Given a general statement such as all ravens are black, a form of the same statement that refers to a specific observable instance of the general class would typically be considered to constitute evidence for that general statement.

Given any statement, the number it is converted to is known as its Gödel number.

Given the statement, " All of Peters friends either like to dance or like to go to the beach ", we can identify key aspects and rewrite using symbols including quantifiers.

Given some statement P, it appears reasonable to ask for a justification for P. If that justification takes the form of another statement, P ', one can again reasonably ask for a justification for P ', and so forth.

Given that Lucian's understanding of Christian traditions has significant gaps and errors, his writing is unlikely to have been influenced by Christians themselves, and he may provide an independent statement about the crucifixion of Jesus.

Given the Cantor – Dedekind axiom, this algorithm can be regarded as an algorithm to decide the truth of any statement in Euclidean geometry.

Given S a statement, the weakest-precondition of S is a

Position Statement Summary: Given that the focus of writing instruction is expanding: the curriculum of composition is widening to include not one but two literacies: a literacy of print and a literacy of the screen and that work in one medium is used to enhance learning in the other, this statement articulates principles of good practice governing these new pedagogical activities for digital literacy.

In a critical statement published in 1955, he asserted that " Given the modern conceptions of the beautiful in literature, given at the very least these essential conceptions, if a work is realistic it has many chances of being good ; if not, supposing even that it has formal qualities, it risks lacking resonance, profundity, that of which all literature has the greatest need -- the human ; from which it follows that it has much less chance of being good -- if only it had some -- than a realistic work.

Given the lack of details and the imprecision contemporary diagnosis and description, Viceroy Revillagigedo's statement official statement that Bodega died " of natural causes " is indisputable.

Given the current state of knowledge, Huxley's statement with regards to " why what we call good is preferable to what we call evil " is still accurate with regards to individual human tastes and predispositions.

Given that the Qur ' an is vague regarding the punishment of homosexual sodomy, Islamic jurists turned to the collections of the hadith and seerah ( accounts of Muhammad's life ) to support their argument for Hudud punishment ; these are perfectly clear but particularly harsh.

Given India's historic position that the original intent of the line was to separate the two nations by the highest mountains in the world, in these locations India extended its forward posts northward to the ridges, regarding this move as compliant with the original border proposal, although the Simla Convention did not explicitly state this intention.

" Given the situation in Spain for several years regarding terrorist attacks, these ties can be considered objectively as a threat to democracy ," the court said, also adding that these parties " contradicted the concept of a ' democratic society ' and presented a major danger to Spain's democracy ".

Given what we knew regarding terrorists ’ interest in acquiring and using chemical weapons against Americans, and given the intelligence assessment provided us regarding the al-Shifa facility, I continue to believe that destroying it was the right decision.

Given the preceding jurisprudence regarding due process, Chief Justice Taney was not entirely breaking ground in his Dred Scott opinion when, without elaboration, he pronounced the Missouri Compromise unconstitutional because an " act of Congress that deprived a citizen of his liberty or property merely because he came himself or brought his property into a particular territory of the United States, and who had committed no offence against the laws, could hardly be dignified with the name of due process of law.

Given the narrow federalist victory in 1995, a reference was made by the Chrétien government to the Supreme Court of Canada in 1996 regarding the legality of a unilateral secession of Quebec.

Given that field experiments necessarily take place in a specific geographic and political setting, the extent to which findings can be extrapolated to formulate a general theory regarding economic behavior is a concern.

Given their relative isolation, several mistaken rumours regarding the Torres Islands and their people have become widespread by way of travel guides, inter-island gossip and the mass media.

Given the success of the earlier DVDs, it was hoped that the sales would encourage Sony to produce a final direct-to-DVD movie to complete the original Homefront Campaign story arc, but there have been no new announcements regarding the Roughneck series.

Given the passionate nature of most Singaporeans regarding food, and Singaporean cuisine, a constantly updated food guide, Makansutra, has been developed, which focuses on the hawker scene in Singapore, and identifies popular stalls in Singapore.

Given that libraries in Milwaukee, Wisconsin were just connecting to the World Wide Web, Flessas gathered and placed information regarding all the services available to the homeless in Milwaukee on the web so service providers to the homeless and the homeless themselves ( who often sought shelter in local libraries ) had equal and rapid access to information about resources available in Milwaukee via the Milwaukee County library system computer network " OMNINET ".

Given this, Spinoza's views regarding causality and modality begin to make much more sense.

Given a diagram F: J → C ( thought of as an object in C < sup > J </ sup >), a natural transformation ψ: Δ ( N ) → F ( which is just a morphism in the category C < sup > J </ sup >) is the same thing as a cone from N to F. The components of ψ are the morphisms ψ < sub > X </ sub >: N → F ( X ).

Given a list of operations and axioms in universal algebra, the corresponding algebras and homomorphisms are the objects and morphisms of a category.

* Given a category C with finite coproducts, a cogroup object is an object G of C together with a " comultiplication " m: G → G G, a " coidentity " e: G → 0, and a " coinversion " inv: G → G, which satisfy the dual versions of the axioms for group objects.

Given objects and in an additive category, we can represent morphisms as-by-matrices

Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that assigns new examples into one category or the other.

Given a concrete category ( C, U ) and a cardinal number N, let U < sup > N </ sup > be the functor C → Set determined by U < sup > N </ sup >( c ) = ( U ( c ))< sup > N </ sup >.

Given the way black music has been named by ( usually ) outsiders ever since the blues, the reaction to the name by artists who ostensibly fit into the ' neo-soul ' category represents a wonderful example of black self-determination in an industry that is still defiantly wedded to narrow definitions and images of black folks ".

Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category or the other.

Given a concrete category C, it is often the case that the opposite category C < sup > op </ sup > per se is abstract.

Given a category C and a morphism

The prime mechanism then appeared to be this: Given a space X carrying a vector bundle, that implied in the homotopy category a mapping from X to a classifying space BG, for the relevant linear group G. For the homotopy theory the relevant information is carried by compact subgroups such as the orthogonal groups and unitary groups of G. Once the cohomology H *( BG ) was calculated, once and for all, the contravariance property of cohomology meant that characteristic classes for the bundle would be defined in H *( X ) in the same dimensions.

Recent findings suggest to differentiate between three types of hoarding, that is: pure hoarding, hoarding plus OCD ( i. e., comorbid OCD ), and OCD-based hoarding Given the aforementioned distinction, it was proposed to increase coverage of compulsive hoarding in the forthcoming Diagnostic and Statistical Manual of Mental Disorders, fifth edition ( DSM-V ), both by creating a distinct category for compulsive hoarding, provisionally named, Hoarding Disorder ( either in the main manual under " obsessive-compulsive spectrum disorders " or in the appendix ), and by including hoarding as a potential symptoms of OCD.

Given an arbitrary category C, a representation of G in the category C is a functor from G to C. Such a functor selects an object of C and a subgroup of automorphisms of that object.

Given a partially ordered class P, we can form a category with P's elements as objects and a single arrow going from one object ( element ) to another if the first is less than or equal to the second.

Given and, a morphism in the coslice category is a map making the following diagram commute:

Given the inherent technical limitations of the visible and palpable signs from these sacroiliac joint mobility maneuvers another broad category of clinical signs have been described called provocative maneuvers.

Given a category C, an idempotent of C is an endomorphism

Given the smaller size of pickup trucks in the Tacoma's category, crash testing for these sized trucks lags with how well most full size trucks perform.

Given a continuous map there is a map defined by This makes into a functor from the category of topological spaces into itself.

Given the size and nature of the mortgage market, many observers classify mortgage lending as a separate category of personal borrowing, and consequently residential mortgages are excluded from some definitions of consumer credit-such as the one adopted by the Federal Reserve in the US.

Ironically, also nominated in the category of Contemporary Male Horse was Point Given who won under Baffert's training the Belmont Stakes, Preakness Stakes, Haskell Invitational Handicap, Travers Stakes and ultimately the Eclipse Award for Horse of the Year.