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According to Gödel mathematical logic was " a science prior to all others, which contains the ideas and principles underlying all sciences.

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## Some Related Sentences

According and Gödel

__According__

**to**his classmate Klepetař

**,**like most residents of

**the**predominantly German Sudetenlaender

**,**

**"**

__Gödel__considered himself always Austrian

**and**an exile in Czechoslovakia

**"**(" ein Österreicher im Exil in der Tschechoslowakei ").

__According__

**to**

**the**fundamental theorem of arithmetic

**,**any number obtained in this way can be uniquely factored into prime factors

**,**so it is possible

**to**recover

**the**original sequence from its

__Gödel__number ( for any given number n of symbols

**to**be encoded ).

According and mathematical

__According__

**to**intuitionists ( anti-realists with respect

**to**

__mathematical__objects ),

**the**truth of

**a**

__mathematical__statement consists in our ability

**to**prove it

**.**

__According__

**to**Husserl

**,**this view of

**logic**

**and**mathematics accounted for

**the**objectivity of

**a**series of

__mathematical__developments of his time

**,**such as n-dimensional manifolds ( both Euclidean

**and**non-Euclidean ), Hermann Grassmann's theory of extensions

**,**William Rowan Hamilton's Hamiltonians

**,**Sophus Lie's theory of transformation groups

**,**

**and**Cantor's set theory

**.**

__According__

**to**Jewish tradition

**,**

**the**Jewish calendar is calculated based on

__mathematical__rules handed down from God

**to**Moses at

**the**moment

**the**command

**was**given

**to**make sure that Passover always falls in

**the**springtime

**.**

__According__

**to**

**the**New Schaff-Herzog Encyclopedia of Religious Knowledge

**,**

**the**Kestoi

**"**appears

**to**have been intended as

**a**sort of encyclopedia of

**the**material

**sciences**with

**the**cognate

__mathematical__

**and**technical branches

**,**but

**to**have contained

**a**large proportion of merely curious

**,**trifling

**,**or miraculous matters

**,**on

**which**account

**the**authorship of Julius has been questioned

**.**

__According__

**to**

**the**principle of ontological parsimony

**,**he holds that we do not need

**to**allow entities in

**all**ten of Aristotle's categories ; we thus do not need

**the**category of quantity

**,**as

**the**

__mathematical__entities are not

**"**real ".

__According__

**to**Formalism

**,**

__mathematical__truths are not about numbers

**and**sets

**and**triangles

**and**

**the**like — in fact

**,**they aren't

**"**about

**"**anything at

**all**

**.**

__According__

**to**Stephen Skinner

**,**

**the**study of sacred geometry has its roots in

**the**study of nature

**,**

**and**

**the**

__mathematical__

**principles**at work therein

**.**

__According__

**to**Sloan Career Cornerstone Center

**,**individuals working in this area

**,**

**"**computational methods are applied

**to**formulate

**and**solve complex

__mathematical__problems in engineering

**and**

**the**physical

**and**

**the**social

**sciences**

**.**

__According__

**to**

**the**Mathematics Genealogy Project

**,**Chebyshev has 7

**,**483

__mathematical__

**"**descendants

**"**as of 2010

**.**

__According__

**to**

**the**renowned neuropsychologist

**and**neurobiologist Roger Wolcott Sperry though

**,**intuition is

**a**right-brain activity while factual

**and**

__mathematical__analysis is

**a**left-brain activity

**.**

__According__

**to**Gauss

**,**who first described it

**,**it is

**the**

**"**

__mathematical__figure of

**the**Earth ",

**a**smooth but highly irregular surface that corresponds not

**to**

**the**actual surface of

**the**Earth's crust

**,**but

**to**

**a**surface

**which**can only be known through extensive gravitational measurements

**and**calculations

**.**

__According__

**to**astrophysicist

**and**math popularizer Mario Livio

**,**since

**the**publication of Luca Pacioli's Divina Proportione in 1509

**,**when

**"**with Pacioli's book

**,**

**the**Golden Ratio started

**to**become available

**to**artists in theoretical treatises that were not overly

__mathematical__

**,**that they could actually use ," many artists

**and**architects have been fascinated by

**the**presumption that

**the**golden rectangle is considered aesthetically pleasing

**.**

__According__

**to**Vandervert

**,**in

**the**emotion-driven prodigy ( commonly observed as

**a**

**"**rage

**to**master ")

**the**cerebellum accelerates

**the**streamlining of

**the**efficiencies of working memory in its manipulation

**and**decomposition / re-composition of visual-spatial content into language acquisition

**and**into linguistic

**,**

__mathematical__

**,**

**and**artistic precocity

**.**

__According__

**to**this restriction

**,**variables are used in

**a**

__mathematical__sense

**,**with identifiers referring

**to**immutable

**,**persistent values

**.**

__According__

**to**Asimov's novels

**,**Hari Seldon devised

**the**Seldon Plan using

**a**

__mathematical__analysis he originally developed

**and**called psychohistory

**.**

__According__

**to**Rosenblum ( 1994 )

**"**volume visualization examines

**a**set of techniques that allows viewing an object without

__mathematical__representing

**the**other surface

**.**

__According__

**to**Noh-Varr

**the**Kree have

**a**

__mathematical__equation that disproves

**the**existence of any deity

**,**

**which**is taught

**to**

**all**Kree around

**"**

**the**same time we learn not

**to**soil ourselves with excrement ".

__According__

**to**

**the**standard

__mathematical__formulation of quantum mechanics

**,**quantum observables such as x

**and**p should be represented as self-adjoint operators on some Hilbert space

**.**

__According__

**to**Searle

**,**no

__mathematical__function can be used

**to**connect

**a**known VIN with its LPN

**,**but

**the**process of assignment is quite simple — namely

**,**

**"**first come

**,**first served "—

**and**can be performed entirely by

**a**computer

**.**

__According__

**to**

**the**NEOS statistics AMPL is

**the**most popular format for representing

__mathematical__programming problems

**.**

According and logic

__According__

**to**

**the**objectivist view

**,**

**the**rules of Bayesian statistics can be justified by requirements of rationality

**and**consistency

**and**interpreted as an extension of

__logic__

**.**

__According__

**to**psychologism

**,**

__logic__would not be an autonomous discipline

**,**but

**a**branch of psychology

**,**either proposing

**a**prescriptive

**and**practical

**"**art

**"**of correct judgement ( as Brentano

**and**some of his more orthodox students did ) or

**a**description of

**the**factual processes of human thought

**.**

__According__

**to**Gould

**,**punctuated equilibrium revised

**a**key pillar

**"**in

**the**central

__logic__of Darwinian theory ".

__According__

**to**these theologians

**,**this law is not

**a**law above God that he assents

**to**but

**,**rather

**,**

__logic__is an eternal part of God's nature

**,**like his omniscience or omnibenevolence

**.**

__According__

**to**Jains

**,**

**the**ultimate principle should always be logical

**and**no principle can be devoid of

__logic__or reason

**.**

__According__

**to**

**the**

__logic__of

**the**eternal return

**,**

**the**site of each such symbolic Center will actually be

**the**Center of

**the**World:

__According__

**to**its website

**,**

**"**The GLP Leaf Party is

**a**libertarian party

**and**it encourages individuals

**and**societies

**to**upgrade their way of solving disputes

**to**

**a**cooperative-game

__logic__

**.**

__According__

**to**S

**.**Jay Olshansky

**and**Bruce Carnes

**,**

**"**there is neither convincing evidence nor scientific

__logic__

**to**support

**the**claim that adherence

**to**

**a**Paleolithic diet provides

**a**longevity benefit

**.**

__According__

**to**Merton

**,**

**"**paradigm ", refers

**to**

**"**exemplars of codified basic

**and**often tacit assumptions

**,**problem sets

**,**key concepts

**,**

__logic__of procedure

**,**

**and**selectively accumulated knowledge that guide

**and**empirical inquiry in

**all**scientific fields ".

__According__

**to**Watts

**,**

**and**in keeping with

**the**common practice of logicians of his day

**,**Watts defined

__logic__as an art ( see liberal arts ), as opposed

**to**

**a**

**science**

**.**

__According__

**to**Watts

**,**as

**a**practical art

**,**

__logic__can be really useful in any of our inquiries

**,**whether they are inquiries in

**the**arts

**,**or inquiries in

**the**

**sciences**

**,**or inquiries of an ethical kind

**.**

__According__

**to**Ibn al-Nadim

**,**al-Kindi wrote at least two hundred

**and**sixty books

**,**contributing heavily

**to**geometry ( thirty-two books ), medicine

**and**philosophy ( twenty-two books each ),

__logic__( nine books ),

**and**physics ( twelve books ).

__According__

**to**Burgess

**,**philosophical

__logic__in this sense

**,**has its center of gravity in theoretical computer

**science**

**,**because many non-classical logics find applications there

**.**

__According__

**to**this

__logic__

**,**if manufacturers ' profits are rising

**,**it follows that they are producing more

**.**

__According__

**to**Geoffrey Hunter

**,**while

__logic__concerns itself with

**the**

**"**truths of

__logic__," metalogic concerns itself with

**the**theory of

**"**sentences used

**to**express truths of

__logic__

**.**

__According__

**to**Hong Kong film critic Perry Lam

**,**writing in Muse magazine

**,**' unpredictable digressions

**and**swift changes of scene can evoke

**a**dreamer's

__logic__

**,**but his sound

**and**images are always sharp

**and**particular

**.**

__According__

**to**another tradition

**,**i

**.**e

**.**

**the**one associated with predicate

__logic__

**and**dependency grammars

**,**

**the**subject is

**the**most prominent overt argument of

**the**predicate

**.**

__According__

**to**

**the**objectivist view

**,**

**the**rules of Bayesian statistics can be justified by requirements of rationality

**and**consistency

**and**interpreted as an extension of

__logic__

**.**

__According__

**to**Foucault

**,**there are several instances where

**the**Western

**,**

**"**liberal art of government

**"**enters into

**a**period of crisis

**,**where

**the**

__logic__of ensuring freedom (

**which**

**was**defined against

**the**background of risk or danger ) necessitates actions

**"**

**which**potentially risk producing exactly

**the**opposite

**.**

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