Logical Types

Logical Types

The principle of logical type was discovered by Bertrand Russell (1908). It was the solution he developed to a certain type of paradox in logic now known as Russell’s Paradox. Most of the existing literature about logical type focus on this rather obscure aspect of formal logic, but the principle itself is very simple. A set of things is a completely different kind of entity to any one of those things, the elements of the set.

A movie film is simply a sequence of still images, but a movie is of course a completely different kind of thing to the still image of a single frame. You can play a movie. You cannot play a single frame. The frame is of the first primitive logical type, and the movie, the set of frames, is of a second logical type. The movie projector is a different kind of thing again. It iterates the frames of any and all movies. It is thus of the class of all possible sets of frames, of a third logical type.

As Russell demonstrated, failing to take logical type into account inevitably produces nonsense results and paradox. This is essentially the problem with the great paradoxes of the new physics. In both pillars of the new physics the paradoxical phenomena are the expressions of different logical types in action. And there is a simple reason why it has not been possible to discover this type of solution in the context of the science of physics. The whole purpose of the science is to discover and define that which is physical, and that which this implies. But in both relativity and quantum theory, that which is physical is a component in a system that is operating at a higher level of logical type. It is like trying to understand the sense of a movie film, and the way the projector works, by studying the science of images, i.e. individual frames.

Quantum Theory

Logical type resolves the problems of quantum theory as touched on in the Home page. As described in World Superposition, quantum theory shows us the physics of a class-of-worlds-as-a-world, a second-logical-type phenomenon. This is here referred to here as the many-worlds reality, and also the QBism world, the world superposition, the class-of-worlds-as-a-world and the personal world. It is all the same thing.

Just as a population is a quite different type of thing to a person, the world one actually encounters is a quite different type of thing to the objective physical world of the current paradigm. Here, the ordinary physical world is the entity of the first or ‘primitive’ logical type. And the world encountered is the superposition of a whole class of worlds of this nature, a second-logical-type phenomenon. Naturally, the idea of superposing whole worlds sounds bizarre, but the superposition principle is fundamental to quantum theory. Physical reality is defined by the ‘wave function’, and wave functions add together and form a superposed sum just like ordinary waves. This picture from the Wikipedia page illustrates the superposition of waves on water. Bizarre though it undoubtedly seems, whole worlds work the same way in the quantum universe.

As explained in depth in the technical pages here, the world one knows as physical reality, the world on which physics experiments are performed, is the class-of-worlds-as-a-world. Quantum theory seems crazy is because it describes the way things operate at this different level of logical type. This, however, is simply the scientific basis of the new paradigm.

In the objective physical world the reality is determinate throughout, just as we automatically assume. Nonetheless, in the class-of-worlds-as-a-world, physical reality is defined solely where observed, exactly as described by QBism. As a result, all the great paradoxes are self-evidently explained. It is the second-logical-type nature of the world superposition that makes complete sense of the physics. It is not that the current paradigm is actually wrong, it is just incomplete. There are two different types of physical reality, existing at different levels of logical type. The result is the indeterminate world of QBism. The many-minds theories that have been proposed also define the same type of world.

Relativity

The superposition of worlds is a completely different kind of thing to the ordinary world of the current paradigm, and the concept of logical type enables us to understand this clearly. It is a second-logical-type phenomenon. The phenomenon that resolves the great paradoxes of relativity is a completely different kind of thing again, a third-logical-type phenomenon.

The great paradoxes of relativity are the passage of time and the Now. All are resolved by Weyl’s simple dictum quoted in Universe Consciousness, but in the worldview of physics this has to be wrong. As he states, consciousness passes along the worldline of the person, and as a result there is the appearance of the passage of time in the static four-dimensional universe. But this is exactly what cannot occur in a system defined exclusively by the physical reality. The resolution is that the experiencing consciousness is a property of the universe itself. Thus it is to the moments of time in space-time as the projector is to the frames of the movie film. It is of a third logical type.

Just as with the movie projector, in order to move the frame of reference you have to have a phenomenon that is contextual to the sequence of frames. Naturally, such a concept is directly at odds with the precepts of physics which holds that all phenomena in reality are physical in origin. Again, therefore, one can never get to the solution of the problem from within physics as currently defined.

Logical type reveals the origin of the paradoxical phenomena in the new physics. These are emergent properties of the universe. This is described in increasing detail in the pages here. The conceptual revolution is that not only is reality different to our current conceptions, so too are we ourselves. We are beings of all three logical types, and centrally relevant to the physical reality each one of us encounters. This is summarised in The Perceiving Subject.