By Roy T. Cook
This important reference introduces undergraduate and post-graduate scholars to the most difficulties and positions of philosophical common sense. parts comprise the most important figures, positions, terminology, and debates inside philosophical good judgment in addition to matters that pertain to comparable, overlapping disciplines, comparable to set idea and the philosophy of arithmetic. Entries are broadly cross-referenced for identity in the context of wider debates.
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Additional info for A Dictionary of Philosophical Logic
Compositionality is often contrasted with views of meaning where additional factors contribute to the meaning of expressions, such as contextualism or holism. See also: Compound Formula, Connective, Formation Rules, Quantifier, Semantics, Truth Functionality COMPOUND EXPRESSION see Compound Statement COMPOUND FORMULA A compound formula (or complex formula, or molecule) is a formula that is composed of other, simpler formulas. Compound formulas are typically formed by prefixing a formula with negation (~), joining two or more statements together with a binary connective such as conjunction (∧), disjunction (v), or material implication (→), or by prefixing a formula with a quantifier (∃, ∀) or modal operator (▫, छ).
In first-order logic supplemented with the membership symbol “∈,” this can be formulated as: (∀x)((∃y)(y ∈ x) → (∃z)(z ∈ x ∧ ~(∃w)(w ∈ z ∧ w ∈ x))) Although the exact import of the axiom of foundation is difficult to summarize, its main role is to rule out the existence of non-wellfounded sets. See also: Anti-Foundation Axiom, Non-Well-Founded Set Theory, Zermelo Fraenkel Set Theory AXIOM OF INFINITY The axiom of infinity asserts that there exists a set A such that (1) the empty set is a member of A, and (2) for any set that is a member of A, its ordinal successor is also a member of A.
See also: Boolean Negation, Dagger, Sheffer Stroke BORDERLINE CASE An object x is a borderline case of a predicate Φ if and only if x is not a clear case of Φ and x is not a clear case of ~ Φ. Borderline cases are often associated with vagueness. ” See also: Falsum, Partial Ordering, Top, Verum BOUND VARIABLE In a formula of first-, second-, or higherorder logic, a variable x is a bound variable if it occurs within the scope of a quantifier. A variable that is not bound by a quantifier is a free variable.