“That makes no sense. You cannot use logic to justify logic. Either you assume the rule work, or you’re an ass. Um, pardon my…”
“The meta-logic rules, I am saying, do not use logic to justify the axioms of logic logically—as you correctly point out, that would be a paradox. But what is the underpinning for logic in the ultimate sense?”
“It works.”
She smiled graciously. “Many philosophers believe this indicates an intimate connection between the laws of physics, the laws of mathematics, and the way the human mind works. Odd, is it not? In an infinite universe, why would we just so happen to evolve brains that could comprehend the laws that just so happen to underpin the physical universe?”
“Not so odd. I’ll tell you why. Natural selection and the damn fool common sense God gave a goose. Lookit here: Animals who thought is was the same as is not might think a predator what is about to eat them up, is not about to dine so fine, and then the natural difference between is and is not would be clear as either-or: namely either you vamoose out from those sharp teeth, or you’ll be an is not in no time.”
“Nicely spoken, but you are familiar with Divarication theory. You are one of its primary authors, are you not? Put any information value you wish into the expression for whatever gene controls the organism’s logic. Somewhere in the little bits of matter that make us up, is something written in our DNA—think of it as a symphony written in a chemical code of four notes—somewhere is the arpeggio that programs us to believe A is A. Estimate the volume needed to carry that abstraction forward between all the generations of organisms possessing neural systems since the pre-Cambrian. Look at how the figure falls out.”
He ran his finger on the mirror surface, and drew out a few calculations. “It’s impossible,” he said at last. “If there was a gene for logic, it would have mutated by now, and cropped up. There would be other creatures with other rules for other types of logic—which is something I can’t imagine, anyhow. I mean, even a mama bird counting her eggs don’t make twice two equal to five.”
“To me, this suggests a simpler and more universal structure to thought,” Rania said. “The laws of optics form a limiting set to the divarication for the principles of how to evolve an eye. Likewise, other laws must form a limit to how logic, language, and thought can evolve. The basic rules of the universe make it so that no organism can evolved into a rational creature for whom A equals not-A.”
“What are you saying?”
She pointed at the mirror: “That! The rules of meta-logic, my champion, is what you have in your brain. A set of neural logic gates which allow you to see meta-logical patterns, and recognize those patterns where they appear. It is your lance to slay my dragon. Because those patterns appear in the Monument: it is written in nothing but patterns.”
“Lady, I still don’t understand, and that is something I am not used to saying.”
“Remember the oldest problem in Sign Theory: How do you communicate with a species so alien that nothing in your psychology or culture is the same? How do you refer to things with no shared references? And I am suggesting we are looking at the handiwork of some race that solved that problem. The mere fact that the Monument exists proves that a universal language is possible, which means that the relation of field theory to physics to molecular chemistry to DNA to brain to brain structures to thought to logic to symbol cannot be arbitrary—despite that our Earthly theories hold them to be.”
“Math, logic, and physics are universal. So I guess that is the only thing aliens can talk with us about.”
“But they are only the beginning of the Monument message. What of other universals? But how do you make a symbol for honesty, for justice, for beauty, for love, for any abstraction?”
“Maybe those things come out of genetic adaptation to game-theory: organisms that don’t play fair enough to cooperate with natural allies can’t compete with mutual foes.”
“No,” she said, “I don’t believe it is merely game-theory. Or, I should say, what is game-theory based on? How do we teach our own children abstractions like truth and justice? Toddlers learn about right and wrong, about yes and no, forbidden and permitted, the basics of law and mercy, long before they learn to count. We do not teach them biology, then genetics, then the theory of the selfish Gene, then the theory of the natural harmony of self-interest, and then tell them it is not in their self-interest not to fib to their fathers. When a child is caught lying, what do you do?”
He straightened up and stepped away from the mirror, partly because the nearness was driving him mad, partly because he wanted to look at her face.
“Lecture ’em good, and take a strap to ’em, so to help remember them the lecture.”
“And what does that suggest?”
“Well—I reckon our kids learn universal concepts the way a baby bird learns birdsongs,” Montrose said. “Pain and pleasure mean ‘yes’ and ‘no.’ The signs we show them, simple things at first, like a swat on the rump, match like lock and key to something in their nervous system. Swat on the rump stimulates the pain centers wired to signal an avoid this behavior. Smiles and touches linked to ganglia wired up to express pleasure. Lock fits key.”
“Then how is it possible to talk to aliens?”
“I am not sure it is. No alien creature, things whose bodies are made of silicon rocks or methane soup or intelligent clouds of smog, things we can’t imagine, they are not going to have any locks in their brains—or whatever part of them does their thinking and fretting—that can possibly fit our keys. Our notions of justice and truth and beauty don’t mean spittle to them. How could you make a language to express things like that? Ideas that only make sense in a certain context? Except…” Menelaus frowned thoughtfully. “Same way we teach our babies, I guess. Teach them in context. Point and grunt. Swat then on the rump. Give a petting and a smile. But you would have to give them our nervous system first.”
“You think as I do. Go on.”
“Go on to what?” He said, exasperated. “You can’t send the context of the message before you send the message! What would that even mean? A language that deciphers itself? How do you do it?”
She smiled, and it was like the sun coming out.
“Simple. You encode the lock and the key both,” she continued. “The human brain is not really a lump of hydrogen and carbon, is it? It is a pattern of information. Anything that you grew in a tank that followed the code-pattern of the human genome would be human, would it not? A human brain made of another substance, provided the nerve cells operated in the same way, or in a way parallel to ours, would be human, would it not?”
“Ghost Del Azarchel thinks so, or so he told me.”
“And what is the human genome but a language, a code of information, a song of four notes, which could be recompiled into any system of other notes, the way a number line can be expressed in base two or base ten?”
He nodded. “I guess so. If you were intelligent, and you wanted to send a message, and the only thing you knew about the recipient was that he occupied the same universe with the same natural laws as you, you’d send the message with the messenger. The messenger would be coded up, expressed as a series of numbers, or logic signs, or something else universal. You show him how to build the lock, tumbler by tumbler, and then you show him where to put all the ridges on the key, tooth by tooth. Is that what you are getting at with all this weird talk of logic and meta-logic? The Monument is instructions on how to build a system that can read the Monument.”