Sentence examples for by considering a wff from inspiring English sources

Some of the uses of the above rules can be illustrated by considering a wff α that contains precisely two free individual variables.

We illustrate one possible interpretation of the wff (7′) (which is closely related to Axiom 6) by considering a situation in which a rancher puts some horses in a corral and leaves for the night.

Thelema is considered a cult by many.

Formation rule 1 is then replaced by: 1′.An expression consisting of a predicate variable or predicate constant of degree n followed by n terms is a wff.

The formation rules are: An expression consisting of a predicate variable of degree n followed by n individual variables is a wff.

If a wff of LPC is considered as a proposition form, instances of it are obtained by replacing all free variables in it by predicates or by names of individuals, as appropriate.

These equivalences are expressed formally by the validity, again for any wff α, of(∃x)(∃y)α ≡ ∼(∀x)(∀y)∼α and(∀x)(∀y)α ≡ ∼(∃x)(∃y)∼α and by the resulting replaceability anywhere in a wff of (∃x)(∃y) by ∼(∀x)(∀y)∼, or of (∀x)(∀y) by ∼(∃x)(∃y)∼.

Consider the closed wff(∀x)(∀y)(ϕxy ⊃ ϕyx),which means that, whenever the relation ϕ holds between one object and a second, it also holds between that second object and the first.

Because the rule of substitution of equivalents can be shown to hold in LPC, it follows that (∃x) may be replaced anywhere in a wff by ∼(∀x)∼, or (∀x) by ∼(∃x)∼, and the resulting wff will be equivalent to the original.

By an LPC substitution-instance of a wff of PC is meant any result of uniformly replacing every propositional variable in that wff by a wff of LPC.

In general, a predicate variable followed by any number of individual variables is a wff of the predicate calculus.