Ignacio Matte Blanco, explained
One keeps things in order. The other lets everything flow both ways. Everyone uses both, all the time.
Tap the arrow
Tidy logic: A is bigger than B. So B is not bigger than A.
10
Tidy Brain and Dream Brain
A clock, two toy cars, a box of crayons and a one-way sign.
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12
Arrows that flip
Arrow cards, a bag of sweets and a dimmer switch.
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16
Symmetry and infinite sets
A mirror, a deck of cards, numbered rows and an onion.
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Who was he?
Ignacio Matte Blanco (1908–1995) was a Chilean psychiatrist and psychoanalyst. He worked in Santiago and later in Rome.
He asked what kind of logic the unconscious uses. His answer, set out in The Unconscious as Infinite Sets (1975) and Thinking, Feeling, and Being (1988), is that the mind mixes two logics. He called the mix bi-logic.
Five words
Asymmetrical logic
Ordinary logic. Relations go one way. Gives us time, order, and part versus whole.
Symmetrical logic
Every relation reverses. No time, no contradiction, part equals whole.
Generalisation
One thing is treated as a member of ever-bigger groups.
Bi-logic
Real thinking is always a mix of the two, in changing amounts.
Infinite sets
Sets where a part can be as big as the whole, which is what symmetrical logic says.
For a 10-year-old
Tidy Brain and Dream Brain
You have two helpers inside your head. I'll call them Tidy Brain and Dream Brain.
Tidy Brain is like a librarian. It puts things in order. I hold up a clock: Tidy Brain knows that breakfast comes before lunch, and lunch comes before bed. I hold up two toy cars, one big and one small: Tidy Brain says "the big one is bigger than the small one, so the small one is NOT bigger than the big one." It likes rules that only go one way, like a one-way street sign.
Dream Brain doesn't work like that. I turn the one-way sign into a two-way sign. For Dream Brain, every road goes both ways. If you are next to your mum, your mum is next to you. That's true. But Dream Brain also thinks: if Mum looks after me, I look after Mum. If the big car is bigger than the small car, the small car is bigger too. Dream Brain doesn't mind that this is silly. It has no clock, so yesterday and tomorrow feel the same.
The street sign
Pick a helper, then flip the sentence.
The big car is bigger than the small car.
Tidy Brain: Yes, that's right.
Here's the most important part. I tip a box of crayons onto the table. Tidy Brain sees lots of different red crayons. Dream Brain sees one red crayon and thinks every red crayon IS that crayon. So if one dog bit you once, Dream Brain decides that every dog is THE dog that bit you. That's why you can feel scared of a friendly dog, even when Tidy Brain knows it's friendly.
The dog that bit you
One dog bit you. Switch helpers and watch the other dogs.
Tidy Brain: only that one dog bit me. The others are different dogs.
Big feelings wake Dream Brain up. When you're very angry, you might shout "You ALWAYS do that!" Tidy Brain knows it isn't always. Dream Brain made it always.
The feelings dial
Turn up the anger and see who takes over.
You forgot to tidy up today.
You need both helpers. Tidy Brain lets you do your maths homework. Dream Brain gives you dreams, stories, music, and feelings. A man called Ignacio Matte Blanco worked out that we use both, all mixed together, all the time.
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For a 12-year-old
Arrows that flip
A doctor called Ignacio Matte Blanco asked a simple question: what kind of logic does the hidden part of your mind use? His answer was that your mind runs on two different logics at once.
I take a card and write "Ali is TALLER than Ben" with an arrow pointing from Ali to Ben. This is normal logic. If I flip the arrow round, it becomes "Ben is taller than Ali", which is a different and false statement. Normal logic cares which way the arrow points. Matte Blanco called this asymmetrical logic. It gives you time, order, and the difference between a part and a whole.
The other logic is symmetrical logic. In it, every arrow points both ways. Flip the card and nothing changes. "Ali is taller than Ben" means the same as "Ben is taller than Ali." That sounds broken, and in the real world it is. But this is how dreams work. Your house can also be your school. Your teacher can also be your aunt. You can be in two places at once.
The arrow card
Choose a relation and a logic, then flip the card.
This is the card the right way round.
The second rule is about groups. I pour a bag of sweets onto the table. One sweet belongs to the group "sweets", which belongs to the group "food", which belongs to "things I like". Symmetrical logic slides down the groups and treats everything in a group as the same thing. So if one teacher tells you off, the hidden mind jumps to "teachers hate me", then "adults hate me", then "everyone hates me". One example becomes the whole group.
Sliding through the groups
Start with one thing. Each press jumps to a bigger group.
Now I put a dimmer switch on the table. Matte Blanco said we're never fully one logic or the other. We slide up and down a dial. When you're calm and doing homework, you're near the tidy end. When you're furious, in love, scared, or dreaming, you slide towards the symmetrical end. Strong feelings push the dial. That's why words like "always", "never", and "everyone" come out when you're upset.
The dimmer switch
Slide from calm to stormy.
He called the mix of the two bi-logic, meaning two logics. It explains why arguing with someone's fear doesn't work. You're using one logic. Their fear is using the other.
Check yourself
Tick every sentence that is true, then press Check.
For a 16-year-old
Symmetry and infinite sets
Freud listed five odd features of the unconscious. It has no sense of time. It doesn't mind contradictions. It treats inner wishes as if they were real events. It shifts feelings from one thing to another (displacement). It squashes several ideas into one (condensation). Freud described these features but never explained why they go together. In The Unconscious as Infinite Sets (1975), Ignacio Matte Blanco claimed that all five follow from just two principles.
Principle of symmetry. The unconscious treats the converse of any relation as identical to the relation. I put a mirror between two objects. "A is the parent of B" reflects into "B is the parent of A". Once every relation reverses, time collapses, because "before" equals "after". Contradiction stops mattering. Part and whole become the same, because "the arm is part of the body" reverses into "the body is part of the arm".
Principle of generalisation. The unconscious treats an individual thing as one member of a set, that set as part of a larger set, and so on. A deck of cards works here. The seven of hearts is a heart, a red card, a card. Combine this with symmetry and every member of a set becomes identical to every other member. That's condensation and displacement explained in one move.
Two principles, five features
Hold a relation up to the mirror, then apply each principle and watch Freud's list fill in.
Now the maths, and the reason for his book title. An infinite set is one where a part can be matched one-to-one with the whole. Write out 1, 2, 3, 4… and under it 2, 4, 6, 8… Every whole number pairs with exactly one even number. The even numbers are only part of the set, yet they're "as big" as the whole set. Matte Blanco's point was that in infinite sets, part = whole is true, and that's exactly what symmetrical logic says. So the unconscious behaves like mathematics of the infinite.
Part as big as the whole
Pair each whole number with an even number. Try to run out.
This links to emotion. Intense feeling pushes thinking towards symmetry, and so towards infinity. When you're in love, the person seems to hold every good quality. When you're terrified, the threat feels total and endless. Emotion, in his view, is partly a way of thinking.
Picture an onion, or ocean depths. On the surface is almost pure asymmetrical logic: science, timetables, arguments. Below that come increasing amounts of symmetry. At the bottom is what he called the indivisible mode, where nothing is separate from anything else. Real thinking is always a mix. He called the mix bi-logic.
Peeling the onion
Go deeper and watch one worry change shape.
Clinically, this explains transference. A patient experiences the therapist as their father: one member of the set "authority figures" becomes identical to another. It also explains why logical reassurance fails against a phobia. You're arguing in one logic with a feeling that lives in the other.
A fair criticism: his model is elegant, but it's a theoretical framework rather than something tested in experiments. Some cognitive scientists argue that ordinary over-generalisation and biased thinking explain the same things without needing infinite sets. Treat it as a powerful lens, not a proven fact.
Check yourself
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