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Path analysis conventionally orders variables from left to right, with those on the left causing those to the right.
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Likewise, if bound first-order variables are assumed to range over sets (as they do in set theory), a commitment to the existence of these sets is incurred.
We let a, b, c, … range over first-order variables.
The charge of ontological bias against Quinean criteria is simply shifted: why allow first-order variables to carry ontological commitment, but not second-order variables?
Observe that no second-order variables are involved in the formulation of the syntax.
We shall identify first-order variables with nominals of hybrid logic.
To make ontological commitment transparent, Quine holds, second-order theories must be transformed into first-order theories by replacing second-order variables with first-order variables ranging over sets, and taking predication to be set membership.
The ontological commitments of second-order theories will then depend on how the second-order variables are interpreted.
Parallel problems admit of parallel solutions: we can eliminate predicates in favor of second-order variables, and take ontological commitment, if any, to be carried by the second-order variables rather than the predicates.
Ramseyfication consists in the replacement of the theoretical terms of a finitely axiomatized theory by bound higher-order variables.
This leads to introducing the taxonomy of deeper-order variables and interaction variables relevant for modeling the physical system.
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