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.

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.

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’).

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.

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. Some common examples are:

d) 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 pÉq. 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 (pÉq) does not in itself imply that the antecedent (p) is true — only that if p were true, q must logically follow from it. 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 (Answers in Genesis takes no position on this issue).

Another good example is Jesus’ statement in Matthew 12:27:

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).

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.

Table 2: Denying the Consequent

There are two types of invalid inference: the fallacies of affirming the consequent (Table 3) and denying the antecedent (Table 4).

Table 4: Denying the Antecedent

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)

2) Jesus’ bones cannot be found (q is true)
\ He rose from the dead (p is true)

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)

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)

The founders of many counterfeit religions still have skeletons mouldering away, which is proof that they are not risen.¹⁴

Reductio ad absurdum

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 Spong¹⁵ 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

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:

1) Animals practise rape and cannibalism;
2) What animals do is OK;
\ Rape and cannibalism are OK.

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.

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:

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.

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.¹⁶

An example of a fallacious reductio ad absurdum is the argument that the Sadducees used against the Resurrection — Matthew 22:23–34

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.

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:

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.

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:

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.

Another example of 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 moon¹⁷). 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.

Logic and science

An example of the fallacy of affirming the consequent is using verified predictions as ‘proof’ of a scientific law.¹⁸ That can be seen if we analyse it:

1) Theory T predicts observation O;
2) O is observed;
\ T is true.

To see why this does not follow, consider:

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.

But I could feel very full for many different reasons.

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.

We can apply this analysis to a major evolutionary argument:

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 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.¹⁹

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).²⁰ 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.^21,22

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:

1) Theory T and auxiliary hypothesis A predict that O will not be observed;
2) O is observed;
\ Either T or A is false.

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.²³

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.

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:

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).

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

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.²⁶ 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.

A genuine example of the fallacy of false alternatives is the following ‘proof’ of the punctuated equilibria version of evolution:

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.

This is basically the form of argument used by Niles Eldredge and Stephen Jay Gould in their seminal paper,²⁷ as pointed out by creationists.²⁸

OTHER COMMON FALLACIES

Hasty Generalisation

So far I have discussed deductive reasoning. 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 1001^st crow will not be an albino.

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.

Genetic Fallacy

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.²⁹ 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.

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 evolutionists³⁰ are often ignored, although these beliefs determine which scientific explanations are acceptable and which are not.

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.

Fallacy of Composition

The opposite to the Fallacy of Division. An example is: all cells are light, therefore all animals containing cells are light.

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:

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) is still Creation Science Foundation Ltd., ACN 010 120 304 (ACN = Australian Company Number). 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.

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:

In a debate between the Christian, William Lane Craig and the atheist, Frank Zindler,³⁴ 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.

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?’³⁵ 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.

The famous Marxist paleontologist Stephen Jay Gould claimed that the mind was an illusion produced by the brain.³⁶ So why should we trust anything Gould says, if his thoughts are 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.

REFERENCES

1. For a good discussion, see Craig, W.L., 1984. Apologetics: An Introduction, Moody Press, Chicago, chapter 1. Return to text

2. For an extensive discussion on the role of logic in Christianity and many examples, see Clark, G.H. 1988. Logic, The Trinity Foundation, Jefferson, MD, USA. Return to text

3. Smith, G. 1995. The ‘Toronto Blessing’. Apologia 4(2):37–40. Return to text

4. A generally first-rate book on the importance of developing a Christ-like mind is Moreland, J.P., 1997. Love Your God With All Your Mind, Navpress, Colorado Springs. Its main disadvantage is that Moreland is ‘sixty-forty in favor of the old-earth position’ (p.107), possibly because of a slight over-emphasis on extra-biblical revelation. Return to text

5. Machen, J.G., 1924. Christianity and Liberalism, Macmillan, New York. Return to text

6. Martin, W.R., 1985. The Kingdom of the Cults, Bethany House Publishers, Minneapolis, MN. Return to text

7. Carroll, L. 1877. Through the looking-glass, and what Alice found there (with fifty illustrations by John Tenniel) Macmillan, London. Return to text

8. One example is Schafersman, S. 1981. Letter. Geotimes, August. Cited in Bird, ref. 26, Vol. II, pp. 77–78. Return to text

9. See How Religiously Neutral are the Anti-Creationist Organisations? Return to text

10. Scott, E., 1997. Dealing with anti-evolutionism. Reports of the National Center for Science Education, 17(4):24–28. Quote on p. 26, with emphasis in original. Return to text

11. Plimer, I.R., 1994. Telling Lies for God, Random House, Australia, p. 289. Return to text

12. See The Ian Plimer Files. Return to text

13. Obviously I can give only a basic outline here. A more formal, in-depth coverage can be found in Hughes, G.E. and Londey, D.G., 1965. The Elements of Formal Logic, Methuen, London. Return to text

14. Thanks to the Wellington Christian logician Ross Powell for this example. Return to text

15. An extensive critique of Spong’s errant and heretical views is Bott, M.R. and Sarfati, J.D., 1995. What’s wrong with Bishop Spong? Apologia 4(1):3–27. See online version. Return to text

16. This argument is dramatised in the form of a Socratic Dialogue in Kreeft, P., n.d. (after 1987). The Unaborted Socrates, IVP, pp. 44–47. Return to text

17. Snelling, A.A. and Rush, D., 1993. Moon dust and the age of the solar system. CEN Tech. J. 7(1):2–42. Return to text

18. Clark, G.H., 1987. The Philosophy of Science and Belief in God, The Trinity Foundation, Jefferson, MD, USA, 2nd Ed. Return to text

19. ReMine, W.J., 1993. The Biotic Message, St Paul Press, St. Paul, Minnesota. Return to text

20. Ann C. Burke, A.C. and Feduccia, A., 1997. Developmental Patterns and the Identification of Homologies in the Avian Hand. Science, 278(5338):666–8. Perspective in the same issue, pp. 596–7 by Hinchliffe, R. The Forward March of the Bird-Dinosaurs Halted? Return to text

21. Oard, M.J., 1998. Bird-dinosaur link challenged. CEN Tech. J. 12(1):5–7. Return to text

22. Sarfati, J.D., 1998. Dino-bird evolution falls flat. Creation Ex Nihilo, 20(2):41. See online version. Return to text

23. For extensive discussion of the views of Popper and Lakatos, and other attempts to define science, see Bird, W.R., 1991. The Origin of Species Revisited, Philosophical Library, New York, Vol. II, chapters 9–10. Return to text

24. Quinn, P., 1984. The Philosopher of Science as Expert Witness. In: Recent Work in the Philosophy of Science, ed. J. Cushing, C. Delaney and G. Gutting, 1984, pp. 32, 43. Cited in Bird, ref. 26, p. 121. Return to text

25. Watson, D.M.S., 1929. Adaptation. Nature 124:233. Return to text

26. Bird, W.R., 1991. The Origin of Species Revisited, Philosophical Library, New York, Vol. II, chapter 11. Return to text

27. Gould, S.J. and Eldredge, N., 1972. Punctuated equilibria: an alternative to phyletic gradualism. In: Models in Paleobiology, T.J.M. Schopf (ed.), Freeman, Cooper and Co., San Francisco, pp. 82–115. Return to text

28. Batten, D.J., 1004. Punctuated equilibrium: come of age? CEN Tech. J., 8(2):131–7. Return to text

29. Ronald Nash has dealt with such claims in detail, for example, Was the New Testament Influenced by Pagan Religions? Return to text

30. Batten, D.J., 1997. A Who’s Who of evolutionists. Creation Ex Nihilo, 20(1):32. See online version. Return to text

31. Clark, ref. 2, pp. 17–18. Return to text

32. Ritchie, A., 1997. Dropping the Pretence: The Creation Science Foundation changes its name. The Skeptic, 17(4):13,15. Return to text

33. Haldane, J.B.S. Possible Worlds, p. 209. Cited in Lewis, C.S., 1960. Miracles, Fontana, London, first published 1947), p. 19. Return to text

34. See Anon., 1996. Atheism vs Christianity: Where does the evidence point? A debate between Mr Frank Zindler and Dr William Lane Craig. Apologia 5(1):21–29, 1996. Return to text

35. Cited by Wieland, C., 1992. Darwin’s real message: have you missed it? Creation Ex Nihilo, 14(4):16–19. See online version. Return to text

36. Gould, S.J., 1990. The Darwinian Revolution in Thought. Lecture, June 6, Victoria University of Wellington, New Zealand. Return to text.