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Conor Grogan
@jconorgrogan
One of my predictions is that pure mathematics is going to realize that it needs to be tightly bound to information theory (specifically defining things by what can't be know)
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Conor Grogan
@jconorgrogan
Longer diatribe: - If information is fundamentally defined by what is not known, then it seems logical that our basic rules of reasoning and inference should also be grounded in this distinction between what is known and what is not known.
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Conor Grogan
@jconorgrogan
-In traditional logic, the basic rules of inference (like modus ponens or modus tollens) are typically defined in terms of the truth values of propositions. A valid inference is one that preserves truth - if the premises are true, then the conclusion must also be true.
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Conor Grogan
@jconorgrogan
-But from an information-theoretic perspective, we might instead define inference in terms of the information content of propositions. A valid inference would be one that preserves or increases information -
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Conor Grogan
@jconorgrogan
if the premises exclude certain possibilities, then the conclusion must exclude at least as many possibilities. This is a subtle but big shift. Instead of focusing on the truth or falsity of propositions, we're focusing on their information content, on the possibilities they exclude.
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Conor Grogan
@jconorgrogan
And I feel like from this perspective it more intuitively explains Gödel!
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