Chapter 11. Zero-trust logic¶
You need all the chapters.
What we learned¶
Let's look back. It all started with an honest machine and a trickster.
Machines. Each one has a table agreed on before the game. The light shows only "true" or "false".
The trickster. He puts his note in after you, and he wants "false". The value of his box is Z. Z is always in the trickster's hands.
Three machines with a secret. On OR put in "true". On NOT-AND — "false". On IF… THEN: if your box is "if", put in "false"; if it is "then", "true". On the others — AND, NOT-OR, EITHER-OR, SAME and the two more from Chapter 5 — the trickster always wins.
NOT. If its only box is the trickster's, the light always says "false".
Chains. The light of one machine is a fixed note for the next. Every machine has its own trickster. That's why it matters how a chain is built: EITHER-OR built from three machines doesn't behave like the single one.
Laws. Without tricksters every law of ordinary logic holds. With tricksters, some hold and some break — check step by step.
Reasoning. The bridge rule: if a = true and IF (a, b) = true, then b = true as well. It passes "true" along, but doesn't make it out of thin air.
Long sentences. In a long OR one "true" of yours is enough. In a long AND one trickster's box ruins everything.
All of this together is ZTL — zero-trust logic.
Where tricksters live today¶
In Chapter 1 we found tricksters in the class chat, in the weather forecast and in the letter x. There are many more.
Rumors: "somebody told me that…". Who told you? You didn't see.
The label on a package: "this juice has no sugar". You didn't measure it.
The answer of a chatbot or a search engine. You asked a question — and got a note that you didn't put in. Maybe a correct one. Maybe not.
Whoever wrote these notes doesn't necessarily want to fool you. The "trickster" in our game is just a way of saying: this isn't up to me. The value of such a box is Z.
What ZTL can do¶
ZTL checks a sentence step by step, machine by machine. At each step the light shows "true" only if that machine's trickster is powerless. Otherwise — "false".
Remember what that means. "False" is not "wrong" but "can't be guaranteed". And a "true" light at the top of a chain doesn't yet mean that every sentence inside is true. Remember Chapter 7: NOT ( NOT (Z) ) = true, yet ZTL still doesn't guarantee the box Z itself.
But once you've worked it out step by step, you can see which parts of the sentence rest on your own notes and which on other people's boxes. And where your note is enough to make the trickster powerless.
What ZTL can't do¶
ZTL doesn't know what is in the trickster's box. It doesn't say the rumor is wrong or that the label on the package is untrue.
ZTL doesn't turn someone else's box into yours. Only you can do that: go and look for yourself, count for yourself, check for yourself. Then the box will hold your own note — and you can work with that.
Zero trust doesn't mean "everybody lies"¶
It may seem that ZTL suspects everyone. Let's be honest: by the rules of ZTL even your mom's word is a box Z until you check it yourself.
But whether to trust is up to you, not ZTL. In life we trust people — and rightly so. ZTL doesn't forbid it. It only shows what your conclusion rests on: on what you know yourself, or on someone else's word.
And when there are no tricksters and everything is known for sure, ZTL is just ordinary logic.
The last puzzle¶
An example first. The sentence: "there is a pen or a pencil in the backpack". You packed the pen yourself — your "true". You don't know about the pencil: maybe mom packed it, maybe not. That is Z.
OR (true, Z) = true
This sentence can be guaranteed, whatever happened to the pencil.
And "there is a pen and a pencil in the backpack"?
AND (true, Z) = false
It can't be guaranteed. That doesn't mean there is no pencil. It means: the pencil isn't up to you.
Now take a simple sentence that you heard or read today — with AND, OR, NOT or IF… THEN. Break it into boxes and work it out step by step. (With IF… THEN, remember which box is "if" and which is "then".)
You already know how to work it out. And which boxes are yours — only you know.
Finally¶
The machines, the boxes and the tricksters will stay in this book. But the question they taught you to ask will go on with you:
What does my conclusion rest on — on something I know myself, or on someone else's word?