Tuesday, June 26, 2018

Causal countability

Say that a set S is causally countable if and only if it is metaphysically possible for someone to causally think through all the items in S. To causally think through the xs is to engage in a step-by-step sequential process of thinking about individual xs such that:

  1. Every individual one of the xs is thought about in precisely one step of the process.

  2. Each step in the process has at most one successor step.

  3. With at most one exception, each step in the process is the successor of exactly one step.

  4. The successor of a step causally depends on it.

Causal finitism then ensures that any causally countable set is countable in the mathematical sense. And, conversely, given some assumptions about reality being rational, any countable set is causally countable.

However, causal countability escapes the Skolem paradox, because of causal finitism and how it is anchored in the non-mathematical notion of causation.

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