Search results
Results from the WOW.Com Content Network
In philosophy, an explanation is a set of statements that renders understandable the existence or occurrence of an object, event, or state of affairs. Among its most common forms are: Causal explanation; Deductive-nomological explanation, involves subsuming the explanandum under a generalization from which it may be derived in a deductive ...
There are two common ways to specify theories: List or describe a set of sentences in the language L σ, called the axioms of the theory. Give a set of σ-structures, and define a theory to be the set of sentences in L σ holding in all these models. For example, the "theory of finite fields" consists of all sentences in the language of fields ...
Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [2] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the ...
A logical connective that represents the "and" relationship between two statements, requiring both to be true. conjunction elimination A rule of inference in propositional logic that allows one to infer a conjunct from a conjunction. conjunction introduction A rule of inference that allows the formation of a conjunction from two individual ...
However, the concept of an infinite set cannot be defined within the system — let alone the cardinality of such a set. The system has at least two different models – one is the natural numbers (isomorphic to any other countably infinite set), and another is the real numbers (isomorphic to any other set with the cardinality of the continuum ...
A variety of basic concepts is used in the study and analysis of logical reasoning. Logical reasoning happens by inferring a conclusion from a set of premises. [3] Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case.
Concrete concept – Metaphysics concept covering the divide between two types of entities; Conjecture – Proposition in mathematics that is unproven; Decision (see Decision-making) Definition – Statement that attaches a meaning to a term; Explanation – Set of statements constructed to describe a set of facts which clarifies causes
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.