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PHILOSOPHY GLOSSARY
..A
abstract
not tangible or concrete
abstract algebra
abstract
not tangible or concrete
abstract algebra
The generalisation of algebraic methods originally concerned with number systems to deal with arbitrary algebraic structures over arbitrary domains.
abstraction
the process or result of forming some abstract idea from a number of more particular or concrete examples
(in set theory)
The process of forming a set, typically by binding a free variable in a formula which expresses the truth condition, for membership in the set, of the value denoted by the variable. Comprehension and separation are particular kinds of set abstraction. Abstraction to properties (predicates or propositional functions) is analogous.
(functional)
Forming a function, typically by binding a free variable in an expression which denotes the value of the function for the argument whose value is denoted by the variable.
ad
the Latin preposition meaning "to" or "towards"
ad hoc
for a particular purpose. An inelegant feature in an otherwise well structured system to fix a particular problem. A hack.
ad hoc polymorphism
(after [CardelliTDP]) a kind of polymorphism in programming languages in which a function taking a polymorphic parameter will execute different code according to the type of the parameter supplied (by contrast with universal polymorphism in which the same code is used). Special cases include overloading and inclusion polymorphism.
algebra
the systematic study of number systems using symbolic formulae involving variables
see also:
abstract algebra
computer algebra
altruism
unselfishness, concern for others
analytic
(logic)
a proof which proceeds by analysis of the desired conclusion showing that it is derivable from accepted premises (from classical Greece). Such proofs are now sometimes known as a backward or goal oriented proofs.
(philosophy)
expressing a relationship between concepts. A statement or proposition which lacks empirical content and is true in virtue of its meaning.
(philosophy)
a kind of philosophy particularly concerned with logical or linguistic analysis (see: Varieties of Philosophical Analysis).
(recursion theory)
definable in second order arithmetic
anarchism
1. the doctrinal abhorrence of coercion, usually including advocacy of the abolition of the state
2. violent opposition to established authorities, especially those considered oppressive
antinomy
a brittle silvery white metalic element
(philosophy)
a paradox or contradiction
a posteriori
knowable or justifiable only on the basis of experience
a priori
knowable or justifiable prior to experience based on purely rational considerations
arithmetization
the process of translating statements or problems from their usual domain into the language of arithmetic, usually so that the methods of arithmetic or logic can be brought to bear on the problem.
arithmetization of analysis
the reduction of the theory of real numbers to that of arithmetic, accomplished by defining a real number as some aggregate of rational numbers, e.g. a Dedkind cut or a Cauchy sequence.
see also:
gödelization
axiom
in a logic or an axiomatic theory an axiom is a sentence which is accepted as true without demonstration. The axioms are the starting points for the derivations of all other theorems.
axiomatic method
a method of doing mathematics in which subject areas are presented and studied as axiomatic theories
axiomatic semantics (computing)
a semantics for a programming language given by defining axioms which permit reasoning about the effects of execution of the various parts of a program.
axiomatic theory
a mathematical (or other) theory presented as a system of axioms.
axiomatisation
The process of formalising some subject as an axiomatic theory.
..B
biconditional
a name used for the logical operator which yields a true proposition iff both its operands have the same truth value. So called because it is equivalent to the conjunction of two conditionals (implications), which is reflected by the usual symbol " ", which consists of the conditional " " overlaid in two directions.
bind
tie or fasten tightly
(in logic)
the effect of various syntactic constructs (such as quantifiers or abstractions) which bind free occurrences of variables (of a certain name), within some expression, to a binding occurrence (of that same name) associated with a binder (e.g. a quantifier). A variable free in some expression, is no longer free in the larger expression formed by binding that variable. e.g. two free occurrences of the variable "x" in the expression "x=x" are bound when the universal closure is formed yielding " x. x=x", in which there are no longer any free occurrences of "x".
bivalent
A logic is bivalent if sentences in the logic can take either of just two truth values, usually named "true" and "false" or "T" and "F".
boolean
(after George Boole) often used as if it means "two-valued" or bivalent, but in fact allows any collection of values which conforms to certain algebraic laws (i.e. is a boolean algebra). A boolean propositional logic, though it admits interpretations in which propositional variables range over more than two values, has just the same set of theorems (the propositional tautologies) as a bivalent propositional logic.
boolean operator
An operator which takes boolean arguments and returns a boolean result.
bound
set bounds to, limit
(in logic)
to limit the scope of a variable, usually by enclosing that scope in some variable binding construction which identifies the variable thus bound.
bound variable
a variable whose scope has been restricted by some variable binding construct or declaration.
..C
c
The name used in Factasia for pure combinatory logic.
calculus ratiocinator
(after Leibniz) a mechanical method of solving problems which have been expressed in a universal language known as a characteristica universalis).
casuist
a person who resolves problems of conscience or duty
cardinal
chief, fundamental
cardinal number
1. numbers denoting quantity ("one", "two", "three", ...), as opposed to ordinal numbers indicating position ("first", "second", "third", ...).
2. An equivalence class generated by the relation "same size as" obtaining when there is a one-one mapping between the elements of two sets.
3. The smallest ordinal number of some size.
see also:
large cardinal
category
a class or division
(philosophy, metaphysics)
one of the fundamental kinds of things (see: Aristotle's Categories)
(mathematics)
a kind of mathematical structure, providing in some respects a very general mathematical counterpart to the notion of a concept. A collection of objects and of morphisms (or arrows) such that each morphism has a domain and codomain which are objects, each object has an identity morphism, and morphisms compose associatively. e.g. corresponding to the mathematical concept of a group there is a category of groups which contains as objects all the groups, and as arrows between these objects the group homomorphisms.
category mistake
a favourite kind of "philosophical puzzlement" to which the Oxford philosopher Gilbert Ryle drew attention. A category mistake occurs when a speaker or writer applies a concept outside the domain in which it can meaningfully be applied (often in the course of formulating some philosophical theory).
see also:
kind
sort
type
characteristica universalis
(after Leibniz) a universal language into which any kind of problem can be translated (and then solved by calculation using a calculus ratiocinator). See: The Method of Mathematics.
class
a collection of persons or things
(logic)
sometimes used interchangeably with or instead of set, sometimes used (e.g. in NBG) for collections which are "too large" to be sets.
coerce
persuade or restrain (an unwilling person) by force
coercion (1)
the act or process of coercing
coercion (2) (computing)
the automatic conversion of a value in a computer program from one type to another as needed for the use made of the value in some particular context, e.g. the conversion of an integer to a floating point number before adding it to some other floating point number.
see also:
anarchism
cofinal
a function into an ordinal is cofinal if its range is unbounded in its codomain.
cofinality
the cofinality of an ordinal , cf( ), is the least ordinal which maps cofinally into .
cognition
knowing, perceiving or conceiving as distinct from emotion or volition.
combinator
a function primitive to or definable in pure combinatory logic
combinatory logic
a form of logic in which bound variables are not used
complex
Not simple. Not atomic. Structured.
complex number
A number formed of two parts, so called real and imaginary parts, both of which are real numbers.
computer
An electronic device which stores and processes data following instructions which are also stored in its memory (and can therefore easily be changed).
computer algebra
the use of computer programs which automate algebraic transformations, e.g. MACSYMA, Maple, Mathematica.
conjunct
One of the immediate constituent sentences of a conjunction, e.g. in "A and B" the conjuncts are "A" and "B".
conjunction
A compound sentence of the form "A and B".
constructive
constructive logic
A logic is constructive if existence proofs in the logic depend upon constructing something with the required property and may not proceed by reductio-absurdum.
contingent
Might have been otherwise.
..D
de
(latin) of or from
de dicto
an ascription of a property or modality to a proposition
de re
an ascription of a property or modality to a thing
decidable
A set is decidable iff there is an effective procedure for deciding whether any object is or is not a member of the set.
deduction
the process of reasoning from premises to conclusions which are logically entailed by those premises. The conclusions of correct deductive inferences cannot possibly be false if the premises are true. See: What is Logic?".
see also:
induction
deductive
by deduction
deductively sound
an inference is deductively sound if it is not logically possible that the premises be true and the conclusion false
definiendum
in a definition, that which is defined
definiens
the body of a definition which gives the meaning to be assigned to the definiendum
definition
a statement in which a meaning (the definiens) is assigned to a word, symbol, phrase, or expression (the definiendum)
deflation
letting the wind out
deflationary conception of truth
the view that the predicate true serves only limited purposes, such as indirect or compendious endorsement and disquotation.
democracy
a system of government involving all, or a large part, of the people governed
See also:
participatory democracy
representative democracy
denote
signify, indicate, mean, convey, name
{philosophy)
after Kripke, a distinction is sometimes made between denotation (which involves reference via a description) and naming in which reference is made without description
denotational semantics (computing)
a semantics for a programming or other language, given by defining mappings from each syntactic category into suitable semantic domains. The mappings are usually expected to be compositional, and "mathematical" semantic domains are often preferred (in which case it may be called a mathematical semantics).
deontic logic
a logic for reasoning about obligations and rights
designate
serve as the name or distinctive mark of
designator
a name or description which designates, or refers to, something
disjunct
one of the immediate constituent formulae or sentences in a disjunction, e.g. in "A or B", "A" and "B" are the disjuncts.
disjunction
a formula or sentence whose principle operator is logical (inclusive) or, e.g. "x>5 x<6"
disquotation
the removal of quotation marks, typically by the use of the predicate "is true", e.g.: "x>5 x<6" is true
disquotation principle
that "'S' is true iff S" for all sentences S
dogmatic
given to asserting or imposing personal opinions
dogmatism
a tendency to be dogmatic
dogmatist
a dogmatic person
(according to pyrrhonism and Sextus Empiricus)
someone who is not a sceptic, and is willing to assert at least one proposition to be true
domain
a sphere of control or influence
- of a function
the collection of values for which the function is defined
- of a relation (in set theory) -
the set of elements or values which relate to some other element under the relation
- in formal semantics
a collection of values which represent the meanings of a certain class of linguistic entities.
dynamic
concerning motion or change
dynamic semantics
that aspect of the semantics of a programming language which is concerned with the effects of executing the program. Also used for the non-static aspects of the semantics of formal specification languages.
..E
effective
effective procedure
An effective procedure is an unambiguous prescription for computing some function or solving a class of problems.
effectively computable
A function is effectively computable if there is an effective procedure for computing the value of the function.
effectively decidable
A class of problems, or a set, is effectively decidable if there exists an effective procedure which will determine the answer to the problem (or membership of the set) terminating with the correct answer within a finite number of steps, for all candidates.
effectively semi-decidable
A class of problems, or a set, is effectively semi-decidable if there exists an effective procedure which terminates with a positive answer whenever the answer to the problem or the membership question is positive, but which may fail to terminate in the case that the answer is negative.
empirical
based on observation or experiment
empiricist
one who emphasises the role of sensory experience or experimental evidence in the justification of knowledge.
epistemology
The theory of knowledge.
epistemic logic
A logic for reasoning about knowledge and belief.
extension
of a set
the membership of the set
of a property
the collection of things which have the property
of a function
the mapping defined by the function, as distinct from any algorithm, rule or formula used to define the function
extensional
of a set theory
A set theory is extensional when two sets are equal iff they have the same extension.
of a higher-order logic
A higher order logic is extensional when two properties or functions are equal iff they have the same extension.
..F
factasy
a genre, treading the line between fact and fantasy
factastic
an adjective used in factasia to describe some of its peculiar doctrines or methods
factastic future engineering
an approach to future engineering advocated in Factasia
FAn
local abbreviation for formal analytic.
FAn oracle
an oracle for FAn conjectures and problems
fictionalism
a doctrine which acts on certain propositions for reasons other than knowledge of or belief in the truth of the proposition, e.g. for pragmatic reasons. See: PS
fideism
a doctrine which accepts sceptical arguments for the unattainability of absolutely certain knowledge but which admits definite affirmative judgements nonetheless. See: PS
field
an area of operation or activity
of a relation (in set theory) -
the field of a relation is the set of all elements which relate to, or are related to by, some other element under the relation. The field is the union of the domain (also called the left field) and the range (also called the right field) of the relation.
first
earliest in time or in some other ordering
first order logic
predicate logic involving quantification only over individuals, not over sets properties or functions (the ordering involved here is the ordering of types of entities in terms of the logical complexity of the entities).
formal
of notations - defined with mathematical precision, machine processable
formal analytic
an analytic truth or falsehood expressed in a formal notation
formalism
a philosophy of mathematics mainly associated with the mathematician Hilbert.
foundation
the solid ground or base on which a building rests.
foundationalism
a term used in epistemology for theories of knowledge in which our knowledge of the "external" world is founded upon evidence provided by our senses. More generally, for knowledge of a certain kind of fact, the theory that this knowledge is derived from premises (often supposed indubitable) of a special kind.
franchise
a right or privilege granted to a person or corporation
free
1. not restricted or impeded, not controlled or bound
2. at no cost
free variable (logic)
a variable which is not bound
fulfil
of self - develop and exploit one's gifts and character to the full.
function
Something which determines for each of a number of possible values for arguments (to the function) a specific value which is the result of the function for that argument.
(in set theory)
a many-one relation (which is sometimes called the graph of the function)
(in computing or constructive mathematics)
an expression or rule which shows how the value of a function may be computed, or is otherwise determined by, the value of the argument to the function.
future
that which is yet to come, what will be
future engineering
the engineering of the future
..G
generalization
A general proposition obtained by inference from particular cases.
(in deductive logic)
An inference from a proposition about an unspecified individual (as a free variable) to a universally quantified proposition. The rule which permits such inferences.
Gödelization
A technique for encoding the formulae of arithmetic as numbers used by Kurt Gödel in his incompleteness proofs [Gödel31].
see also:
arithmetization (Gödelization is a technique for the arithmetization of logical syntax)
Gödel number
A number assigned to some syntactic entity by Gödelization.
Gödel numbering
see Gödelization
groupware
Software which facilitates collaboration.
..H
hack
cut or chop roughly, mangle
(Computing, 1)
to write a program hastily with little concern for elegance and structure
(Computing 2)
to attempt to gain unauthorised access to computer systems, usually through electronic networks
hacker
Someone who hacks.
The connotations of this term vary widely depending on who is using it. In the tradition now associated with the "open source" movement (which credits itself as the main source of the software infrastructure for the internet) a hacker is a hero who has made significant contributions to the development of open source software. In other milieu the term may be associated with over hasty and poorly engineered software development. In the popular press the term has been primarily associated with the practice of attempting illegally to penetrate computer systems and networks (i.e. nothing much to do with software development). A vigorous campaign by open source advocates to dissuade the press from this usage has had some marginal success (so small that I can't bring to mind the term which they are supposed to use instead).
halting problem
the problem of deciding for an arbitrary Turing machine and initial configuration (tape + position on tape + initial state) whether the Turing machine started in that configuration would ever halt.
historicism
This term was coined by Karl Popper as a label for those kinds of social philosophy which engage in sweeping historical prophesy and assert the inevitability of the prophesied course of history.
HOL
Higher Order Logic (1)
A logical system, usually a Type Theory, with multiple ranges of quantification (usually called types) some of which contain sets or functions. See also: Church's Simple Theory of Types, Pure Type Systems
Higher Order Logic (2)
A proof tool, originally developed by the Hardware Verification Group at The University of Cambridge Computer Laboratories. Now available as several variants (HOL88, HOL90, HOL98, HOL Light), supporting the construction and checking of proofs in Higher Order Logic. There are also many more proof tools for variants of Higher Order Logic or for logical Type Theories which do not go under the name "HOL". There is an annual international workshop concerned with the development and application of these proof tools.
hyper-rational
An exacting standard of rationality based on the assertion only of formally proven analytic propositions.
hypostasis
an underlying substance, as opposed to an attribute or that which is insubstantial
hypostatise
reify, possibly fallaciously
..I
I
In combinatory logic, the identity combinator, a function which, when applied to some value always returns that same value.
I = x. x
iff
if and only if
impredicative
not predicative
include
A includes B if everything in B is also in A
inclusion polymorphism
a kind of polymorphism found in the type systems of object oriented programming languages in which some types are included in others. A type of object consisting of multiple named components would typically include the types whose objects have the same set of named components together with some additional components.
induction
(mathematical)
a method of proving a general truth affirming that every one of a set of mathematical objects (e.g. the natural numbers) has a certain property (e.g. has exactly one prime factorisation). The method depends upon their being a systematic way of constructing all the elements of the set by starting with one of a finite set of basis elements and repeatedly applying a finite number of constructions (for the natural numbers the basis is the number 0, and the method of construction is addition of 1). An inductive proof then consists of a proof that the basis elements each have the required property and a proof that the construction, when applied to elements having the property, will yield an element also having the property. Mathematical induction is in fact a kind of deduction. It is also called structural induction.
(scientific)
scientific induction is the process of concluding empirical generalisations from particular instances, where this is not deductively sound because not all possible instances are premises
intersection
where two things lie across each other
(in set theory)
the intersection of two sets a and b is that set whose members are those things which are members both of a and of b
intuitionism
a position in the Philosophy of Mathematics mainly associated with L.E.J.Brouwer
intension
the meaning or internal content of a concept, as contrasted with its extension
the strenuous exertion of the mind or will
intensional
of a logic
not extensional
of an act
intended
intention
thing intended
intentional
intended
in error, or perhaps correctly in American English: intensional
intentional stance
the attempt to understand an artefact by second guessing the intentions of its designer [[Dennett95] ch.9 p.229]
intentional systems
Systems whose behaviour can be - at least sometimes - explained and predicted by relying on ascriptions to the system of beliefs and desires (and hopes, fears, intentions, hunches,...). [also from Dennett]
..J
judgement
The critical faculty whereby we assess the truth of claims, an application of, or the result of applying this faculty.
in formal logic
in some formal logics the theorems of the system are called judgements and there may be a single form of judgement (as in Frege's Begriffsschrift, where a judgement always takes the form of the assertion, using a vertical bar, of a content formed using a horizontal bar), or multiple forms (as, for example, in the contructive type theories of Per Martin Löf).
justify
Show the justice or rightness of.
justification
that which justifies (or warrant's)
in epistemology
knowledge may be explained or defined as "justified true belief", in which case the question what (if anything) counts as justification of a claim to knowledge becomes a central problem
..K
K
(combinatory logic)
the constant combinator. A function which, when applied to some value, yields a constant function which always returns that value.
K = x y. x
kind
considerate, generous, affectionate
Class, type, sort, variety.
(logic)
a polymorphic logical type theory which has operations over types may have a second tier of typing in which types and operators over them are assigned to kinds.
knowledge
justified true belief
..L
lambda
the greek letter
lambda abstraction
a syntactic construct denoting a function, beginning with the lambda symbol which binds a variable in an expression which denotes the value of the function for the argument whose value is denoted by the variable, e.g. " x. x*x" is a lambda expression denoting the square function.
lambda calculus
a notation and calculus involving lambda abstraction, widely used logic and in theoretical computer science
large cardinal
a cardinal number at least as large as the first strongly inaccessible cardinal
limit
that beyond which something may not pass
(in mathematics)
a quantity which the value of a function or sequence or the sum of a series approaches arbitrarily closely
limit ordinal
an ordinal number which is not a successor ordinal
logic
As a subject
The study of reasoning
a logic
a (usually formal) system encoding principles of reasoning.
logical atomism
A philosophical position associated with Bertrand Russell and Ludwig Wittgenstein involving logical analysis of propositions into atomic propositions and their correspondence with the structure of reality (in the form of facts).
logical construction
A method (advocated by Bertrand Russell and originating in his philosophy of mathematics) permitting parsimonious ontologists to maximise their use of Occam's razor by "logically constructing" entities as complexes of simpler things to which one is already committed. Most notoriously, of physical objects from sense data
logical necessity
A proposition is logically necessary if it is true in all possible worlds.
logical positivism
The name adopted by the Vienna Circle (including Rudolf Carnap and Alfred Ayer) for their philosophical position, most famous for introducing the verification principle as a criterion for meaning of synthetic propositions, and for dismissing metaphysics as meaningless
..M
meaning
what is meant by, or the significance or importance of, a word, sentence or event
meaning-truth platitude
the principle that the truth value of a statement depends only on its meaning and the state of the world in certain respects
means
What it takes to realise some end. Maybe material or intellectual resources, maybe methods.
mechanisation
arranging to be accomplished by machinery (possibly by computers or calculators)
mechanisation of mathematics
The automation of mathematical methods, usually by programming digital computers.
metaphysics
that branch of philosophy which is concerned with ontology and other a priori aspects of the nature of the universe
meme
a unit of cultural transmission or of imitation (coined by Richard Dawkins in The Selfish Gene [Dawkins89] ).
memetics
the science (or pseudo science) of memes.
memetic future engineering
the use of memetics in future engineering
method
A prescription, recipe or algorithm describing how to achieve some purpose or end.
modal
(philosophy)
concerning possibility, impossibility, necessity or contingency
modal logic
a diverse family of logics involving modal operators, usually rendered and . The original interpretation of these symbols was for "necessarily" and "possibly" respectively, but other applications of modal logics have introduced alternative interpretations, e.g. in relation to time (always, sometime), provability (provable, consistent), and knowledge (know, believe).
model
a representation of something, possibly smaller (scale model), simplified, made more precise (mathematical model), or idealised.
(of a first order theory)
A model of a first order theory is an interpretation of the language of the theory which satisfies all the non-logical axioms of the theory.
(mathematical)
An abstract model, defined with mathematical precision, of some thing or phenomenon, which may be used to reason about or calculate its behaviour. Often used in engineering design to ensure that a design will fulfill its intended purpose.
model theory
A major branch of mathematical logic which studies the models of first order theories.
..N
natural
existing in, or caused by, nature
natural meaning
the meaning or significance of some natural entity or phenomenon
non-natural meaning
the meaning of words and sentences
natural number
The non-negative whole numbers, zero and those numbers which can be reached by counting upwards from zero. Occasionally used to mean the strictly positive whole numbers, excluding zero.
naturalistic
Imitating nature closely.
naturalistic fallacy
Phrase used by the philosopher G.E.Moore for the fallacy of supposing that the good is susceptible of definition.
necessary
could not possibly be otherwise
See also:
logical necessity
number
A kind of mathematical object on which computations are performed.
numeral
A written expression (i.e. a bit of syntax) which denotes a number, as distinct from the number itself. e.g. the numeral which denotes 45 is "45".
Analogous to the disquotional principle (concerning truth) we might put forward a disquotational principle for numerals: that "'n' denotes n" for all numerals n.
..O
ontology
a branch of metaphysics dealing with the nature of being
ontological
pertaining to ontology
ontological conception of vagueness
the theory that some vagueness is inherent in the nature of things themselves, rather than in the language we use to talk about them (see also: semantic conception of vagueness)
opaque
not permitting the transmission of light, or of enlightenment
opacity
the property of being opaque
open
undisguised, public, manifest; not exclusive or limited
open brand
a brand which is not limited to use by some particular organisation but is made generally available under terms similar to those for Open Source software.
open mind
a mind open to new ideas, lacking in prejudice, not dogmatic.
open sesame
a way of acquiring or achieving something which would not normally be possible (magic words used in The Arabian Nights)
open society
a society with wide dissemination of information and freedom of belief. See: [Popper45a/b].
open source
a software development ethos in which the product and its sources are licenced without charge under very liberal licencing conditions. See OpenSource.org.
operational
concerning methods of working
operational semantics
a semantics for a programming language, given by defining how the program should (or could) be evaluated or compiled
See also:
structured operational semantics
oracle
a person or thing regarded as infallible
(recursion theory)
the study of relative recursiveness involves reasoning about the capabilities of Turing machines equipped with an oracle capable of answering a problem the Turing machine could not otherwise have answered (e.g. an oracle for the halting problem).
see also:
FAn oracle
ordinal
of or concerning and order
ordinal number
numbers denoting position ("first", "second", "third", ...), as opposed to cardinal numbers indicating quantity ("one", "two", "three", ...).
See also:
successor ordinal
limit ordinal
overload
load excessively
overloading (computing)
a kind of polymorphism in programming languages involving the use of the same name to denote several different values or operations.
oxymoron
a figure of speech which is apparently self contradictory
..P
parameter
a value which controls the effect of some operation or procedure
parametric polymorphism
a kind of polymorphic type system in which a polymorphic function takes an (implicit or explicit) type parameter and processes in a uniform manner arguments of a polymorphic type involving a type variable which is instantiated by the type parameter.
participate
take part in
participatory democracy
a democracy in which people may participate directly in decision making processes rather than indirectly throught the election of representatives.
See also:
representative democracy
piecemeal
piece by piece, gradually
piecemeal engineering
a kind of social engineering advocated by Karl Popper.
See also:
utopian engineering
philosophy
the search for truth through reason
performative utterence
an utterence which, while appearing to make a statement, should (according to J.L.Austin) be understood as performing an action, e.g. "I promise...".
physicalism
the doctrine that physical reality is all that there is
platonism
(after Plato) the doctrine that abstract entities really do exist (often specialised to some particular domain, e.g. mathematics)
pleonasm
the use of more words than are needed to give the sense
polymorphic
Coming in various different forms, e.g. the caterpillar and the butterfly are different forms of one polymorphic insect.
polymorphic type
a generic type, usually involving a type variable, which can be instantiated to multiple specific types
polymorphic type system
a type system is polymorphic if it is possible in it to define functions which operate over more than one type of data. Such a function would have a polymorphic type.
polymorphism
the property of being polymorphic.
see also:
ad hoc polymorphism
coercion
inclusion polymorphism
overloading
parametric polymorphism
universal polymorphism
positivism
Positivist philosophy in its broadest sense is a general tendency in philosophy which embraces aspects of the thought of many philosophers including Humean scepticism, the work of Comte (who coined the term), elements of utilitarianism and pragmatism, and logical positivism. The term also has application in other disciplines, e.g. legal positivism.
predicate
that part of a sentence which affirms something of the subject of the sentence
predicate logic
a logic in which the internal structure of propositions is exposed by constructing atomic propositions from predicate applied to some subject, or relation expressed between several. By contrast with a propositional logic in which atomic propositions are not further be analysed.
predicative
formed or contained in the predicate
predicative type theory
a type theory in which objects may be defined using predicates involving quantification over some whole of which the defined object is an element
private
known only to an individual or to a select group
private language (1)
a language which can, in principle, only be understood by one person
private language (2)
a language in which it is possible for an individual to talk (or write) about things which are private to him
program (computing)
a set of instructions for a computer prescribing how some task is to be performed
programming language (computing)
a language designed for programming computers
projectivism
a projectivist theory about some domain of discourse is one which claims that statements about that domain are not objective claims about reality but are projections onto the world of feelings or other mental states of the speaker, e.g. the position of David Hume and of logical positivism about ethical statements.
proof theoretic strength
a measure of the strength of a formal logical system.
proposition
that which is expressed by a statement
propositional connective
a word used to construct a compound proposition from one or more constituent propositions, e.g. and, or, not.
propositional function
in the context of some logic, a function whose value is a proposition or a truth value, as appropriate. In classical logic, a boolean valued function. Examples include the boolean operators.
propositional logic
an elementary form of logic concerned with truth functional combinations of atomic propositions
propositional tautology
a valid formula of propositional logic
See also:
tautology
psychologism
the intrusion of psychological considerations into logic (also used similarly in relation to other disciplines)
pure
unmixed, unadulterated
pure type system (logic)
a type system presented in a systematic way devised by Henk Barendregt. This presentation is helpful (inter alia) in making clear the interpretation of these type theories as logics under the propositions-as-types interpretation.
pyrrhonism
the philosophy of Pyrrho of Elis (c300 b.c.), the ultimate scepticism
..Q
quantification
the use of a quantifier
quantifier
a linguistic construct in which an assertion is made using a variable which ranges over some domain of discourse
see also:
universal quantifier
quiddity
the essence of a person or thing
(see also: [Quine87])
quine
the verb "to quine" was coined by the tortoise in Douglas Hofstadter's Gödel, Escher, Bach [Hofstadter80] as the name of a process devised by W.V.Quine which is helpful in explaining Gödel's proof of the incompleteness of arithmetic [Gödel31]. To quine a phrase is to form a larger phrase or sentence (or nonesense) by writing the phrase first in quotation marks, and then once more without the quotation marks. In brief, to precede the phrase by its quotation.
For example, the phrase "yields falsehood when preceded by its quotation", when quined gives:
"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation
a variant of the liar paradox. This technique is used (together with gödelization) to explain Gödel's construction of a sentence of arithmetic which asserts its own unprovability.
quine corner
The symbols " " and " ", used by W.V.Quine as Gödelizing braces, are sometimes known as "quine corners". The expression formed by enclosing an expression or formula of first order arithmetic in quine corners (as in 45+7=50 ) is a "shorthand" for the Gödel numeral of the enclosed expression and therefore denotes the relevant Gödel number.
..R
range
the area over which a thing is distributed
- of a relation (in set theory) -
the set of elements or values which are related to some other element under the relation
rational
based on reason
rational number
a number which is either zero or the ratio of two non-zero whole numbers
see also:
hyper-rational
rationalist
one who emphasises the role of reason in the justification of knowledge.
real
not imaginary
real number
the limit of a convergent sequence of rationals
realism
belief in objective existence, often relative to some type of entity
recursive
involving self-reference
(in computer science and logic)
a definition of a function or procedure is recursive if it involves reference to the function or procedure being defined, i.e. if during evaluation the function or procedure may invoke itself (usually with different arguments).
recursive function (logic)
a recursive function is one which is effectively computable, whose evaluation always terminates with a result.
recursive set (logic)
a set is recursive if the question of membership in the set is effectively decidable.
recursively enumerable (logic)
a set is recursively enumerable if there is an effective procedure for enumerating the members of the set. Equivalently, if its membership question is semi-decidable.
regular
conforming to a standard, complete, thorough, absolute
regular ordinal
an ordinal is regular if it is a limit ordinal whose cofinality, cf( ), is .
rhetoric
the art of effective or persuasive speaking or writing
relation
what one person or thing has to do with another
(logic, set theory)
a correspondence between two sets (say A, B) represented by a set of ordered pairs, each containing one element from A and one from B.
reify
convert into a thing, materialise
(computing, formal methods)
to realise an abstract specification as an executable program
see also:
hypostasis
representative
consisting of elected deputies
representative democracy
a democracy in which government effected by elected representatives of the people
see also:
participatory democracy
rigid
inflexible, strict
rigid designator
a name or description which designates the same object in every possible world
nonrigid designator
a designator which is not rigid
..S
sceptic
someone inclined to doubt accepted opinions
scepticism
systematic doubt. See also: PS
See also:
pyrrhonism
second
1. a unit of time
2. coming immediately after the first, in time or in some other ordering
second order logic
a logic in which entities are typed, each type forming a domain of quantification, among which there is type of individuals and a type of second order entities (sets, properties, relations or functions of or over individuals) but no types of higher than second order.
semantic
concerning meaning
semantic conception of vagueness
the theory that vagueness originates in language and is not an objective feature of the world (see also: ontological conception of vagueness)
semantic creativity
the ability of users of a language to understand sentences which they have never previously encountered
semantic holism
the idea that the meaning of linguistic constructs is dependent on the rest of the language of which they are a part
semantic irrealism
the denial that there are any semantic facts
semantic naturalism
theories which consider natural language semantics to be definable in terms of the concepts of the natural sciences.
See also:
axiomatic semantics
denotational semantics
dynamic semantics
operational semantics
static semantics
structured operational semantics
semi-decidable
see: effectively semi-decidable
semiotics
the study of signs and symbols
set
an unstructured collection
set theory
a theory of sets, e.g. ZF.
See also:
class
skyhook
an imaginary means of suspension in the sky
solecism
a mistake of grammar or of idiom
sort
(noun)
a group of things with common attributes, a type or kind. Typically used in preference to type in the context of a first order logical system (as in "many-sorted first-order logic"). Also used by Barendregt in his pure type systems as a generic term covering types, kinds et.al.
(verb)
to rearrange a list or sequence according to a prescribed ordering relation
sound
a logic is sound with respect to its semantics if only true sentences are derivable under the inference rules from premises which are themselves all true.
speculation
formation of theories or conjectures, especially without a firm factual basis
static
unmoving or unchanging
static semantics
that aspect of the semantics of a computer programming language which is concerned with type constraints (which are usually checked by a compiler before execution of the program). Also used for similar aspects of formal specification languages, which however need not be decidable.
static type checking
a type system for a programming language allows for static type checking if it is possible to check conformance to the type constraints at compile time.
strong
powerful
strong type checking
a type system for a programming language allows for strong type checking if a type correct program will give no data type related errors during execution.
strongly rigid designator
a rigid designator of a necessary object
See also:
proof theoretic strength
structure
a set of interconnected parts of any complex thing
structured operational semantics
an operational semantics presented as an axiom system permitting the derivation of transformations over a canonical syntax
successor
something which immediately follows
successor ordinal
an ordinal number which immediately follows some other ordinal number, i.e. which is obtained by adding one to an ordinal
See also:
limit ordinal
syntax
that aspect of the study or definition of languages which concerns rules governing which constructs in a language are well-formed
synthetic
says something about the real world
..T
tautology
1. the saying of the same thing twice over in different words
2. a statement in which the predicate asserts no more than is contained in the meaning of the subject
3. an instance of a valid formula of propositional logic
4. a complex proposition which is true independently of the truth values of its constituent atomic propositions
5. a statement that is necessarily true
6. an analytic statement
see also:
propositional tautology
temporal logic
A modal logic in which one can reason about time.
TOE - Theory Of Everything
A term used for the elusive goal of the quest to unify the fundamental (but incompatible) theories of physics, viz. general relativity and quantum theory. This would supposedly yield a single coherent (and true) theory (a TOE) to which all other scientific theories would be in principle reducible (which is where the everything comes from). (e.g. string theory)
token
an instance of a type
transitive
transitive relation
a relation is transitive iff for all elements x, y and z in the field of the relation, if x is related to y and y related to z then x is related to z.
transitive set
a set s is transitive iff every member of s is a subset of s.
truth
the property of being true
Turing machine
a kind of automaton invented by the logician Alan Turing for the purpose of establishing the existence of unsolvable problems
type
a collection of things or persons having common characteristics
type checking (computing)
a stage in the compilation or interpretation of computer programs in which the conformance of the program to defined typing rules is checked.
see also:
static type checking
strong type checking
type sentence (philosophy)
Used by some philosophers to distinguish a syntactical object from its instances (which are then called tokens). This sentence might then be called a type sentence of which the instance occurring on the screen in front of you is a token.
type system (computing)
a system for classifying data values manipulated by computer programs, usually specific to a particular high level programming language
see also:
polymorphic type system
pure type system
type theory (logic)
a logical system in which the domain of discourse consists of a number of types, each of which is a collection of elements (of that type), and in which logical variables are associated with a type and range over the elements of that type.
type variable (computing and logic)
In a typed programming language or logical system a type variable is a variable which ranges over some or all of the available types.
..U
union
a whole resulting from combination of parts or members
(in set theory)
the union of two sets a and b is that set whose members are those things which are either members of a or of b (or of both)
urelement
an individual or element, in the domain of a set theory, which is not a set
universal
completely general
(philos)
that (if anything) which is referred to by general terms (e.g. virtuousness)
universal polymorphism
(after [CardelliTDP]) those kinds of polymorphism in programming languages in which a polymorphic function uses a single algorithm independent of the type of its arguments, e.g. inclusion polymorphism and parametric polymorphism.
universal characteristic (philosophy)
an english translation of Characteristica Universalis, the name given by Leibniz to his proposed universal language in which all things be expressed and which would also be universally intelligible. See: The Method of Mathematics.
universal quantifier (logic)
a variable binding construct used in a logic to express the proposition that some expression is true of every element in a domain of discourse or of a type
utopia
An imagined perfect place or state of things, e.g. The Factasian Utopia.
utopian engineering
Term used by Karl Popper in [Popper45a] for approaches to social engineering which involve first drawing a blueprint (i.e. describing the desired utopia) and then devising an implementation plan. Utopian engineering is contrasted with historicism, which is fatalistic and therefore may regard blueprints and plans as superfluous, and piecemeal engineering, which, fearful of repeating past blunders of utopian engineering, confines itself to a kind of sociological firefighting.
..V
value
values
Principles or standards, one's judgement of what is valuable or important.
value agent
A non-profit value-promoting agent in the Factasia Value Net.
value net
The economic infrastructure of Factasia.
value system
A coherent, organised collection of values, e.g. The Factasia Value System.
variable
changeable
(logic)
a name used in a formal notation, either for an unspecified value (of some particular type) (a free variable) or in a variable binding construct (such as universal quantification or lambda abstraction) (a bound variable).
see also:
type variable
verification
The process of establishing the truth of a proposition.
the verification principle
A principle of logical positivism to the effect that the meaning of a statement lies in its method of verification, and that a statement is meaningful iff it can in principle be verified.
Vienna Circle
A group of philosophical scientists and scientific philosophers which flourished in Vienna during the late 1920s and early 1930s and was the source of the philosophy of logical positivism.
virtual
Apparent, not real.
virtual brand
A brand (as in product marketing) promoted in its own right, not closely associated with tangible product. A branded vision or ideology promulgated through cyber-space.
virtual corporation
(1 - strong)
A company with few or no employees and no physical assets, possibly identified with a virtual brand.
(2 - weak)
A company which conducts a significant part of its business electronically, or which makes use of telecommuting.
virtue
Moral excellence, goodness.
vision
Imaginative insight or foresight.
..W
warrant
anything that authorises a person or an action
epistemic warrant
that which justifies a claim to knowledge
weltanschauung
a particular philosophy or view of life
..Z
Z
Zermelo Set Theory
The first axiomatisation of set theory published by Ernst Zermelo in 1908 [Zermelo08] in response to the antinomies found in informal set theory by Russell and others. Intended to provide a consistent foundation for mathematics, its consistency remains unimpeached, though it has been found necessary to augment the theory with the axiom of replacement (see ZF) to provide an adequate foundation for modern mathematics. Zermelo's system includes the axiom of choice, but the letter "Z" is now normally used to refer to his system with the axiom of choice omitted.
The Z specification language
A language developed by Jean Raymond Abrial and others at the University of Oxford, broadly similar in strength and character to Zermelo set theory (though the etymology seems uncertain), but with a much richer syntax oriented to applications in the specification of software.
ZF
Zermelo-Fraenkel set theory, an axiomatisation of set theory consisting of Zermelo set theory (see above) strengthened with the axiom of replacement, due to Abraham Fraenkel, the effect of which is to ensure that any collection of sets which can be shown to be no greater in size than an existing set is itself a set.
ZFC
Zermelo-Fraenkel set theory augmented by the axiom of choice.
..A
abstract
not tangible or concrete
abstract algebra
abstract
not tangible or concrete
abstract algebra
The generalisation of algebraic methods originally concerned with number systems to deal with arbitrary algebraic structures over arbitrary domains.
abstraction
the process or result of forming some abstract idea from a number of more particular or concrete examples
(in set theory)
The process of forming a set, typically by binding a free variable in a formula which expresses the truth condition, for membership in the set, of the value denoted by the variable. Comprehension and separation are particular kinds of set abstraction. Abstraction to properties (predicates or propositional functions) is analogous.
(functional)
Forming a function, typically by binding a free variable in an expression which denotes the value of the function for the argument whose value is denoted by the variable.
ad
the Latin preposition meaning "to" or "towards"
ad hoc
for a particular purpose. An inelegant feature in an otherwise well structured system to fix a particular problem. A hack.
ad hoc polymorphism
(after [CardelliTDP]) a kind of polymorphism in programming languages in which a function taking a polymorphic parameter will execute different code according to the type of the parameter supplied (by contrast with universal polymorphism in which the same code is used). Special cases include overloading and inclusion polymorphism.
algebra
the systematic study of number systems using symbolic formulae involving variables
see also:
abstract algebra
computer algebra
altruism
unselfishness, concern for others
analytic
(logic)
a proof which proceeds by analysis of the desired conclusion showing that it is derivable from accepted premises (from classical Greece). Such proofs are now sometimes known as a backward or goal oriented proofs.
(philosophy)
expressing a relationship between concepts. A statement or proposition which lacks empirical content and is true in virtue of its meaning.
(philosophy)
a kind of philosophy particularly concerned with logical or linguistic analysis (see: Varieties of Philosophical Analysis).
(recursion theory)
definable in second order arithmetic
anarchism
1. the doctrinal abhorrence of coercion, usually including advocacy of the abolition of the state
2. violent opposition to established authorities, especially those considered oppressive
antinomy
a brittle silvery white metalic element
(philosophy)
a paradox or contradiction
a posteriori
knowable or justifiable only on the basis of experience
a priori
knowable or justifiable prior to experience based on purely rational considerations
arithmetization
the process of translating statements or problems from their usual domain into the language of arithmetic, usually so that the methods of arithmetic or logic can be brought to bear on the problem.
arithmetization of analysis
the reduction of the theory of real numbers to that of arithmetic, accomplished by defining a real number as some aggregate of rational numbers, e.g. a Dedkind cut or a Cauchy sequence.
see also:
gödelization
axiom
in a logic or an axiomatic theory an axiom is a sentence which is accepted as true without demonstration. The axioms are the starting points for the derivations of all other theorems.
axiomatic method
a method of doing mathematics in which subject areas are presented and studied as axiomatic theories
axiomatic semantics (computing)
a semantics for a programming language given by defining axioms which permit reasoning about the effects of execution of the various parts of a program.
axiomatic theory
a mathematical (or other) theory presented as a system of axioms.
axiomatisation
The process of formalising some subject as an axiomatic theory.
..B
biconditional
a name used for the logical operator which yields a true proposition iff both its operands have the same truth value. So called because it is equivalent to the conjunction of two conditionals (implications), which is reflected by the usual symbol " ", which consists of the conditional " " overlaid in two directions.
bind
tie or fasten tightly
(in logic)
the effect of various syntactic constructs (such as quantifiers or abstractions) which bind free occurrences of variables (of a certain name), within some expression, to a binding occurrence (of that same name) associated with a binder (e.g. a quantifier). A variable free in some expression, is no longer free in the larger expression formed by binding that variable. e.g. two free occurrences of the variable "x" in the expression "x=x" are bound when the universal closure is formed yielding " x. x=x", in which there are no longer any free occurrences of "x".
bivalent
A logic is bivalent if sentences in the logic can take either of just two truth values, usually named "true" and "false" or "T" and "F".
boolean
(after George Boole) often used as if it means "two-valued" or bivalent, but in fact allows any collection of values which conforms to certain algebraic laws (i.e. is a boolean algebra). A boolean propositional logic, though it admits interpretations in which propositional variables range over more than two values, has just the same set of theorems (the propositional tautologies) as a bivalent propositional logic.
boolean operator
An operator which takes boolean arguments and returns a boolean result.
bound
set bounds to, limit
(in logic)
to limit the scope of a variable, usually by enclosing that scope in some variable binding construction which identifies the variable thus bound.
bound variable
a variable whose scope has been restricted by some variable binding construct or declaration.
..C
c
The name used in Factasia for pure combinatory logic.
calculus ratiocinator
(after Leibniz) a mechanical method of solving problems which have been expressed in a universal language known as a characteristica universalis).
casuist
a person who resolves problems of conscience or duty
cardinal
chief, fundamental
cardinal number
1. numbers denoting quantity ("one", "two", "three", ...), as opposed to ordinal numbers indicating position ("first", "second", "third", ...).
2. An equivalence class generated by the relation "same size as" obtaining when there is a one-one mapping between the elements of two sets.
3. The smallest ordinal number of some size.
see also:
large cardinal
category
a class or division
(philosophy, metaphysics)
one of the fundamental kinds of things (see: Aristotle's Categories)
(mathematics)
a kind of mathematical structure, providing in some respects a very general mathematical counterpart to the notion of a concept. A collection of objects and of morphisms (or arrows) such that each morphism has a domain and codomain which are objects, each object has an identity morphism, and morphisms compose associatively. e.g. corresponding to the mathematical concept of a group there is a category of groups which contains as objects all the groups, and as arrows between these objects the group homomorphisms.
category mistake
a favourite kind of "philosophical puzzlement" to which the Oxford philosopher Gilbert Ryle drew attention. A category mistake occurs when a speaker or writer applies a concept outside the domain in which it can meaningfully be applied (often in the course of formulating some philosophical theory).
see also:
kind
sort
type
characteristica universalis
(after Leibniz) a universal language into which any kind of problem can be translated (and then solved by calculation using a calculus ratiocinator). See: The Method of Mathematics.
class
a collection of persons or things
(logic)
sometimes used interchangeably with or instead of set, sometimes used (e.g. in NBG) for collections which are "too large" to be sets.
coerce
persuade or restrain (an unwilling person) by force
coercion (1)
the act or process of coercing
coercion (2) (computing)
the automatic conversion of a value in a computer program from one type to another as needed for the use made of the value in some particular context, e.g. the conversion of an integer to a floating point number before adding it to some other floating point number.
see also:
anarchism
cofinal
a function into an ordinal is cofinal if its range is unbounded in its codomain.
cofinality
the cofinality of an ordinal , cf( ), is the least ordinal which maps cofinally into .
cognition
knowing, perceiving or conceiving as distinct from emotion or volition.
combinator
a function primitive to or definable in pure combinatory logic
combinatory logic
a form of logic in which bound variables are not used
complex
Not simple. Not atomic. Structured.
complex number
A number formed of two parts, so called real and imaginary parts, both of which are real numbers.
computer
An electronic device which stores and processes data following instructions which are also stored in its memory (and can therefore easily be changed).
computer algebra
the use of computer programs which automate algebraic transformations, e.g. MACSYMA, Maple, Mathematica.
conjunct
One of the immediate constituent sentences of a conjunction, e.g. in "A and B" the conjuncts are "A" and "B".
conjunction
A compound sentence of the form "A and B".
constructive
constructive logic
A logic is constructive if existence proofs in the logic depend upon constructing something with the required property and may not proceed by reductio-absurdum.
contingent
Might have been otherwise.
..D
de
(latin) of or from
de dicto
an ascription of a property or modality to a proposition
de re
an ascription of a property or modality to a thing
decidable
A set is decidable iff there is an effective procedure for deciding whether any object is or is not a member of the set.
deduction
the process of reasoning from premises to conclusions which are logically entailed by those premises. The conclusions of correct deductive inferences cannot possibly be false if the premises are true. See: What is Logic?".
see also:
induction
deductive
by deduction
deductively sound
an inference is deductively sound if it is not logically possible that the premises be true and the conclusion false
definiendum
in a definition, that which is defined
definiens
the body of a definition which gives the meaning to be assigned to the definiendum
definition
a statement in which a meaning (the definiens) is assigned to a word, symbol, phrase, or expression (the definiendum)
deflation
letting the wind out
deflationary conception of truth
the view that the predicate true serves only limited purposes, such as indirect or compendious endorsement and disquotation.
democracy
a system of government involving all, or a large part, of the people governed
See also:
participatory democracy
representative democracy
denote
signify, indicate, mean, convey, name
{philosophy)
after Kripke, a distinction is sometimes made between denotation (which involves reference via a description) and naming in which reference is made without description
denotational semantics (computing)
a semantics for a programming or other language, given by defining mappings from each syntactic category into suitable semantic domains. The mappings are usually expected to be compositional, and "mathematical" semantic domains are often preferred (in which case it may be called a mathematical semantics).
deontic logic
a logic for reasoning about obligations and rights
designate
serve as the name or distinctive mark of
designator
a name or description which designates, or refers to, something
disjunct
one of the immediate constituent formulae or sentences in a disjunction, e.g. in "A or B", "A" and "B" are the disjuncts.
disjunction
a formula or sentence whose principle operator is logical (inclusive) or, e.g. "x>5 x<6"
disquotation
the removal of quotation marks, typically by the use of the predicate "is true", e.g.: "x>5 x<6" is true
disquotation principle
that "'S' is true iff S" for all sentences S
dogmatic
given to asserting or imposing personal opinions
dogmatism
a tendency to be dogmatic
dogmatist
a dogmatic person
(according to pyrrhonism and Sextus Empiricus)
someone who is not a sceptic, and is willing to assert at least one proposition to be true
domain
a sphere of control or influence
- of a function
the collection of values for which the function is defined
- of a relation (in set theory) -
the set of elements or values which relate to some other element under the relation
- in formal semantics
a collection of values which represent the meanings of a certain class of linguistic entities.
dynamic
concerning motion or change
dynamic semantics
that aspect of the semantics of a programming language which is concerned with the effects of executing the program. Also used for the non-static aspects of the semantics of formal specification languages.
..E
effective
effective procedure
An effective procedure is an unambiguous prescription for computing some function or solving a class of problems.
effectively computable
A function is effectively computable if there is an effective procedure for computing the value of the function.
effectively decidable
A class of problems, or a set, is effectively decidable if there exists an effective procedure which will determine the answer to the problem (or membership of the set) terminating with the correct answer within a finite number of steps, for all candidates.
effectively semi-decidable
A class of problems, or a set, is effectively semi-decidable if there exists an effective procedure which terminates with a positive answer whenever the answer to the problem or the membership question is positive, but which may fail to terminate in the case that the answer is negative.
empirical
based on observation or experiment
empiricist
one who emphasises the role of sensory experience or experimental evidence in the justification of knowledge.
epistemology
The theory of knowledge.
epistemic logic
A logic for reasoning about knowledge and belief.
extension
of a set
the membership of the set
of a property
the collection of things which have the property
of a function
the mapping defined by the function, as distinct from any algorithm, rule or formula used to define the function
extensional
of a set theory
A set theory is extensional when two sets are equal iff they have the same extension.
of a higher-order logic
A higher order logic is extensional when two properties or functions are equal iff they have the same extension.
..F
factasy
a genre, treading the line between fact and fantasy
factastic
an adjective used in factasia to describe some of its peculiar doctrines or methods
factastic future engineering
an approach to future engineering advocated in Factasia
FAn
local abbreviation for formal analytic.
FAn oracle
an oracle for FAn conjectures and problems
fictionalism
a doctrine which acts on certain propositions for reasons other than knowledge of or belief in the truth of the proposition, e.g. for pragmatic reasons. See: PS
fideism
a doctrine which accepts sceptical arguments for the unattainability of absolutely certain knowledge but which admits definite affirmative judgements nonetheless. See: PS
field
an area of operation or activity
of a relation (in set theory) -
the field of a relation is the set of all elements which relate to, or are related to by, some other element under the relation. The field is the union of the domain (also called the left field) and the range (also called the right field) of the relation.
first
earliest in time or in some other ordering
first order logic
predicate logic involving quantification only over individuals, not over sets properties or functions (the ordering involved here is the ordering of types of entities in terms of the logical complexity of the entities).
formal
of notations - defined with mathematical precision, machine processable
formal analytic
an analytic truth or falsehood expressed in a formal notation
formalism
a philosophy of mathematics mainly associated with the mathematician Hilbert.
foundation
the solid ground or base on which a building rests.
foundationalism
a term used in epistemology for theories of knowledge in which our knowledge of the "external" world is founded upon evidence provided by our senses. More generally, for knowledge of a certain kind of fact, the theory that this knowledge is derived from premises (often supposed indubitable) of a special kind.
franchise
a right or privilege granted to a person or corporation
free
1. not restricted or impeded, not controlled or bound
2. at no cost
free variable (logic)
a variable which is not bound
fulfil
of self - develop and exploit one's gifts and character to the full.
function
Something which determines for each of a number of possible values for arguments (to the function) a specific value which is the result of the function for that argument.
(in set theory)
a many-one relation (which is sometimes called the graph of the function)
(in computing or constructive mathematics)
an expression or rule which shows how the value of a function may be computed, or is otherwise determined by, the value of the argument to the function.
future
that which is yet to come, what will be
future engineering
the engineering of the future
..G
generalization
A general proposition obtained by inference from particular cases.
(in deductive logic)
An inference from a proposition about an unspecified individual (as a free variable) to a universally quantified proposition. The rule which permits such inferences.
Gödelization
A technique for encoding the formulae of arithmetic as numbers used by Kurt Gödel in his incompleteness proofs [Gödel31].
see also:
arithmetization (Gödelization is a technique for the arithmetization of logical syntax)
Gödel number
A number assigned to some syntactic entity by Gödelization.
Gödel numbering
see Gödelization
groupware
Software which facilitates collaboration.
..H
hack
cut or chop roughly, mangle
(Computing, 1)
to write a program hastily with little concern for elegance and structure
(Computing 2)
to attempt to gain unauthorised access to computer systems, usually through electronic networks
hacker
Someone who hacks.
The connotations of this term vary widely depending on who is using it. In the tradition now associated with the "open source" movement (which credits itself as the main source of the software infrastructure for the internet) a hacker is a hero who has made significant contributions to the development of open source software. In other milieu the term may be associated with over hasty and poorly engineered software development. In the popular press the term has been primarily associated with the practice of attempting illegally to penetrate computer systems and networks (i.e. nothing much to do with software development). A vigorous campaign by open source advocates to dissuade the press from this usage has had some marginal success (so small that I can't bring to mind the term which they are supposed to use instead).
halting problem
the problem of deciding for an arbitrary Turing machine and initial configuration (tape + position on tape + initial state) whether the Turing machine started in that configuration would ever halt.
historicism
This term was coined by Karl Popper as a label for those kinds of social philosophy which engage in sweeping historical prophesy and assert the inevitability of the prophesied course of history.
HOL
Higher Order Logic (1)
A logical system, usually a Type Theory, with multiple ranges of quantification (usually called types) some of which contain sets or functions. See also: Church's Simple Theory of Types, Pure Type Systems
Higher Order Logic (2)
A proof tool, originally developed by the Hardware Verification Group at The University of Cambridge Computer Laboratories. Now available as several variants (HOL88, HOL90, HOL98, HOL Light), supporting the construction and checking of proofs in Higher Order Logic. There are also many more proof tools for variants of Higher Order Logic or for logical Type Theories which do not go under the name "HOL". There is an annual international workshop concerned with the development and application of these proof tools.
hyper-rational
An exacting standard of rationality based on the assertion only of formally proven analytic propositions.
hypostasis
an underlying substance, as opposed to an attribute or that which is insubstantial
hypostatise
reify, possibly fallaciously
..I
I
In combinatory logic, the identity combinator, a function which, when applied to some value always returns that same value.
I = x. x
iff
if and only if
impredicative
not predicative
include
A includes B if everything in B is also in A
inclusion polymorphism
a kind of polymorphism found in the type systems of object oriented programming languages in which some types are included in others. A type of object consisting of multiple named components would typically include the types whose objects have the same set of named components together with some additional components.
induction
(mathematical)
a method of proving a general truth affirming that every one of a set of mathematical objects (e.g. the natural numbers) has a certain property (e.g. has exactly one prime factorisation). The method depends upon their being a systematic way of constructing all the elements of the set by starting with one of a finite set of basis elements and repeatedly applying a finite number of constructions (for the natural numbers the basis is the number 0, and the method of construction is addition of 1). An inductive proof then consists of a proof that the basis elements each have the required property and a proof that the construction, when applied to elements having the property, will yield an element also having the property. Mathematical induction is in fact a kind of deduction. It is also called structural induction.
(scientific)
scientific induction is the process of concluding empirical generalisations from particular instances, where this is not deductively sound because not all possible instances are premises
intersection
where two things lie across each other
(in set theory)
the intersection of two sets a and b is that set whose members are those things which are members both of a and of b
intuitionism
a position in the Philosophy of Mathematics mainly associated with L.E.J.Brouwer
intension
the meaning or internal content of a concept, as contrasted with its extension
the strenuous exertion of the mind or will
intensional
of a logic
not extensional
of an act
intended
intention
thing intended
intentional
intended
in error, or perhaps correctly in American English: intensional
intentional stance
the attempt to understand an artefact by second guessing the intentions of its designer [[Dennett95] ch.9 p.229]
intentional systems
Systems whose behaviour can be - at least sometimes - explained and predicted by relying on ascriptions to the system of beliefs and desires (and hopes, fears, intentions, hunches,...). [also from Dennett]
..J
judgement
The critical faculty whereby we assess the truth of claims, an application of, or the result of applying this faculty.
in formal logic
in some formal logics the theorems of the system are called judgements and there may be a single form of judgement (as in Frege's Begriffsschrift, where a judgement always takes the form of the assertion, using a vertical bar, of a content formed using a horizontal bar), or multiple forms (as, for example, in the contructive type theories of Per Martin Löf).
justify
Show the justice or rightness of.
justification
that which justifies (or warrant's)
in epistemology
knowledge may be explained or defined as "justified true belief", in which case the question what (if anything) counts as justification of a claim to knowledge becomes a central problem
..K
K
(combinatory logic)
the constant combinator. A function which, when applied to some value, yields a constant function which always returns that value.
K = x y. x
kind
considerate, generous, affectionate
Class, type, sort, variety.
(logic)
a polymorphic logical type theory which has operations over types may have a second tier of typing in which types and operators over them are assigned to kinds.
knowledge
justified true belief
..L
lambda
the greek letter
lambda abstraction
a syntactic construct denoting a function, beginning with the lambda symbol which binds a variable in an expression which denotes the value of the function for the argument whose value is denoted by the variable, e.g. " x. x*x" is a lambda expression denoting the square function.
lambda calculus
a notation and calculus involving lambda abstraction, widely used logic and in theoretical computer science
large cardinal
a cardinal number at least as large as the first strongly inaccessible cardinal
limit
that beyond which something may not pass
(in mathematics)
a quantity which the value of a function or sequence or the sum of a series approaches arbitrarily closely
limit ordinal
an ordinal number which is not a successor ordinal
logic
As a subject
The study of reasoning
a logic
a (usually formal) system encoding principles of reasoning.
logical atomism
A philosophical position associated with Bertrand Russell and Ludwig Wittgenstein involving logical analysis of propositions into atomic propositions and their correspondence with the structure of reality (in the form of facts).
logical construction
A method (advocated by Bertrand Russell and originating in his philosophy of mathematics) permitting parsimonious ontologists to maximise their use of Occam's razor by "logically constructing" entities as complexes of simpler things to which one is already committed. Most notoriously, of physical objects from sense data
logical necessity
A proposition is logically necessary if it is true in all possible worlds.
logical positivism
The name adopted by the Vienna Circle (including Rudolf Carnap and Alfred Ayer) for their philosophical position, most famous for introducing the verification principle as a criterion for meaning of synthetic propositions, and for dismissing metaphysics as meaningless
..M
meaning
what is meant by, or the significance or importance of, a word, sentence or event
meaning-truth platitude
the principle that the truth value of a statement depends only on its meaning and the state of the world in certain respects
means
What it takes to realise some end. Maybe material or intellectual resources, maybe methods.
mechanisation
arranging to be accomplished by machinery (possibly by computers or calculators)
mechanisation of mathematics
The automation of mathematical methods, usually by programming digital computers.
metaphysics
that branch of philosophy which is concerned with ontology and other a priori aspects of the nature of the universe
meme
a unit of cultural transmission or of imitation (coined by Richard Dawkins in The Selfish Gene [Dawkins89] ).
memetics
the science (or pseudo science) of memes.
memetic future engineering
the use of memetics in future engineering
method
A prescription, recipe or algorithm describing how to achieve some purpose or end.
modal
(philosophy)
concerning possibility, impossibility, necessity or contingency
modal logic
a diverse family of logics involving modal operators, usually rendered and . The original interpretation of these symbols was for "necessarily" and "possibly" respectively, but other applications of modal logics have introduced alternative interpretations, e.g. in relation to time (always, sometime), provability (provable, consistent), and knowledge (know, believe).
model
a representation of something, possibly smaller (scale model), simplified, made more precise (mathematical model), or idealised.
(of a first order theory)
A model of a first order theory is an interpretation of the language of the theory which satisfies all the non-logical axioms of the theory.
(mathematical)
An abstract model, defined with mathematical precision, of some thing or phenomenon, which may be used to reason about or calculate its behaviour. Often used in engineering design to ensure that a design will fulfill its intended purpose.
model theory
A major branch of mathematical logic which studies the models of first order theories.
..N
natural
existing in, or caused by, nature
natural meaning
the meaning or significance of some natural entity or phenomenon
non-natural meaning
the meaning of words and sentences
natural number
The non-negative whole numbers, zero and those numbers which can be reached by counting upwards from zero. Occasionally used to mean the strictly positive whole numbers, excluding zero.
naturalistic
Imitating nature closely.
naturalistic fallacy
Phrase used by the philosopher G.E.Moore for the fallacy of supposing that the good is susceptible of definition.
necessary
could not possibly be otherwise
See also:
logical necessity
number
A kind of mathematical object on which computations are performed.
numeral
A written expression (i.e. a bit of syntax) which denotes a number, as distinct from the number itself. e.g. the numeral which denotes 45 is "45".
Analogous to the disquotional principle (concerning truth) we might put forward a disquotational principle for numerals: that "'n' denotes n" for all numerals n.
..O
ontology
a branch of metaphysics dealing with the nature of being
ontological
pertaining to ontology
ontological conception of vagueness
the theory that some vagueness is inherent in the nature of things themselves, rather than in the language we use to talk about them (see also: semantic conception of vagueness)
opaque
not permitting the transmission of light, or of enlightenment
opacity
the property of being opaque
open
undisguised, public, manifest; not exclusive or limited
open brand
a brand which is not limited to use by some particular organisation but is made generally available under terms similar to those for Open Source software.
open mind
a mind open to new ideas, lacking in prejudice, not dogmatic.
open sesame
a way of acquiring or achieving something which would not normally be possible (magic words used in The Arabian Nights)
open society
a society with wide dissemination of information and freedom of belief. See: [Popper45a/b].
open source
a software development ethos in which the product and its sources are licenced without charge under very liberal licencing conditions. See OpenSource.org.
operational
concerning methods of working
operational semantics
a semantics for a programming language, given by defining how the program should (or could) be evaluated or compiled
See also:
structured operational semantics
oracle
a person or thing regarded as infallible
(recursion theory)
the study of relative recursiveness involves reasoning about the capabilities of Turing machines equipped with an oracle capable of answering a problem the Turing machine could not otherwise have answered (e.g. an oracle for the halting problem).
see also:
FAn oracle
ordinal
of or concerning and order
ordinal number
numbers denoting position ("first", "second", "third", ...), as opposed to cardinal numbers indicating quantity ("one", "two", "three", ...).
See also:
successor ordinal
limit ordinal
overload
load excessively
overloading (computing)
a kind of polymorphism in programming languages involving the use of the same name to denote several different values or operations.
oxymoron
a figure of speech which is apparently self contradictory
..P
parameter
a value which controls the effect of some operation or procedure
parametric polymorphism
a kind of polymorphic type system in which a polymorphic function takes an (implicit or explicit) type parameter and processes in a uniform manner arguments of a polymorphic type involving a type variable which is instantiated by the type parameter.
participate
take part in
participatory democracy
a democracy in which people may participate directly in decision making processes rather than indirectly throught the election of representatives.
See also:
representative democracy
piecemeal
piece by piece, gradually
piecemeal engineering
a kind of social engineering advocated by Karl Popper.
See also:
utopian engineering
philosophy
the search for truth through reason
performative utterence
an utterence which, while appearing to make a statement, should (according to J.L.Austin) be understood as performing an action, e.g. "I promise...".
physicalism
the doctrine that physical reality is all that there is
platonism
(after Plato) the doctrine that abstract entities really do exist (often specialised to some particular domain, e.g. mathematics)
pleonasm
the use of more words than are needed to give the sense
polymorphic
Coming in various different forms, e.g. the caterpillar and the butterfly are different forms of one polymorphic insect.
polymorphic type
a generic type, usually involving a type variable, which can be instantiated to multiple specific types
polymorphic type system
a type system is polymorphic if it is possible in it to define functions which operate over more than one type of data. Such a function would have a polymorphic type.
polymorphism
the property of being polymorphic.
see also:
ad hoc polymorphism
coercion
inclusion polymorphism
overloading
parametric polymorphism
universal polymorphism
positivism
Positivist philosophy in its broadest sense is a general tendency in philosophy which embraces aspects of the thought of many philosophers including Humean scepticism, the work of Comte (who coined the term), elements of utilitarianism and pragmatism, and logical positivism. The term also has application in other disciplines, e.g. legal positivism.
predicate
that part of a sentence which affirms something of the subject of the sentence
predicate logic
a logic in which the internal structure of propositions is exposed by constructing atomic propositions from predicate applied to some subject, or relation expressed between several. By contrast with a propositional logic in which atomic propositions are not further be analysed.
predicative
formed or contained in the predicate
predicative type theory
a type theory in which objects may be defined using predicates involving quantification over some whole of which the defined object is an element
private
known only to an individual or to a select group
private language (1)
a language which can, in principle, only be understood by one person
private language (2)
a language in which it is possible for an individual to talk (or write) about things which are private to him
program (computing)
a set of instructions for a computer prescribing how some task is to be performed
programming language (computing)
a language designed for programming computers
projectivism
a projectivist theory about some domain of discourse is one which claims that statements about that domain are not objective claims about reality but are projections onto the world of feelings or other mental states of the speaker, e.g. the position of David Hume and of logical positivism about ethical statements.
proof theoretic strength
a measure of the strength of a formal logical system.
proposition
that which is expressed by a statement
propositional connective
a word used to construct a compound proposition from one or more constituent propositions, e.g. and, or, not.
propositional function
in the context of some logic, a function whose value is a proposition or a truth value, as appropriate. In classical logic, a boolean valued function. Examples include the boolean operators.
propositional logic
an elementary form of logic concerned with truth functional combinations of atomic propositions
propositional tautology
a valid formula of propositional logic
See also:
tautology
psychologism
the intrusion of psychological considerations into logic (also used similarly in relation to other disciplines)
pure
unmixed, unadulterated
pure type system (logic)
a type system presented in a systematic way devised by Henk Barendregt. This presentation is helpful (inter alia) in making clear the interpretation of these type theories as logics under the propositions-as-types interpretation.
pyrrhonism
the philosophy of Pyrrho of Elis (c300 b.c.), the ultimate scepticism
..Q
quantification
the use of a quantifier
quantifier
a linguistic construct in which an assertion is made using a variable which ranges over some domain of discourse
see also:
universal quantifier
quiddity
the essence of a person or thing
(see also: [Quine87])
quine
the verb "to quine" was coined by the tortoise in Douglas Hofstadter's Gödel, Escher, Bach [Hofstadter80] as the name of a process devised by W.V.Quine which is helpful in explaining Gödel's proof of the incompleteness of arithmetic [Gödel31]. To quine a phrase is to form a larger phrase or sentence (or nonesense) by writing the phrase first in quotation marks, and then once more without the quotation marks. In brief, to precede the phrase by its quotation.
For example, the phrase "yields falsehood when preceded by its quotation", when quined gives:
"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation
a variant of the liar paradox. This technique is used (together with gödelization) to explain Gödel's construction of a sentence of arithmetic which asserts its own unprovability.
quine corner
The symbols " " and " ", used by W.V.Quine as Gödelizing braces, are sometimes known as "quine corners". The expression formed by enclosing an expression or formula of first order arithmetic in quine corners (as in 45+7=50 ) is a "shorthand" for the Gödel numeral of the enclosed expression and therefore denotes the relevant Gödel number.
..R
range
the area over which a thing is distributed
- of a relation (in set theory) -
the set of elements or values which are related to some other element under the relation
rational
based on reason
rational number
a number which is either zero or the ratio of two non-zero whole numbers
see also:
hyper-rational
rationalist
one who emphasises the role of reason in the justification of knowledge.
real
not imaginary
real number
the limit of a convergent sequence of rationals
realism
belief in objective existence, often relative to some type of entity
recursive
involving self-reference
(in computer science and logic)
a definition of a function or procedure is recursive if it involves reference to the function or procedure being defined, i.e. if during evaluation the function or procedure may invoke itself (usually with different arguments).
recursive function (logic)
a recursive function is one which is effectively computable, whose evaluation always terminates with a result.
recursive set (logic)
a set is recursive if the question of membership in the set is effectively decidable.
recursively enumerable (logic)
a set is recursively enumerable if there is an effective procedure for enumerating the members of the set. Equivalently, if its membership question is semi-decidable.
regular
conforming to a standard, complete, thorough, absolute
regular ordinal
an ordinal is regular if it is a limit ordinal whose cofinality, cf( ), is .
rhetoric
the art of effective or persuasive speaking or writing
relation
what one person or thing has to do with another
(logic, set theory)
a correspondence between two sets (say A, B) represented by a set of ordered pairs, each containing one element from A and one from B.
reify
convert into a thing, materialise
(computing, formal methods)
to realise an abstract specification as an executable program
see also:
hypostasis
representative
consisting of elected deputies
representative democracy
a democracy in which government effected by elected representatives of the people
see also:
participatory democracy
rigid
inflexible, strict
rigid designator
a name or description which designates the same object in every possible world
nonrigid designator
a designator which is not rigid
..S
sceptic
someone inclined to doubt accepted opinions
scepticism
systematic doubt. See also: PS
See also:
pyrrhonism
second
1. a unit of time
2. coming immediately after the first, in time or in some other ordering
second order logic
a logic in which entities are typed, each type forming a domain of quantification, among which there is type of individuals and a type of second order entities (sets, properties, relations or functions of or over individuals) but no types of higher than second order.
semantic
concerning meaning
semantic conception of vagueness
the theory that vagueness originates in language and is not an objective feature of the world (see also: ontological conception of vagueness)
semantic creativity
the ability of users of a language to understand sentences which they have never previously encountered
semantic holism
the idea that the meaning of linguistic constructs is dependent on the rest of the language of which they are a part
semantic irrealism
the denial that there are any semantic facts
semantic naturalism
theories which consider natural language semantics to be definable in terms of the concepts of the natural sciences.
See also:
axiomatic semantics
denotational semantics
dynamic semantics
operational semantics
static semantics
structured operational semantics
semi-decidable
see: effectively semi-decidable
semiotics
the study of signs and symbols
set
an unstructured collection
set theory
a theory of sets, e.g. ZF.
See also:
class
skyhook
an imaginary means of suspension in the sky
solecism
a mistake of grammar or of idiom
sort
(noun)
a group of things with common attributes, a type or kind. Typically used in preference to type in the context of a first order logical system (as in "many-sorted first-order logic"). Also used by Barendregt in his pure type systems as a generic term covering types, kinds et.al.
(verb)
to rearrange a list or sequence according to a prescribed ordering relation
sound
a logic is sound with respect to its semantics if only true sentences are derivable under the inference rules from premises which are themselves all true.
speculation
formation of theories or conjectures, especially without a firm factual basis
static
unmoving or unchanging
static semantics
that aspect of the semantics of a computer programming language which is concerned with type constraints (which are usually checked by a compiler before execution of the program). Also used for similar aspects of formal specification languages, which however need not be decidable.
static type checking
a type system for a programming language allows for static type checking if it is possible to check conformance to the type constraints at compile time.
strong
powerful
strong type checking
a type system for a programming language allows for strong type checking if a type correct program will give no data type related errors during execution.
strongly rigid designator
a rigid designator of a necessary object
See also:
proof theoretic strength
structure
a set of interconnected parts of any complex thing
structured operational semantics
an operational semantics presented as an axiom system permitting the derivation of transformations over a canonical syntax
successor
something which immediately follows
successor ordinal
an ordinal number which immediately follows some other ordinal number, i.e. which is obtained by adding one to an ordinal
See also:
limit ordinal
syntax
that aspect of the study or definition of languages which concerns rules governing which constructs in a language are well-formed
synthetic
says something about the real world
..T
tautology
1. the saying of the same thing twice over in different words
2. a statement in which the predicate asserts no more than is contained in the meaning of the subject
3. an instance of a valid formula of propositional logic
4. a complex proposition which is true independently of the truth values of its constituent atomic propositions
5. a statement that is necessarily true
6. an analytic statement
see also:
propositional tautology
temporal logic
A modal logic in which one can reason about time.
TOE - Theory Of Everything
A term used for the elusive goal of the quest to unify the fundamental (but incompatible) theories of physics, viz. general relativity and quantum theory. This would supposedly yield a single coherent (and true) theory (a TOE) to which all other scientific theories would be in principle reducible (which is where the everything comes from). (e.g. string theory)
token
an instance of a type
transitive
transitive relation
a relation is transitive iff for all elements x, y and z in the field of the relation, if x is related to y and y related to z then x is related to z.
transitive set
a set s is transitive iff every member of s is a subset of s.
truth
the property of being true
Turing machine
a kind of automaton invented by the logician Alan Turing for the purpose of establishing the existence of unsolvable problems
type
a collection of things or persons having common characteristics
type checking (computing)
a stage in the compilation or interpretation of computer programs in which the conformance of the program to defined typing rules is checked.
see also:
static type checking
strong type checking
type sentence (philosophy)
Used by some philosophers to distinguish a syntactical object from its instances (which are then called tokens). This sentence might then be called a type sentence of which the instance occurring on the screen in front of you is a token.
type system (computing)
a system for classifying data values manipulated by computer programs, usually specific to a particular high level programming language
see also:
polymorphic type system
pure type system
type theory (logic)
a logical system in which the domain of discourse consists of a number of types, each of which is a collection of elements (of that type), and in which logical variables are associated with a type and range over the elements of that type.
type variable (computing and logic)
In a typed programming language or logical system a type variable is a variable which ranges over some or all of the available types.
..U
union
a whole resulting from combination of parts or members
(in set theory)
the union of two sets a and b is that set whose members are those things which are either members of a or of b (or of both)
urelement
an individual or element, in the domain of a set theory, which is not a set
universal
completely general
(philos)
that (if anything) which is referred to by general terms (e.g. virtuousness)
universal polymorphism
(after [CardelliTDP]) those kinds of polymorphism in programming languages in which a polymorphic function uses a single algorithm independent of the type of its arguments, e.g. inclusion polymorphism and parametric polymorphism.
universal characteristic (philosophy)
an english translation of Characteristica Universalis, the name given by Leibniz to his proposed universal language in which all things be expressed and which would also be universally intelligible. See: The Method of Mathematics.
universal quantifier (logic)
a variable binding construct used in a logic to express the proposition that some expression is true of every element in a domain of discourse or of a type
utopia
An imagined perfect place or state of things, e.g. The Factasian Utopia.
utopian engineering
Term used by Karl Popper in [Popper45a] for approaches to social engineering which involve first drawing a blueprint (i.e. describing the desired utopia) and then devising an implementation plan. Utopian engineering is contrasted with historicism, which is fatalistic and therefore may regard blueprints and plans as superfluous, and piecemeal engineering, which, fearful of repeating past blunders of utopian engineering, confines itself to a kind of sociological firefighting.
..V
value
values
Principles or standards, one's judgement of what is valuable or important.
value agent
A non-profit value-promoting agent in the Factasia Value Net.
value net
The economic infrastructure of Factasia.
value system
A coherent, organised collection of values, e.g. The Factasia Value System.
variable
changeable
(logic)
a name used in a formal notation, either for an unspecified value (of some particular type) (a free variable) or in a variable binding construct (such as universal quantification or lambda abstraction) (a bound variable).
see also:
type variable
verification
The process of establishing the truth of a proposition.
the verification principle
A principle of logical positivism to the effect that the meaning of a statement lies in its method of verification, and that a statement is meaningful iff it can in principle be verified.
Vienna Circle
A group of philosophical scientists and scientific philosophers which flourished in Vienna during the late 1920s and early 1930s and was the source of the philosophy of logical positivism.
virtual
Apparent, not real.
virtual brand
A brand (as in product marketing) promoted in its own right, not closely associated with tangible product. A branded vision or ideology promulgated through cyber-space.
virtual corporation
(1 - strong)
A company with few or no employees and no physical assets, possibly identified with a virtual brand.
(2 - weak)
A company which conducts a significant part of its business electronically, or which makes use of telecommuting.
virtue
Moral excellence, goodness.
vision
Imaginative insight or foresight.
..W
warrant
anything that authorises a person or an action
epistemic warrant
that which justifies a claim to knowledge
weltanschauung
a particular philosophy or view of life
..Z
Z
Zermelo Set Theory
The first axiomatisation of set theory published by Ernst Zermelo in 1908 [Zermelo08] in response to the antinomies found in informal set theory by Russell and others. Intended to provide a consistent foundation for mathematics, its consistency remains unimpeached, though it has been found necessary to augment the theory with the axiom of replacement (see ZF) to provide an adequate foundation for modern mathematics. Zermelo's system includes the axiom of choice, but the letter "Z" is now normally used to refer to his system with the axiom of choice omitted.
The Z specification language
A language developed by Jean Raymond Abrial and others at the University of Oxford, broadly similar in strength and character to Zermelo set theory (though the etymology seems uncertain), but with a much richer syntax oriented to applications in the specification of software.
ZF
Zermelo-Fraenkel set theory, an axiomatisation of set theory consisting of Zermelo set theory (see above) strengthened with the axiom of replacement, due to Abraham Fraenkel, the effect of which is to ensure that any collection of sets which can be shown to be no greater in size than an existing set is itself a set.
ZFC
Zermelo-Fraenkel set theory augmented by the axiom of choice.
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