## diagonal procedure

## Barcan formula

## Barcan formula Quick reference

### The Oxford Dictionary of Philosophy (3 ed.)

...formula A fundamental thesis in quantified modal logic, first isolated by the 20th-century American philosopher Ruth Barcan Marcus . It was originally the schema that ◊(∃ x )A x strictly implies (∃ x )◊A x (informally: if possibly something is A, then something is possibly A). Adding this to a standard modal logic is equivalent to adding ◊(∃ x )A x → (∃ x )◊A x or (∀ x )□ F x → □(∀ x )F x , and either of these may be called the Barcan formula. Informally the latter means that if everything is necessarily F, then necessarily everything is F. The...

## logical laws Reference library

### The Oxford Companion to Philosophy (2 ed.)

...x ) –( Fx . – Fx ) ‘For any x , it is not the case that x is F and x is not F ’In propositional calculus the law of identity is:( p → p ), ‘If p then p ’in predicate calculus:(∀ x ) ( Fx → Fx ), ‘For any x , if x is F then x is F ’in predicate calculus with identity:(∀ x ) ( x = x ), ‘For any x , x is x ’in modal predicate calculus with identity:□(∀ x ) ( x = x ), ‘Necessarily, for any x , x is x ’In propositional calculus the law of excluded middle is: p ∨ – p , ‘Either p or not p ’in predicate calculus:(∀ x ) ( Fx ...

## Marcus, Ruth Charlotte Barcan (1921–) Reference library

### The Dictionary of Modern American Philosophers

...as in the case of 9 and “the number of planets”) between two interpretations of the initial premises. The first is: (x is a mathematician → x is rational) & ~ (x is a mathematician →x is two-legged) [where “~” is the negation operator (“not”)]? (x is a bicyclist →x is two-legged) & ~ (x is a bicyclist →x is rational)While the second is: x is a mathematician → ( x is rational & ~ x is two-legged) x is a bicyclist → ( x is two-legged & ~ x is rational) On the first interpretation, the premises are true but are not sufficient in QML to generate the...

## Baconthorpe, John (c.1290–c.1348) Reference library

### The Continuum Encyclopedia of British Philosophy

...those he wills and judges to be saved. Besides Peter Auriol , Baconthorpe also criticizes certain views of Thomas Wylton and Thomas Bradwardine . He criticizes Wylton's view that in the consequence ‘God knows that X will exist; therefore X will exist’ the antecedent (‘God knows that X will exist’) is necessary, but the consequent (‘X will exist’) is contingent. Moreover, in his quaestiones canonicae , Baconthorpe attacks Bradwardine's claim that it is impossible from the viewpoint of God's ordained power ( de potentia Dei ordinata ) that future events...

## Butchvarov, Panayot Krustev (1933–) Reference library

### The Dictionary of Modern American Philosophers

...is the work on identity, elaborated in Being Qua Being . Butchvarov focuses on the problem of accounting for the apparent distinctness of material identicals. Genuine informative identity statements of the form a = b , in contrast to mere instances of the law of identity ( x )( x = x ), are always about things that are presented as two but, when the statement is true, are in fact one. He understands such identity in terms of two objects – in effect, intentional objects, though not necessarily actually intended by anyone – being one entity ....

## Donnellan, Keith Sedgwick (1931–) Reference library

### The Dictionary of Modern American Philosophers

...like “the present king of France is bald” should be analyzed as “There exists one and only one entity x that is the present king of France, and x is bald.” Donnellan argues that in natural languages, there are actually two different kinds of uses of definite descriptions. Russell’s analysis picks out the “attributive” use of definite descriptions. When we use a definite description (“the F ”) this way, we mean to make statements about the unique entity x that is F . However, Donnellan notes that we also sometimes use definite descriptions “referentially”...

## Copi, Irving Marmer (1917–2002) Reference library

### The Dictionary of Modern American Philosophers

...Dame Journal of Formal Logic 12 (1971): 454–8. Fang, Joong, “ The ‘User-hostile’ Logic: ‘Logic’ versus ‘Illogic’, ” Philosophia Mathematica 2 (1987): 77–109. Johnson, Frederick A. “ Copi’s Method of Induction, ” Notre Dame Journal of Formal Logic 20 (1979): 295–300. Leblanc, Hughes “ Minding Ones X’s and Y’s, ” Logique et Analyse 8 (1965): 207–8. Peirce, Charles S. “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic,” Memoirs of the American Academy 9 (1870):...

## Thomson, Judith Jarvis (1929–) Reference library

### The Dictionary of Modern American Philosophers

...– the situation with “good” is more extreme than the situation with “big.” In the latter case, a statement of the form “X is big” uniformly permits expansion into a statement of the form “X is a big F.” Not so for “good.” Sometimes a statement of the form “X is good” permits this sort of expansion. But sometimes it does not, permitting instead expansion to “X is good at doing F” or “X is good for F-ing” or “X is good to Fs” or “X is good with Fs” and perhaps others. Thomson summarizes these points in the slogan: all goodness is goodness in a way, and goes...

## Fogelin, Robert John (1932–) Reference library

### The Dictionary of Modern American Philosophers

...“X knows that the king is in check” is broken down into the warrant-carrying operator “X knows that” and the statement “The king is in check.” The warrant component then can be given precise analysis, to be determined by the particular subject matter. On the account of “knows that” which Fogelin offers, the full analysis in this case yields “X commands adequate grounds for the statement: ‘The king is in check’.” The knowledge claim is true or false depending on whether X in fact has such grounds for the statement. Similar analyses can be provided for “X sees...

## Tarski, Alfred (1901–83) Reference library

### The Dictionary of Modern American Philosophers

...languages, in collaboration with Robert Lawson Vaught in their “Arithmetical Extensions of Relational Systems,” was published in 1956 . The chief criteria for this definition were formal correctness and material adequacy. Formally it is required that (∀ x ) True ( x ) if and only if φ( x ), where “True” does not occur in φ, and the definition meets the requirement for material adequacy when we have φ( s ) if and only if ψ where s is the name of a sentence S of the language L and ψ is a copy of S in the metalanguage M for S . Tarski...

## Relativism Reference library

### The Continuum Encyclopedia of British Philosophy

...Relativism is not one doctrine but many. Different forms of relativism can be categorized with the help of the schema: X is relative to Y. For instance, epistemic relativism replaces X with knowledge or justification, ontological relativism with world, facts or objects, semantic relativism with meaning or truth , and moral relativism with virtues, values or norms. The position of Y has been given to the individual ( Protagorean relativism), culture, frameworks, historical periods or the human species. It is widely believed that most forms...

## logic Reference library

### The Continuum Encyclopedia of British Philosophy

...goes across, such as the distributive law, x ¥ ( y + z ) = ( x ¥ y ) + ( x ¥ y ) , but some new laws hold in this domain that fail in arithmetic – for example, x ¥ x = x , which Boole took to be characteristic of this non-numerical algebra. By algebraic manipulation, one may resolve logical inferences. Boole was prepared to pass through a sequence of manipulations in which the interim ones may have no well-specified meaning. To say that all X are Y is the same as saying that no X is non-Y , which Boole writes as x (1 − y ) = 0. Here ‘1’ stands for the...

## Jones, William Thomas (1910–98) Reference library

### The Dictionary of Modern American Philosophers

...the interested novice. His approach insists upon placing philosophical theories in their appropriate cultural contexts, but is guided throughout by his conviction that “nothing takes the place of a direct, patient, and painstaking study of a great and subtle mind” (1975, vol. 1, p. x). Jones’s History was an immediate success, rapidly adopted as required reading in history of philosophy curricula at many universities. It has sold hundreds of thousands of copies to date, and is still in wide use. In The Romantic Syndrome , Jones develops a methodology to...

## Aune, Bruce Arthur (1933–) Reference library

### The Dictionary of Modern American Philosophers

...on issues in epistemology and philosophy of mind. His article, “Hypotheticals and ‘Can': Another Look,” (1967), and his contribution, “Can,” to the Encyclopedia of Philosophy (1967) have both played major roles in the philosophical literature exploring analyses of “S can do X.” In the 1970s, Aune's interests broadened to include Kant, leading to a book, Kant's Theory of Morals (1980), and a teaching interest that he maintained until his retirement. Aune is also interested in a variety of issues in ontology, in which he maintains a broadly nominalist...

## Skyrms, Brian (1938–) Reference library

### The Dictionary of Modern American Philosophers

...” Journal of Philosophy 79 (1982): 695–711. “ Dynamic Coherence and Probability Kinematics, ” Philosophy of Science 54 (1987): 1–20. “ Carnapian Inductive Logic for Markov Chains, ” Erkenntnis 35 (1991): 439–60. Ed. with Wolfgang Spohn and Bas van Fraassen , Existence and Explanation: Essays Presented in Honor of Karel Lambert (Dordrecht, 1991). “ Sex and Justice, ” Journal of Philosophy 91 (1994): 305–20. “ The Structure of Radical Probabilism, ” Erkenntnis 45 (1997): 285–97. “ Subjunctive Conditionals and Revealed Preference ” Philosophy...

## mathematics, philosophy of Reference library

### The Continuum Encyclopedia of British Philosophy

...correspond to the symbol standing for the unknown ( x ), and still less how, in an expression with several unknowns, the idea corresponding to x should differ from the idea corresponding to y . With algebraic notation we can draw inferences simply by manipulating the symbols correctly, without having any idea in mind that would give those symbols meaning. The notation itself suggests speculations that go beyond the available stock of ideas. Thus the modern notation for exponents, x y , originally meant ‘ x multiplied by itself y times’, but given this...

## Harrod, Roy Forbes (1900–78) Reference library

### The Continuum Encyclopedia of British Philosophy

...future concomitance of a proposition X with property A given a number of past observations of the same concomitance is high (probability is defined in terms of logical frequency, that is as the ‘proportion of times that the conclusion from evidence of a certain character is true’, Foundations of Inductive Logic , p. 241). The argument runs by means of an analogy of a traveller walking on a continuous extent of unknown length (a desert, for instance): the traveller's hypothesis that the extent continues for at least 1/ x th of the time he has already been on...

## Hanson, Norwood Russell (1924–67) Reference library

### The Dictionary of Modern American Philosophers

...same data, though their eyesight is normal and they are visually aware of the same object” (1958, p. 4). Appealing to both gestalt optical illusions and episodes in the history of astronomy, Hanson argued that “seeing is a ‘theory-laden’ undertaking. Observation of x is shaped by prior knowledge of x” (1958, p. 19). Because a strict division between observational and theoretical languages was a standard feature of then-dominant logical empiricist conceptions of science, Hanson’s view can be seen as an early revision of what came to be seen as logical empiricist...