Fallacies
formal, informal,rhetorical & sta2s2cal

Formal fallacies• A logical argument that is not valid– Valid: The premises ﬁt & prove the conclusion– For example:
All S is M.
All P is M.
Therefore, all S is P.

Formal fallacies• A logical argument that is not valid– For example:
All rabbits run fast.
Homare Sawa runs fast.
Therefore, Homare Sawa is a rabbit.

Formal fallacies• A logical argument that is not valid
Compare a valid example:
All rabbits run fast.
Homare Sawa is a rabbit.
Therefore, Homare Sawaruns fast.

Picture Materials : KNIHA KRÁLÍCI A HLODAVCI – PRAKTICKÁ ENCYKLOPEDIE – ESTHER VERHOEFVERHALLEN

Rhetorical (informal) fallacies• (Some) ARempts to convince without logic– People instead of premises, data
Everybody says it, so it must be true.
Stupid people say it, so it must be false.
– Ignorance/knowledge instead of logic
We don’t know it’s not true...
This is a good idea, so it must be true.

Sta2s2cal fallacies• Misunderstanding / misrepresen2ng sta2s2cs
It’s significant (p<0.01), so it’s important.
The temperature has been going down since
September. By June we’ll be freezing.

• Calcula2ng incorrectly, improperly
All my friends agree with me.
Therefore, everyone agrees with me.

Chocolate & Nobel Prizes

Messrli2012Chocolate & Nobel Prizes

Maurageet al.
2013

Chocolate & Nobel Prizes

Maurageet al.
2013

Chocolate & Nobel Prizes

Maurageet al.
2013

Sunlight correlates with vaca2ons

Courtesy oftylervigen.com

Japanese cars & US suicides

Courtesy oftylervigen.com

Government
Can you spot the fallacy?

Bri2sh poli2cians’ bargain• 2011: Bri2sh poli2cians say government
wastes £10bn (Y2兆) per year
• Ben Goldacre read the report to check theircalcula2on.

hRp://www.badscience.net/2012/04/is-this-the-worst-government-sta2s2c-ever-created/Bri2sh poli2cians’ bargain
Government workers’ mobile phones are from
anexpensive
If theirmobilePhones
phonesMost
spendingcompany.
is not for mobile
phones.
were
a different company,
theyyear.
would
cost fromthe government£600,000 per
If be20%
theycheaper.
save 20%, that is £120,000 (£0.00012bn).
Extrapola)on
fallacyCitygovernment
spends £50bn per year on allprograms. If they can save 20%, that is £10bn.

Bad charts
50,000,020
50,000,000
49,999,980
49,999,960
49,999,940
49,999,920
49,999,900
49,999,880
49,999,860
49,999,840
49,999,820

Bad charts
50,000,000

45,000,000

40,000,000

35,000,000

30,000,000

25,000,000

Both charts based on
the same numbers

Bad charts
50,000,020
50,000,000
49,999,980
49,999,960
49,999,940
49,999,920
49,999,900
49,999,880
49,999,860
49,999,840
49,999,820

But this one is only thetop 0.0004% of the range

Be careful
50,000,000

45,000,000

40,000,000

35,000,000

30,000,000

25,000,000

This is the top
50% of the range

Language, Psychology
Can you spot the fallacy?

Word aversion
Many English speakers say they hate the word moist.
They say they dislike its sound, but maybe they
actually dislike its meaning. Thibodeau et al. (2015)
asked people to rate whether they like or dislike
several words. Although 21% dislike moist, those same
people did not dislike hoist or rejoiced. Therefore,people who dislike the word moist dislike its meaning,
not its sound.

Word aversion
Many English speakers say they hate the word moist.
They say they dislike its sound, but maybe they
“A is False”
not necessarily
actually
dislikedoes
its meaning.
Thibodeaumean
et al. (2015)“B is people
True.”to rate whether they like or dislike
asked
several words. Although 21% dislike moist, those same
False Dilemma
people did not dislike hoist or rejoiced. Therefore,
people who dislike the word moist dislike its meaning,
not its sound.Economics
Can you spot the fallacy?

Growth vs. debt
Reinhart & Rogoff (2010) compared economic growthand government debt. They found little connection.
But when debt is more than 90% of GDP, growth
drops dramatically.
Herndon et al. (2013) couldn’t duplicate Reinhart &Rogoff’s findings. Eventually they found that Reinhart& Rogoff had made a computer error that caused
their statistics to be calculated incorrectly.

GDP Growth vs. Public Debt
4.5
4
3.5
3
2.5
2
1.5
1Reinhart & Rogoﬀ 2010
Herndon et al. 2013

0.50-0.5

0-30

30-60

60-90

>90

Growth vs. debt
Reinhart & Rogoff, who oppose big debt for politicalreasons, found that big debt is bad.
Herndon et al. found that big debt does not havemuch effect. (Small debt has a good effect, butpoliticians don’t argue about that.)
1. Garbage in, garbage out
2. Beware of ﬁnding what you are looking for.

Sociology and Communica2on
Can you spot the fallacy?

Canvassing
People rarely change their political positions. Lacour& Green (2014) found that when an interviewer saysthat he or she is gay, the people being interviewed are
more likely to change their positions about gay
marriage.

Canvassing
This was not a fallacy – it was a lie. Lacour made up
fake data to “prove” the effectiveness of his
canvassing techniques.
The respected journal Science published the paperand peer reviewers accepted it in part because Greenis a very well-known and respected scholar in thisfield. One reviewer said, “I trust anything Don Greensays.”
When he discovered the lie, Green asked Science toretract the paper.

The fallacy fallacy

Videos are available on YouTube from PBS Idea Channel