There are a lot of ways to slip up in logic, and one web site that lists the major ones is here, and it's where I found the examples quoted in this post. I think it’s fun to note all the ways arguments can be unfairly twisted, and I believe people in general and Christians particularly ought to be very careful not to fall into any of them. Yet it happens every day.
Some denominations believe we ought not worry too much about “human logic” and just “take God’s Word for it.” But of course that in itself is a logical fallacy, because what it really means is, I insist that the places where my theology breaks down are the places where I'm being most faithful, in accepting the contradictions. I’ll go with my/our own interpretation even if it contradicts itself. If my theological system teaches, for example, that (1) grace is universal, (2) man can do absolutely nothing whatsoever toward his salvation, and (3) not everyone is saved, well all three of those are true, even though they can't all be. It's just plain sad when such contradictions do not even cause their proponents to hesitate, to consider that there may be a problem in their teaching, when not even logic or common sense deters them or brings them to sound doctrine.
It’s true that God’s ways are “past finding out,” as St. Paul tells us. But that is not at all the same as – in fact it is the exact opposite of – saying His ways insult our intelligence. It means His intelligence is infinitely greater than ours. Though the Truth will always surpass our ability to understand it, it will not fail to meet reason’s basic requirements. If any doctrine does, it isn’t from the Logos. (That's the root of our word, logic, and another name for the Second Hypostasis or Person of the Holy Trinity.) It is also true that Christian faith has a logic different from that of secular faith (Yes, secularism and materialism and humanism are all faiths.) but it is still logical in its own terms.
Here, then, are a few of my favorite logical fallacies. (The following are not my words, except as clearly labeled; they are excerpts from the above-mentioned website.)
The fallacy of equivocation is committed when a term is used in two or more different senses within a single argument.
For an argument to work, words must have the same meaning each time they appear in its premises or conclusion. Arguments that switch between different meanings of words equivocate, and so don’t work. This is because the change in meaning introduces a change in subject. If the words in the premises and the conclusion mean different things, then the premises and the conclusion are about different things, and so the former cannot support the latter.
(1) The church would like to encourage theism.
(2) Theism is a medical condition resulting from the excessive consumption of tea.
(3) The church ought to distribute tea more freely.
This argument is obviously fallacious because it equivocates on the word theism. The first premise of the argument is only true if theism is understood as belief in a particular kind of god; the second premise of the argument is only true if theism is understood in a medical sense.
(1) Christianity teaches that faith is necessary for salvation.
(2) Faith is irrational, it is belief in the absence of or contrary to evidence.
(3) Christianity teaches that irrationality is rewarded.
This argument, which is a reasonably familiar one, switches between two different meanings of “faith”. The kind of faith that Christianity holds is necessary for salvation is belief in God, and an appropriate response to that belief. It does not matter where the belief and the response come from; someone who accepts the gospel based on evidence (e.g. Doubting Thomas) still gets to heaven, according to Christianity.
For the kind of faith for which (1) is true, (2) is therefore false. Similarly, for the kind of faith for which (2) is true, (1) is false. There is no one understanding of faith according to which both of the argument’s premises are true, and the argument therefore fails to establish its conclusion.
Another example, this time from Anastasia:
(1) Double Predestination means God chooses whom to save and whom not to save.
(2) Single Predestination means God only chooses whom to save, but does not actually choose to damn anyone.
(3) We believe in Single Predestination but not in Double Predestination.
This is an equivocation on “choose”; it overlooks the fact that in real life, “not to decide is to decide.” Not to choose to save someone is practically (and morally!) identical to choosing not to save him.
CIRCULAR ARGUMENTS (BEGGING THE QUESTION)
An argument is circular if its conclusion is among its premises, if it assumes (either explicitly or not) what it is trying to prove. Such arguments are said to beg the question. A circular argument fails as a proof because it will only be judged to be sound by those who already accept its conclusion.
Anyone who rejects the argument’s conclusion should also reject at least one of its premises (the one that is the same as its conclusion), and so should reject the argument as a whole. Anyone who accepts all of the argument’s premises already accepts the argument’s conclusion, so can’t be said to have been persuaded by the argument. In neither case, then, will the argument be successful.
(1) The Bible affirms that it is inerrant.
(2) Whatever the Bible says is true.
(3) The Bible is inerrant.
This argument is circular because its conclusion--The Bible is inerrant--is the same as its second premise--Whatever the Bible says is true. Anyone who would reject the argument’s conclusion should also reject its second premise, and, along with it, the argument as a whole.
Note from Anastasia: The issue here is not the inerrancy of the Bible, but the fact that anyone who wishes to make a logical argument for inerrancy will need to do better than this.
The above argument is a straightforward, real-world example of a circular argument. Other examples can be a little more subtle.
Typical examples of circular arguments include rights-claims: e.g., “I have a right to say what I want, therefore you shouldn’t try to silence me”; “Women have a right to choose whether to have an abortion or not, therefore abortion should be allowed”; “The unborn has a right to life, therefore abortion is immoral”.
Having a right to X is the same as other people having an obligation to allow you to have X, so each of these arguments begs the question, assuming exactly what it is trying to prove.
Other Examples from Anastasia:
(1) Scripture is all trustworthy.
(2) Our confessions are drawn entirely from Scripture
Therefore, our confessions are the correct way to interpret Scripture.
The circularity lies in the fact that ones confessions are always his interpretation of Scripture. The argument in effect says, "Our interpretations of Scripture [confessions, creeds] are correct because they are [our interpretation of] Scripture."
We believe in the Bible because of Christ – and in Christ because of the Bible.
The fallacist's fallacy involves rejecting an idea as false simply because the argument offered for it is fallacious. Having examined the case for a particular point of view, and found it wanting, it can be tempting to conclude that the point of view is false. This, however, would be to go beyond the evidence.
It is possible to offer a fallacious argument for any proposition, including those that are true. One could argue that 2+2=4 on the basis of an appeal to authority: "Simon Singh says that 2+2=4". Or one could argue that taking paracetamol relieves headaches using a post hoc: "I took the paracetamol and then my headache went away; it worked!"
Each of these bad arguments has a true conclusion. A proposition therefore should not be dismissed because one argument offered in its favour is faulty.
"People argue that there must be an afterlife because they just can't accept that when we die that's it.”
‘NO TRUE SCOTSMAN'
The no true Scotsman fallacy is a way of reinterpreting evidence in order to prevent the refutation of one’s position. Proposed counter-examples to a theory are dismissed as irrelevant solely because they are counter-examples, but purportedly because they are not what the theory is about.
If Angus, a Glaswegian, who puts sugar on his porridge, is proposed as a counter-example to the claim No Scotsman puts sugar on his porridge, the ‘No true Scotsman’ fallacy would run as follows:
(1) Angus puts sugar on his porridge.
(2) No (true) Scotsman puts sugar on his porridge.
(3) Angus is not a (true) Scotsman.
(4) Angus is not a counter-example to the claim that no Scotsman puts sugar on his porridge.
This fallacy is a form of circular argument, with an existing belief being assumed to be true in order to dismiss any apparent counter-examples to it. The existing belief thus becomes unfalsifiable.
An argument similar to this is often arises when people attempt to define religious groups. In some Christian groups, for example, there is an idea that faith is permanent, that once one becomes a Christian one cannot fall away. Apparent counter-examples to this idea, people who appear to have faith believe but subsequently lose it, are written off using the ‘No True Scotsman’ fallacy: they didn’t really have faith, they weren’t true Christians. The claim that faith cannot be lost is thus preserved from refutation. Given such an approach, this claim is unfalsifiable, there is no possible refutation of it.
Note from Anastasia: A claim that is unfalsifiable is not necessarily untrue; it's just not supported by a the unfalsifiable argument.
(It just so happens, however, that this particular example does have a refutation of a different sort. It's found in John 15:2, in which Jesus tells us that any "branch IN ME" that doesn't bear fruit will be cut off.)