smartigoTraining logical thinking: four traps and how to get around them
Logical thinking sounds like textbooks and IQ tests. In daily life it's something much more hands-on: noticing that a sentence doesn't say what you're hearing in it. And the good news is that you need no special talent for it, only a few habits.
Trap 1: The answer that comes too fast
A bat and a ball cost $1.10 together. The bat costs one dollar more than the ball. How much is the ball?
Almost everyone first thinks "10 cents". That's wrong: then the bat would be $1.10 and both together $1.20. The ball costs 5 cents, the bat $1.05. If you caught yourself, you're in good company. The puzzle comes from Shane Frederick's research, and the error rate is high, even among students at good universities. It shows that a first impression is often a suggestion you have to check before accepting it.
Habit: when an answer feels instantly right, calculate against it once.
Trap 2: If-then gets turned around
"If it rains, the street is wet." The street is wet. Did it rain? Not necessarily, it could have been a street sweeper. That sounds trivial, yet it's the mix-up behind many claims: "Whoever earns well is hard-working. You're hard-working, so you earn well." Or: "Whoever cheats looks nervous. He looks nervous, so he's cheating."
For practice there's Peter Wason's famous card task. Four cards lie in front of you, each with a letter on one side and a number on the other. You see: E, K, 4, 7. The rule is: "If there's a vowel on one side, there's an even number on the other." Which cards do you need to turn over to test the rule?
Answer
E and 7. With E you have to check that an even number is behind it. With 7 you have to check that no vowel is behind it, because that would break the rule. The 4 is the popular wrong choice: whether a vowel is behind the 4 or not, it refutes nothing. And K doesn't matter.
Most people choose E and 4. We prefer to look for confirmation instead of refutation. That's human, and it can be practised.
Trap 3: "Some" is not "all"
All roses are flowers. Some flowers wilt quickly. So do some roses wilt quickly? You can't derive that from the two sentences. The quickly wilting flowers could be nothing but tulips. Such tasks are called syllogisms, and it's remarkable how often we wrongly say yes when the conclusion sounds plausible. It's called belief bias: we want to see confirmed what we believe, and the inference slides through.
Habit: at every "so", ask whether the result follows from the sentences or from your expectation.
Trap 4: Forgetting the counterexample
"All politicians lie." "All tradesmen turn up late." "It's always like that here." Whoever says "all" or "always" claims something that a single counter-case refutes. That is one of the most useful habits there is: look for the one case that doesn't fit. You usually find it quickly, and the statement shrinks to what it really wanted to say: "often".
How do you train this?
Not by solving logic puzzles by the dozen. More by keeping three habits:
- Turn it around. When a sentence says "if A, then B", ask what applies when B occurs without A.
- Look for the counterexample. At every "all" and "never", spend a second looking for the outlier.
- Brake. With answers that feel instantly right, check. Especially with bills, offers and messages in a hurry.
Whether this carries over to many areas of life is open. Research on transfer is reserved (see Brain training: does it actually work?). But it is plausible: once you've seen these patterns, you recognise them again. For example in messages that apply pressure and offer a simple conclusion, as described in Spotting phishing.
One last small observation: these tasks seem easier when they're in front of you and you know there's a trap. In real life the trap doesn't announce itself.
An example from daily life
An offer for a phone contract: "Only $9.99 a month." In the small print: "24-month term, one-time $39.99 activation fee, $19.99 from month 13." Someone who only skims has "about ten dollars" in mind. Someone who calculates gets: 12 times 9.99 is about 120, twelve months at 19.99 about 240, plus $40 activation. That's roughly $400 over 24 months, or about $17 a month.
That isn't higher math, nor higher logic. It's the plain habit of not confusing the headline with the result. That's also the core of the four traps above: the first impression is a claim, not a finding.
It's worth collecting such cases deliberately now and then. Not to be annoyed at providers, but to see how often the same mechanism recurs: a low price at the front, a high one at the back; an "all" at the start, a single example as evidence; a "so" that comes out of nowhere. Once you've seen three such cases, you spot the fourth immediately.
In Smartigo, tasks like these appear as small everyday scenes, with a second chance and without giving the answer away at once. The core features are free.