When faced with the exigencies of existence, suspension of choice is not an option.
A large body of empirical work has suggested the existence of a "choice overload" effect in consumer decision making: when faced with large menus of alternatives, decision makers often avoid/indefinitely defer choice.
Finally, all that the Trailheaders knew was terror, and the existence of a choice — they could fight or run from the horror.
Later on he lists Axiom IV, which, as noted, asserts the existence of a choice set for any set of disjoint non-empty sets.
The existence of a choice function $f:\{X,Y\} \rightarrow \{0,1\}$ choosing an element from $X$ and $Y$ would imply $(A \vee \neg A)$.
Note that some references (e.g., [80]) introduce persistent homology by defining the birth and death of generators without using the existence of a choice of compatible bases, as given by the Fundamental Theorem of Persistent Homology.
For the set \(P\) of potential choice functions on an indexed family of sets \(\sA\) is clearly nonempty and is readily shown to be strongly inductive; so Zorn's lemma yields the existence of a choice function on \(\sA\).
But in the case of an infinite collection, even when each of its members is finite, the question of the existence of a choice function or a transversal is problematic[4].
But logic, which deals only in right and wrong answers, certainly can disprove the existence of free choice.
