A Brief Guide to Critical Thinking

Bridge 8 and animator James Hutson have created six two-minute animations on various aspects of critical thinking. The videos are designed for kids ages 8 to 10 but are also useful for grown-ups who might want an introduction to the basics of logic and the scientific method, as well as to psychological missteps like confirmation bias and the Gambler’s Fallacy.

The Anthropological Argument: Part 2

In this post a specific anthropological argument for God’s existence is stated and defended, and then examined if it is a good and convincing argument.

A Familiar Conversation: Part 1

Those familiar with past conversations on this blog will be familiar with the voice of our objector. In this article I shall refer to our objector as Didymus, in memory of the one who doubted the Apostles’ word, but came to believe when Christ appeared to him saying, “Blessed are those who have not seen yet believed.”

The following will seem like we’re treading familiar water. That’s because we will be. This is, as the title declares, a familiar conversation.[1] First, take note of few of Didymus’ statements;

Stuart: Failing to make an argument is failing to reason.

Didymus: I’m not failing to make an argument, I’m refusing to make a philosophical one. . . One argument of mine is that I just don’t see god. This is an evidentiary argument.

In response, making an argument, but not making a philosophical argument is impossible. All arguments require and use in some way philosophy, even if it’s just the basic laws of logic (rules of right-thinking) that are employed. Logic is a sub-discipline of philosophy, and because logic must be used in an argument, refusing to make a philosophical argument is refusing to make an argument.

An evidentiary argument is one that provides evidence. Evidence by itself tells us nothing until reason is applied. Good reason requires good philosophy, and bad reasoning uses bad philosophy. So evidence is always used in philosophical arguments, and this is the case for the cosmological, teleological, moral and historical arguments for God’s existence. Because I look favourably on the use of such arguments, I am an evidentialist apologist. The ontological argument is supposed to only use premises that can be derived purely from inside the mind instead of tangible evidence from the world of sight and sound. Still, one could construe this argument to be evidentiary in the sense that it, as a purely philosophical argument can be used as evidence in the case for God’s existence (that is, if one thinks it is a good argument).

Also take note of Didymus’ response to this question.

Stuart: What arguments for Atheism[2] do you find convincing?

Didymus: I see no evidence for god.

“I see no evidence for god” is supposed to be taken as a serious argument for Atheism.[2] Witness the implied syllogism.

Step (1) I see no evidence for god.
Step (2) Therefore, God does not exist.

Clearly this is not an argument. Arguments need at least two premises to reach a conclusion. There is no logical law of inference that would conclude (2) – that God does not exist – from (1) – I see no evidence for God. In order to conclude atheism one would have to add an extra premise between (1) and (2), bumping the conclusion to step (3). Let us presume that the lack of Didymus finding evidence is reason enough to conclude that there is no evidence for God.

Step 1) There is no evidence for god.
Step 2) The absence of evidence is evidence of absence.
Step 3) Therefore, God does not exist.

Now this is a logically valid argument. That is the argument breaks no formal or informal rules of inference. The argument though is far from sound. For an argument to be sound it needs to be logically valid and have true premises.

The evidence for God is vast. There are two broad categories each with a diverse variety: philosophical evidence and experiential evidence. The philosophical evidence is listed above, and frequently discussed here at the Thinking Matters website. The experiential evidence can be everything from a full-blown Christophany[3] to the quiet witness of the Holy Spirit to the believer. Other experiential evidence might include miracles of healing, signs and wonders, deliverance from demonic activity, the functioning of spiritual gifts such as prophecy or words of knowledge and wisdom.

So as there is evidence for God, premise (1) is false. Nothing more is needed to invalidate the argument. However, you will recall that we were operating under Didymus’ belief that there is no evidence for God. So more important for my purpose here is to point out that premise (2) is also false. The absence of evidence is not evidence of absence.

When there is an absence of evidence for belief P it may be reasonable to remain sceptical or doubtful about belief P, but to conclude from only this that there is an actual absence of P is to overstep the boundary of what one can rationally claim. There are many cases where the failure to provide evidence does not mean said occurrence did not happen, or said entity does not exist. Four examples shall suffice.


A body is found. Investigators are able to deduce a time and cause of death, and come to suspect that it took place in a well-known haunt where other illegal activity often occurs. As it happens, the murder did occur there and their suspicions are correct, though they do not know it. The problem is the place they suspect is clean of all the expected bloodstains and bullet casings. They find no evidence that the crime was committed there. This is because the murder scene was scrubbed clean and put in perfect order by an expert team, who then fled the country leaving no witnesses. Scenarios like this make “The absence of evidence is not evidence of absence” an axiom in forensic science.


Prior to the advent of heliocentricism,[4] championed by Copernicus and Galileo, it was thought by more than a few that the earth was the centre of the Solar System and that the sun revolved around the earth. Suppose heliocentricism was proposed before any of the evidence for it was found. One would understandably be sceptical, as this new idea would be totally different from what had always been taught and previously believed by everyone else. The people who ask for evidence get no reply – none yet has been discovered. They conclude then that geocentricism[5] is better because there is no evidence for heliocentricism. In this case the inability to prove something was not proof that that something was false.


Take the moral claim “cannibalism (to eat another human’s flesh) while the person is still alive is wrong.” When asked to prove this moral assertion, the person making the claim is not able to do it. One argues that is wrong to knowingly inflict harm on someone else, and thus this case of cannibalism is wrong, but this response itself relies on other unproven and un-evidenced moral assertions. The point here is you can know something is wrong, without knowing how something is wrong. Morality is very much an instinctual process, and one grasps that something is wrong without necessarily reasoning out the “why?” beforehand. So here you have a moral claim that is true but is unable to be shown to be true, yet it remains reasonable to believe true. Again, the inability to prove something was not proof that that something was false.


Before the Seventeenth Century it was supposedly thought that there was no such thing as a black swan. However, during the expansion of Europe people traveled widely and, lo and behold, some black swans were discovered. Prior to this there was an absence of evidence for black swans, but this did not mean that there were no such things as black swans.

Next time in Part 2 we shall continue with this familiar conversation, and see how Didymus generally responds to this.

[1] My reason for posting here is so when this argument again pops up, as it inevitably will, I can simply refer said proponent to this post.

[2] Atheism is the idea that God does not exist

[3] An appearance of Christ in the flesh, such as to Saul/Paul on the road to Damascus.

[4] The belief that the earth revolves around the sun.

[5] The belief that the earth is in the centre of the universe, and all revolves around it.

A "Grab Bag" of Self-Refuting Positions

In his Introduction to Logic, Harry Gensler defines a self-refuting statement as “[A] statement that makes negative claims so sweeping that it ends up denying itself.” [1] In other words, it results when an argument or position is undercut by its own criteria  (An example of this would be saying, “I cannot speak a word of English” in English).  Off the top of my head and in no particular order, here’s a grab-bag of several self-refuting positions which I’ve documented over the years:

  1. Truth does not exist (Is that a true statement?)
  2. Nothing is absolute (Is that absolutely true?)
  3. I do not exist (You must exist to deny that you exist)
  4. Science is the only way to know (Can you scientifically prove that?)
  5. Only what can be perceived by the five senses exists (Can you prove that by the five senses?)
  6. Nobody can know anything for sure (Do you know that for sure?)
  7. Nobody can know anything about God (How do you know that?)
  8. Talk about God is meaningless (Since it is a statement about God, this statement is meaningless too)
  9. Reality is just your interpretation, objective reality does not exist (That’s just your interpretation)
  10. “‘Everything we think and do is the function of our genes/nervous system'”: Is this belief itself just the result of genetic/neutral activity? If so, why trust it — or any belief we have? If your belief happens to be right, it’s just by accident” [2]
  11. There are no beliefs (You expect me to believe that?) [3]
  12. Everything is meaningless (So is that statement)

I’ll be adding to this as they keep coming to me, suggestions are welcome!


[1] – Harry J. Gensler, Introduction to Logic (New York, NY: Routledge 2002)p:396
[2] – Paul Copan, Loving Wisdom: Christian Philosophy of Religion (Danvers, MA: Chalice 2007) p.62
[3] – Victor Reppert, C. S. Lewis’s Dangerous Idea (Downers Grove, IL: InterVarsity 2003)p.75

"The single most incompetent logical argument ever made"

David B. Hart has written a favourable review of The Greatest Show on Earth: The Evidence for Evolution over at First Things, but has some pretty strong passing comments of Richard Dawkins’ previous work:

[W]hat makes The God Delusion so frustrating to any reader who has a shred of decent philosophical training and who knows the history of ideas is its special combination of encyclopedic ignorance and thuggish bluster. Repeatedly, Dawkins discusses such issues as Thomas’ “five ways” (which he, as many do, mistakes for Thomas’ chief “proofs” for the “existence” of God); but he never bothers to consult anyone who could explain these issues to him. And he is desperately in need of such explanations, given how utterly bewildered he is on every significant point. He cannot distinguish questions regarding the existence of the universe from questions regarding its physical origin; he does not grasp how assertions regarding the absolute must logically differ from assertions regarding contingent beings; he does not know the differences between truths of reason and empirical facts; he has no concept of ontology, in contradistinction to, say, physics or evolutionary biology; he does not understand how assertions regarding transcendental perfections differ from assertions regarding maximum magnitude; he clumsily imagines that the idea of God is susceptible to the same argument from infinite regress traditionally advanced against materialism; he does not understand what the metaphysical concept of simplicity entails; and on and on. His own pet proof of “why there almost certainly is no God” (a proof in which he takes much evident pride) is one that a usually mild-spoken friend of mine (a friend who has devoted too much of his life to teaching undergraduates the basic rules of logic and the elementary language of philosophy) has described as “possibly the single most incompetent logical argument ever made for or against anything in the whole history of the human race.”

That may be an exaggeration. My friend has spent little time among theologians. But that is neither here nor there. All of these failings would be pardonable if Dawkins were capable of correction. But his habitual response to any concept whose meaning he has not taken the time to learn is to dismiss it as meaningless, with the sort of truculent affectation of contempt that suggests he really knows, at some level, that he is out of his depth.

Read the whole thing.

Hart is the author of Atheist Delusions: The Christian Revolution and Its Fashionable Enemies.

For a collection of reviews of The God Delusion, visit this page.

(Source: Justin Taylor)

What makes a good argument?

Edited by by Dominic Bnonn Tennant: 07/01/2009

An Introduction to Logic

I often tell people that the most useful and fundamental tool in the apologist’s tool-kit is logic. However, it’s depressing how often I see basic logical mistakes being made. Even more depressing is when an opponent or detractor of an argument actually thinks he or she is making a good point, when a basic mistake is obvious. To help with avoiding this, I’m going to lay out a few ground rules for debating: what logic is, and how to use it.

Logic is the study of the rules for right thinking. This is often not properly understood. People tend to use “logic” as a popular synonym for “common sense,” but it is actually a highly technical sub-discipline of philosophy, akin to mathematics. It’s a discipline that itself has many sub-disciplines, and like mathematics, it’s very easy to understand the basics and to use them correctly. For now, we’ll just be surveying basic deductive logic, by asking the question: what makes a good argument?

For our purposes, I’m taking a good argument to be one which is persuasive to a broad range of people. It is one which would persuade a reasonable person, and ideally even an unreasonable person. There are four criteria which make a good argument.

I. It must be formally valid

Formal validity means that the conclusion of the argument follows necessarily from its premises. Such an argument can be structured into a syllogism, which is a way of writing it with its various premises, and a conclusion, as in the examples below. If an argument breaks one of the rules of inference, it is formally invalid. We’ll look at the nine essential rules of inference, first using proper notation, and then using plain language with an example. Leibniz, the German philosopher who formulated many of these rules and gave them their notation, believed that all thought was constructed from these simple rules.

1. Modus ponens

Modus ponens is Latin. It means “the mode which affirms”. Knowing the English translation makes it very easy to follow:

  1. P ? Q
  2. P
  3. Q

In plain English: if P, then Q; P, therefore Q. “P” and “Q” represent propositions, so it’s helpful to substitute in simple phrases for them, to get a better idea of what the rule is saying. For example, let P mean “it is raining”, and let Q mean “the ground is wet”. So:

  1. If it is raining, then the ground is wet.
  2. It is raining.
  3. Therefore, the ground is wet.

As you see, this is really a very simple and obvious rule—as you’ll find that all the fundamental rules of logic are.

2. Modus tollens

Like modus ponens, modus tollens is also Latin. It means “the mode which denies”. Again, this gives a helpful clue as to its form:

  1. P ? Q
  2. ¬ Q
  3. ¬ P

In plain English: P implies Q; not Q, therefore not P. Substituting in some propositions:

  1. If it tastes sweet, then I like it.
  2. It don’t like it.
  3. Therefore, it doesn’t taste sweet.

3. Hypothetical syllogism

  1. P ? Q
  2. Q ? R
  3. P ? R

If P implies Q, and Q implies R, then P implies R.

  1. If it is cheese, then it is delicious.
  2. If it is delicious, then I want to eat it.
  3. Therefore, if it is cheese, then I want to eat it.

4. Conjunction

  1. P
  2. Q
  3. P ? Q

If P, and if Q, then P and Q.

  1. I have chocolate.
  2. I have cheese.
  3. Therefore, I have chocolate and cheese.

5. Simplification

  1. P ? Q
  2. Q

If P and Q, then Q. This isn’t a trick rule; you shouldn’t read it to be excluding P by stating the conclusion Q. It’s just saying that if two things are true, then one of those things is true. Of course, the other is also true, so we can equally say, if P and Q, then P. Both are valid simplifications of the same premise.

  1. I like chocolate and I like cheese.
  2. Therefore, I like cheese.
  1. I like chocolate and I like cheese.
  2. Therefore, I like chocolate.

6. Absorption

  1. P ? Q
  2. P ? ( P ? Q )

If P implies Q, then P implies both P and Q.

  1. If it is raining, then the grass is wet.
  2. If it is raining, then it is raining and the grass is wet.

7. Addition

This is also known as the disjunction introduction, since it introduces disjunctions (“and/or” statements).

  1. P
  2. P ? Q

P, therefore P or Q. In other words, given some proposition P, either P is true, or some unrelated proposition Q is true. The truth of Q doesn’t exclude the truth of P, though typically it is assumed.

  1. The sun rises in the east.
  2. Therefore, the sun rises in the east, or I have a secret identity as a superhero.

8. Constructive Dilemma

  1. ( P ? Q ) ? ( R ? S )
  2. P ? R
  3. Q ? S

If P implies Q, and R implies S, P or Q is true; so R or S is true.

  1. If Yvette comes along on the trip, then Jim will be happy; and if Jim goes on the trip without Yvette, then he will be lonely.
  2. Either Yvette comes along on the trip or Jim goes on the trip without Yvette.
  3. Therefore, either Jim will be happy or he will be lonely.

9. Disjunctive syllogism

This is basically an “either/or” statement:

  1. P ? Q
  2. ¬ P
  3. Q

P or Q; not P, therefore Q. Of course, the converse is also true: P or Q; not Q, therefore P.

  1. I am allowed either two plain biscuits or one chocolate biscuit.
  2. I choose to eat the one chocolate.
  3. Therefore, I don’t choose to eat the two plain.

II. It must be informally valid

The second of the criteria of a good argument is informal validity. Being formally valid is not enough; it must also not commit any informal fallacy. There are many kinds of informal fallacies—far too many to list here. However, I’ll cover the eight of the most common. When an argument commits any of these fallacies, it is informally invalid.

1. The strawman

This is misrepresenting your opponent’s position in some way—either by caricaturing it, or assuming that he holds to the most vulnerable possible variant of it—and then arguing against that misrepresentation as if it were his actual position. For example:

      Person A: “Life got here by creation.”


    Person B: “That’s impossible because the earth could not possibly have been created in six 24-hour days.”

2. Begging the question

Arguing in a circle and providing no reason for accepting a premise in your argument, other than the conclusion of the argument itself.

      Person A: “I know that God exists because the Bible says He does.”


      Person B: “How do you know the Bible is telling the truth?”


    Person A: “Because the Bible was written by God.”

3. The genetic fallacy

Arguing for or against some belief based on the origin of that belief.

  • Because of our fear and ignorance of nature we invented God. Therefore he does not exist.
  • This fellow often produces shoddy research, so his latest paper should be dismissed.

4. Argument from ignorance

Arguing that a belief is false because there is insufficient evidence for it.

  • No one can disprove the existence of God. Therefore, God exists.
  • There’s no evidence that the Red Sea was ever parted. Therefore, the account in Exodus is a myth. (Notice, though, that an argument saying that there is evidence that the Red Sea was not ever parted would not be fallacious.)

5. Equivocation

Using a word or category in such a way that it has more than one meaning.

  1. Margarine is better than nothing.
  2. Nothing is better than butter.
  3. Therefore, margarine is better than butter.

6. Amphiboly

Formulating a premise in such a way as its meaning is ambiguous.

  • No food is better than our food.

7. Composition

Inferring that a whole has a certain property because all of its parts have that property.

  • Every part of an infinite past can be traversed. Therefore, an infinite past can be traversed.
  • Every tile on the floor was cheap, therefore the tiled floor is cheap.

8. Ad hominem.

Attacking the person and not the argument (Latin: “at the man”).

  • What he says can’t be correct because he’s a religious nut.
  • Calvinism is awful because John Calvin burned Servetus at the stake. (Notice how this example also constitutes the genetic fallacy.)

Is this a good argument?

  1. Either I am crazy, or I am dead.
  2. I am not crazy.
  3. Therefore, I am dead.

This disjunctive syllogism is both formally and informally valid, making it logically valid. But obviously this not a good argument. On reflection premise one is rather spurious. Why should anyone accept the dilemma presented there? There is also cause to doubt premise two. Therefore, logical validity is not all that is required to make a good, convincing argument. A good argument requires something else.

III. It must have true premises

The third criterion is that a good argument must have true premises. When an argument is formally and informally valid and has true premises, it is sound. But if it is invalid, or it has false premise, it is unsound. When an argument is sound the conclusion follows necessarily and inescapably from its premises. It doesn’t matter if you don’t like it. If you disagree, then you are wrong. When an argument is sound the conclusion is true. Of course, if we don’t know that some premise is true, then we can’t know if the argument is sound. But not knowing the truth of a premise does not make the argument unsound.

You’ll remember that we defined a good argument as one which will persuade a broad range of people, convince a reasonable man and hopefully even an unreasonable man. When an argument is sound, does this mean it is a good argument? This brings us to our final criterion.

IV. Premises more probable than their contradictories

When constructing an argument it would be a tall order indeed if we had to prove the truth of every premise. If that were the case we would be lost in utter scepticism, for we would have to prove the premises of the arguments for the premises of the argument, and the premises of those arguments backwards ad infinitum.

To save us from scepticism a good argument must have premises which are at least more probable than their contradictories. In other words, a premise should be more plausibly true than false. We need not know for certain a premise is true; we need only know that the alternative is less likely.

Obviously there are many differing opinions on many differing subjects, and we live in a very divergent and contrary world. The most powerful arguments will therefore be those structured on premises which are widely accepted and are the hardest to deny. The strength of an argument will depend on the strength of its premises.

Now, plausibility is a person-dependent notion, so in cases of disagreement we need to dig a little deeper to see what reasons we have for accepting or rejecting a premise. When we do, we may find that we have made the mistake—but we also may find that our opponent’s rejection is based on misinformation, ignorance of evidence, or a fallacious objection. Thus we may be able to persuade the other by giving better evidence, information, or gently correcting their error.