Recursive definitionIn mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set. A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs.
DenotationIn linguistics and philosophy, the denotation of an expression is its literal meaning. For instance, the English word "warm" denotes the property of being warm. Denotation is contrasted with other aspects of meaning including connotation. For instance, the word "warm" may evoke calmness or coziness, but these associations are not part of the word's denotation. Similarly, an expression's denotation is separate from pragmatic inferences it may trigger.
Universality (philosophy)In philosophy, universality or absolutism is the idea that universal facts exist and can be progressively discovered, as opposed to relativism, which asserts that all facts are relative to one's perspective. Absolutism and relativism have been explored at length in contemporary analytic philosophy. Also see Kantian and Platonist notions of "universal", which are considered by most philosophers to be separate notions. Moral universalism When used in the context of ethics, the meaning of universal refers to that which is true for "all similarly situated individuals".
ExplanationAn explanation is a set of statements usually constructed to describe a set of facts which clarifies the causes, context, and consequences of those facts. It may establish rules or laws, and may clarify the existing rules or laws in relation to any objects or phenomena examined. Explanation, in philosophy, is a set of statements that makes intelligible the existence or occurrence of an object, event, or state of affairs.
Coherence theory of truthCoherence theories of truth characterize truth as a property of whole systems of propositions that can be ascribed to individual propositions only derivatively according to their coherence with the whole. While modern coherence theorists hold that there are many possible systems to which the determination of truth may be based upon coherence, others, particularly those with strong religious beliefs, hold that the truth only applies to a single absolute system. In general, truth requires a proper fit of elements within the whole system.
Atomic sentenceIn logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences. For example, "The dog ran" is an atomic sentence in natural language, whereas "The dog ran and the cat hid" is a molecular sentence in natural language. From a logical analysis point of view, the truth or falsity of sentences in general is determined by only two things: the logical form of the sentence and the truth or falsity of its simple sentences.
Boolean-valued functionA Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e., a single bit of information. In the formal sciences, mathematics, mathematical logic, statistics, and their applied disciplines, a Boolean-valued function may also be referred to as a characteristic function, indicator function, predicate, or proposition.
