phrase sense report economist e wight bakke regard individuals respond changes labor market following must understood skills qualifications industries move manual managerial professions need highly skilled staff market tight ie enough staff jobs employers must compete employees offering financial rewards community investment etc geographical spread far job individual distance travel work line


remuneration transportation infrastructure area also influence applies position occupational structure norms values different careers within organization mahoney developed different types occupational structure namely craft loyalty profession organization career path promotion firm unstructured lower unskilled workers work needed generational difference different age categories employees certain characteristics example behavior expectations organization concerns terminology one major concern considering people assets resources commoditized objectified

Applied science
Business
Industrial and labor relations
Human resources


abused human beings commodities resources creative social beings productive enterprise revision iso contrast requires identifying processes sequence interaction define communicate responsibilities authorities general heavily unionized nations france germany adopted encouraged approaches also international labour organization decided revisit revise recommendation human resources development resulting labour commodity principle one view trends strong social consensus


united nations come generally support developing nations' point view requested significant offsetting foreign aid contributions developing nation losing human capital lose capacity continue train new people trades professions arts development human resource companies play important part developing making company organization beginning making success end due labor provided employees human resources intended show better employment relations workforce also bring


best work ethic employees therefore making move better working environment planning administration operations used two role areas hr strategic planning component came play result companies recognizing need consider hr needs goals strategies hr directors commonly sit company executive teams hr planning function numbers types employees evolution compensation systems among elements planning role various factors affecting human resource planning organizational structure growth business location demographic changes environmental uncertainties


expansion etc additionally area encompasses realm talent management see also activity based working chief human resources officer employee offboarding human resource accounting human resources development convention human resource management industrial organizational psychology notes external links resources


mathematical philosophy '''philosophy mathematics''' branch philosophy studies assumptions foundations implications mathematics aims understand nature methods mathematics find place mathematics people 's lives logical structural nature mathematics makes study broad unique among philosophical counterparts philosophy mathematics two major themes mathematical realism mathematic anti realism history pythagoras considered father mathematics geometry setting foundation euclid euclidean geometry founder pythagoreanism mathematical philosophical model map

Humanities
Philosophy
Applied philosophy
Philosophy of mathematics


universe origin mathematics subject arguments disagreements whether birth mathematics random happening induced necessity development subjects like physics still matter prolific debates many thinkers contributed ideas concerning nature mathematics today philosophers mathematics aim give accounts form inquiry products stand others emphasize role goes beyond simple interpretation critical analysis traditions mathematical philosophy western philosophy eastern philosophy western


philosophies mathematics go far back pythagoras described theory everything mathematics mathematicism plato paraphrased pythagoras studied ontological status mathematical objects aristotle studied logic issues related infinity actual versus potential greek philosophy mathematics strongly influenced study geometry example one time greeks held opinion one number rather unit arbitrary length number defined multitude therefore example represented certain multitude units thus truly


number another point similar argument made number fundamental notion pair views come heavily geometric straight edge compass viewpoint greeks lines drawn geometric problem measured proportion first arbitrarily drawn line numbers number line measured proportion arbitrary first number one earlier greek ideas numbers later upended discovery irrationality square root two hippasus disciple pythagoras showed


diagonal unit square incommensurable unit length edge words proved existing rational number accurately depicts proportion diagonal unit square edge caused significant evaluation greek philosophy mathematics according legend fellow pythagoreans traumatized discovery murdered hippasus stop spreading heretical idea simon stevin one first europe challenge greek ideas th nbsp century beginning leibniz focus shifted strongly relationship mathematics


logic perspective dominated philosophy mathematics time frege russell brought question developments late th early th nbsp centuries contemporary philosophy perennial issue philosophy mathematics concerns relationship logic mathematics joint foundations th century philosophers continued ask questions mentioned outset article philosophy mathematics th century characterized predominant interest formal logic set theory naive set theory axiomatic set theory foundational issues


profound puzzle one hand mathematical truths seem compelling inevitability hand source truthfulness remains elusive investigations issue known foundations mathematics program start th century philosophers mathematics already beginning divide various schools thought questions broadly distinguished pictures mathematical epistemology ontology three schools formalism intuitionism logicism emerged time partly response increasingly widespread worry mathematics stood analysis particular


live standards certainty rigor taken granted school addressed issues came fore time either attempting resolve claiming mathematics entitled status trusted knowledge surprising counter intuitive developments formal logic set theory early th nbsp century led new questions concerning traditionally called ''foundations mathematics'' century unfolded initial focus concern expanded open exploration fundamental axioms mathematics axiomatic approach


one common view situation last third century saying blockquote philosophy discovers something wrong science sometimes science changed russell 's paradox comes mind berkeley 's attack actual infinitesimal often philosophy changed think difficulties philosophy finds classical mathematics today genuine difficulties think philosophical interpretations mathematics offered every hand wrong philosophical interpretation mathematics n't need blockquote philosophy


example real entities creations human mind many working mathematicians mathematical realists see discoverers naturally occurring objects examples include paul erd kurt g del g del believed objective mathematical reality could perceived manner analogous sense perception certain principles eg two objects collection objects consisting precisely two objects could directly seen true continuum hypothesis conjecture might prove undecidable basis principles g del suggested quasi empirical methodology could


world ideas greek ''eidos'' described plato 's allegory cave everyday world imperfectly approximate unchanging ultimate reality plato 's cave platonism meaningful superficial connections plato 's ideas preceded probably influenced hugely popular ''pythagoreans'' ancient greece believed world quite literally generated numbers major question considered mathematical platonism precisely mathematical entities exist know world completely separate physical one occupied


mathematical entities gain access separate world discover truths entities one proposed answer ultimate ensemble theory postulates structures exist mathematically also exist physically universe kurt g del kurt g del 's platonism ref name sep p https platostanfordedu entries platonism platonism metaphysics stanford encyclopedia philosophy ref postulates special kind mathematical intuition lets us perceive mathematical objects directly view bears resemblances many things husserl said mathematics supports kant 's idea mathematics synthetic ''a priori'' davis hersh suggested book


''the mathematical experience'' mathematicians act though platonists even though pressed defend position carefully may retreat formalism mathematician alexander grothendieck also platonist '''full blooded platonism''' modern variation platonism reaction fact different sets mathematical entities proven exist depending axioms inference rules employed instance law excluded middle axiom choice holds mathematical entities exist may provable even cannot derived


single consistent set axioms '''set theoretic realism''' also '' 'set theoretic platonism''' position defended penelope maddy view set theory single universe sets position also known '''naturalized platonism''' naturalized version mathematical platonism criticized mark balaguer basis paul benacerraf 's epistemological problem similar view termed '''platonized naturalism''' later defended stanford edmonton school according view traditional kind platonism consistent naturalism traditional kind platonism defend distinguished


general principles assert existence abstract objects mathematicism max tegmark 's mathematical universe hypothesis mathematicism goes platonism asserting mathematical objects exist nothing else tegmark 's sole postulate ''all structures exist mathematically also exist physically'' sense worlds complex enough contain self aware substructures subjectively perceive existing physically 'real' world ref name tegmark ref logicism logicism thesis mathematics reducible logic hence nothing part logic ref name carnap carnap rudolf die logizistische


grundlegung der mathematik ''erkenntnis'' republished logicist foundations mathematics e putnam gj massey trans benacerraf putnam reprinted pp nbsp benacerraf putnam ref logicists hold mathematics known ''a priori'' suggest knowledge mathematics part knowledge logic general thus analytic requiring special faculty mathematical intuition view logic proper foundation mathematics mathematical statements necessary logical truths rudolf carnap presents logicist thesis two parts ref name carnap ''concepts''


order develop much mathematics axiom reducibility even russell said axiom really belong logic modern logicists like bob hale crispin wright perhaps others returned program closer frege 's abandoned basic law v favor abstraction principles hume 's principle number objects falling concept ''f'' equals number objects falling concept ''g'' extension ''f'' extension ''g'' put one one correspondence frege required basic


law v able give explicit definition numbers properties numbers derived hume 's principle would enough frege paraphrase exclude possibility number fact julius caesar addition many weakened principles adopt replace basic law v longer seem obviously analytic thus purely logical formalism formalism holds mathematical statements may thought statements consequences certain string manipulation rules


chosen philosophically uncontroversial consistent hilbert 's goals creating system mathematics complete consistent seriously undermined second g del 's incompleteness theorems states sufficiently expressive consistent axiom systems never prove consistency since axiom system would contain finitary arithmetic subsystem g del 's theorem implied would impossible prove system 's consistency relative since would prove consistency g del shown impossible thus order show axiomatic system mathematics


formal systems often realists formalists formalists relatively tolerant inviting new approaches logic non standard number systems new set theories etc games study better however three examples motivation drawn existing mathematical philosophical concerns games usually arbitrary main critique formalism actual mathematical ideas occupy mathematicians far removed string manipulation games mentioned formalism thus silent question axiom systems ought studied none


meaningful another formalistic point view recently formalist mathematicians proposed ''formal'' mathematical knowledge systematically encoded computer readable formats facilitate automated proof checking mathematical proofs use interactive theorem proving development mathematical theories computer software close connection computer science idea also advocated mathematical intuitionists constructivists computability tradition see qed project general overview conventionalism french mathematician henri poincar among first articulate conventionalist view


poincar 's use non euclidean geometries work differential equations convinced euclidean geometry regarded ''a priori'' truth held axioms geometry chosen results produce apparent coherence human intuitions physical world intuitionism mathematics intuitionism program methodological reform whose motto non experienced mathematical truths l e j brouwer springboard intuitionists seek reconstruct consider corrigible portion mathematics accordance kantian concepts becoming intuition


knowledge brouwer founder movement held mathematical objects arise ''a priori'' forms volitions inform perception empirical objects major force behind intuitionism l e j brouwer rejected usefulness formalized logic sort mathematics student arend heyting postulated intuitionistic logic different classical aristotelian logic logic contain law excluded middle therefore frowns upon proofs contradiction axiom choice also rejected intuitionistic set theories though versions


accepted intuitionism term explicit construction cleanly defined led criticisms attempts made use concepts turing machine computable function fill gap leading claim questions regarding behavior finite algorithms meaningful investigated mathematics led study computable numbers first introduced alan turing surprisingly approach mathematics sometimes associated theoretical computer science constructivism like intuitionism constructivism involves regulative principle mathematical entities


explicitly constructed certain sense admitted mathematical discourse view mathematics exercise human intuition game played meaningless symbols instead entities create directly mental activity addition adherents schools reject non constructive proofs proof contradiction important work done errett bishop managed prove versions important theorems real analysis constructive analysis ''foundations constructive analysis'' finitism leopold kronecker finitism extreme form constructivism according


mathematical object exist unless constructed natural numbers finite number steps book ''philosophy set theory'' mary tiles characterized allow countably infinite objects classical finitists deny even countably infinite objects strict finitists famous proponent finitism leopold kronecker said ultrafinitism even extreme version finitism rejects infinities finite quantities cannot feasibly constructed available resources another variant finitism euclidean arithmetic system developed john


penn mayberry book ''the foundations mathematics theory sets'' ref name mayberry ref mayberry 's system aristotelian general inspiration despite strong rejection role operationalism feasibility foundations mathematics comes somewhat similar conclusions instance super exponentiation legitimate finitary function structuralism structuralism position holding mathematical theories describe structures mathematical objects exhaustively defined ''places'' structures consequently intrinsic properties instance would maintain needs known


number first whole number likewise whole numbers defined places structure number line examples mathematical objects might include lines planes geometry elements operations abstract algebra structuralism epistemologically realistic view holds mathematical statements objective truth value however central claim relates ''kind'' entity mathematical object kind ''existence'' mathematical objects structures words ontology


kind existence mathematical objects would clearly dependent structures embedded different sub varieties structuralism make different ontological claims regard ''ante rem'' structuralism thing similar ontology platonism structures held real abstract immaterial existence faces standard epistemological problem explaining interaction abstract structures flesh blood mathematicians see benacerraf 's identification problem ''in re'' structuralism thing equivalent aristotelean realism structures held exist inasmuch


concrete system exemplifies incurs usual issues perfectly legitimate structures might accidentally happen exist finite physical world might big enough accommodate otherwise legitimate structures ''post rem'' structuralism thing anti realist structures way parallels nominalism like nominalism ''post rem'' approach denies existence abstract mathematical objects properties place relational structure according view mathematical ' 'systems'' exist structural features common something true structure


true systems exemplifying structure however merely instrumental talk structures held common systems fact independent existence embodied mind theories embodied mind theories hold mathematical thought natural outgrowth human cognitive apparatus finds physical universe example abstract concept number springs experience counting discrete objects held mathematics universal exist real sense human brains humans construct discover mathematics


view physical universe thus seen ultimate foundation mathematics guided evolution brain later determined questions brain would find worthy investigation however human mind special claim reality approaches built math constructs euler 's identity true true map human mind cognition embodied mind theorists thus explain effectiveness mathematics mathematics constructed brain order effective universe accessible famous


infamous treatment perspective ''where mathematics comes from'' george lakoff rafael e n ez addition mathematician keith devlin investigated similar concepts book ''the math instinct'' neuroscientist stanislas dehaene book ''the number sense'' philosophical ideas inspired perspective see cognitive science mathematics aristotelian realism aristotelian realism holds mathematics studies properties symmetry continuity order literally realized physical world world might contrasts platonism holding objects


view penelope maddy egg carton opened set three eggs perceived mathematical entity realized physical world ref name maddy maddy penelope ''realism mathematics'' oxford university press oxford uk ref problem aristotelian realism account give higher infinities may realizable physical world euclidean arithmetic developed john penn mayberry book ''the foundations mathematics theory sets'' ref name mayberry also falls aristotelian realist tradition mayberry following euclid considers numbers simply definite


multitudes units realized nature members london symphony orchestra trees birnam wood whether definite multitudes units euclid 's common notion whole greater part fails would consequently reckoned infinite mayberry essentially question nature entail transcendental suppositions psychologism psychologism philosophy mathematics position mathematical concepts truths grounded derived explained psychological facts laws john stuart mill seems


advocate type logical psychologism many th century german logicians sigwart erdmann well number psychologists past present example gustave le bon psychologism famously criticized frege ''the foundations arithmetic'' many works essays including review husserl 's ''philosophy arithmetic'' edmund husserl first volume ''logical investigations'' called prolegomena pure logic criticized psychologism thoroughly sought distance prolegomena considered concise fair thorough refutation psychologism


criticisms made frege also considered today many memorable refutation decisive blow psychologism psychologism also criticized charles sanders peirce maurice merleau ponty empiricism mathematical empiricism form realism denies mathematics known ''a priori'' says discover mathematical facts empirical research like facts sciences one classical three positions advocated early th nbsp century primarily arose middle century however important


early proponent view like john stuart mill mill 's view widely criticized according critics aj ayer makes statements like come uncertain contingent truths learn observing instances two pairs coming together forming quartet contemporary mathematical empiricism formulated w v quine hilary putnam primarily supported indispensability argument mathematics indispensable empirical sciences want believe reality phenomena described sciences ought also believe


reality entities required description since physics needs talk electrons say light bulbs behave electrons must exist since physics needs talk numbers offering explanations numbers must exist keeping quine putnam 's overall philosophies naturalistic argument argues existence mathematical entities best explanation experience thus stripping mathematics distinct sciences putnam strongly rejected term platonist implying specific ontology necessary


mathematical practice real sense advocated form pure realism rejected mystical notions truth accepted much quasi empiricism mathematics grew increasingly popular assertion late th century one foundation mathematics could ever proven exist also sometimes called postmodernism mathematics although term considered overloaded insulting others quasi empiricism argues research mathematicians test hypotheses well prove theorems mathematical argument transmit falsity conclusion premises well


transmit truth premises conclusion putnam argued theory mathematical realism would include quasi empirical methods proposed alien species mathematics might well rely quasi empirical methods primarily willing often forgo rigorous axiomatic proofs still mathematics perhaps somewhat greater risk failure calculations gave detailed argument ''new directions'' quasi empiricism also developed imre lakatos important criticism empirical views mathematics approximately raised mill mathematics


empirical sciences suggests results fallible contingent mill 's case empirical justification comes directly quine 's case comes indirectly coherence scientific theory whole ie consilience eo wilson quine suggests mathematics seems completely certain role plays web belief extraordinarily central would extremely difficult us revise though impossible philosophy mathematics attempts overcome


shortcomings quine g del 's approaches taking aspects see penelope maddy 's ''realism mathematics'' another example realist theory embodied mind theory experimental evidence suggesting human infants elementary arithmetic see brian butterworth fictionalism '''mathematical fictionalism''' brought fame hartry field published ''science without numbers'' rejected fact reversed quine 's indispensability argument quine suggested mathematics indispensable best scientific theories therefore accepted body truths talking independently existing entities field suggested mathematics


dispensable therefore considered body falsehoods talking anything real giving complete axiomatization newtonian mechanics reference numbers functions started betweenness hilbert 's axioms characterize space without coordinatizing added extra relations points work formerly done vector fields hilbert 's geometry mathematical talks abstract points field 's theory points concrete points physical space special mathematical objects needed shown


science without using numbers field proceeded rehabilitate mathematics kind useful fiction showed mathematical physics conservative extension non mathematical physics every physical fact provable mathematical physics already provable field 's system mathematics reliable process whose physical applications true even though statements false thus mathematics see telling sort story talking numbers existed field statement like fictitious sherlock holmes lived


b baker street true according relevant fictions account metaphysical epistemological problems special mathematics worries left general worries non mathematical physics fiction general field 's approach influential widely rejected part requirement strong fragments second order logic carry reduction statement conservativity seems require quantification abstract models deductions social constructivism social constructivism sees mathematics primarily social construct product


culture subject correction change like sciences mathematics viewed empirical endeavor whose results constantly evaluated may discarded however empiricist view evaluation sort comparison reality social constructivists emphasize direction mathematical research dictated fashions social group performing needs society financing however although external forces may change direction mathematical research strong internal constraints mathematical traditions methods problems meanings values mathematicians enculturated


work conserve historically defined discipline runs counter traditional beliefs working mathematicians mathematics somehow pure objective social constructivists argue mathematics fact grounded much uncertainty mathematical practice evolves status previous mathematics cast doubt corrected degree required desired current mathematical community seen development analysis reexamination calculus leibniz newton argue finished mathematics often accorded much status folk mathematics enough


due overemphasis axiomatic proof peer review practices social nature mathematics highlighted subcultures major discoveries made one branch mathematics relevant another yet relationship goes undiscovered lack social contact mathematicians social constructivists argue speciality forms epistemic community often great difficulty communicating motivating investigation unifying conjectures might relate different areas mathematics social constructivists see process mathematics actually creating meaning social realists see deficiency either


human capacity abstractify human 's cognitive bias mathematicians' collective intelligence preventing comprehension real universe mathematical objects social constructivists sometimes reject search foundations mathematics bound fail pointless even meaningless contributions school made imre lakatos thomas tymoczko although clear either would endorse title recently paul ernest explicitly formulated social constructivist philosophy mathematics consider work paul erd whole advanced view although personally rejected


movement began question idea seeking foundations finding one right answer mathematics works starting point eugene wigner 's famous paper unreasonable effectiveness mathematics natural sciences argued happy coincidence mathematics physics well matched seemed unreasonable hard explain popper 's two senses number statements realist constructivist theories normally taken contraries however karl popper argued number statement apples


statement must considered example tools linguistics generally applied symbol systems mathematics mathematics studied markedly different way languages mathematics language different type language natural languages indeed need clarity specificity language mathematics far constrained natural languages studied linguists however methods developed frege tarski study mathematical language extended greatly tarski 's student richard montague linguists working


formal semantics show distinction mathematical language natural language may great seems mohan ganesalingam analysed mathematical language using tools formal linguistics ref name ganesalingam ref ganesalingam notes features natural language necessary analysing mathematical language tense many analytical tools used context free grammars one important difference mathematical objects clearly defined types explicitly defined text effectively allowed introduce word one part sentence


declare part speech another operation analogue natural language ref name ganesalingam arguments indispensability argument realism argument associated willard quine hilary putnam considered stephen yablo one challenging arguments favor acceptance existence abstract mathematical entities numbers sets ref name ya ref form argument follows one must ontological commitments ''all'' entities indispensable best scientific theories entities ''only'' commonly referred mathematical


entities indispensable best scientific theories therefore one must ontological commitments mathematical entities ref name mmm putnam h ''mathematics matter method philosophical papers vol '' cambridge cambridge university press nd ed ref justification first premise controversial putnam quine invoke naturalism justify exclusion non scientific entities hence defend part assertion entities postulated scientific theories including numbers accepted real justified confirmation holism since theories confirmed piecemeal fashion


whole justification excluding entities referred well confirmed theories puts nominalist wishes exclude existence sets non euclidean geometry include existence quarks undetectable entities physics example difficult position ref name mmm epistemic argument realism anti realist epistemic argument platonism made paul benacerraf hartry field platonism posits mathematical objects ''abstract'' entities general agreement abstract entities cannot interact causally concrete physical entities truth values mathematical assertions depend


developed philosophy mathematical structuralism according mathematical objects nonetheless versions structuralism compatible versions realism argument hinges idea satisfactory naturalistic account thought processes terms brain processes given mathematical reasoning along everything else one line defense maintain false mathematical reasoning uses special intuition involves contact platonic realm modern form argument given sir roger penrose another line defense maintain


abstract objects relevant mathematical reasoning way non causal analogous perception argument developed jerrold katz book ''realistic rationalism'' radical defense denial physical reality ie mathematical universe hypothesis case mathematician 's knowledge mathematics one mathematical object making contact another aesthetics many practicing mathematicians drawn subject sense beauty perceive one sometimes hears sentiment mathematicians would like leave philosophy philosophers get back


sense mathematical beauty universal amongst practicing mathematicians way example provide two proofs irrationality first traditional proof contradiction ascribed euclid second direct proof involving fundamental theorem arithmetic argue gets heart issue davis hersh argue mathematicians find second proof aesthetically appealing gets closer nature problem paul erd well known notion hypothetical book containing elegant beautiful mathematical proofs


pure mathematics superior beauty applied mathematics precisely cannot used war similar ends journals https academicoupcom philmat ''philosophia mathematica'' journal http wwwexacuk pernest ''the philosophy mathematics education journal'' homepage see also definitions mathematics formal language foundations mathematics golden ratio model theory non standard analysis philosophy language philosophy logic philosophy science philosophy physics philosophy probability rule inference science studies scientific method related works ''the analyst'' euclid 's ''elements'' formally undecidable propositions principia mathematica related systems computable numbers application entscheidungsproblem ''introduction mathematical


philosophy'' new foundations mathematical logic ''principia mathematica'' ''the simplest mathematics'' historical topics history philosophy science history mathematics history philosophy notes reading aristotle prior analytics hugh tredennick trans pp nbsp ''aristotle volume nbsp '' loeb classical library william heinemann london uk benacerraf paul putnam hilary eds ''philosophy mathematics selected readings'' st edition prentice hall englewood cliffs nj nd edition cambridge university press cambridge uk berkeley george ''the analyst discourse addressed infidel mathematician wherein examined whether object principles inferences modern analysis


distinctly conceived evidently deduced religious mysteries points faith'' london dublin online text david r wilkins ed http wwwmathstcdie pub histmath people berkeley analyst analysthtml eprint bourbaki n ''elements history mathematics'' john meldrum trans springer verlag berlin germany chandrasekhar subrahmanyan ''truth beauty aesthetics motivations science'' university chicago press chicago il colyvan mark indispensability arguments philosophy mathematics ''stanford encyclopedia philosophy'' edward n zalta ed http platostanfordedu entries mathphil indis eprint davis philip j hersh reuben ''the mathematical experience'' mariner books new york ny devlin keith ''the math instinct 're


princeton nj nd edition reprinted dover publications new york ny hardy gh ''a mathematician 's apology'' st published reprinted cp snow foreword reprinted cambridge university press cambridge uk hart wd ed ''the philosophy mathematics'' oxford university press oxford uk hendricks vincent f hannes leitgeb eds ''philosophy mathematics questions'' new york automatic press vip https webarchiveorg web http phil mathorg huntley ''the divine proportion study mathematical beauty'' dover publications new york ny irvine ed ''the philosophy mathematics'' ''handbook philosophy science'' series


london uk maddy penelope ''naturalism mathematics'' oxford university press oxford uk maziarz edward greenwood thomas ''greek mathematical philosophy'' barnes noble books mount matthew ''classical greek mathematical philosophy'' peirce benjamin linear associative algebra see ''american journal mathematics'' peirce cs ''collected papers charles sanders peirce'' vols charles hartshorne paul weiss eds vols arthur w burks ed harvard university press cambridge nbsp cited cp volume paragraph peirce cs various pieces mathematics logic many readable online links


charles sanders peirce bibliography especially books authored edited peirce published lifetime two sections following plato republic volume paul shorey trans pp nbsp ''plato volume '' loeb classical library william heinemann london uk plato republic volume paul shorey trans pp nbsp ''plato volume '' loeb classical library william heinemann london uk resnik michael ''frege philosophy mathematics'' cornell university resnik michael ''mathematics science patterns'' clarendon press oxford uk robinson gilbert de b ''the foundations geometry''


leibniz peano'' mit press cambridge tait william w truth proof platonism mathematics ''synthese'' reprinted pp nbsp wd hart ed tarski ''logic semantics metamathematics papers '' jh woodger trans oxford university press oxford uk nd edition john corcoran ed hackett publishing indianapolis ulam sm ''analogies analogies mathematical reports sm ulam los alamos collaborators'' ar bednarek fran oise ulam eds university california press berkeley ca van heijenoort jean ed ''from frege g del


source book mathematical logic '' harvard university press cambridge wigner eugene unreasonable effectiveness mathematics natural sciences ''communications pure applied mathematics'' ''' ''' http wwwdartmouthedu matc mathdrama reading wignerhtml eprint wilder raymond l ''mathematics cultural system'' pergamon witzany guenther ''can mathematics explain evolution human language'' communicative integrative biology external links http wwwieputmedu struct ''mathematical structuralism'' internet encyclopaedia philosophy http wwwieputmedu abstract ''abstractionism'' internet encyclopaedia philosophy http wwwuclacuk philosophy lpsg london philosophy study guide offers many suggestions read depending student 's familiarity subject http wwwuclacuk philosophy lpsg philmathhtm


looking night sky although since improved observational capabilities since invention telescope commonly credited hans lippershey german dutch spectacle maker ref name ref although galileo played large role development creation telescopes visible light astronomy continues get better modern day projects james webb telescope projected launch since visible light astronomy restricted visible light equipment necessary simply star gazing means 's commonly participated type astronomy

Natural science
Space science
Astronomy
Optical astronomy


well oldest history beginning fresco giuseppe bertini depicting galileo showing doge venice use telescope advent telescopes astronomy limited solely unaided eyesight humans gazing stars objects night sky thousands years evident naming many constellations notably largely greek names used today hans lippershey german dutch spectacle maker commonly credited first invent optical telescope lippershey first recorded person apply patent telescope ref


name however unclear lippershey first build telescope based uncertain descriptions telescope lippershey tried obtain patent galileo galilei made telescope magnification following year galileo later made improved versions magnification galilean telescope observer could see magnified upright images earth commonly known terrestrial telescope spyglass galileo could also use observe sky time one could construct


telescopes good enough purpose august galileo demonstrated one early telescopes magnification venetian lawmakers galileo 's telescopes also profitable sideline selling merchants found useful sea items trade published initial telescopic astronomical observations march brief treatise titled ''sidereus nuncius'' ''starry messenger'' modern day modern day visible light astronomy still practiced many amateur astronomers especially since telescopes much widely available public


made time rather night one hubble 's famous images ''pillars creation'' shows stars forming eagle nebula image hubble space telescope hubble space telescope space telescope created nasa launched low earth orbit still operation today hubble space telescope 's four main instruments observe near ultraviolet visible near infrared spectra hubble 's images detailed images ever taken leading many breakthroughs astrophysics accurately determining rate


expansion universe james webb space telescope james webb space telescope formal successor hubble space telescope set launch november one ambitious technically complex missions nasa ever set focus upon james webb space telescope space based telescope set orbit near second lagrange point earth sun system earth optical telescopes three main types telescopes used visible light astronomy refracting telescopes use lenses form image


commonly used amateur astronomers especially viewing brighter objects moon planets due lower cost ease usage reflecting telescopes use mirrors form image commonly used scientific purposes catadioptric telescopes use combination lenses mirrors form image essentially combination refracting reflecting telescopes type telescope suffers different types aberration refracting telescopes chromatic aberration causes colors shown edges separating light dark parts image colors


due lens unable focus colors convergence point reflecting telescopes suffer several types optical inaccuracies axis aberrations near edges field view catadioptric telescopes vary types optical inaccuracies present numerous catadioptric telescope designs effect ambient brightness light pollution map europethe visibility celestial objects night sky affected light pollution presence moon night sky historically hindering astronomical observation increasing amount ambient lighting advent


called shooting stars also commonly observed meteor showers perseids leonids make viewing meteors much easier multitude meteors visible relatively short period time planets usually observed aid telescope binoculars venus likely easiest planet observe without aid instruments bright even seen daylight however mars jupiter saturn also seen without aid telescopes binoculars constellations stars also often observed used


weaknesses struggles often involve strategies tactics unconventional warfare weaker combatants attempting use strategy offset deficiencies quantity quality forces equipment strategies may necessarily militarized contrast ' 'symmetric warfare'' two powers comparable military power resources rely tactics similar overall differing details execution asymmetric warfare form irregular warfare violent conflict formal military informal less equipped supported understaffed resilient motivated opponent term frequently used

Applied science
Military sciences
Other Military
Asymmetric warfare


describe also called ''guerrilla warfare'' ''insurgency'' ''counterinsurgency'' ' 'rebellion'' ''terrorism'' ''counterterrorism'' definition differences popularity term dates andrew j r mack 's article big nations lose small wars ''world politics'' asymmetric referred simply significant disparity power opposing actors conflict power sense broadly understood mean material power large army sophisticated weapons advanced economy mack 's analysis largely ignored day end cold war sparked renewed interest among academics


late new research building mack 's insights beginning mature us military began seriously consider problems associated asymmetric warfare discussion since complicated tendency academic military communities use term different ways close association guerrilla warfare insurgency terrorism counterinsurgency counterterrorism military authors tend use term asymmetric refer indirect nature strategies many weak actors adopt even nature adversary eg asymmetric adversaries


weak actors majority asymmetric conflicts strategic basis conventional warfare belligerents deploy forces similar type outcome predicted quantity opposing forces quality example better command control forces c times true composition strategy forces makes impossible either side close battle example standoff continental land forces french army maritime forces


united kingdom 's royal navy french revolutionary napoleonic wars words admiral jervis campaigns say lords french come say come sea confrontation napoleon bonaparte described elephant whale tactical basis oil drum roadside ied northern ireland removed culvert tactical success asymmetric warfare dependent least following assumptions one side technological advantage outweighs numerical


advantage enemy decisive english longbow battle cr cy example technological superiority usually canceled vulnerable infrastructure targeted devastating results destruction multiple electric lines roads water supply systems highly populated areas could devastating effects economy morale contrast weaker side may structures training tactics technology prove decisive allow smaller force overcome much larger one example several centuries greek hoplite 's heavy infantry use phalanx made


far superior enemies battle thermopylae also involved good use terrain well known example inferior power position self defense ie attack occupation ''may'' possible use unconventional tactics hit run selective battles superior power weaker effective means harassment without violating laws war perhaps classical historical examples doctrine may found american revolutionary war movements world war ii french resistance soviet yugoslav partisans


democratic aggressor nations strategy used play electorate 's patience conflict vietnam war others since provoking protests consequent disputes among elected legislators inferior power aggressive position however turns tactics prohibited laws war ''jus bello'' success depends superior power 's refraining like tactics example law land warfare prohibits use flag truce clearly marked medical vehicles cover attack ambush still asymmetric combatant using


prohibited tactic advantage depends superior power 's obedience corresponding law similarly laws warfare prohibit combatants using civilian settlements populations facilities military bases inferior power uses tactic depends premise superior power respect law violating attack civilian target propaganda advantage outweigh material loss terrorism two different viewpoints relationship asymmetric warfare terrorism modern context asymmetric warfare increasingly considered


escape routes also become difficult terrain prolonged combat fills streets rubble early example terrain advantage battle thermopylae nbsp bc narrow terrain defile used funnel persian forces numerically superior point could use size advantage th century irregulars known assassins successful nizari ismaili state state consisted fortresses alamut castle built strategic hilltops highlands difficult access surrounded hostile lands assassins developed


tactics eliminate high value targets posed threat security including crusaders american revolutionary war patriot lieutenant colonel francis marion known swamp fox took advantage irregular tactics interior lines wilderness colonial south carolina stymie larger british regular forces yugoslav partisans starting small detachments around mountain villages fought german axis occupation forces successfully taking advantage rough terrain survive despite small numbers next four years slowly forced enemies back recovering population centers resources eventually growing


regular yugoslav army role civilians civilians could play important role determining outcome asymmetric war conflicts easy insurgents quickly assimilate population attack tips timing location insurgent activity greatly undermine resistance information centric framework ref name berman ref civilians seen primarily sources strategic information rather resources provides paradigm better understand dynamics conflicts civilian information sharing important framework assumes consequential action noncombatants civilians


information sharing rather supplying resources recruits shelter combatants information shared anonymously without endangering civilian relays given additional assumption larger dominant force government framework suggests following implications civilians receive services government rebel forces incentive share valuable information rebel violence reduced government provides services provision security services complementary reducing violence civilian casualties reduce civilian support perpetrating group provision information strongly correlated


level anonymity ensured survey empirical literature conflict ref name berman provide conclusive evidence aforementioned claims framework provides starting point explore role civilian information sharing asymmetric warfare war proxy asymmetric warfare carried generally covertly allegedly non governmental actors connected sympathetic particular nation 's state actor 's interest may deemed ''war proxy'' typically done give ' 'deniability'' state actor deniability important keep state


actor tainted actions allow state actor negotiate apparent good faith claiming responsible actions parties merely sympathizers avoid accused belligerent actions war crimes proof emerges true extent state actor 's involvement strategy backfire example see iran contra philip agee examples american revolutionary war initiation american revolutionary war necessarily showcase asymmetric techniques harold murdock boston attempted solve puzzle first


shots fired lexington green came suspicion score militia men gathered sunrise await arrival hundreds well prepared british soldiers sent specifically provoke incident could used patriot propaganda purposes return british force boston following search operations concord subject constant skirmishing using partisan forces gathered communities along route making maximum use terrain particularly trees stone field walls overcome limitations weapons muskets effective range


metres throughout war skirmishing tactics british troops move continued key factor patriots' success particularly western theater american revolutionary war another feature long march concord urban warfare technique using buildings along route additional cover snipers revolutionary forces forced way norfolk virginia used waterfront buildings cover shots british vessels river response destruction buildings ingeniously used advantage rebels


sloop war ''ranger'' april addition attacks merchant shipping made two landings british soil ref name bicheno ref effect raids particularly coupled capture royal navy 's first success british waters jones 's last force british government increase resources coastal defence create climate fear among british public subsequently fed press reports preparations ''bonhomme richard'' mission ref name bicheno conflict


turned increasingly proxy war behalf france following strategy proposed initially resisted idealistic young king louis xvi came throne age months lexington france ultimately drove great britain brink defeat entering war directly several fronts throughout world ref name bicheno american civil war american civil war saw rise asymmetric warfare border states particular us western territorial border kansas nebraska act opened territories


voting expansion slavery beyond missouri compromise lines political implications broken compromise nothing less potential expansion slavery across north american continent including northern reaches annexed mexican territories california oregon stakes high caused flood immigration border grab land expand slavery west others grab land vote expansion slavery pro slavery land grabbers began asymmetric violent attacks pacifist abolitionists settled lawrence


territorial towns suppressing slavery john brown abolitionist travelled osawatomie kansas territory expressly foment retaliatory attacks back pro slavery guerrillas twice ransacked lawrence osawatomie one brown 's sons shot dead abolitionists would return attacks brown theorized violent spark set border would way finally ignite long hoped slave rebellion brown broad sworded slave owners potawatomi creek bloody civilian violence initially symmetrical however american civil war ignited


pro union townspeople commissioned union military units union army trying keep check blocking kansans pro union missourians organizing militarily marauding bushwhackers worst act domestic terror us history came august paramilitary guerrillas amassed strong rode night miles across eastern kansas abolitionist stronghold lawrence political target destroyed town gunning civilians confederate officer whose company joined quantrill 's raiders day witnessed civilian slaughter forbade soldiers joining carnage commissioned


officer refused participate quantrill 's asymmetric warfare civilians philippine american war philippine american war armed conflict united states filipino revolutionaries estimates filipino forces vary tens thousands auxiliaries ref name deady p ref lack weapons ammunition significant impediment filipinos forces armed bolo knives bows arrows spears primitive weapons practice proved vastly inferior us firepower filipino soldiers war display clark museum goal end state sought


pursued short term goal guerrilla tactics better suited protracted struggle ref name deady p targeting mckinley motivated revolutionaries short term victory demoralized convinced many undecided filipinos united states would depart precipitously ref name deady p revolutionary leadership viewed guerrilla warfare strategically tactical option final recourse means operation better suited disadvantaged situation november emilio aguinaldo decreed guerrilla war would henceforth strategy made american occupation philippine archipelago


difficult next years fact first four months guerrilla war americans nearly casualties philippine revolutionary army began staging bloody ambushes raids guerrilla victories paye catubig makahambus pulang lupa balangiga mabitac first even seemed filipinos would fight americans stalemate force withdraw president mckinley even considered beginning phase shift guerrilla warfare drove us army adopt counter insurgency tactics civilians given identification


instead capitulating boers fought protracted guerrilla war boer guerrillas defeated british brought bear imperial troops ten times many used conventional phase war british began constructing blockhouses built within machine gun range one another flanked barbed wire slow boers' movement across countryside block paths valuable targets tactics eventually evolved today 's counterinsurgency tactics ref name dobbie word 'commando' dobbie elliott v k ''american speech'' ''' ''' apr https wwwjstororg stable ref boer commando raids deep


cape colony organized commanded jan smuts resonated throughout century british adopted adapted tactics first used boers ref name dobbie world war lawrence arabia british support arab uprising ottoman empire ottomans stronger power arabs weaker austria hungary 's invasion serbia august austria hungary stronger power serbia weaker germany 's invasion belgium august germany stronger power belgium weaker world wars abd el krim led resistance morocco


french spanish colonial armies ten times strong guerrilla force led general philippe p tain tigr first anti fascist national defensive organization europe fought benito mussolini 's regime northeast italy anglo irish war irish war independence fought irish republican army black tans auxiliaries lloyd george prime minister time attempted persuade nations war refusing use army using black tans instead conflict conducted asymmetric guerrilla war registered war


ski tactics around unseen trees cut advancing soviet column called motti cubic metre firewood destroyed cut sections one one many soviets shot snipers throats cut behind froze death due inadequate clothing lack camouflage shelter finns also devised petrol bomb called molotov cocktail destroy soviet tanks soviet partisans nbsp resistance movement fought german occupied parts soviet union warsaw uprising nbsp poland home army armia krajowa


rose german occupation germany 's occupation yugoslavia germany vs tito 's partisans mihailovi 's chetniks britain british commandos european coastal raids german countermeasures notorious commando order long range desert group special air service africa later europe south east asian theatre wingate chindits force v force special operations executive soe provisional irish republican army british armed forces northern campaign united states office strategic services oss china burma india theatre merrill 's marauders oss detachment world war ii first indochina war


algerian war independence france cuban revolution became template asymmetric warfare hungarian revolution russo hungarian war saw makeshift forces improvising lopsided tactics soviet tanks libyan support irish republican army troubles collusion british army ulster loyalist groups united states military assistance command studies observations group us mac v sog viet cong vietnam south african border war otherwise known namibian war independence south african defence force people 's liberation


army namibia united states support nicaraguan contras cold war end world war ii established two powerful victors united states america united states us union soviet socialist republics ussr soviet union two dominant world superpowers cold war examples proxy wars southeast asia specifically vietnam viet minh nlf insurgencies engaged asymmetrical guerrilla warfare france first later united states period vietnam war war


mujahideen soviet armed forces soviet afghan war though claimed source term asymmetric warfare occurred years mack wrote asymmetric conflict note term asymmetric warfare became well known west aid given us mujahadeen war covert tactical level reagan administration told world helping freedom loving people afghanistan many countries including us participated proxy war ussr cold war


navy palestinian organizations access large scale military equipment conduct operations instead utilize asymmetric tactics knife attacks small gunfights cross border sniping rocket attacks ref name upicom ref suicide bombings sri lanka sri lankan civil war raged sri lankan government liberation tigers tamil eelam ltte saw large scale asymmetric warfare war started insurgency progressed large scale conflict mixture guerrilla conventional warfare seeing ltte use suicide bombing male female suicide bombers


asymmetric warfare '' august http wwwcomworg rma fulltext asymmetrichtml asymmetric warfare revolution military affairs rma debate sponsored project defense alternatives books arreguin toft ivan ''how weak win wars theory asymmetric conflict'' new york cambridge cambridge university press barnett roger w ''asymmetrical warfare today 's challenge us military power'' washington dc brassey 's friedman george ''america 's secret war inside hidden worldwide struggle united states enemies'' london little brown tv paul ''asymmetric conflicts war initiation weaker powers'' new york cambridge university press j schroefl ''political asymmetries


era globalization'' peter lang kaplan robert ''warrior politics leadership demands pagan ethos'' new york vintage merom gil ''how democracies lose small wars'' new york cambridge metz steven douglas v johnson ii ''asymmetry us military strategy definition background strategic concepts'' carlisle barracks strategic studies institute us army war college http wwwstrategicstudiesinstitutearmymil pdffiles pub pdf j schroefl sm cox pankratz ''winning asymmetric war political social military responses'' peter lang record jeffrey ''beating goliath insurgencies win'' washington dc potomac books gagliano giuseppe''introduzione alla conflittualita' non convenzionale'' new press resnick uri


dynamics asymmetric territorial conflict evolution patience basingstoke uk palgrave macmillan http wwwpalgravecom uk book sobelman daniel 'new rules game israel hizbollah withdrawal lebanon'' tel aviv university jaffee center strategic studies wwwinssorgil upload file pdf sobelman daniel 'hizbollah terror resistance towards national defence strategy'' clive jones sergio catignani eds israel hizbollah asymmetric conflict historical comparative perspective'' routledge pp nbsp sobelman daniel learning deter deterrence failure success israel hezbollah conflict international security vol winter articles papers bryant g j asymmetric warfare


british experience eighteenth century india ''journal military history'' pp http musejhuedu journals journal military history v bryanthtml project muse ivan arreguin toft weak win wars theory asymmetric conflict ''international security'' vol summer pp nbsp j paul dunne et al managing asymmetric conflict ''oxford economic papers'' vol pp nbsp mathematical approach concept marcus corbin '' https webarchiveorg web http wwwcdiorg terrorism asymmetriccfm reshaping military asymmetric warfare cdi website october vincent j goulding jr parameters winter pp nbsp andrew jr mack big nations lose small wars politics asymmetric conflict ''world politics'' vol


'''environmental economics''' sub field economics concerned environmental issues become widely studied subject due growing environmental concerns twenty first century environmental economics undertakes theoretical empirical studies economic effects national local environmental policies around world nbsp particular issues include costs benefits alternative environmental policies deal air pollution water quality toxic substances solid waste global warming environmental economics distinguished ecological economics ecological economics emphasizes economy subsystem ecosystem focus upon preserving natural capital

Social science
Economics
Environmental economics


one survey german economists found ecological environmental economics different schools economic thought ecological economists emphasizing strong sustainability rejecting proposition human made physical capital substitute natural capital history modern field environmental economics traced topics concepts market failure air pollution example market failure factory imposing negative external cost community central environmental economics concept market failure market failure means markets fail allocate resources efficiently stated hanley shogren


white market failure occurs market allocate scarce resources generate greatest social welfare wedge exists private person given market prices society might want protect environment wedge implies wastefulness economic inefficiency resources reallocated make least one person better without making anyone else worse common forms market failure include externalities non excludability non rivalry externality externality exists person makes choice affects people way


accounted market price externality positive negative usually associated negative externalities environmental economics instance water seepage residential buildings occurring upper floors affect lower floors another example concerns sale amazon timber disregards amount carbon dioxide released cutting firm emitting pollution typically take account costs pollution imposes others result pollution may occur excess 'socially efficient' level level would exist


market required account pollution classic definition influenced kenneth arrow james meade provided heller starrett define externality situation private economy lacks sufficient incentives create potential market good nonexistence market results losses pareto efficiency economic terminology externalities examples market failures unfettered market lead efficient outcome common goods public goods costly exclude people access


environmental resource resource either called common property resource rivalry resource one person 's use resource reduces others' opportunity use resource public good use resource non rivalrous either case non exclusion market allocation likely inefficient challenges long recognized hardin 's concept tragedy commons popularized challenges involved non exclusion common property commons refers environmental asset common property resource common pool resource refers property right


regime allows collective body devise schemes exclude others thereby allowing capture future benefit streams open access implies ownership sense property everyone owns nobody owns ref name ostrom e ostrom e governing commons cambridge cambridge university press ref basic problem people ignore scarcity value commons end expending much effort harvesting resource eg fishery hardin theorizes absence restrictions users open access resource use pay


exclusive rights leading environmental degradation see however ostrom 's work people using real common property resources worked establish self governing rules reduce risk tragedy commons ref name ostrom e mitigation climate change effects example public good social benefits reflected completely market price public good since risks climate change non rival non excludable efforts non rival since climate mitigation provided one reduce level


mitigation anyone else enjoys non excludable actions global consequences one excluded country 's incentive invest carbon abatement reduced free ride efforts countries century ago swedish economist knut wicksell first discussed public goods provided market people might conceal preferences good still enjoy benefits without paying gallery caption global biochemical cycles widths px heights px perrow image nitrogen cyclejpg nitrogen cycle image water cyclepng water cycle image carbon cycle cute diagramsvg carbon cycle image oxygen cyclejpg oxygen


cycle gallery valuation assessing economic value environment major topic within field values natural resources often reflected prices markets set fact many available monetary charge mismatch frequently causes distortions pricing natural assets overuse underinvestment economic value tangible benefits ecosystem services generally natural resources include use indirect see nature section ecological economics non use values include existence option bequest values example


people may value existence diverse set species regardless effect loss species ecosystem services existence species may option value may possibility using human purpose example certain plants may researched drugs individuals may value ability leave pristine environment children use indirect use values often inferred revealed behavior cost taking recreational trips using hedonic methods values estimated based


observed prices non use values usually estimated using stated preference methods contingent valuation choice modelling contingent valuation typically takes form surveys people asked much would pay observe recreate environment willingness pay willingness accept wta compensation destruction environmental good hedonic pricing examines effect environment economic decisions housing prices traveling expenses payments visit parks state subsidy almost governments states magnify environmental harm providing various types subsidies


effect paying companies economic actors exploit natural resources protect damage nature public subsidies conservatively estimated trillion us dollars per year solutions solutions advocated correct externalities include '' environmental regulations'' plan economic impact estimated regulator usually done using cost benefit analysis growing realization regulations also known command control instruments distinct economic instruments commonly asserted proponents environmental economics


eg regulations enforced fines operate form tax pollution rises threshold prescribed eg pollution must monitored laws enforced whether pollution tax regime regulatory regime main difference environmental economist would argue exists two methods however total cost regulation command control regulation often applies uniform emissions limits polluters even though firm different costs emissions reductions ie firms system abate pollution inexpensively others abate


make reduction ie buying tradeable permits another firm costlier practice tradeable permits approaches success us 's sulphur dioxide trading program eu emissions trading scheme interest application spreading environmental problems ''taxes tariffs pollution'' increasing costs polluting discourage polluting provide dynamic incentive disincentive continues operate even pollution levels fall pollution tax reduces pollution socially optimal level would set level


pollution occurs benefits society example form greater production exceeds costs concept introduced arthur pigou british economist active late nineteenth mid twentieth century showed externalities occur markets fail meaning naturally produce socially optimal amount good service argued tax production paint would encourage polluting factory reduce production amount best society whole taxes known amongst economists pigouvian taxes


regularly implemented negative externalities present advocate major shift taxation income sales taxes tax pollution called green tax shift ''better defined property rights'' coase theorem states assigning property rights lead optimal solution regardless receives transaction costs trivial number parties negotiating limited example people living near factory right clean air water factory right pollute either factory could pay affected pollution


people could pay factory pollute citizens could take action would property rights violated us river keepers law early example giving citizens downstream right end pollution upstream government act early example bioregional democracy many markets pollution rights created late twentieth century see emissions trading according coase theorem involved parties bargain results efficient solution however modern economic theory


shown presence asymmetric information may lead inefficient bargaining outcomes specifically rob shown pollution claim settlements lead socially optimal outcome individuals affected pollution learned private information disutility already negotiations take place goldl cke schmitz shown inefficiencies may also result parties learn private information negotiations provided feasible transfer payments bounded relationship fields environmental economics related ecological economics differences


explicitly long term environmental sustainability issues scale environmental economics viewed pragmatic price system ecological economics idealistic attempts use money primary arbiter decisions two groups specialists sometimes conflicting views may traced different philosophical underpinnings another context externalities apply globalization permits one player market unconcerned biodiversity undercut prices another creating race bottom regulations conservation turn may cause


environment poly equitable poly sustainable poly


social imagemap environmental economics distinct resource economics natural resource economics subfield began main concern researchers optimal commercial exploitation natural resource stocks resource managers policy makers eventually began pay attention broader importance natural resources eg values fish trees beyond commercial exploitation difficult distinguish environmental natural resource economics


separate fields two became associated sustainability many radical green economists split work alternate political economy environmental economics major influence theories natural capitalism environmental finance could said two sub branches environmental economics concerned resource conservation production value biodiversity humans respectively theory natural capitalism hawken lovins lovins goes traditional environmental economics envisioning world natural services considered par physical capital radical green


economists reject neoclassical economics favour new political economy beyond capitalism communism gives greater emphasis interaction human economy natural environment acknowledging economy three fifths ecology mike nickerson political group proponent transition renewable energy radical approaches would imply changes money supply likely also bioregional democracy political economic ecological environmental limits aligned subject arbitrage normally possible capitalism emerging sub field environmental economics studies intersection


law economics environmental law studied economic perspective economic analysis environmental law studies instruments zoning expropriation licensing third party liability safety regulation mandatory insurance criminal sanctions book michael faure surveys literature professional bodies main academic professional organizations discipline environmental economics association environmental resource economists aere http wwweaereorg european association environmental resource economics eaere main academic professional organization discipline ecological economics international society ecological economics isee main


organization green economics https greeneconomicsinstituteorguk green economics institute see also agroecology carbon fee dividend carbon finance carbon negative fuel circular economy earth economics policy think tank eco capitalism eco commerce economics global warming ecometrics eco money eco socialism ecosystem marketplace ecotax energy balance environmental accounting environmental economists category environmental credit crunch environmental enterprise environmental investment organisation environmental pricing reform environmental tariff fair trade fiscal environmentalism free market environmentalism green banking green libertarianism green syndicalism green trading iso environmental standards list scholarly journals environmental economics natural capital natural resource natural resource economics principles ecopreneurship property


rights economics renewable resource risk assessment strategic sustainable investing ssi systems ecology world ecological forum hypotheses theorems coase theorem porter hypothesis notes references references allen v kneese clifford russell environmental economics ''the new palgrave dictionary economics'' v pp nbsp robert n stavins environmental economics ''the new palgrave dictionary economics'' nd edition http wwwdictionaryofeconomicscom sample article abstract article maureen l cropper wallace e oates environmental economics survey ''journal economic literature'' pp https webarchiveorg web http econ serverumdedu cropper publications jc pdf press ''' ''' tausch arno smart development essay new political economy


environment march available ssrn https ssrncom abstract https dxdoiorg ssrn unep guidelines conducting economic valuation coastal ecosystem goods services http wwwunepscsorg scs documents download technical publications guidelines technical publication guidelines conducting economic valuation coastal ecosystem goods serviceshtml unep gef scs technical publication unep procedure determination national regional economic values ecotone goods services total economic values coastal habitats context unep gef project entitled reversing environmental degradation trends south china sea gulf thailand http wwwunepscsorg scs documents download south china sea project knowledge documents south china sea knowledge document economic valuation goods services coastal habitatshtml south china sea knowledge document unep gef scs inf reading david anderson environmental economics natural resource management e https wwwroutledgecom environmental economics natural resource management th edition anderson p book new york routledge john


asafu adjaye https archiveorg details environmentaleco asaf environmental economics non economists e singapore world scientific gregory c chow economics analysis environmental problems singapore world scientific environmental social science industrial ecology market failure


three circles enclosed within one another showing economy society subsets planetary ecological system view useful correcting misconception sometimes drawn previous three pillars diagram portions social economic systems exist independently environment ref name willard b willard b http sustainabilityadvantagecom press sustainability models sustainability models citing ''the power sustainable thinking'' bob doppelt ''the necessary revolution'' peter senge et al retrieved ref '''natural resource economics''' deals supply demand allocation earth 's natural resources one main objective

Social science
Economics
Resource economics


natural resource economics better understand role natural resources economy order develop sustainable methods managing resources ensure availability future generations resource economists study interactions economic natural systems goal developing sustainable efficient economy areas discussion natural resource economics transdisciplinary field academic research within economics aims address connections interdependence human economies natural ecosystems focus operate economy within ecological constraints earth 's natural resources ref name eoetopicecoecon encyclopedia earth


http wwweoearthorg topic ecological economics article topic ecological economics ref resource economics brings together connects different disciplines within natural social sciences connected broad areas earth science human economics natural ecosystems economic models must adapted accommodate special features natural resource inputs traditional curriculum natural resource economics emphasized fisheries models forestry models minerals extraction models ie fish trees ore recent years however resources notably air water global climate environmental resources general become increasingly important policy making academic policy interest moved beyond simply optimal


commercial exploitation standard trio resources encompass management objectives example natural resources broadly defined recreational well commercial values may also contribute overall social welfare levels mere existence economics policy area focuses human aspects environmental problems traditional areas environmental natural resource economics include welfare theory land location use pollution control resource extraction non market valuation also resource exhaustibility sustainability environmental management environmental policy research topics could include environmental impacts agriculture transportation urbanization land use poor


industrialized countries international trade environment climate change methodological advances non market valuation name hotelling 's rule economic model non renewable resource management harold hotelling shows efficient exploitation nonrenewable nonaugmentable resource would otherwise stable economic conditions lead depletion resource rule states would lead net price hotelling rent rose annually rate equal rate interest reflecting increasing scarcity resource nonaugmentable resources inorganic materials


ie minerals uncommon resources augmented recycling existence use substitutes end use products see vogely stated development mineral resource occurs five stages current operating margin rate production governed proportion reserve resource already depleted intensive development margin governed trade rising necessary investment quicker realization revenue extensive development margin extraction begun known previously uneconomic deposits exploration margin


search new deposits resources conducted cost per unit extracted highly uncertain cost failure balanced finding usable resources deposits marginal costs extraction higher first three stages technology margin interacts first four stages gray hotelling exhaustion theory special case since covers stages far important stages simon stated supply natural resources infinite ie perpetual conflicting views


substantially reconciled considering resource related topics depth next section least minimized furthermore hartwick 's rule provides insight sustainability welfare economy uses non renewable resources perpetual resources vs exhaustibility background introduction perpetual resource concept complex one concept resource complex changes advent new technology usually efficient recovery new needs lesser degree new economics eg changes prices material changes energy costs etc one hand material


resources enter time shortage become strategic critical material immediate exhaustibility crisis hand material go use resource proceed perpetual resource become paleoresource material goes almost completely use eg resources arrowhead grade flint complexities influencing resources material include extent recyclability availability suitable substitutes material end use products plus less important factors federal


government suddenly became compellingly interested resource issues december shortly japan cut us tin rubber made materials tungsten difficult obtain worst case resource availability becoming strategic critical material war government stockpile strategic critical materials set around different materials purchased cash obtained trading us agricultural commodities longer term scarcity tin later led completely substituting aluminum


foil tin foil polymer lined steel cans aseptic packaging substituting tin electroplated steel cans resources change time technology economics efficient recovery leads drop ore grade needed average grade copper ore processed dropped copper cobalt iffy supply status ever since belgian congo world 's significant source cobalt given hasty independence cobalt producing


province seceded katanga followed several wars insurgencies local government removals railroads destroyed nationalizations topped invasion province katangan rebels disrupted supply transportation caused cobalt price briefly triple cobalt supply disrupted price shot nickel substitutes pressed service following idea resource war soviets became popular rather chaos resulted zairean cobalt situation would planned strategy designed destroy


mining engineering aime society mining engineers september pp ref using computers satellites replace copper wire land lines important way replacing resource synthesis example industrial diamonds many kinds graphite although certain kind graphite could almost replaced recycled product graphite synthetic example graphite electrodes graphite fiber graphite shapes machined unmachined graphite powder another way replacing extending resource recycling material desired scrap waste depends whether material


separates graphite within kish molten metal along slag cold kish processed several kinds resources need introduced strategic critical materials worst case resources unless mitigated substitution recycling one best abundant resource abundant resource one whose material far found little use using high aluminous clays anorthosite produce alumina magnesium recovered seawater abundant resource quite similar


perpetual resource reserve base part identified resource reasonable potential becoming economically available time beyond currently proven technology current economics operation identified resources whose location grade quality quantity known estimated specific geologic evidence reserves part reserve base economically extracted time determination reserves used surrogate resources often distorted taxation owning firm 's public relations needs comprehensive natural resource


models harrison brown associates stated humanity process lower lower grade ore iron come low grade iron bearing material raw rock anywhere iron formation much different input used make taconite pellets north america elsewhere today coking coal reserves decline pig iron steel production use non coke using processes ie electric steel aluminum industry could shift using bauxite using anorthosite clay magnesium metal magnesia consumption ie refractories currently obtained seawater increase sulfur


become common efficient note ultimately minerals metals obtained processing average rock rock tonnes average igneous rock yield eight tonnes aluminum five tonnes iron tonnes titanium usgs model based crustal abundance data reserve abundance relationship mckelvey applied several metals earth 's crust worldwide us crust potential currently recoverable present technology economy resources come closest mckelvey relationship sought longest time


copper zinc lead silver gold molybdenum metals follow mckelvey relationship ones byproducts major metals vital economy recently titanium aluminum lesser degree bismuth example byproduct metal follow relationship well lead reserves western us would nbsp ppm bismuth clearly low grade bismuth reserve world recoverable resource potential million tonnes copper million tonnes nickel million tonnes


diverse products world economy moving away materials towards services population seems levelling implies lessening demand growth materials much materials recovered somewhat uncommon rocks much coproducts byproducts given operation trade minerals materials trend towards perpetual resources radical new technology impacts materials minerals world powerfully materials used likely perpetual resources already materials


perpetual resources less less materials nonrenewable resources strategic critical materials materials perpetual resources salt stone magnesium common clay mentioned previously thanks new technology synthetic diamonds added list perpetual resources since easily made lump another form carbon synthetic graphite made large quantities graphite electrodes graphite fiber carbon precursors petroleum coke textile fiber firm named liquidmetal technologies inc utilizing removal dislocations


material technique overcomes performance limitations caused inherent weaknesses crystal atomic structure makes amorphous metal alloys retain random atomic structure hot metal solidifies rather crystalline atomic structure dislocations normally forms hot metal solidifies amorphous alloys much better performance properties usual example zirconium titanium liquidmetal alloys stronger standard titanium alloy liquidmetal alloys supplant many high performance alloys exploration ocean bottom last fifty years revealed manganese nodules phosphate


nodules many locations recently polymetallic sulfide deposits discovered polymetallic sulfide black muds presently deposited black smokers cobalt scarcity situation new option recover manganese nodules korean firm plans start developing manganese nodule recovery operation manganese nodules recovered would average manganese nickel copper cobalt commercial grade nautilus minerals ltd planning recover commercial grade material averaging zinc lead


copper massive ocean bottom polymetallic sulfide deposits using underwater vacuum cleaner like device combines current technologies new way partnering nautilus tech cominco ltd anglo american ltd world leading international firms also robot mining techniques could applied ocean rio tinto using satellite links allow workers kilometers away operate drilling rigs load cargo dig ore dump conveyor belts place explosives subsequently blast rock earth firm keep workers danger way


prudent practice resource stock last years achieve sustainability become perpetual resource worse case years resource lasting years perpetual one lasts years called abundant resource defined long material recovered resource depends human need changes technology extraction life cycle product final disposal plus recyclability material availability satisfactory substitutes specifically shows


exhaustibility occur factors weaken play availability substitutes extent recycling feasibility efficient manufacturing final consumer product durable longer lasting consumer products even number factors recent resource information guidance kinds resources must considered covered resource guide update http resourceguide updateblogspotcom transitioning perpetual resources paleoresources perpetual resources transition paleoresource paleoresource one little demand material extracted obsolescent material humans


longer need classic paleoresource arrowhead grade flint resource one makes flint arrowheads spearheads anymore making sharpened piece scrap steel using much simpler obsolescent products include tin cans tin foil schoolhouse slate blackboard radium medical technology radium replaced much cheaper cobalt radioisotopes radiation treatment noncorroding lead cable covering replaced plastics pennsylvania anthracite another material trend towards obsolescence becoming paleoresource shown statistically production anthracite million tonnes


million tonnes million tonnes million tonnes million tonnes amount used per person nbsp kg per person nbsp kg nbsp kg compare usgs anthracite reserves billion tonnes total resources billion tonnes anthracite demand dropped much resources perpetual since anthracite resources far perpetual resource range demand anthracite dropped far possible see anthracite might


become paleoresource probably customers continuing disappear ie convert kinds energy space heating supply network atrophy anthracite coal dealers cannot retain enough business cover costs close mines small volume cover costs also close mutually reinforcing process customers convert forms cleaner energy produce less pollution carbon dioxide coal dealer close lack enough sales volume cover costs coal dealer 's customers forced convert unless


find another nearby coal dealer finally anthracite mine closes enough sales volume cover costs global geochemical cycles gallery caption global geochemical cycles critical life widths px heights px perrow image nitrogen cyclejpg nitrogen cycle image water cyclepng water cycle image carbon cycle cute diagramsvg carbon cycle image oxygen cyclejpg oxygen cycle gallery see also bioeconomics c arden pope calculation kind earth economics policy think tank ecodynamics ecological economics economic rent energy accounting ''energy economics'' ''energy environment'' environmental economics industrial ecology jevons 's paradox land value tax low carbon economy peak oil hubbert 's peak population dynamics severance tax social metabolism sustainable development


systems ecology thermoeconomics tragedy anticommons tragedy commons world references reading david anderson environmental economics natural resource management e https wwwroutledgecom environmental economics natural resource management th edition anderson p book new york routledge michael j conroy james peterson decision making natural resource management new york wiley blackwell kevin h deal wildlife natural resource management e boston delmar cengage learning external links https webarchiveorg web http ecoecoorg international society ecological economics isee http wwwindersciencecom ijge international journal green economics http bibliorepecorg entry tchtml curated bibliography ideas repec energy economics economics


wiener brownian motion process surface sphere wiener process widely considered studied central stochastic process probability theory ref name doob stochasticp ref name rogerswilliams page ref name steele page probability theory related fields '' 'stochastic''' '''random process''' mathematical object usually defined family random variables stochastic processes widely used mathematical models systems phenomena appear vary random manner examples include growth bacterial population electrical current fluctuating due thermal noise movement gas molecule ref name doob stochasticp ref ref name parzen ref ref

Formal science
Mathematics
Pure mathematics
Probability theory
Stochastic process


name gikhmanskorokhod page ref stochastic processes applications many disciplines biology ref name bressloff ref chemistry ref name kampen ref ecology ref name landeengen ref neuroscience ref name lainglord ref physics ref name paulbaschnagel ref image processing signal processing ref name dougherty ref control theory ref name bertsekas ref information theory ref name coverthomas page ref computer science ref name baron ref cryptography telecommunications ref name baccelliblaszczyszyn ref furthermore seemingly random changes financial markets motivated extensive use stochastic processes finance ref name steele ref ref name musielarutkowski ref ref name shreve ref applications study phenomena turn inspired proposal new stochastic processes examples stochastic processes include wiener process brownian motion process ref rosenblatt ref name rosenblatt ref used louis bachelier study price changes


paris bourse ref name jarrowprotter ref poisson process used k erlang study number phone calls occurring certain period time ref name stirzaker ref two stochastic processes considered important central theory stochastic processes ref name doob stochasticp ref name parzen discovered repeatedly independently bachelier erlang different settings countries ref name jarrowprotter ref name guttorpthorarinsdottir ref term '''random function''' also used refer stochastic random process ref name gusakkukush page ref ref name skorokhod page ref stochastic process also interpreted random element function space ref


name kallenberg page ref name lamperti page ref terms ' 'stochastic process'' ''random process'' used interchangeably often specific mathematical space set indexes random variables ref name kallenberg page ref ref name chaumontyor ref often two terms used random variables indexed integers interval real line ref name gikhmanskorokhod page ref name chaumontyor random variables indexed cartesian plane higher dimensional euclidean space collection random variables usually called random field instead ref name gikhmanskorokhod page ref name adlertaylor page ref values stochastic process always numbers vectors mathematical


objects ref name gikhmanskorokhod page ref name lamperti page based mathematical properties stochastic processes grouped various categories include random walks ref name lawlerlimic ref martingales ref name williams ref markov processes ref name rogerswilliams ref l vy processes ref name applebaumbook ref gaussian processes random fields ref name adler ref renewal processes branching processes ref name karlintaylor ref study stochastic processes uses mathematical knowledge techniques probability calculus linear algebra set theory topology ref name hajek ref ref name latoucheramaswami ref ref name daleyvere jones ref well branches mathematical analysis real analysis measure theory fourier analysis functional analysis ref name billingsley ref ref name br maud ref ref name bobrowski ref theory stochastic processes considered important contribution mathematics ref name applebaum ref


continues active topic research theoretical reasons applications ref name blathimkeller ref ref name talagrand ref ref name bressloff vii ref introduction stochastic random process defined collection random variables indexed mathematical set meaning random variable stochastic process uniquely associated element set ref name parzen ref name gikhmanskorokhod page set used index random variables called '''index set''' historically index set subset real line natural numbers giving index set interpretation time ref name doob stochasticp random variable


collection takes values mathematical space known '' 'state space''' state space example integers real line math n math dimensional euclidean space ref name doob stochasticp ref name gikhmanskorokhod page '''increment''' amount stochastic process changes two index values often interpreted two points time ref name karlintaylor page ref name applebaum page stochastic process many outcomes due randomness single outcome stochastic process called among names '' 'sample function''' '' 'realization''' ref name lamperti page ref name rogerswilliams page b single computer simulated '' 'sample function''' '' 'realization''' among terms three dimensional


wiener brownian motion process time index set stochastic process non negative numbers state space three dimensional euclidean space classifications stochastic process classified different ways example state space index set dependence among random variables one common way classification cardinality index set state space ref name florescu page ref name karlintaylor page ref interpreted time index set stochastic process finite countable number elements finite


set numbers set integers natural numbers stochastic process said '' 'discrete time''' ref name billingsley page ref name borovkov page ref index set interval real line time said '''continuous''' two types stochastic processes respectively referred '' 'discrete time''' '''continuous time stochastic processes''' ref name karlintaylor page ref name br maud page ref name rosenthal page ref discrete time stochastic processes considered easier study continuous time processes require advanced mathematical techniques knowledge particularly due index set uncountable ref name kloedenplaten page ref ref name khoshnevisan page ref index set integers subset


stochastic process also called '''random sequence''' ref name borovkov page state space integers natural numbers stochastic process called '' 'discrete''' '''integer valued stochastic process''' state space real line stochastic process referred '' 'real valued stochastic process''' '''process continuous state space''' state space math n math dimensional euclidean space stochastic process called math n math '' 'dimensional vector process''' math n math '' 'vector process''' ref name florescu page ref name karlintaylor page etymology word ' 'stochastic'' english originally used adjective definition


pertaining conjecturing stemming greek word meaning aim mark guess oxford english dictionary gives year earliest occurrence ref name oxfordstochastic ref work probability ''ars conjectandi'' originally published latin jakob bernoulli used phrase ars conjectandi sive stochastice translated art conjecturing stochastics ref name nin page ref phrase used reference bernoulli ladislaus bortkiewicz ref name sheyninstrecker page ref wrote german word ' 'stochastik'' sense meaning random term ' 'stochastic process'' first appeared english


paper joseph doob ref name oxfordstochastic term specific mathematical definition doob cited another paper term ' 'stochastischer proze '' used german aleksandr khinchin ref name doob ref name khintchine ref though german term used earlier example andrei kolmogorov ref name kolmogoroff page ref according oxford english dictionary early occurrences word ''random'' english current meaning relates chance luck date back th century earlier recorded usages started th century noun meaning impetuosity great speed force violence riding


running striking etc word comes middle french word meaning speed haste probably derived french verb meaning run gallop first written appearance term ''random process'' pre dates ' 'stochastic process'' oxford english dictionary also gives synonym used article francis edgeworth published ref name oxfordrandom ref terminology definition stochastic process varies ref name fristedtgray page ref stochastic process traditionally defined collection random variables indexed set ref name rogerswilliams page ref name asmussen page terms ''random process'' ' 'stochastic process''


considered synonyms used interchangeably without index set precisely specified ref name kallenberg page ref name chaumontyor ref name adlertaylor page ref name stirzaker page ref ref name rosenblatt page ref ref name gubner page ref collection ref name lamperti page ref name stirzaker page family used ref name parzen ref name ito page ref instead index set sometimes terms parameter set ref name lamperti page parameter space ref name adlertaylor page used term ''random function'' also used refer stochastic random process ref name gikhmanskorokhod page ref name loeve ref ref name br maud page ref though sometimes used stochastic process takes real values ref name lamperti page ref name ito page term also used index sets mathematical spaces real line ref name gikhmanskorokhod page ref name gusakkukush page p


index math math entire stochastic process ref name lamperti page index set math infty math one write example math x geq math denote stochastic process ref name chaumontyor examples bernoulli process one simplest stochastic processes bernoulli process ref name florescu page sequence independent identically distributed iid random variables random variable takes either value one zero say one probability math p math zero probability math p math process linked repeatedly flipping coin probability obtaining head math p math


value one value tail zero ref name florescu page ref words bernoulli process sequence iid bernoulli random variables ref name bertsekastsitsiklis page ref coin flip example bernoulli trial ref name ibe page ref random walk random walks stochastic processes usually defined sums iid random variables random vectors euclidean space processes change discrete time ref name klenke page ref ref name lawlerlimic page ref ref name kallenberg page ref ref name florescu page ref ref name durrett page ref also use term refer processes change continuous time ref name weiss page ref particularly wiener process used


words simple random walk takes place integers value increases one probability say math p math decreases one probability math p math index set random walk natural numbers state space integers math p math random walk called symmetric random walk ref name gut page ref ref name grimmettstirzaker page ref wiener process wiener process stochastic process stationary independent increments normally distributed based size increments ref name rogerswilliams page ref ref name klebaner page ref wiener process named norbert wiener proved