Tag Archives: philosophy

The hypothetical barking dog: a lesson in logic

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Sherlock Holmes (wikipedia)


This month our church is hosting a Senior Seminar. In this seminar we invite graduating seniors to join us as we attempt to give them a crash course in the big choices they will face as they head off to college or the work force. One of these areas we explore in the seminar is worldviews and philosophy.

Honoring the fact that the Presidential election has gone to the dogs (a sad commentary on political discourse), this post uses dogs to examine the basic hypothetical form of a philosophical argument. To set up the scenario we are going to use the barking dog hypothesis found in the Sherlock Holmes adventure – Silver Blaze.

Colonel Ross still wore an expression which showed the poor opinion which he had formed of my companion’s ability, but I say by the inspector’s face that his attention had been keenly aroused.

“You consider that to be important?” he asked.

“Exceedingly so.”

“Is there any point to which you would wish to draw my attention?”

“To the curious incident of the dog in the night-time.”

“The dog did nothing in the night-time.”

“That was the curious incident,” remarked Sherlock Holmes.

…

“Before deciding that question I had grasped the significance of the silence of the dog, for one true inference invariably suggests others. The Simpson incident had shown me that a dog was kept in the stables, and yet, though someone had been in and had fetched out a horse, he had not barked enough to arouse the two lads in the loft. Obviously the midnight visitor was someone whom the dog knew well.”

That basis of Holmes argument starts with the hypothesis that when a dog detects an intruder it will bark.

Writing this out as a premise in an argument would look like this:

If (a dog detects an intruder) then (the dog will bark)

This seems like a premise that that has a high degree of probability of being true most of the time. Of course there are unstated assumptions like the dog is healthy and can see, smell, and hear, is not drugged, and can actually bark. Holmes assumes this hypothesis is reliable, having the testimony that dog is used as a guard dog along with the lads to make sure the horse is not stolen.

In a hypothetical form of a philosophical argument the concept of a dog detecting an intruder is called the antecedent. It represents a cause and is often represented by a P.

The concept of the dog barking is called the consequent. It represents an effect and is often represented by a Q.

Using this as a starting point, we can look at the hypothesis and 4 different ways to arrive at a conclusion based on what the second premise in the argument attempts to either confirm or deny.

Note the hypothetical stays the same in all 4 cases, in which we have asserted that P is a cause of the effect Q. We are also assuming that this hypothesis is true. We are only attempting to verify the conclusion that each argument is making. If this hypothesis is false then the conclusion of each argument would also be false (or at least unproven by the argument).

Modus Ponens: Affirming the Antecedent

hypothetical If (a dog detects an intruder) then (the dog will bark)
premise The dog detects an intruder
conclusion Therefore the dog barks
  • If P is really a cause of Q and the premise that the dog detected an intruder is true (P is true), it will be true that the dog barked (Q is true).

Modus Tollens: Denying the Consequent

hypothetical If (a dog detects an intruder) then (the dog will bark)
premise The dog did not bark
conclusion Therefore the dog did not detect an intruder
  • If P is really a cause of Q and the premise that the dog did not bark is true (not Q), it will be true that the dog did not detect an intruder (not P).
    • The dog did not bark so the cause was missing, which was how Holmes arrived at the conclusion that the person who took the horse could not have been a stranger to the dog.

Fallacy: Denying the Antecedent

hypothetical If (a dog detects an intruder) then (the dog will bark)
premise The dog did not detect an intruder
conclusion Therefore the dog did not bark
  • If P is really a cause of Q and the premise that the dog did not detect an intruder is true (not P), it will not necessarily be true that the dog did not bark (not Q).
    • This is a fallacy because Q may occur for other reasons
    • The dog may have barked because it was hungry or playing etc.

Fallacy: Affirming the Consequent

hypothetical If (a dog detects an intruder) then (the dog will bark)
premise The dog barks
conclusion Therefore the dog detects an intruder
  • If P is really a cause of Q and the premise that the dog barks is true (Q), it will not necessarily be true that the dog detected an intruder (P).
    • This is a fallacy because Q may occur for other reasons
    • The dog may not have barked because of an intruder, but because it was hungry or playing etc.

Once we have established these valid and invalid forms of an argument we can apply them to more interesting cases.

Give this one a try:

hypothetical If (humans and chimps have a common ancestor) then (humans and chimps have similar genetic makeup)
premise humans and chimps have similar genetic makeup
conclusion Therefore humans and chimps have a common ancestor

Is this a valid argument?

Reason Rally or Atheist Assembly?

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Today on the National Mall in Washington DC, people will gather together at an event called the Reason Rally. What is the purpose of the gathering? According to the web site it is a “coming out of the closet” for secularists. Here is how the Washington Post is describing it:

Reason Rally will show that all the cool people are atheists now and that the days of consent by silence are over. It’s an appeal to millions of hidden atheists to come out of their closets and join the fun.

One of the speakers, is Richard Dawkins, who poses the question who is against reason?

How have we come to the point where reason needs a rally to defend it? To base your life on reason means to base it on evidence and logic. Evidence is the only way we know to discover what’s true about the real world. Logic is how we deduce the consequences that follow from evidence. Who could be against either?

Sadly, Dawkins concludes that anyone who is not a secularist is against reason, logic, and evidence. He lauds science and reason comparing the building of planes, rockets, Mars rovers, the ability to cure diseases,  and the fact that the Earth spins to other things “we know”. Things like the age of the universe, the age of the earth, and the fact that we all evolved from other species.

This is not something new, Dawkins is known for this famous (or is it infamous) quote:

It is absolutely safe to say that if you meet somebody who claims not to believe in evolution, that person is ignorant, stupid or insane (or wicked, but I’d rather not consider that).

He, by his own count says 4x in the article that the “Reason Rally is not for you” if you have not outgrown the supernatural.

Tom Gilson over at Thinking Christian wrote the following:

The new atheists–participants in the contemporary anti-religion movement led by Richard Dawkins, Sam Harris, the late Christopher Hitchens, among others–are working overtime to tell the world that reason favors atheism, and atheism alone.

In this article and in this blog entry, he demonstrates where Dawkins fails to apply the reason he is rallying for.

Unfortunately, the notion that anyone who is religious must be against reason is ridiculous. Questioning the conclusions of science in areas like evolution is not rejecting reason or hiding from evidence. It is however recognizing that some things are probable and can’t be known with absolute certainty.

One of my favorite bloggers and theologians, C. Michael Patton has written on the idea of our need for certainty in a provocative entry “Why I am not completely sure Christianity is true”:

We don’t want probability! People can poke holes in that. We want absolute certainty. We want to be indubitable!” Indubitability ultimately equates to infallible knowledge—knowledge that can’t be wrong.

The science of aerodynamics can be proven with absolute certainty. I happen to live near an airport and see the evidence flying overhead every day. As we look overhead at these engineering marvels it is easy to think that science can prove anything in a similar manner. If scientists can build that plane then they can prove things like evolution too. However, this is committing the fallacy of faulty generalization.

  • Science has proven flight is possible by building a plane.
  • Science proposes that all living things evolved.
  • Therefore all living things have evolved because science proves things.

Enns and other theologians have assumed this as a starting point as they grapple with the impacts to theology. But that depends on what we mean by “know” and “prove”. In evaluating Enns claims, I have written about the difference between science that deals with the present, like putting rockets on the moon, and science that deals with the past and events that are a singularity, like the beginning of the universe.

We must all wrestle with the evidences we have available to answer these types of questions regarding what it is true. That even includes our own belief in God as Creator and in Jesus’ death and resurrection. Belief or faith by definition requires trusting something that can’t be proven certain, but does not mean that we are forced to take a “blind leap” that throws reason to the wind.

Christianity is a rational faith based on the historic reality of God interacting with His creation by sending His Son into the world to conquer death and save sinners during the first century. Can we know this with absolute certainty? No.  But having examined the evidence I have come to the logical conclusion that it is probable that Christianity is true.

And, if the Reason Rally is a coming out party for atheists to assert how cool they are then,Dawkins is right it is not for me. But then this event is not really a rally for reason, it is just an assembly of atheists.