Why are monadic predicates not sufficient for a complete description of the world?

Conversely, monadic predicate calculus is not significantly more expressive than term logic.

The validities of monadic predicate calculus with identity are decidable, however.

According to Peirce, a genuinely monadic predicate characteristically expresses quality.

In 1922 Behmann proved that the monadic predicate calculus is decidable.

Inferences in term logic can all be represented in the monadic predicate calculus.

The absence of polyadic relation symbols severely restricts what can be expressed in the monadic predicate calculus.

The formal system described above is sometimes called the pure monadic predicate calculus, where "pure" signifies the absence of function letters.

Taking propositional logic as given, every formula in the monadic predicate calculus expresses something that can likewise be formulated in term logic.

Monadic predicate calculus can be contrasted with polyadic predicate calculus, which allows relation symbols that take two or more arguments.

While instantiating the predicates can be characterized by their logical properties of relations, quantifiers and cardinality as monadic predicates of these predicate objects.

These include propositional logic and monadic predicate logic, which is first-order logic restricted to unary predicate symbols and no function symbols.

For evidently we need both reflexive and non-reflexive polyadic predicates, as well as monadic predicates, if we are to be able to describe at all adequately the world around us.

They are to monadic predicate logic what Boolean algebras are to propositional logic, and what polyadic algebras are to first-order logic.

In short, any explanation of "x is greater than y", it seems, still leaves us with a two-term relation whereas the reductivist, if his argument is going to work, needs a monadic predicate.

A predicate F is distributive if, whenever some things are F, each one of them is F. But in standard logic, every monadic predicate is distributive.

Mentions that sentential logic, monadic predicate logic, the modal logic S5, and the Boolean logic of (un)permuted relations, are all fragments of PFL.

Simons (1987) and Casati and Varzi (1999) show that the calculus of individuals can be grounded in either in a bit of set theory, or in monadic predicates, schematically employed.

The existential fragment (EMSO) of Monadic predicate calculus second-order logic (MSO) is second-order logic without universal second-order quantifiers, and without negative occurrences of existential second-order quantifiers.

It is so weak that, unlike the full predicate calculus, it is decidable - there is a decision procedure that determines whether a given formula of monadic predicate calculus is logically valid (true for all nonempty domains).

In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols in the signature are monadic (that is, they take only one argument), and there are no function symbols.