apodictic machine-checked praxeology

1.10. Claims no theorem uses🔗

Two claims at the centre of the doctrine are used by no theorem here, and so are not on the list. The first is the bridge from what a man actually does to what he prefers — demonstrated preference, in Rothbard's sense. It is written out below in the form it would take, and then set aside:

/-- PARKED: the bridge from actual action to preference. Carried by no theorem; lives in the document, not the library. -/ structure DemonstratedPreference (praxis : ActionFrame) : Prop where bridge : act : Action praxis, givenUp act.forgone, praxis.Prefers act.agent act.time {act.chosen} {givenUp}

The second is the claim that there is any action at all. Action itself is a definition here, and no theorem uses it yet.

🔗structure
Apodictic.Action (praxis : ActionFrame) : Type
Apodictic.Action (praxis : ActionFrame) : Type

An action: an agent, at a time, uses means in the belief that they will bring about a chosen end, giving up at least one alternative end in doing so.

The fields hold together as a package — nothing with fewer parts counts as an action — but this is a definition, so it asserts nothing. Shape: our-reconstruction. No theorem uses it yet; the law of marginal utility rests on the counterfactual plan alone.

agent : praxis.Agent

The acting person.

time : praxis.Time

When the action happens.

chosen : praxis.End

The end aimed at.

means : praxis.Means

The means employed.

forgone : Set praxis.End

The ends given up by acting — the raw material of opportunity cost. Just a set: saying "the next-best alternative" would presuppose a ranking this file does not have.

forgone_nonempty : self.forgone.Nonempty

Action is choice: something is always given up, if only doing nothing.

chosen_not_forgone : self.chosen  self.forgone

The chosen end is not among the forgone.

belief : praxis.Believes self.agent self.time self.means self.chosen

The agent believes the means used will bring about the chosen end.