems with gradualism (absence of fossil intermediates, and inability to construct a functional series);
∴ Life must have evolved via punctuated equilibria.
|The other origin theories have been largely falsified, so premise 1 is fairly safe to claim.|
Other common fallacies
|So far I have discussed deductive reasoning.||And mistaken inductive arguments for it. To continue the pattern of errors, he also mistakes deductive arguments for inductive reasoning in this section.|
|As discussed, inductive arguments reason from a finite set of examples to a general rule. The reason they are less important is that they don’t guarantee the truth of the conclusion—they are formally invalid by the definition of validity in logic. For example, just because we find that 1000 crows are black, it does not follow that the 1001st crow will not be an albino.||True; however, there is a very high probability that the 1001st crow will be black.|
|Science by its nature is inductive, not deductive. Science always uses a finite number of measurements, each of which has an uncertainty, so science can never give a complete picture of reality. Hence, although science can be useful, it can never be a threat to the Christian Faith.||Here is a little deductive argument: Science by its nature is inductive; creationists believe that inductive arguments are less important than deductive ones; therefore, creationists do not think science is very important.
Although it is true that scientific statements can never be proven absolutely, they can be falsified absolutely; a single contradictory observation can do that. If CMI insists that the "Christian Faith" stands or falls on the truth of some scientific statement, that statement can be falsified and with it the "Faith."|
|The error of trying to disprove a belief by tracing it to its source. For example, Kekulé thought up the (correct) ring structure of the benzene (C6H6) molecule after a dream of a snake grasping its tail, but chemists don’t need to worry about correct ophiology to analyse benzene!|
|However, many anti-Christians commit this fallacy when they try to disprove Christianity by pointing out alleged parallels in pagan mythology.||Although creationists really get in a snit if one insinuates that the Divinely Inspired and Literally True Holy Bible is in any way similar to those satanic pagan myths, the presence of the Deluge in many mythologies has been used in the past to argue that the Deluge actually happened; the Old Catholic Encyclopedia says, "The Deluge is referred to in several passages of Scripture as a historical fact ... and this view of the subject is confirmed by the numerous variants under which the Flood tradition lives in the most distant nations of the earth."|
|Another example is: ‘You only believe Christianity because you were indoctrinated by your parents and culture; if you came from a Hindu family and culture you would be a Hindu’, with the spoken or unspoken impression ‘thus Christianity need not be preferred over Hinduism’. In neither case can anything be inferred about the truth of Christianity from reasons a Christian’s belief allegedly originated.||This is true from a strictly logical point of view, but it works to discredit arguments as to the "obviousness" or "intuitiveness" of one's birth-religion compared to other religions.
However, the argument belongs more to the deductive than the inductive category.|
|Many evolutionist propagandists believe that they simply need to demonstrate that a creationist has a ‘fundamentalist’ religious belief to discredit his purely scientific claims. The double standards are glaring—the radical atheist or even Marxist beliefs of many leading evolutionists are often ignored, although these beliefs determine which scientific explanations are acceptable and which are not.||Ah, Red-baiting; the old die-hard. Unfortunately for CMI, it is also highly fallacious in this instance: whether the scientists are communists is of no consequence, because (unlike the promoters of Lysenkoism) they do not mix their communist political views with their scientific work, so mentioning it constitutes an ad hominem. Similarly, atheist scientists do not tend to mix their atheism with their scientific work. On the other hand, creationists' fundamentalism by their own admission forms the entire basis of their work in creationism.|
Fallacy of Division
|For example: a truck is heavy, therefore all its atoms are heavy. This example is obviously fallacious, but other equally fallacious arguments are advanced in all seriousness. Some New Agers like Teilhard de Chardin claim that because living beings are conscious, then their atoms must have some consciousness.||Very few people adhere to this sort of reductionism. Those who do, are called cranks.|
Fallacy of Composition
|The opposite to the Fallacy of Division. An example is: all cells are light, therefore all animals containing cells are light.||Truly a fallacy. However, creationists use a very similar fallacy in their arguments about mutations when they say, "All mutations are minuscule. Therefore, many generations of mutations cannot bring about speciation."|
Post hoc ergo propter hoc
|This is Latin for ‘after this, therefore because of this’. But just because B happened after A, it doesn’t mean B was caused by A. Gordon Clark gives the following example of this fallacy:
“”‘In the late seventies the Internal Revenue Service [USA] undertook to harass Christian schools…. [They] tried to revoke the tax exemption status of Christian schools, holding them guilty of race discrimination until they could prove themselves innocent by certain processes impossible to fulfil in some localities. One of the arguments the IRS used was that those schools were organized just after laws of racial discrimination were enacted. Post hoc ergo propter hoc. One of the defenses used by the Christians was that the schools were organized just after the Supreme Court banned the Bible and Prayer. One might add that they were organized after violence, drugs and sex became intolerable in the public schools.’
A more recent example of this fallacy is the claim by the atheist, Alex Ritchie:
Of course, Answers in Genesis in the USA changed its ministry name three years before this, and the official company name of Answers in Genesis (Australia) at the time still remained Creation Science Foundation Ltd., ACN 010 120 304 (ACN = Australian Company Number).
“”‘I suggest that the name change from Creation Science Foundation [Australia] to Answers in Genesis is a shrewd and timely precaution to safeguard this religious organisation from the possibility of legal action, following the precedent of the Plimer/Roberts case.’
|The reason for the change in ministry name is explained in this article: the ministry’s axioms are the propositions of the Bible, not the theories of fallible scientists. [Ed. Note: In 2006, the ministries in Australia, Canada, NZ and South Africa all changed their names to Creation Ministries International]||Translation: "We don't do science; we do Biblical exegesis."|
The basis for logic
|A final question is, why should logic work at all? Not only can unbelievers not make a sound case against Christianity, but an atheistic world-view attacks the very basis of reasoning itself. This was realised by the famous Communist evolutionist biologist, J.B.S. Haldane:
“”‘If my mental processes are determined wholly by the motions of atoms in my brain, I have no reason to suppose my beliefs are true … and hence I have no reason for supposing my brain to be composed of atoms.’
|Snarl word overload there. But in any event, firstly, one can also turn this argument around on the creationists: why should a divinely-designed brain -- especially one that believes in Jesus and hence gets all of God's brain-power, as described above -- ever not be correct? Secondly, the nice thing about logical arguments is that they verify themselves: even if an argument comes out of the most fallible atom-swirl of a brain ever imaginable, one can still verify its correctness.|
|In a debate between the Christian, William Lane Craig and the atheist, Frank Zindler, Zindler claimed that our logical processes evolved for survival value. Craig pointed out that this provides no reason for us to trust their validity, only their value in survival.||Richard Dawkins, among others, believes that the "delusion" of religion came about in this way. However, the ability to make correct empirical observations is a very useful survival skill, so that argument falls on its face.|
|Even Darwin wrote in an early private notebook, ‘Why is thought, being a secretion of brain, more wonderful than gravity as a property of matter?’ But this argument is self-defeating. For it applies to that thought of Darwin’s too, and to every thought about evolution, hence we have no reason to trust them.||A quote mine of Darwin. To take a wild guess, he was probably attacking the Platonic idea that ideas or "Forms" are more real than matter.|
|The famous Marxist paleontologist Stephen Jay Gould claimed that the mind was an illusion produced by the brain. So why should we trust anything Gould says, if his thoughts are illusions?||Firstly, saying that the mind is an illusion is not the same thing as saying that thoughts are illusions; secondly, it is nonsense to say that thoughts, being immaterial, are in any wise "illusions."|
|This only shows that many atheistic theories actually refute themselves. Thus there is no need for independent empirical tests for them. Conversely, the Christian doctrine that we are created in the image of a logical God is an excellent explanation for our logical faculties.||Although it is true that some "atheistic" theories are self-refuting, atheism itself is not, as it does not even contain a belief to refute. Nor do any of the refutations in this section hold water.|