Informal Logic 101: How to Think and Argue Better, Part 4

Part 4: Three Ways to Argue

Meanwhile, at the clinic…
Client (Michael Palin): “Aha! If you’re arguing, I must have paid.”
Mr. Barnard (John Cleese): “Not necessarily. I could be arguing in my spare time….”

OK, if you aren’t a Monty Python fan (and I am only marginally) and you don’t understand the above quote, you are forgiven. But, I urge you to look up the Monty Python skit “Argument Clinic” (or similar title) on YouTube. Go ahead. We’ll wait…. And, I assure you, those aren’t the kinds of arguments we’ll examine here. (Yes, it is! No, it isn’t!) By the way, notice that Palin’s character had it right. He said, “An argument is a collective series of statements to establish a definite proposition.” A fair definition, yet mostly what he got for his money was unsupported contradictions.

There are three types of logical argument, or ways of reasoning, if you will — deductive, inductive, and abductive. Most people have heard of the first two but are unaware of the third. (I know I wasn’t familiar with it until several years back.) Each has its strengths and proper area of usage.

Sherlock Holmes - Basil RathboneDeductive

Most arguments result in conclusions that are, at best, probable. If your reasoning is both sound and valid, the odds that your conclusion is correct are strongly in your favor. The main strength of a deductive argument, properly constructed, is that the proper conclusion necessarily follows from the premises. The conclusion is certain by logical necessity. Unfortunately, deductive argumentation can rarely be used outside of formal logic.

Perhaps the most recognizable example of deductive reasoning is the classic:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

But, there are three other, popular forms of the deductive argument that we need to examine. We’ll even learn a little Latin in the process. They are modus ponens, modus tollens, and disjunctive syllogism, and their formulations all refer to an antecedent (‘P’) and a consequent (‘Q’).

Modus Ponens (Affirming the Antecedent)

If P, then Q.
Therefore, Q.


If the Bible is historically reliable, then it must be taken seriously.
The Bible has proven to be historically reliable.
Therefore, it must be taken seriously.

(Yes, I realize that the second statement is controversial in some circles and itself the conclusion of another argument, but just go with me on this, OK?)

Modus Tollens (Denying the Consequent)

If P, then Q.
Not Q.
Therefore, not P.


If there is an attractive female guest star, Captain Kirk will flirt with her.
Captain Kirk did not flirt in this episode.
Therefore, there must not have been any attractive female guest stars.

Disjunctive Syllogism (Denying the Disjunct)

Either P or Q.
Not Q.
Therefore, P.


The foreign dignitary must either be an official ambassador or the king himself.
He is clearly not the king.
Therefore, he must be an official ambassador.

By the way, see that word “syllogism”? Get used to it. It refers to the 2-premises-plus-1-conclusion formula for an argument. If there are a lot of possibilities other than P or Q, then technically the argument hasn’t been boiled down enough for a proper deductive argument.

chemist in a labInductive

Notice that in deductive cases, you typically begin with a more general statement, then look at a particular case, and finish by concluding whether or not the particular fits the general. (This often involves causes and effects.) With inductive reasoning, however, the argument begins with several particulars, or individual examples, and concludes with a general statement. As previously mentioned, another difference is that a deductive argument guarantees a truthful conclusion, whereas an inductive argument merely deals in what is (im)probable. This makes sense, since most things in life involve limited knowledge and lots of uncertainty.

If the premises of an inductive argument are not sufficient to support the conclusion, we say that the argument is “weak”. On the other hand, sufficient support results in a (highly?) likely or probable conclusion, so we call it a “strong” argument. Some inductive arguments are stronger than others, and even the strength of a particular inductive argument may vary as more information related to the premises comes to light. Whereas deduction requires validity and soundness, induction deals in strength and cogency. “Cogency”, in this context, means the same as “soundness” — i.e., that all the premises must be true or acceptable.

Alright, let’s try an inductive argument:

The first pesticide developed with new Chemical X caused harmful mutations in the crops.
The second pesticide developed with new Chemical X caused harmful mutations in the crops.
The third pesticide developed with new Chemical X caused harmful mutations in the crops.
The fourth pesticide developed with new Chemical X caused harmful mutations in the crops.
The fifth pesticide developed with new Chemical X caused harmful mutations in the crops.
The sixth pesticide developed with new Chemical X caused harmful mutations in the crops.
The seventh pesticide developed with new Chemical X caused harmful mutations in the crops.
The eighth pesticide developed with new Chemical X caused harmful mutations in the crops.
Therefore, it is likely — perhaps even highly likely — that the next pesticide developed with new Chemical X will cause harmful mutations in the crops.

Not certainty. But, assuming an objective analysis indicates no other factors could have caused the mutations, a conclusion with (high?) probability can be reached. (Note: It is important in cases like this to not mistake correlation for causation.)

Now, what about this strange bird called “abduction”? Sounds kind of alien to me….

Abductive (aka “inference to the best explanation”)

Think of it as sort of a “big picture” approach to problem-solving or case-making. Basically, abductive reasoning is when one takes a whole bunch of data — i.e., a series of facts, or various lines of evidence — regarding an event and attempts to infer the best explanation for what happened. Abduction is more like induction than deduction, in that it yields probables rather than certainties. But, instead of trying to produce or predict a specific outcome, the goal is to come up with a superior explanatory hypothesis. Spock at viewerFor example, Christian apologists like William Lane Craig and Gary Habermas use abductive reasoning to make a case for the bodily resurrection of Jesus Christ. Scientists and philosophers will use abductive reasoning to develop and argue for theories about the origin of man or of the universe or the Cartesian argument for global skepticism. (Yeah, I don’t have a clue what that is, either.)

Here is an everyday example of abductive reasoning that I found in the online Stanford Encyclopedia of Philosophy:

“One morning you enter the kitchen to find a plate and cup on the table, with breadcrumbs and a pat of butter on it, and surrounded by a jar of jam, a pack of sugar, and an empty carton of milk. You conclude that one of your house-mates got up at night to make him- or herself a midnight snack and was too tired to clear the table. This, you think, best explains the scene you are facing. To be sure, it might be that someone burgled the house and took the time to have a bite while on the job, or a house-mate might have arranged the things on the table without having a midnight snack but just to make you believe that someone had a midnight snack. But these hypotheses strike you as providing much more contrived explanations of the data than the one you infer to.”

So, how do I figure out which hypothesis is best? While there is no settled way to determine that one hypothesis is superior to another, Professor Samples says there are six generally-accepted criteria used and recommended by logicians. A solid case…

1) demonstrates balance between complexity and simplicity;
2) shows coherence;
3) corresponds to the facts;
4) avoids unwarranted presumptions and ad hoc explanations;
5) is testable; and
6) successfully adjusts to accommodate possible counterevidence.

The one that scores highest on these should have the most explanatory power and scope and is, therefore, the one most rational to accept, however tentatively. Now, if I could just figure out how to do all that in an objective manner. Simple, right?! Seriously, though,… Abductive arguments are being used more and more by academics and “normal folk” alike. They are recognized as being extremely useful, preferable even, especially in thinking about more complex issues.

Had enough for today? OK. In Part 5 we’ll dive into the really fun part of all this — identifying logical fallacies! Yee-haw!


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