TL;DR
This paper investigates the logical consistency of w-ordered collections using a supertask that challenges the assumptions of actual infinity by highlighting contradictions between completeness and uncompletability.
Contribution
It introduces a supertask framework to analyze the paradoxes surrounding w-ordered collections and their compatibility with the concept of actual infinity.
Findings
Identifies contradictions in the assumption of w-ordering with supertasks
Demonstrates the supertrap challenges the coherence of w-ordered collections
Highlights implications for the philosophy of infinity
Abstract
This paper examines the consistency of w-order by means of a supertask that functions as a supertrap for the assumed existence of w-ordered collections, which are simultaneously complete (as is required by the Actual infinity) and uncompletable (because no last element completes them).
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Taxonomy
TopicsAdvanced Algebra and Logic · Logic, Reasoning, and Knowledge · Computability, Logic, AI Algorithms