Logical Types

Just as a class of people is a quite different type of thing to a single person, the superworld is a quite different type of domain to the objective physical world of the current worldview. As has been described, the superworld is the effect of many ordinary worlds superposed. In other words, the ordinary world is the primitive, first-logical-type element of the system, and the personal world is a second-logical-type phenomenon. This is a ‘class-of-worlds-as-a-world’.

This is the ontology of the personal world. It exists at a different level of logical type to the ordinary world. It is an entity of ‘higher’ logical type.

The crucial point is that the class will have different properties, properties that an element of the class cannot have. You cannot change the colour of a red glass marble. But you can easily change the colour of a jarful of red marbles. You pour out the red marbles and fill it up with green ones. The same logic applies to the relative world.

Because the world hologram changes, the class of worlds that contain the world hologram is changed. In effect, in the reality of the world hologram, the quantum state of the world changes on observation. The collapse dynamics operates. This is the transition illustrated in this image – full explanation in Schrödinger’s Cat. The class of worlds changes from the green class to either the blue class or the yellow class.

The class of lifelines in the Schrödinger's cat thought experiment. (Lockwood, 1989)
The class of lifelines in the Schrödinger’s cat thought experiment. (Lockwood, 1989)

Category Error

The reason quantum theory seems crazy is because it describes the way things operate at both these different levels of logical type. The linear dynamics is the time evolution of each version of the physical world. The paradoxical collapse dynamics is the operation of a class-of-worlds-as-a-world.

The problem is simply that we have been trying to explain how the ordinary world could behave like this. As stated by Feynman, quoted in The Science, it absolutely cannot make sense. This is because we have been trying to apply it all to the ordinary world. That is the origin of the measurement problem. The assumption of only one type of world is a fundamental ‘category error‘. The concept of category errors is addressed in detail in the Stanford Encyclopedia of Philosophy. It means a mistaken assumption about what kind of thing something is.

The measurement problem is essentially the huge puzzle of why, and how, observing the real world causes it to change. The resolution is that it does not, but effectively it does. This is exactly what Hugh Everett said in his many-worlds theory. The solution is that what changes is a different type of world, the class-of-worlds-as-a-world. And that is why it comes to be like that, to Feynman’s great frustration.

Kuhn showed that each great new step requires a new vocabulary, a new ‘lexicon’. This is the collection of new terms that define the key features of the new explanation, and without which it does not make sense. This may be a new ‘taxonomy’, a new classification system. Logical type is a new classification in this field, and this makes sense of the measurement problem.

Classifying the relative world as a second logical type phenomenon explains the nature of the worlds described in ‘Relational Quantum Mechanics‘ and ‘Quantum Bayesianism‘. The Many-Minds theories that have been proposed also define the same type of world. These relative worlds are defined by the observations and thus indeterminate except where observed. The class-of-worlds-as-a-world is the ontology for that type of world.

The next section is The Block Universe