%&5&3.*/*4. Barry Loewer %FUFSNJOJTNJTBDPOUJOHFOUNFUBQIZTJDBMDMBJNBCPVUUIFGVOEBNFOUBMOBUVSBMMBXT UIBUIPMEJOUIFVOJWFSTF*UTBZT The natural laws and the way things are at time t determine the way things will be at later times. 5IF NBUIFNBUJDJBO 1JFSSF4JNPO -BQMBDF FYQSFTTFE IJT CFMJFG UIBU EFUFS- minism is true this way: 8F PVHIU UP SFHBSE UIF QSFTFOU TUBUF PG UIF VOJWFSTF BT UIF FGGFDU PG JUT antecedent state and as the cause of the state that is to follow. An intel- MJHFODF LOPXJOH BMM UIF GPSDFT BDUJOH JO OBUVSF BU B HJWFO JOTUBOU BT XFMM as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were suf!ciently QPXFSGVMUPTVCKFDUBMMEBUBUPBOBMZTJTUPJUOPUIJOHXPVMECFVODFSUBJO UIF future as well as the past would be present to its eyes. The perfection that the human mind has been able to give to astronomy affords but a feeble outline of such intelligence. 5IF QIZTJDT PG -BQMBDFT EBZ UIF àSTU EFDBEFT PG UIF OJOFUFFOUI DFOUVSZ XBT /FXUPOJBO DMBTTJDBM NFDIBOJDT*TBBD/FXUPOGPSNVMBUFEQSJODJQMFTUIBUIFUIPVHIU FYQSFTTUIFMBXTEFTDSJCJOHIPXGPSDFTEFUFSNJOFUIFNPUJPOTPGCPEJFT F ma) and IPXUIFQPTJUJPOTPGCPEJFTBOEPUIFSGBDUPSTEFUFSNJOFHSBWJUBUJPOBMBOEPUIFSLJOET PGGPSDFT6TJOHUIFTFQSJODJQMFT /FXUPOBOEQIZTJDJTUTGPMMPXJOHIJNXFSFBCMFUP QSFEJDUBOEFYQMBJOUIFNPUJPOTPGDFMFTUJBMBOEUFSSFTUSJBMCPEJFT'PSFYBNQMF UIFTF laws account for the orbits of the planets, the trajectories of cannon balls, and the QFSJPET PG QFOEVMVNT-JLF/FXUPO -BQMBDFEJE OPULOPX BMM UIFGPSDFTUIFSF BSF but he envisioned that, once those forces (and the corresponding force laws) were LOPXO /FXUPOJBO QIZTJDT XPVME CF B complete physical theory. That is, its laws would account for the motions of all material particles. And since he thought that FWFSZUIJOH UIBU FYJTUT JO TQBDF JT DPNQPTFE PG WBSJPVT LJOET PG WFSZ TNBMM NBUFSJBM #"33:-0&8&3 QBSUJDMFT PSBUPNT IFUIPVHIUUIBU/FXUPOJBONFDIBOJDT PODFBMMUIFGPSDFTXFSF LOPXO XPVMECFXIBUUPEBZXFXPVMEDBMMthe theory of everything. *UTFFNFEDMFBS UP IJN UIBU UIF DPNQMFUFE /FXUPOJBO UIFPSZ XPVME CF EFUFSNJOJTUJD BOE UIBU JU would thus be in principle possible accurately to predict the future (and retrodict UIFQBTU GSPNDPNQMFUFLOPXMFEHFPGUIFQSFTFOU*UTIPVMECFOPUFE IPXFWFS UIBU UIFSFBSFTVCUMFUJFTDPODFSOJOHXIFUIFS/FXUPOJBONFDIBOJDTJTEFUFSNJOJTUJDJOUIF XBZ-BQMBDFJNBHJOFEJUUPCF*UIBTCFFOTIPXOUIBUUIFSFBSFJOJUJBMDPOEJUJPOT compatible with the laws for which the laws do not determine all future positions. )PXFWFS UIPTFDPOEJUJPOTBSFVOVTVBMBOEJUJTQMBVTJCMFUIBUUIFZDBOCFSVMFEPVU as obtaining in our world. .BOZQFPQMFàOEUIFJEFBPGEFUFSNJOJTNBCIPSSFOUBOEJODSFEJCMF*UJTGFMUUP CF BCIPSSFOU CZ UIPTF XIP UIJOL UIBU EFUFSNJOJTN JT JODPNQBUJCMF XJUI GSFF XJMM BOE IVNBO EJHOJUZ *U NBZ TFFN UIBU JG EFUFSNJOJTN PCUBJOT UIFO QFPQMF BSF MJLF NBSJPOFUUFTXIPTFNPWFNFOUTBSFVOEFSUIFDPOUSPMPGJNQFSTPOBMMBXTPGOBUVSF*U BMTPTUSJLFTNBOZBTJODSFEJCMFCFDBVTFJUTFFNTUIBUTPNVDIPGXIBUIBQQFOTmOPU KVTUEFMJCFSBUFIVNBOBDUJPO CVUBMTPUIFXFBUIFS UIFTUPDLNBSLFU GBMMJOHJOMPWF BOETPPOmJTJSSFNFEJBCMZVOQSFEJDUBCMFBOETP UIFZUIJOL DPOTUJUVUFTQSPPGUIBU determinism is false. 0OUIFPUIFSIBOE TPNFQFPQMFàOEEFUFSNJOJTNUPCFBOBUUSBDUJWFBOEFWFO JOTQJSJOHNFUBQIZTJDBMWJFX*UTFFNTUPJNQMZUIBUFWFSZFWFOU FYDFQUQFSIBQTUIF !rst event, if there is one) has a scienti!c explanation. And while it is granted that we cannot predict much of the future it might be argued that the reason is not that deter- NJOJTNJTGBMTF CVU BT-BQMBDFTVHHFTUT UIBUPVSJOUFMMFDUJTUPPGFFCMFUPBDRVJSFUIF SFMFWBOUJOGPSNBUJPOBOENBLFUIFSFRVJSFEDBMDVMBUJPOT 8IBUFWFS WJTDFSBM SFBDUJPO POF IBT UP EFUFSNJOJTN JU JT XJEFMZ CFMJFWFE UIBU EFCBUFTDPODFSOJOHJUCFMPOHUPBQSFWJPVTFSBTJODFJUJTOPXLOPXOUIBU/FXUPOJBO NFDIBOJDTJTGBMTFBOEUIFUIFPSJFTUIBUSFQMBDFJUmJOQBSUJDVMBSRVBOUVNNFDIBOJDT m BSFOPUEFUFSNJOJTUJD#VU BTXFXJMM TFF UIFTJUVBUJPOJT NPSFDPNQMJDBUFEBOE interesting. Clarifying determinism *OUIFGPSNVMBUJPOPGEFUFSNJOJTN iEFUFSNJOFuNFBOTiMPHJDBMMZOFDFTTJUBUFTu5IF /FXUPOJBO MBXT BSF NPEVMP UIF SFNBSL BCPVU VOVTVBM JOJUJBM DPOEJUJPOT BCPWF two-way deterministic because they and the state at t logically necessitates both the future and the past of t4PNFQIJMPTPQIFSTIBWFTPNFUIJOHTUSPOHFSJONJOECZ iEFUFSNJOFTu5IFJSJEFBJTUIBUUIFQSFTFOU BOEUIFMBXT EPOPUKVTUMPHJDBMMZJNQMZ the future but that they bring about GVUVSFTUBUFT0OUIJTVOEFSTUBOEJOH BUFNQPSBM EJSFDUJPOJTCVJMUJOUPUIFDIBSBDUFSJ[BUJPOPGEFUFSNJOJTNTJODFXFUIJOLPGUIFQBTU BT CSJOHJOH BCPVU UIF GVUVSF CVU OPU UIF PUIFS XBZ BSPVOE * XJMM TBZ NPSF BCPVU iCSJOHJOHBCPVUuXIFOEJTDVTTJOHlaws. The state at tJTFYQMBJOFEJOUFSNTPGUIFTQBDFmUJNFBOEUIFGVOEBNFOUBMPOUPMPHZ BOENBHOJUVEFT5IFFYJTUFODFPGUIFTUBUFBUtQSFTVQQPTFTBWJFXBCPVUTQBDFmUJNF and fundamental ontology on which there is a complete temporal ordering of all %&5&3.*/*4. FWFOUTBOEUIFGVOEBNFOUBMNBHOJUVEFTBSFFYFNQMJàFEJOTUBOUBOFPVTMZ5IFWBMVFT of all these quantities specify the state at t*O/FXUPOJBONFDIBOJDTUIFTUBUFBUt is TQFDJàFEJOUFSNTPGUIFQPTJUJPOT NPNFOUVNBOEJOUSJOTJDRVBOUJUJFT MJLFNBTTBOE charge, of each particle at time t*OàFMEUIFPSJFTUIFTUBUFBUt is speci!ed in terms of the !eld values (which can be vectors) at all spatial points at time t. There are GVOEBNFOUBMUIFPSJFTUIBUQPTJUTQBDFmUJNFTBOEPOUPMPHJFTUIBUEPOPUTIBSFUIPTF QSFTVQQPTJUJPOT'PSFYBNQMF JOUIFTQBDFmUJNFTPG&JOTUFJOTUIFPSZPGTQFDJBMBOE HFOFSBMSFMBUJWJUZUIFSFBSFFWFOUTUIBUBSFOPUUFNQPSBMMZDPNQBSBCMF/FWFSUIFMFTT WFSTJPOTPGEFUFSNJOJTNDBOCFGPSNVMBUFEGPSNBOZPGUIPTFTQBDFmUJNFTCZàOEJOH something that plays the role of the state at a time such that it and the laws determine UIFFWFOUTUISPVHIPVUBMMPGUIFTQBDFmUJNF &BSNBO The most controversial and philosophically signi!cant concept in the charac- terization of determinism is that of law of nature. The idea that there are laws of nature and that it is the job of the sciences to discover them developed during the seventeenth and eighteenth centuries with the rise of classical mechanics. An overly TJNQMFTVHHFTUJPOUIBUNBZIBWFBHSBJOPGUSVUIJTUIBUMBXTBTUIFCBTJTPGFYQMBOBUJPO DBNFUPCFTFFOBTBOJOUFSNFEJBSZCFUXFFO(PETXJMMBOEIJTDSFBUJPOPSFWFOBT BSFQMBDFNFOUGPSUIFPMPHJDBMFYQMBOBUJPO*UCFDBNFBDFOUSBMUFOFUPGQIZTJDT BOE NBOZPGUIFPUIFSTDJFODFT UIBULOPXMFEHFPGUIFMBXTPGOBUVSFJTUIFLFZUPTDJFO- UJàDFYQMBOBUJPOBOESFMJBCMFQSFEJDUJPO/PUFWFSZUSVFHFOFSBMJ[BUJPO FRVBUJPOPS GVODUJPOUIBUNBQTFBDITUBUFPOUPJUTGVUVSF JTPSJTBTTPDJBUFEXJUIBMBX*GJUXFSF UIFOEFUFSNJOJTNXPVMECFUSJWJBM4PUIFRVFTUJPOJT 8IBUNBLFTBHFOFSBMJ[BUJPO PSFRVBUJPOMBXGVM 1BSUPGUIFBOTXFSJTQSPWJEFECZUIFDPOOFDUJPOTCFUXFFOMBXT BOEPUIFSDFOUSBMOPUJPOTJOUIFTDJFODFT JOQBSUJDVMBSFYQMBOBUJPO DPVOUFSGBDUVBMT DBVTBUJPO BOE DPOàSNBUJPO &YQMBOBUJPOT PGUFO JOWPMWF TQFDJGZJOH IPX B MBX BOE JOJUJBMDPOEJUJPOTFOUBJMUIFFWFOUUPCFFYQMBJOFE-BXTTVQQPSUDPVOUFSGBDUVBMTUBUF- NFOUTGPSFYBNQMF JGUIFEJTUBODFCFUXFFOUIFFBSUIBOEUIFTVOXFSFr meters then 2 the gravitational force between them would be F Gmems/r . Further, propositions UIBUBSFBQUGPSFYQSFTTJOHMBXGVMHFOFSBMJ[BUJPOTBSFDPOàSNFECZUIFJSJOTUBODFT 8IJMFUIFGFBUVSFTKVTUNFOUJPOFEIFMQUPJEFOUJGZMBXT UIFSFJTTUJMMBRVFTUJPOPG what laws are. There are two main philosophical positions concerning the metaphysics PGMBXT XIJDI*XJMMDBMMi)VNFBOuBOEiNFUBQIZTJDBMuBDDPVOUT5IFNPTUTPQIJT- UJDBUFE WFSTJPO PG UIF )VNFBO WJFX JT EVF UP %BWJE -FXJT BOE UIF NPTU TPQIJTUJDBUFEWFSTJPOPGUIFNFUBQIZTJDBMWJFXJTEVFUP5JN.BVEMJO TFF.BVEMJO 2007). 0O -FXJTT BDDPVOU UIF MBXT BSF DPOUJOHFOU HFOFSBMJ[BUJPOT JNQMJFE CZ UIF best systematization PGUIFEJTUSJCVUJPOPGGVOEBNFOUBMFOUJUJFT NBHOJUVEFT FUD)FSFJTUIF JEFB-FULCFBMBOHVBHFXIPTFBUPNJDQSFEJDBUFTFYQSFTTPOMZGVOEBNFOUBMNBHOJ- tudes and relations and mathematical notions and let W be the set of all truths of L. 5IFMBXT DBMMUIFNi-MBXTu BSFEFàOFEBTGPMMPXT 5BLF BMM EFEVDUJWF TZTUFNT XIPTF UIFPSFNT BSF USVF 4PNF BSF TJNQMFS CFUUFSTZTUFNBUJ[FEUIBOPUIFST4PNFBSFTUSPOHFS NPSFJOGPSNBUJWF UIBO others. These virtues compete: an uninformative system can be very simple, #"33:-0&8&3 an unsystematized compendium of miscellaneous information can be very JOGPSNBUJWF5IFCFTUTZTUFNJTUIFPOFUIBUTUSJLFTBTHPPEBCBMBODFBTUSVUI XJMMBMMPXCFUXFFOTJNQMJDJUZBOETUSFOHUI)PXHPPEBCBMBODFUIBUJTXJMM EFQFOEPOIPXLJOEOBUVSFJT"SFHVMBSJUZJTBMBXJGGJUJTB<DPOUJOHFOU> UIFPSFNPGUIFCFTUTZTUFN -FXJT "DDPSEJOHUP.BVEMJOTNFUBQIZTJDBMBDDPVOU MBXT DBMMUIFNi.MBXTu BSFOPU themselves generalizations or regularities but rather fundamental elements of the XPSMETPOUPMPHZUIBUproduce UIFMBXGVMSFHVMBSJUJFT.BVEMJOTBZTMJUUMFNPSFBCPVU XIBUMBXTBSFBOEFYBDUMZIPXBMBX produces SFHVMBSJUZ)JTJEFBTFFNTUPCFUIBUMBXT are described by dynamical equations (e.g., F ma). Given the state of the universe at t the laws evolve that state into subsequent states, producing a regularity satisfying the equation. 5IFRVFTUJPOJTXIFUIFSUIFGVOEBNFOUBMMBXTPGPVSXPSMEBSF-MBXTPS.MBXT PSTPNFPUIFSBDDPVOU 0O-FXJTTBDDPVOUUIFCFTUTZTUFNPGBXPSMEJTEFUFSNJOFE CZUIFFOUJSFIJTUPSZPGTUBUFTPGUIFVOJWFSTF*UGPMMPXTUIBUUIF-MBXTsupervene on UIFUPUBMJUZPGTUBUFT*ODPOUSBTU .MBXT JGUIFSFBSFBOZ EPOPUTVQFSWFOFPOUIF totality of states since different laws can produce the same total histories. For some BEWPDBUFT PG .MBXT UIJT DPOUSBTU JT FOPVHI UP FTUBCMJTI UIBU -MBXT BSF UPP XFBL UPEPUIFXPSLUIBUMBXTBSFTVQQPTFEUPEP5IFZTBZUIBU-MBXTBSFJODBQBCMFPG FYQMBJOJOHTUBUFFWPMVUJPOTJODFUIFZBSFEFUFSNJOFECZUIFTUBUFT#VUUIFJTTVFJT NPSFTVCUMFTJODF-MBXTBOEUIFTUBUFEPentail TVCTFRVFOUTUBUFT"EWPDBUFTPG-MBXT HPPOUPTBZUIBUXFIBWFOPJEFBPGIPX.MBXTproduce TUBUFT8FDBOOPUTFUUMFUIF issue here but will note some other differences between the two accounts. The two accounts of laws may render different verdicts concerning