Toddler logic

How old are people when they first start being able to reason?

I vaguely recall reading somewhere in the psychological literature on the development of reasoning skills that kids are able to reason as early as 4.  However even that may underestimate how early these skills emerge.

Our daughter is 3 years and one month old.  Here’s a conversation we had this evening.

Lillian (singing): “I’m the king of the castle, and you the dirty bascal.”

Us: “Its rascal, not bascal.”

“No, its BASCAL.”

“OK, well, grown-ups say rascal.  Little babies say bascal.”

Lillian ponders for a moment, then smiles. “I’m a baby!”

She had performed the following inference:

Babies say bascal.
I say bascal.
Therefore, I’m a baby.

This of course is an invalid inference; she might be something other than a baby which also says bascal.

However logical perfection is a lot to ask of a three year old.  In context, despite not being deductively valid, it wasn’t a bad inferential move to make.

She’s been making these sorts of inferences for a while – indeed, since well before she was three.  And explicit or verbalised inference was preceded by patterns of behavior which seemed to indicate an implicit understanding of certain inferential patterns.

So we can say the following with certainty: Reasoning abilities of a rudimentary kind are, at least sometimes, exhibited by humans before they turn 3.

Support is transitive?

On the news tonight there was coverage of protests in Washington against the Iraq war. There was a soundbite of an Iraq veteran saying “You can’t support the troops and oppose the war, because the troops support the war.”

These thoughts flashed through my mind in quick succession:

1. Argument.
2. Argument, very concisely expressed.
3. Bad argument.
4. Bad, but interesting.

Why interesting? Well, consider what this fellow must be assuming. Put another way, what co-premise would, if true, make this argument strong?

Presumably something like, “if you support somebody, you have to support what they support”.

This is similar to the technical notion of transitivity: if A supports B and B supports C, then A supports C. Conversely, if A doesn’t support C, then A doesn’t really support B.

So we get:

Now it seems to me that this assumption is obviously wrong as a general principle. For example I can support my child without thereby being obliged to adopt whatever ill-considered attitude they might adopt.

From a “critical thinking” perspective, the argument is really a “fallacy of equivocation” – i.e. an argument that is fallacious because it “equivocates” on a key term, meaning that it uses a key term in different ways in different places.

The term “support” means one thing when you talk about supporting the troops, and another thing when you talk about supporting or opposing the war.

But there is a deeper issue here – the idea that allegiance to a group requires allegiance to the beliefs of that group. Something profound (and presumably of evolutionary origin) in the human psyche makes us tend this way. Many human organisations promote the idea and owe their continued existence to its power. But it is of course a dangerous idea.

Critical Thinking – Where to Really Start

It turns out that my recent post Critical Thinking – Where to start?, with its list of 10 or so good books on critical thinking, has generated far more hits than any other entry on this humble blog. Many of those came from Gary Curtis’ blog on his excellent Fallacy Files site, where the list is described as “a list of books for improving critical thinking skills”.

Trouble is, if you really want to improve your critical thinking skills, the list of books isn’t going to do much for you. Skills only improve through practice, which means engaging in critical thinking activities and working on your performance. In this regard, critical thinking is just like any other skill. You’d never get better at tennis just by reading books about it.

So, where would you start practicing critical thinking? Some of the books on the list have exercises, and they might be worth doing. But if you want to

• get going right away
• with something that is free, and
• proven to have real benefits,

then a good place to start is the Austhink argument mapping tutorials – though you would need to actually do the exercises.

Argument mapping is certainly not the whole story about critical thinking, and I’d recommend that you do other things as well, such as read some of the books on the list. But practicing argument mapping builds your core reasoning and argument skills, and these are central to critical thinking.