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 articles 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. 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 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 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 also referred to here as a personal world, the QBism world and the inside view. 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. 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 a different level of logical type.

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, and thus personal, exactly as described by QBism: all the 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 personal world of QBism, and the many personal worlds of the many-minds theories. 

Relativity

Logical type resolves the problems of relativity by bringing in a third level of logical type. 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. The phenomenon that resolves the great paradoxes of relativity is a completely different kind of thing again.

The great paradoxes of relativity are the passage of time and the Now. All are resolved by Weyl’s simple dictum quoted in The Conceptual Revolution, 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, as described in Universe Consciousness, 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 fames 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 of the logical type of all the frames of reference addressed. 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.

The Frame of Reference

The frame of reference is absolutely fundamental to science of every kind, and physics is the ultimate arbiter. But exactly this issue is the problem in the great paradoxes of the new physics. In both cases a frame of reference of a different logical type is axiomatic: as soon as the solution is glimpsed it is obvious.

In quantum theory the key point is that the frame of reference encountered as physical reality is a completely different kind of thing to the frame of reference in an ordinary world. This cannot make sense in physics without the concept of world superposition, a second-logical-type phenomenon. But it is the fundamental cause of this phenomenon which is completely unreachable starting from physics.

As explained in the technical area of this site, the world encountered is not the world of the observer, the physical entity, but the individual defined by the state of the memory, the record of observations. This is the crucial component of quantum mechanics, as described in Many Worlds, but it has not been recognised as such. It means the protagonist of the dynamics in quantum mechanics is this structure of information.

It seems this could not possibly be so centrally relevant, but this is the whole problem of approaching the paradoxes from the physics worldview. Nonetheless, this is the meaning of Everett’s famous many worlds theory, taken absolutely literally. So it is hardly surprising it has not be understood let alone accepted. The physical reality encountered is defined by the record of observations, the central component of Everett’s formulation of quantum mechanics. Thus the primary definition is information.

Although it has been incomprehensible without this lens, with it Everett’s theory is transparently correct, as described in Time & Quantum Time. The explanatory principle is even more impossible to arrive at in the context of physics. The frame of reference in operation is not that of the physical observer, as is always, perfectly naturally, assumed. It is the world hologram, the state of the memory in Everett’s formulation of quantum mechanics. The essential mechanics of his formulation is presented in Many Worlds.

A similar transformation appears in the paradoxes of relativity. The only possible resolution to the passage of time and the Now, the present moment, is a moving frame of reference. This cannot exist in the physical world, which is why there is a paradox because as Weyl states this is exactly what consciousness does. He is describing a moving frame of reference, but there can be no such moving changing frame of reference in physical reality.

If the dynamics described by physics, and defined in the equations, are to actually operate, there must be a moving frame of reference. At present this is beyond all of physics to explain because we now know that the universe is a four-dimensional space-time domain, and it is static. The situation is resolved by taking this moving frame of reference to be an emergent property of the universe itself: it is to the moments in space-time as the movie projector is to the frames of the movie film. This precisely explains the appearance of the passage of time, and the Now, the moving present moment; thus the great paradoxes are resolved.