PINKER, WASON, and GRICE

Speranza

A TRIVIU M

The medieval curriculum comprised seven liberal arts, divided into the lower-level trivium (grammar, logic, and rhetoric) and the upper-level quadrivium (geometry, astronomy, arithmetic, and music).

Trivium originally meant three roads, then it meant crossroads, then commonplace (since common people hang around crossroads), and finally trifling or immaterial.

The etymology is, in a sense, apt: with the exception of astronomy, none of the liberal arts is about anything.

They don't explain plants or animals or rocks or people; rather, they are intellectual tools that can be applied in any realm.

Like the students who complain that algebra will never help them in the real world, one can wonder whether these abstract tools are useful enough in nature for natural selection to have inculcated them in the brain. Let's look at a modified trivium: logic, arithmetic, and probability.

"Contrariwise," continued Tweedledee, "if it was so, it might be, and if it were so, it would be; but as it isn't, it ain't. That's logic!"

Logic, in the technical sense, refers not to RATIONALITY in general but to inferring the truth of one statement from the truth of other statements based only on their form, not their content.

I am using logic when I reason as follows.

P
If P, Q.
Therefore Q

P and Q.
Therefore, P is true.

P or Q.
~P
Therefore Q.

If P  Q,
~Q.
Therefore ~P.

I can derive all these truths not knowing whether P means

i. There is a unicorn in the garden.
ii. Iowa grows soybeans.
iii. My car has been eaten by rats.

Does the brain do logic?

College students' performance on logic problems is not a pretty sight.

There are some archeologists, biologists, and chess players in a room.

None of the archeologists are biologists.

All of the biologists are chess players.

What, if anything, follows?

A majority of students conclude that none of the archeologists are chess players, which is not valid.

None of them conclude that some of the chess players are not archeologists, which is valid.

In fact, a fifth claim that the premises allow no valid inferences.

Spock always did say that humans are illogical.

But as the psychologist John MacNamara has argued, that idea itself is barely logical.

The rules of logic were originally seen as a formalization of the laws of thought.

That went a bit overboard.

Logical truths are true regardless of how people think.

But it is hard to imagine a species discovering logic if its brain did not give it a feeling of certitude when it found a logical truth.

There is something peculiarly compelling, even irresistible, about

P
If P, Q.
Therefore, Q.

With enough time and patience, we discover why our own logical errors are erroneous.

We come to agree with one another on which truths are necessary.

And we teach others not by force of authority but Socratically, by causing the pupils to recognize truths by their own standards.

People surely do use some kind of logic.

All languages have logical terms (or "formal devices", as Grice called them at Harvard) like "not", "and", "if", "same", "equivalent", and "opposite".

Children use "not", "and", "or," and "if" appropriately before they turn three, not only in English but in half a dozen other languages that have been studied.

 Logical inferences are ubiquitous in human thought, particularly when we understand language.

Here is a simple example from the psychologist Martin Braine:

John went in for lunch.
The menu showed a soup-and-salad special, with free beer or coffee.
Also, with the steak you got a free glass of red wine.
John chose the soup-and-salad special with coffee, along with something else to drink.

(a) Did John get a free beer?
(Yes, No, Can't Tell) ---- NO.

(b) Did John get a free glass of wine?
(Yes, No, Can't Tell) ----- NO.

Virtually everyone deduces that the answer to (a) is no.

Our knowledge of restaurant menus tells us that the or in free beer or coffee implies "not both"—you get only one of them free.

If you want the other, you have to pay for it.

Farther along, we learn that John chose coffee.

From the premises "not both free beer and free coffee" and "free coffee," we derive "not free beer" by a logical inference.

The answer to question (b) is also no.

Our knowledge of restaurants reminds us that food and beverages are not free unless explicitly offered as such by the menu.

We therefore add the conditional

"if not steak, no free red wine."

John chose the soup and salad, which suggests he did not choose steak.

We conclude, using a logical inference, that he did not get a free glass of wine.

Logic is indispensable in inferring true things about the world from piecemeal facts acquired from other people via language or from one's own generalizations.

Why, then, do people seem to flout logic in stories about archeologists, biologists, and chess players?

One reason is that logical words in everyday languages like English are ambiguous, often denoting several formal logical concepts.

The English word "or" can sometimes mean the logical connective OR (A or B or both) and can sometimes mean the logical connective XOR (exclusive or: A or B but not both).

Wood notes this in his review in "Mind". "OR" implicates "XOR".

The context often makes it clear which one the speaker intended, but in bare puzzles coming out of the blue, readers can make the wrong guess.

Another reason is that logical inferences cannot be drawn out willynilly.

Any true statement can spawn an infinite number of true but useless new ones.

From:

ii. Iowa grows soybeans.

we can derive

iv. Iowa grows soybeans or the cow jumped over the moon.
v. Iowa grows soybeans and either the cow jumped over the moon or it didn't.

ad infinitum. (This is an example of the "frame problem").

Unless it has all the time in the world, even the best logical inferencer has to guess which implicatures to explore and which are likely to be blind alleys.

Some rules have to be inhibited, so valid inferences will inevitably be missed.

The guessing can't itself come from logic.

Generally, it comes from assuming that the utterer is a Griceian cooperative conversational partner conveying relevant information and not, say, a hostile lawyer or a tough-grading logic professor trying to trip one up. (Grice taught logic, but he never tried to trip Strawson up).

Perhaps the most important impediment is that mental logic is not a hand-held calculator ready to accept any As and B's and C's as input.

It is enmeshed with our system of knowledge about the world.

A particular step of mental logic, once set into motion, does not depend on world knowledge, but its inputs and outputs are piped directly into that knowledge.

In the restaurant story, for example, the links of inference alternate between knowledge of menus and applications of logic.

Some areas of knowledge have their own inference rules that can either reinforce or work at cross-purposes with the rules of logic.

A famous example comes from the psychologist Peter Cathcart Wason.

Wason was inspired by the philosopher Sir Karl Popper's ideal of scientific reasoning: a hypothesis is accepted if attempts to falsify it fail.

Wason wanted to see how ordinary people do at falsifying hypotheses.

In his A3D7 'card selection task', Wason told ordinary people that a set of cards had letters on one side and numbers on the other, and asked them to test the 'if' utterance

vi. If a card has a vowel on one side, it has an odd number on the other.

-- a simple If P, Q statement.

The Wason subjects were shown 4 cards and were asked which ones they would have to turn over to see if the rule was true.

Try it.

Most people choose either the D card or the D card and the 3 card.

The correct answer is D and 7.

~(p ⊃ q) iff p & ~q.

The 3 card is irrelevant.

The 'if' utterance iplicates that Ds have 3s, not that 3s have Ds.

The 7 card is crucial.

If it had a D on the other side, the 'if' utterance would be false.

Only about five to ten percent of the people who are given the test select the right cards.

Even people who have taken logic courses get it wrong

Incidentally, it's not that people interpret "If D, 3" as "If D, 3 and vice versa."

If they did interpret it that way but otherwise behaved like logicians, they would turn overall four cards.

Dire implications were seen.

John Q. Public was irrational, unscientific, prone to confirming his prejudices rather than seeking evidence that could falsify them.

But when the arid numbers and letters are replaced with real-world events, sometimes — though only sometimes — people turn into logicians.

You are a bouncer in a bar, and are enforcing the rule "If a person is drinking beer, he must be eighteen or older."

You may check what people are drinking or how old they are.

Which do you have to check: a beer drinker, a Coke drinker, a twenty-five-year-old, a sixteen-year-old?

Most people correctly select the beer drinker and the sixteen-year-old.

But mere concreteness is not enough.

The if-utterance

vii. If a person eats hot chili peppers, he drinks cold beer.

is no easier to falsify than the D's and 3's.

L. Cosmides discovers that people get the answer right when the 'if' utterance is a contract, an exchange of benefits.

In those circumstances, showing that the rule is false is equivalent to finding cheaters.

A contract is an implication of the form "

viii. If you take a benefit, you must meet a requirement.

Cheaters take the benefit without meeting the requirement.

Beer in a bar is a benefit that one earns by proof of maturity, and cheaters are underage drinkers.

Beer after chili peppers is mere cause and effect, so Coke drinking (which logically must be checked) doesn't seem relevant.

Cosmides shows that people do the logical thing whenever they construe the Ps and Qs as benefits and costs, even when the events are exotic, like eating duiker meat and finding ostrich eggshells.

It's not that a logic module is being switched on, but that people are using a different set of rules.

These rules, appropriate to detecting cheaters, sometimes coincide with logical rules and sometimes don't.

When the cost and benefit terms are flipped, as in

ix. If a person pays $20, he receives a watch.

people still choose the cheater card (he receives the watch, he doesn't pay $20) — a choice that is neither logically correct nor the typical error made with meaningless cards.

In fact, the very same story can draw out logical or non-logical choices depending on the reader's interpretation of who, if anyone, is a cheater.

x. If an employee gets a pension, he has worked for ten years.

Who is violating the rule?

If people take the employee's point of view, they seek the twelve-year workers without pensions.

If they take the employer's point of view, they seek the eight-year workers who hold them.

The basic findings have been replicated among the Shiwiar, a foraging people in Ecuador.

The mind seems to have a cheater-detector with a logic of its own.

When standard logic and cheater-detector logic coincide, people act like logicians.

When they part company, people still look for cheaters.

What gave Cosmides the idea to look for this mental mechanism?

It was the evolutionary analysis of altruism.

Natural selection does not select public-mindedness.

A selfish mutant would quickly outreproduce its altruistic competitors.

Any selfless behavior in the natural world needs a special explanation.

One explanation is reciprocation.

A creature can extend help in return for help expected in the future.

But favour-trading is always vulnerable to cheaters.

For it to have evolved, it must be accompanied by a cognitive apparatus that remembers who has taken and that ensures that they give in return.

The evolutionary biologist Robert Trivers had predicted that humans, the most conspicuous altruists in the animal kingdom, should have evolved a hypertrophied cheater-detector algorithm.

Cosmides appears to have found it.

Cosmides, L. Deduction or Darwinian algorithms? An explanation of the "elusive" content effect on the Wason selection task. Ph.D. dissertation, Harvard University.

So is the mind logical in the logician's sense?

Sometimes yes, sometimes no.

A better question is, Is the mind well-designed in the biologist's sense?

Here the "yes" can be a bit stronger.

Logic by itself can spin off trivial truths and miss consequential ones.

The mind does seem to use logical rules, but they are recruited by the processes of language understanding, mixed with world knowledge, and supplemented or superseded by special inference rules appropriate to the content.