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Posted by Harvey on September 18, 2001 21:07:36 UTC

Mark,

This is a continuation of the thread we were discussing down a little further...

You mentioned a number of means to make an apparently false mathematical statement into a correct statement by modifying certain parameters. This is not what I am referring to when I am speaking of a paradox caused by assuming that 'everything is math'.

As you'll recall, I said that if everything is math then everything must conform to mathematical description. However, certain aspects of human conduct certainly are not mathematical. For example, if someone is lying they are offering propositions which contradict another proposition (intentionally or non-intentionally is not a factor), or they are offering a proposition that does not match a state of affairs. Another related issue is mathematical mistakes which cannot be 'corrected' through re-interpretation.

The reason why this philosophical issue is a genuine stumbling block is because we have the following scenarios to consider (not comprehensive list):

1. Everything is mathematical even mistakes, lies, contradictions, etc but these anomalies are not actual anomalies (i.e., pseudo-anomalies).

2. Everything is mathematical even mistakes, lies, contradictions, etc and these are anomalies that exist, but anomalies exist at any level of math or logic and this for whatever reason is not a threat to mathematical order.

3. Everything is mathematical even mistakes, lies, contradictions, etc and anomalies do exist, but there is some firewall built between 'us' and the true mathematical reality which cannot tolerate anomalies such as what we see by human behavior.

4. Everything is mathematical but not everything is computable (or some other yet-to-be-discovered property). If some process is based on uncomputable results then this mathematical order cannot be extended to this uncomputable realm. Therefore, the aspects of life which are uncomputable can escape the 'gravitational effects' of this mathematical order (i.e., the full restrictions of 'mathematicalness' do not apply to uncomputable processes - or whatever process we wish to identify).

5. The thesis that everything is mathematical is incorrect in that strong reductionism is false. That is, something being mathematical might only be a trait by elementary particles which are 'free' from being fully mathematical in behavior and therefore further up the chain of natural structure the less and less mathematical things really are. In this sense, biology, sociology, etc may not be reducible to solely mathematical processes.

6. The thesis that everything is mathematical is just false. Nothing is mathematical, everything is only approximately mathematical - nothing exact.

7. Nothing is mathematical it is only a limitation in human thinking which gives us this impression.

Warm regards, Harv

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