Logical Types

Logical Types

The principle of logical type was discovered by the polymath Bertrand Russell in 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 class of things is a completely different type of entity to any one of those things, the elements of the class. And as a result it has different properties, properties that an element of the class cannot have. For example, a population can have different numbers of people at different times, a concept that is meaningless with respect to a single person. 

A movie is an ideal example. A movie film is a completely different type of thing to the still image of a single frame. The frame is of the first, ‘primitive’, logical type, and the movie, the class of frames in sequence on the film, is of a second ‘higher’, logical type. The movie film thus has the property that it can be played, and thus give rise to the motion picture, a second-logical-type phenomenon. You cannot play a frame.
The movie projector is a different kind of thing again. It is the iterator for the class of any and all movies. It is a third-logical-type phenomenon. It thus has the property of bringing the movie to life.

Category Error

Although the principle is It is quite simple, it is of vital significance in analysing systems. As Russell made clear, failure to make this distinction inevitably leads to 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 way a movie projector works by studying the science of images, the individual frames. The problem is a fundamental ‘category error‘, a concept addressed in detail in the Stanford Encyclopedia of Philosophy.

Quantum Theory

Logical type resolves the problems of quantum theory as described in Quantum Theory. The world hologram is present in a great number of worlds, and the resulting physical reality is the superposition of all of them, a ‘superworld’. This is a class-of-worlds-as-a-world, a second-logical-type phenomenon. This provides the ontology of the QBism world because it is indeterminate except where observed, by definition. 

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. The ordinary physical world is the component, of the first or ‘primitive’ logical type in this context. 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 as described in Quantum Theory.

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, the great paradoxes, measurement and locality, 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 Relativity. 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 where nothing exists except 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 viewpoint you have to have a phenomenon that is contextual to the sequence of frames. Naturally, such a concept is directly at odds with the current 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 at different levels of logical type. 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 we are, each one of us in our personal worlds, centrally relevant to the events in the physical reality.

The Perceiving Subject

As explained by Mermin, quoted in The Inside View, the central problem with the physics is not something undiscovered, but something that has been very specifically omitted. The great paradoxes in both pillars of the new physics come about because the perceiving subject has been excluded from the science, and all are resolved by including it. His quote is given in The Inside View. The key point is that the perceiving subject is a being of three logical types. The active transtemporal subject is the world hologram as has been described. This entity lives in a world that is a second-logical-type phenomenon. The perceiving is the consciousness that is a third-logical-type phenomenon. The body is the instantiation of the world hologram.

Scientific Revolution

As Tegmark states, important scientific discoveries go though three phases:

… first they are completely ignored, then they are violently attacked, and finally they are brushed aside as well known. Everett’s discovery was no exception: it took more than a decade before it started getting noticed. But it was too late for Everett, who left academia disillusioned.
Everett’s no-collapse idea is not yet at stage three, but after being widely dismissed as too crazy during the 1970s and 1980s, it has gradually gained more acceptance. At an informal poll taken at a conference on the foundations of quantum theory in 1999, physicists rated the idea more highly than the alternatives, although many more physicists were still ‘undecided’. I believe the upward trend is clear.
Why the change? I think there are several reasons. Predictions of other types of parallel universes from cosmological inflation and string theory have increased tolerance for weird-sounding ideas. New experiments have demonstrated quantum weirdness in ever larger systems. Finally, the discovery of a process known as decoherence has answered crucial questions that Everett’s work had left dangling.

So the world is coming around. It seems increasingly obvious Everett is right. The remaining puzzles persist because the final hurdle has not been cleared. This is the nature of the identity of the subject of the dynamics, the protagonist in the reality defined by the equations. This is the entity ‘in here’, the record of observations, in human observers the world hologram, to common parlance the mind. In the world of this type of entity the physical reality is a holographic universe, which resolves all the puzzles and paradoxes. The world encountered is the superworld, a second-logical-type phenomenon. The  consciousness that brings all of creation to life is a third-logical-type phenomenon.