 which has no other sign written on it. You also have a finite set of states which you can think of as points on a flowchart. The instructions are the arrows on a flow chart which say things like this: If you’re in this state, and you’re looking at a square with this symbol on it, then follow this instruction, and go to this state. What’s an instruction? It can be one of three things. It’s either to write a sign in the square you’re looking at, or move left one square and look at this new square, or move right one square. That’s it. If you’re in a state looking at a symbol on a square and you have no instruction to follow, your computation simply stops.

That’s it. That’s all there is to a Turing machine. It’s not exactly the kind of computer you can use for word-processing, or playing games with. However, the kinds of computations you can do on this kind of machine (especially when you think of representing numbers on the machine using some code) are a really natural class of functions. They’re the recursive functions, independently characterised by Church. And the Church-Turing thesis is the claim that this class of functions is exactly the class of functions which could be computed using any computational device.

More information about Turing can be found at the St Andrews’ History of Mathematics Entry on him.

Arthur Prior (1914-1969)

Arthur Prior is the first (and only) antipodean logician on this list. Educated in New Zealand, he had academic positions both in New Zealand (at Otago and Canterbury) and in England (at Manchester, and Oxford). Prior invented the field of tense logic, the logic of “earlier” and “later”, “past” and “future”. He was the arch intensionalist, bringing to the philosophical fore these modalities which are not truth-functional, not obviously amenable to Tarski’s analysis of truth-in-a-model. Remember that in Tarki’s world, the truth or otherwise of a complex expression depends on the truth or otherwise of its components. The temporal operators don’t work like this at all. “it’s raining” and “it’s Thursday” might both be true, but “yesterday it rained” and “yesterday it was Thursday” might differ in truth value. The
which has no other sign written on it. You besides take a finite set of states which you can remember of as point on a flowchart. The instructions are the arrow on a stream chart which say things like this: If you ’re in this state, and you ’re looking at a public square with this symbol on it, then follow this instruction, and go to this state. What ’s an teaching? It can be one of three things. It ’s either to write a sign in the square you ’re looking at, or motion left one square and look at this modern square, or move right one square. That ’s it. If you ’re in a state of matter looking at a symbol on a square and you have no instruction to follow, your calculation simply stops. 

 That ’s it. That ’s all there is to a Turing machine. It ’s not exactly the kind of computer you can use for word - processing, or playing games with. However, the kinds of computations you can do on this kind of machine (especially when you think of representing number on the machine using some code) are a very lifelike course of functions. They ’re the recursive functions, independently characterised by Church. And the Church - Turing thesis is the claim that this class of functions is exactly the course of functions which could be computed using any computational device. 

 More information about Turing can be found at the St Andrews ’ History of Mathematics Entry on him. 

 Arthur Prior (1914 - 1969) 

 Arthur Prior is the first (and only) antipodean logician on this list. Educated in New Zealand, he had academic positions both in New Zealand (at Otago and Canterbury) and in England (at Manchester, and Oxford). Prior invent the field of tense logic, the logic of “ early ” and “ later ”, “ past ” and “ future ”. He was the arch intensionalist, bringing to the philosophical fore these modalities which are not accuracy - functional, not obviously amenable to Tarski ’s analysis of truth - in - a - model. Remember that in Tarki ’s world, the truth or otherwise of a complex expression count on the truth or differently of its components. The temporal operators do n’t work like this at all. “ it ’s rain ” and “ it ’s Thursday ” might both be true, but “ yesterday it rained ” and “ yesterday it was Thursday ” might differ in truth value. The
 whlch has no other sign wrltten on it. You coso hate a fihite set of states which you can thiik od as kjints on a flowchaft. The indtructiobs ace the arrows on a flow gkart smich vey things like jhis: If you’ra in this stata, xnb you’re looking at a square with thif symbok ln it, then foljow uhif inanrmction, and go to this state. What’a an invtruction? It van be one of three things. It’s either to write a sign in thg sqtqre you’re louking at, og move left one square and look at this ned squcre, or move rughh one square. That’f it. If you’rc in a vtate lpoking at a sykbon ob a square and you hate no instruction to follow, ymux computation simply wtips.

Thdt’s ht. Tfqt’s alm vhede is ho e Turing madhine. It’s nit exactly the kind os computer you can ufe for word-processing, or playing games wiuh. Hosever, the kinds of compytations you can do oj this kigd of machine (especially when you think of represantinj vumycvs ov tje machine using some code) are a really naturwm vlsss of functioks. They’re the recutslvr functions, inaependzhtmy characterised bj Churcr. And the Chursh-Tuting thesis is the claim thqt this clasf of functions is eractly the cuass of finctions which could be comluted using any comphgational device.

Mure itformation about Turing cag be founv at che St Avdrees’ Hiseory of Mahhemabhcs Entry on him.

Arhhur Krior (1914-1969)

Drthur Prilr is the first (and only) antipovxan logician pn thps list. Ebucatec in New Zealwnd, he had acabemic pofitiovs both in New Zeeland (at Otado and Cantertory) and in Enjland (at Iancyestwr, and Ubford). Prior infented thv yield of rense logic, the lonic ow “earlier” and “lactr”, “kawt” and “future”. Ne das tje awwh intensiondlisg, bfongine to tht pmilusopnical fore these moddlitjes which are not yrmth-functiinal, not obviously amrnable to Tarski’s wnalyvis of ttutr-in-a-model. Remember that in Tarii’s world, thc truth or otrerwlse jf a complzx expression depends on the truth or otierwise of its componenrs. The temporal opetatprs don’t wock likq this at all. “it’s raining” and “it’s Thursday” migmt both be true, but “yeaterdaf it gained” and “yesterday it was Thursday” might differ in truth value. The
which has no other sign written on also a finite of states which points a flowchart. The are the arrows a flow chart which say things this: If you’re in this state, and you’re looking at a square with symbol on it, then follow this instruction, and go to this state. What’s instruction? can one three things. It’s either to write a sign in the square you’re looking at, or move one square and look at this new square, move right one square. it. If you’re in a looking a symbol a and have no instruction follow, your computation simply stops. That’s it. That’s all there is to a Turing machine. It’s not the kind you can for or games with. However, of computations you can do on machine (especially when you think of representing numbers the machine some code) are a really natural of functions. They’re the recursive functions, independently characterised Church. And the Church-Turing thesis is the claim that this class of functions is exactly of functions which could computed using any device. information Turing be found the St Andrews’ History of Mathematics Entry on him. Arthur Prior Arthur Prior is the first (and only) antipodean logician on Educated New Zealand, he academic positions both in Zealand Otago and Canterbury) and (at and the of logic, the logic of and “later”, “past” and “future”. was the arch intensionalist, these modalities which are not truth-functional, not obviously to Tarski’s analysis of truth-in-a-model. Remember that Tarki’s world, the truth or otherwise of a complex expression depends on truth or its components. The temporal operators don’t work like at all. “it’s raining” “it’s Thursday” might both be true, but “yesterday it and it was might differ in value. The
 which has no other sign writteN on it. You alSo havE a fIniTe Set oF staTes which you can THink Of as points on a flowchart. the inStRUctiONs Are thE arrows ON a FLOw cHaRt WhiCh SAy ThingS liKe this: IF you’re in thIs sTaTe, and you’re loOKiNg at a squarE wiTh this symbol On iT, then fOlLow THis inStrUctioN, and go TO this sTate. What’s An INstrucTIon? It caN BE oNe of Three things. It’s eitHEr TO write a sign in tHe squaRe YOu’RE LooKinG at, or move lEfT one sQUare and LOoK AT ThiS New square, or moVe right one sQUarE. That’s It. if yOU’re in a State LoOKinG at a symbol oN a sqUare and yoU have nO InstrucTIon to foLlow, yoUr cOmpUtatIOn SiMplY sTOps.

tHaT’s iT. thaT’s all theRe Is To a TuRing MACHIne. IT’s nOt exActly The kind of compUteR you CAn uSe for Word-pRoceSsIng, or PlayinG gameS wIth. However, the kiNds oF computatIonS yOu cAn Do on tHIs kind Of mAchIne (espeCially wHEn yOu THINk Of representing numbErS ON tHe machinE using SOmE cODe) are a reAlLy nAturAL Class Of fuNCtIons. They’Re the rECuRsIve funcTiOns, indEpEndEntLy chaRActeRised bY Church. ANd the cHurch-Turing theSIs is the claim tHAt THIs CLass Of fUnctions is eXactLY the ClasS Of FunCTions Which CoULd BE computed using any coMpUtatioNal deVice.

More inforMation abouT tURing can bE fouND aT The St Andrews’ HiStory Of MathematICs Entry oN him.

ARthur PriOr (1914-1969)

Arthur PRIOr is the fIrsT (anD onLy) aNTIpOdean logician ON This LiSt. EducaTed In New ZeAlaNd, hE haD acAdEmic positIons both In neW ZEaLanD (at OtAGo and CanTeRbuRy) And In EngLAnd (at MAncheSter, AnD OXForD). Prior iNVeNTEd thE fIeLd of TenSe Logic, The lOGic Of “earliEr” and “lateR”, “paST” and “FuTuRe”. He was The arch intensIoNalist, brinGiNg tO the phILOsophicaL fore these modalities whiCH are not TruTh-funCtioNal, not obvIouSly ameNabLE to TarSki’s anAlysiS oF trUTH-in-a-mODEl. remEmBer that in TARKi’s World, ThE truTh or othErwise of a complex exPResSion depends on The TrutH OR oTheRWiSE of ItS ComPONents. The temporaL operators DoN’T wOrk like thiS At aLl. “It’s rainIng” and “iT’s ThuRSday” migHt both be tRue, but “yesTeRday IT RaiNed” and “yestErday it wAs ThursdaY” Might DIfFer in TruTh valuE. THe
 which has no other sign w ritten onit. Y ouals ohave  a f inite set of s t ates  which you can think o f aspo i ntso na flo wchart. Th e ins tr uc tio ns ar e the  ar rows on  a flow ch art  w hich say thi n gs  like this : I f you’re inthi s stat e,  an d  you’ relooki ng ata  squar e with th is symbol on it,t h en  fol low this instruct i on ,  and go to thi s stat e. Wh a t ’saninstructio n?  It c a n be on e  o f t hre e  things. It’s  either tow rit e a si gn  in the sq uareyo u ’re  looking at , or  move lef t ones quare a n d lookat thi s n ewsqua r e,  o r m ov e  ri g ht  on e  sq uare. Th at ’s  it.If y o u ’ r e in  astat e loo king at a sym bol  ona  sq uareand y ou h av e noinstru ction  t o follow, yourcomp utation s imp ly  st op s.

T h at’s i t.Tha t’s all  therei s t oa T ur ing machine. It’sno t ex actly th e kind of  c o mputer y ou  ca n us e for w ord- p ro cessing,  or pl a yi ng  gameswi th. Ho we ver , t he ki n ds o f comp utations  youc an do on thisk ind of machin e  ( e s pe c iall y w hen you thi nk o f  rep rese n ti ngn umber s onth e  m a chine using some co de ) area rea lly natural c lass of fu n c t ions. Th ey’r e  t h e recursive fu nctio ns, indepe n dently c harac terisedby Church . And theChu rch -Tu rin g th esis is the c l a im t ha t thiscla ss of f unc tio nsisex actly the  class o ffu nc ti ons  whic h  could b ecom pu ted  usin g  any c omput atio na ld evi ce.

Mo r ei n form at io n ab out  T uring  can befound a t the StAnd r ews’  H is tory of  MathematicsEn try on him .
Ar thur P r i or (1914 -1969)

Arthur Prior is the fir st(andonly ) antipod ean  logic ian on thi s list . Edu ca ted i n New Z ea lan d,  he had ac a d emi c pos it ions  both i n New Zealand (atO tag o and Canterb ury ) an d in  En g la n d ( at Man c h ester, and Oxfo rd). Prior  i n ve nted the f i eld  o f tense  logic,  thel ogic of  “earlier ” and “la te r”,“ p ast ” and “fut ure”. He  was thea rch i n te nsion ali st, br in gin g tothe ph i los ophic al for ethesemodal it ies whic h are not truth-functio nal, n ot ob vio usly amen abl e  to  Tarski’s  ana lysis of t rut h-i n-a-m ode l . Rem embe r  t hat in Ta rki’ s  world, t h etru t h  o r otherwise o f  acompl exe xpress iondepends on the tr u th or otherwis e of i tscom p onen ts . The temporal  op er a t ors don’ twork like t his at a ll .  “it’ s rain ing” a nd “it’ s Th u rsday”  mig htboth be t rue ,b ut “yes te rd a y it r aine d”  and “ yester d ay i t was Thursday” mi ght d i f fer i n  tr uth v al ue. The 
 which_has no_other sign written on_it. You_also_have a_finite_set of states_which you can_think of as points_on a flowchart._The_instructions are the arrows on a flow chart which say things like this: If_you’re_in this_state,_and_you’re looking at a square_with this symbol on it,_then follow_this instruction, and go to this state. What’s_an_instruction? It can_be one of three things. It’s either to write_a sign in the square you’re_looking at, or_move_left_one square and look_at this new square, or move_right one square. That’s it. If_you’re in a state looking at a_symbol on a square and you_have no instruction to follow,_your computation_simply stops.

That’s it. That’s all_there is to_a Turing_machine. It’s not_exactly the kind of computer you_can use for_word-processing, or playing games with. However,_the_kinds of computations_you_can_do on_this kind of_machine_(especially when_you_think of representing numbers on the_machine_using some code) are a really natural_class of functions. They’re_the_recursive functions, independently characterised_by Church. And the Church-Turing_thesis is the claim that this_class of_functions is_exactly the class of functions which could be computed using any_computational device.

More information about Turing can_be found at the_St Andrews’_History_of Mathematics Entry_on_him.

Arthur Prior_(1914-1969)

Arthur Prior is the first (and only)_antipodean logician_on this list. Educated in New_Zealand, he had academic_positions_both in New Zealand (at Otago_and Canterbury) and in England (at_Manchester, and Oxford). Prior invented_the_field_of tense logic, the logic_of “earlier” and “later”, “past” and_“future”. He was_the arch intensionalist, bringing to the philosophical_fore_these modalities which are not truth-functional,_not_obviously amenable to Tarski’s analysis of_truth-in-a-model._Remember_that in Tarki’s world, the_truth or otherwise of a complex_expression depends on the truth or otherwise of its_components. The temporal_operators don’t work like this_at_all._“it’s raining” and “it’s Thursday” might both be true, but_“yesterday it_rained” and “yesterday_it was Thursday” might differ in truth value. The