Friday, January 07, 2011


Deductive Arguments are arguments where, if its premise is true, the conclusion must also be true. They are also called “valid” arguments. Here is an an interesting classification of deductive arguments -

Modus ponens (“mode of putting”)

If the letters p and q stand for declarative sentences:

If p then q.
Therefore q.

If there is no chance factor in chess, then chess is a game of pure skill.
There is no chance factors in chess.
Therefore, chess is a game of pure skill.

Modus tollens (“mode of talking”)

If p then q.
Therefore, not-p.

Eg., Sherlock Holmes in A.C. Doyle’s “The Adventure of Silver Blaze” –
A dog was kept in the stables, and yet, though someone had been in and fetched out a horse [the dog] had not barked…Obviously the …visitor was someone whom the dog knew well.

In Modus tollens form –

If the visitor was a stranger, then the dog would have barked.
The dog did not bark.
Therefore, the visitor was not a stranger.

Hypotherical Syllogism

If p then q.
If q then r.
Therefore, if p then r.

If you study other cultures, then you start to realize the variety of human customs.
If you start to realize the variety of human customs, then you become more tolerant.
Therefore, if you study other cultures, then you become more tolerant.

Disjunctive Syllogism

p or q.
Therefore, q.

Eg., - Bertand Russell in Skeptical Essays (1935)
Either we hope for progress by improving morals or we hope for progress by improving intelligence.
We can’t hope for progress by improving morals.
Therefore, we must hope for progress by improving intelligence.


Ad hominem (“to the man”) – attacking the person of a source rather than his qualifications or reliability, or the actual argument he makes.
Eg., - It is no surprise that Carl Sagan argues for life in Mars – after all, he was a well-known atheist. I don’t believe it for a minute.

Ad ignorantium (“appeal to ignorance”) – arguing that a claim is true because it has not been shown to be false.
Eg., Senator Joseph McCarthy when asked for evidence to back up his accusation that a certain person was a Communist: “I don’t have much information on this except the general statement of the agency that there is nothing in the files to disprove his Communist connections.”

Ad misericordiam (“appeal to pity”) – appealing to pity as an argument for special treatment
Eg.: I know I flunked every exam, but if I don’t pass this course,I’ll have to retake it in summer school. You have to let me pass!

Ad populum – appealing to emotions of a crowd; also appealing to a person to go along with the crowd (“Everybody’s doing it!”)

Affirming the consequent – a deductive mistake of the form –
If p then q.
Therefore p. (it overlooks alternatives)

When the roads are icy, the mail is late.
The mail is late.
Therefore, the roads are icy.

Begging the question / Circular argument / petition principii implicitly using your conclusion as a premise.
Eg., -
The Bible is true, because God wrote it.
The Bible says that God exists.
Therefore, God exists.

Complex question – posing a question in such a way that people cannot agree or disagree with you without committing themselves to some other claim you wish to promote.

Eg.,: “Are still as self-centered as you used to be?”

Denying the antecedent – overlooking alternatives in modus tollens

False dilemma – reducing options you consider to just two, often diametrically opposed to each other and unfair to the people against whom the dilemma is posed.
Eg., - “America: Love It or Leave It” (again overlooks alternatives).

Non sequitur (“does not follow”) – a conclusion that is not a reasonable inference from the evidence.

Poisoning the well – using loaded language to disparage an argument before even mentioning it –
Eg., - “I’m confident you haven’t been taken in by those few holdouts who still haven’t outgrown the superstition that…” (more subtly – No sensitive person thinks that…)

Post hoc, ergo propter hoc (“after this, therefore because of this”) – assuming causation merely on the basis of mere succession in time.

Red herring – introducing an irrelevant subject and thereby diverting attention from the main subject.
Eg., In a discussion on the relative safety of cars, the issue of cars made in America is a red herring.

Straw man – a caricature of an opposing view, exaggerated from what anyone is likely to hold, so it is easy to refute.
Weston, Antony (2009). A Rulebook of Arguments. Hackett Publishing Co. Cambridge.

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