Deep (Principal) Limits     Lead: Robin Covey

4/2/2001

Summary by Swapnil Bhatia:

The topic of the discussion was "Deep (Principal) Limits on Science (Goedel's Theorem)". The discussion began with the appropriate question of the kinds of limits that are involved when we think about science. A suggestion offered was that since science is the pursuit of a form of knowledge, a limit on science would be a limit on things that we can know. Thus, the topic of the discussion could be rephrased to mean a discussion of the things that are fundamentally unknowable. However, the key point here was that these were unknowable only through the scientific method, i.e. empirically.

Limits in Science?

A clarification was proposed as to what we really mean by science and the scientific method. Science involves the building of models to explain phenomena occurring in nature. These are thus, only models, which are imposed upon nature. They may not be exact equivalents of what there really is. Another aspect of the scientific method is observation. Without observation there cannot be any empirical science. It was suggested that this was another fundamental limit on science. Not all things in nature fall into the observable category. For example, a large part of the Universe is unobservable (at the present time) by any scientific means. Thus, if the scientific method rests on observation, it will definitely remain limited as long as there are things that remain unavailable to the method of observation.

Theories such as the multiple-universes theory were discussed in this context as being theories put forth by science to explain the unobservable portion of the Universe. One such theory suggested, was the many-worlds hypothesis based on quantum physics. Briefly, if at each moment a quantum possibility is to be realized, then it is proposed that in reality all possibilities are realized. However, one of them is observed in the world that we live in, whereas all the others are realized in other multiple universes.

Limits of the Mind?

The discussion then turned toward investigating whether there were any fundamental limits on mind. One suggestion was that there definitely are limits on how well mind can understand itself. There are limits, for example, on how accurately a mathematical system can represent itself. A question was raised whether representation was essential for knowing or understanding.

Representation of a concept, such as 'snow', was not, knowing what snow is, such as by experience. The issue at hand was whether description of an object is essential to knowing about the object, or whether direct experience without representation was sufficient. A point suggested to help discuss this aspect was Kant's idea that there cannot be any perception without concepts and that there cannot be any concepts without perception.

Experiencing

The discussion seemed to be moving toward the idea that science can never accurately model experience. The question then raised was whether, that, was the goal of science. Does science aspire to create experience? Isn't science just concerned with explanations, descriptions and modeling of nature? Explanations are not expected to create experience but are only verbal reports of why or how something occurs. In response, a question such as "What is love?" was put forth as a challenge to science. It was argued that science cannot even explain a concept such as love.

Sources of Knowledge

To take the discussion in a new direction, the question of the various sources of our knowledge was raised. What are the various ways that we can know things? This was not investigated in further detail. Instead a more fundamental point regarding methods of knowledge was proposed. The suggestion was that since every event in nature is caused, it would be sufficient to trace the causal chain. However, it was argued that this would not lead to complete knowledge since all knowledge is not necessarily about causation. For example, knowledge in mathematics is not about causation. This led to a discussion about the nature of causation. There was disagreement on the answer. However, an interesting point made was that it may be possible to give an account of things such as causation from the point of view of a scientist as well as a priest. Both accounts may be different and accurate.

(In)Completeness

The discussion was then focused toward the question of proof and evidence. As an example, mathematical systems and Hilbert's ambitious program was discussed. Hilbert aspired to prove everything that there was to prove in any mathematical system. However, Goedel proved that Hilbert's program is impossible to achieve. The proof that the foundations of any mathematical system are valid requires a meta-system to prove it in. Thus, it would never be possible to prove a mathematical system completely. Goedel on the other hand thought that it was possible to perceive mathematical truths such as 2+2=4 in exactly the same way as one would perceive an ordinary object in nature. This turned out to be untrue.

Toward the end of the discussion, there were some questions about the nature of the scientific method. To resolve these, it was suggested that all that science really did was to come up with a model or concept of a natural phenomena from a third person's point of view. Thus, science required the duality of the subject and the object to come up with an explanation. This was fundamentally necessary for observation, which is the basis of any empirical science. Thus, this ruled out any means by which science could explain subjective experiences such as what it was like to be a serial killer, or what it felt like to taste old wine.

April 30, 2001