Simultaneous substitutions for several "variable ideas" in the same proposition also have their place in Bolzano's logic.
In the general case, Bolzano's deducibility is a triadic relation between the premises, the conclusion and the variable ideas.
Let us examine some examples: Such a deduction works with two variable ideas, "Leipzig" and "Dresden", and depends also on astronomical knowledge.
A sentential form, or equivalently the corresponding proposition "in which certain ideas are considered variable", can generate a whole class of propositions if appropriate ideas are substituted for the variable ideas.
To consider one or several ideas in a given proposition variable means to take the class of all propositions which have the same structure and contain the same ideas except at places occupied by the "variable ideas".
If we take into account not the initial Bolzanian concept of deducibility relative to given variable ideas, but logical derivability, and either adapt or cancel the requirement of consistency of the premises, the distance seems rather short.
Now Bolzano can define compatibility for propositions in complete analogy with compatibility for ideas: The propositions A, B, C, D, … are all mutually compatible with respect to the variable ideas i, j, … common to all of them if there is a sequence of ideas which, substituted for the variables i, j, …, makes all these propositions true (Bolzano 1837, § 154).
An example using the VS-MMPF methodology is presented in [36] where user selected number of particles can be used in each mode of the filter by making use of the so-called "variable-mass" idea.
This approach is based upon the extension of the variable sampling period idea with a new packet based control methodology.
