Concepts in logic

In mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. For example, the formula x+3=y is satisfiable because it is true when x=3 and y=6, while the formula x+1=x is not satisfiable over the integers. The dual concept to satisfiability is validity; a formula is valid if every assignment of values to its variables makes the formula true. For example, x+3=3+x is valid over the integers, but x+3=y is not.

in a mathematical game, a statement that players know and also know that other players know (ad infinitum)

In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality, which is concerned with whether the internal definitions of objects are the same. ==In mathematics== The extensional definition of function equality, discussed above, is commonly used in mathematics. A similar extensional definition is usually employed for relations: two relations are said to be equal if they have the same extensions.

expression in propositional calculus

200px|thumbnail|right|Trivialism in First-order logic#Logical symbols|symbolic logic; Read as "given any proposition, it is a true proposition."

possibility considered in a counterfactual

group of things derived from extensional or intensional definition (philosophy)

basic element of strings in a formal language

Predicable (Lat. praedicabilis, that which may be stated or affirmed, sometimes called quinque voces or five words) is, in scholastic logic, a term applied to a classification of the possible relations in which a predicate may stand to its subject. It is not to be confused with 'praedicamenta', the scholastics' term for Aristotle's ten Categories.

when universalizable abstract principles are reflectively found to be in equilibrium with particular intuitive judgements

form for logical arguments, obtained by abstracting from the subject matter of its content terms

In mathematics, logic and philosophy of mathematics, something that is impredicative is a self-referencing definition. Roughly speaking, a definition is impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set that contains the thing being defined. There is no generally accepted precise definition of what it means to be predicative or impredicative. Authors have given different but related definitions.

Reasoning that is rationally compelling, though not deductively valid

fundamental philosophical abstraction; the recognition of difference

term in model theory and related areas of mathematics

A supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. Supertasks are called hypertasks when the number of operations is uncountable. A hypertask that includes one task for each ordinal number is called an ultratask. The term "supertask" was coined by the philosopher James F. Thomson, who devised Thomson's lamp. The term "hypertask" derives from Clark and Read in their paper of that name.

statement that asserts that a certain premise is true

logical principle

theoretical universal logical calculation framework

concept in logic; syntactic transformation on formal expressions

totality of intensions, that is, properties or qualities, that an object possesses

latin terms

In mathematical logic (a subtopic within the field of formal logic), two formulae are equisatisfiable if the first formula is satisfiable whenever the second is and vice versa; in other words, either both formulae are satisfiable or neither is. The truth values of two equisatisfiable formulae may nevertheless disagree for a particular assignment of variables. As a result, equisatisfiability differs from logical equivalence, since two equivalent formulae always have the same models, whereas equisatisfiable ones need only share satisfiability status. More formally, the equisatisfiability meta fo

concept in metaphysics and logic

Finiteness, finitude, or being finite, is the state of being limited or having an end, and is a counter to the concept of infinity. Humans are considered to be in this state because of their limited life span, uniformly ending in death. Each natural number is considered to be in this state, because counting up to that number stops when the number is reached. The concept appears across disciplines, from mathematics and linguistics to philosophy, where it is used to describe quantities, structures, and conditions. In mathematics, a set or number is finite if it is limited in size, while in lingu

term used to model certain phenomena that cannot be adequately handled using ordinary possible worlds

in mathematical logic, property of formula that has the same truth value in each of some class of structures

principle in epistemology