Kreisel demonstrated that the informal notion of 'constructive ordinal' resists full formalization within any single accepted theory, making the ascending condition semantically indeterminate.

?Rate how convincing each reason is below to see the overall strength.

No one has weighed in yet. Be the first to share reasons for or against this statement.

Ascending condition(the specific aspect of ordinals being discussed): A rule or property describing something that grows, increases, or progresses in a definable way according to certain steps.
Constructive mathematics(the broader field this discussion belongs to): A branch of math that only accepts objects or truths if you can actually construct or prove them through explicit steps, rather than proving something exists just by showing that it can't not exist.
Constructive ordinal(the key concept Kreisel investigated): A way of ordering or ranking mathematical objects based on operations you can actually perform or build step-by-step, rather than just imagining them abstractly.
Formalization(describing what Frege did with existence): The process of taking an idea and expressing it precisely using logical symbols and strict rules, like translating messy everyday language into mathematical logic.

Based on where you are in your exploration