Eksempler på brug af Principia mathematica på Engelsk og deres oversættelser til Dansk
{-}
-
Colloquial
-
Official
-
Medicine
-
Financial
-
Ecclesiastic
-
Official/political
-
Computer
It is fundamentally weak in its reliance on the logic of Principia Mathematica….
The book is called Philosophiae Principia Mathematica Naturali Natural Philosophy, Mathematical Principles.
Bogen hedder Philosophiae Naturali Principia Mathematica Matematiske Principper for Natural Philosophy.One major attempt had been by Bertrand Russell with Principia Mathematica 1910-13.
Et vigtigt forsøg havde været ved Bertrand Russell med Principia Mathematica 1910/13.As the Principia Mathematica neared completion, Whitehead turned his attention to the philosophy of science.
Som Principia Mathematica neared afslutning, Whitehead vendte hans opmærksomhed på den filosofi, videnskab.Cantor had hoped to meet with Russell who had just published the Principia Mathematica.
Cantor havde håbet at mødes med Russell der netop havde offentliggjort Principia Mathematica.The first volume of Principia Mathematica was published in 1910, the second in 1912, and the third in 1913.
Den første bind af Principia Mathematica blev offentliggjort i 1910, det andet i 1912, og den tredje i 1913.The significant event for Post's career had been the publication of Russell and Whitehead 's Principia Mathematica.
Den markant begivenhed for Post's karriere var offentliggørelsen af Russell og Whitehead's Principia Mathematica.He produced, in 1905, an edition of Russell 's Principia Mathematica with a commentary on contemporary works on the subject.
Han er produceret i 1905, en udgave af Russell's Principia Mathematica med en kommentar til nutidige værker om emnet.When Post began his graduate studies it was an exciting new development andPost participated in Cassius J Keyser's seminar at Columbia which studied the Principia Mathematica.
Når Post begyndte hans studier var det en spændende ny udvikling ogPost deltaget i Cassius J Keyser's seminar på Columbia som studeret Principia Mathematica.In this work he accepted the claim by Russell andWhitehead made in the Principia Mathematica that mathematics is a part of logic.
I dette arbejde, han har accepteret kravet som Russell ogWhitehead sted i Principia Mathematica, at matematik er en del af logikken.This culminated in Isaac Newton 's Principia Mathematica(1687), in which Newton derived Kepler's laws of planetary motion from a force-based theory of universal gravitation.
Det kulminerede i Isaac Newtons Principia Mathematica(1687), hvori Newton fik Keplers love om planetarisk bevægelse fra en kraft-baseret teori om universel gravitation.Over a year later(1687)Newton published the Philosophiae naturalis principia mathematica or Principia as it is always known.
Over et år senere(1687)Newton offentliggjort Philosophiae Naturalis principia Mathematica eller In Principia Mathematica, Whitehead and Russell were able to provide detailed derivations of many major theorems in set theory, finite and transfinite arithmetic, and elementary measure theory.
I Principia Mathematica, Whitehead og Russell var i stand til at give detaljerede afledning af mange store teoremer i sæt teorien finite og transfinite regne, og elementære foranstaltning teori.First defended in his Principles, andlater in more detail in Principia Mathematica, Russell's logicism consisted of two main theses.
Første forsvares i hans principper, ogsenere mere detaljeret i Principia Mathematica, Russell's logicism bestod af to vigtigste afhandlinger.Their collaboration on Principia Mathematica appears to have begun near the end of 1900, although both men failed to remember the exact time their collaboration began when interviewed late in their lives.
Deres samarbejde om Principia Mathematica synes at have begyndt i nærheden udgangen af 1900, selv om både mænd undladt at huske den nøjagtige tidspunkt deres samarbejde begyndte, da interviewet sent i deres liv.Thesis, in which he proved the completeness andconsistency of the propositional calculus described in the Principia Mathematica by introducing the truth table method.
Afhandling, hvor han viste fuldstændighed ogsammenhæng i de propositional calculus beskrevet i Principia Mathematica ved at indføre sandheden tabellen metode.In this work he accepted the claim by Russell andWhitehead made in the Principia Mathematica that mathematics is a part of logic. Ramsey's aim in this paper, however, was to improve on the Principia Mathematica and he did so in two ways.
I dette arbejde, han har accepteret kravet som Russell ogWhitehead sted i Principia Mathematica, at matematik er en del af logikken. Ramsey's mål på dette papir, dog var at forbedre det Principia Mathematica, og han gjorde det på to måder.We now turn to Post's Ph.D. thesis, in which he proved the completeness andconsistency of the propositional calculus described in the Principia Mathematica by introducing the truth table method.
Vi går nu over til Post's Ph.D. afhandling, hvor han viste fuldstændighed ogsammenhæng i de propositional calculus beskrevet i Principia Mathematica ved at indføre sandheden tabellen metode.She used the third Latin edition of Philosophiae naturalis principia mathematica, edited by H Pemberton under Newton 's supervision, which had been published in London in 1726.
Hun brugte en tredjedel latinsk udgave af Philosophiae Naturalis principia Mathematica, redigeret af H Pemberton under Newton's tilsyn, som var blevet offentliggjort i London i 1726.Bernays wrote a second habilitation in which he established the completeness of propositional logic;this was in fact is a study of Russell and Whitehead 's Principia Mathematica, and uses ideas from Schröder.
Bernays skrev en anden habilitationsprocedure, hvor han er etableret fuldstændighed propositional logik;dette var i virkeligheden er en undersøgelse af Russell og Whitehead's Principia Mathematica, og bruger ideer fra Schröder.Had the genius to recognise the even greater mathematical genius of Newton,to urge him to write the Principia Mathematica, and then pay for the costs of publication out of his own pocket because the Royal Society was currently broke….
Havde geni at erkende endnu større matematisk geni af Newton,til at opfordre ham til at skrive Principia Mathematica, og derefter betale for omkostningerne i forbindelse med offentliggørelsen af sin egen lomme, fordi Royal Society var i færd med brød….He was employed as a half-time instructor in mathematics by Harvard during the first semester of 1926-27 andit was around this time that he read the first volume of Whitehead and Russell 's Principia Mathematica which had been published in 1910.
Han blev ansat som halv tid instruktør i matematik ved Harvard i løbet af første halvår af 1926-27, ogdet var omkring denne tid, at han læst første bind af Whitehead og Russell's Principia Mathematica, som var blevet offentliggjort i 1910.In this he proved that if an axiomatic system of set theory of the type proposed by Russell and Whitehead in Principia Mathematica is consistent, then it will remain so when the axiom of choice and the generalized continuum-hypothesis are added to the system.
I denne han vist, at hvis en indlysende system af sæt teori af den type, som foreslået af Russell og Whitehead i Principia Mathematica er konsekvent, så vil det fortsat være sådan, når aksiom valg og den generelle kontinuum-hypotese er tilføjet til systemet.Although first introduced by Russell in 1903 in the Principles, his theory of types finds its mature expression in his 1908 article Mathematical Logic as Based on the Theory of Types andin the monumental work he co-authored with Alfred North Whitehead, Principia Mathematica 1910, 1912, 1913.
Selvom første gang indført ved Russell i 1903 i de principper, hans teori om typer finder sin modne udtryk i hans 1908 artiklen Matematisk logik som Baseret påteorien om Typer og i den monumentale arbejde, han co-forfattet med Alfred North Whitehead, Principia Mathematica 1910, 1912, 1913.A fellow student suggested that he would find reading Bertrand Russell 's works interesting andindeed reading Russell and Whitehead 's Principia Mathematica quickly convinced Quine that he should study mathematics as his major subject with the philosophy of mathematics as a secondary topic.
En stipendiat studerende foreslog, at han ville finde behandling Bertrand Russell's værker interessante ogfaktisk læse Russell og Whitehead' s Principia Mathematica hurtigt overbevist om, Quine, at han skal studere matematik som hans vigtigste emne med filosofien om matematik som et sekundært emne.These lecture notes were later edited by Wilhelm Ackermann and published as Grundzüge der theoretischen Logik. Bernays wrote a second habilitation in which he established the completeness of propositional logic;this was in fact is a study of Russell and Whitehead 's Principia Mathematica, and uses ideas from Schröder.
Disse Lecture Notes senere blev redigeret af Wilhelm Ackermann og offentliggjort som Grundzüge der theoretischen Logik. Bernays skrev en anden habilitationsprocedure, hvor han er etableret fuldstændighed propositional logik;dette var i virkeligheden er en undersøgelse af Russell og Whitehead's Principia Mathematica, og bruger ideer fra Schröder.Their collaboration on Principia Mathematica appears to have begun near the end of 1900, although both men failed to remember the exact time their collaboration began when interviewed late in their lives. In fact they had attended the International Congress of Mathematicians in Paris in 1900 and there they had learnt about Peano 's work on the foundations of mathematics.
Deres samarbejde om Principia Mathematica synes at have begyndt i nærheden udgangen af 1900, selv om både mænd undladt at huske den nøjagtige tidspunkt deres samarbejde begyndte, da interviewet sent i deres liv. Faktisk havde de deltog i det internationale kongres af Matematikere i Paris i 1900, og der de havde lært om Peano's arbejde om grundlaget for matematik.He published A formulation of the simple theory of types in 1940 in which he attempted to give a system related to that of Whitehead and Russell 's Principia Mathematica which was designed to avoid the paradoxes of naive set theory.
Han offentliggjorde en formulering af den simple teori på typer i 1940, hvor han forsøgte at give et system relateret til det, Whitehead og Russell's Principia Mathematica, som havde til formål at undgå de paradokser af naive sæt teorien.The correctness of this result is clearly entirely dependent on the trustworthiness of the analysis leading to the above generalisation… it is fundamentally weak in its reliance on the logic of Principia Mathematica… for full generality a complete analysis would have to be given of all possible ways in which the human mind could set up finite processes for generating sequences.
Rigtigheden af dette resultat er naturligvis helt afhængig af pålideligheden af den analyse, der førte til ovennævnte generalisering… Det er fundamentalt svag 
