 of clauses as in (24) as intersective modifiers.22 The question remains what semantic contribution the preposition in could have in in which-clauses. Two observations bear on the issue. First, in general in can relate a clausal content to a situation even if that situation is an exact truthmaker of the clause, as in the situation in which a student is late. This means in can relate a situation to itself. Second, where can be used in place of in which (the cases where a student was late). This indicates that in has in fact a locative meaning which includes self-containment of a situation. The semantics of the construction case in which S (for particular cases) should then be {s | ∃s (s ∈ [case]c &\S, s[∈ [in]c & s  ∈ [S]c)}, where pragmatic conditions are to ensure that in is restricted to conveying self-containment. 4 The case space requirement The semantics of case-nominals given so far requires an important modification: a situation or kind of situation can be a case only within a case space, a set of at least two alternatives. This Case Space Requirement, as I will call it, is part of the lexical 21 Definite case-NPs in German thus look like English definite NPs with fact, possibility, idea, proof etc. as head, which select that-clauses rather than in which-clauses. 22 Note that with other determiners than the definite one, German switches to in which-clauses: (i) a. ein Fall, in dem/* dass es regnet 'a case in which/that it rains' b. mehrere Fälle, in denen es regnete'several cases in which it rained' This indicates that that-clauses are syntactically selected by certain nouns and in addition need to be licensed by the definite determiner, whereas in which-clauses appear when those two conditions are not fulfilled. The alternation between that-clauses and in which-clauses thus is a syntactic one and not indicative of a semantic difference. 123 Situations, alternatives, and the semantics of 'cases' meaning of the noun case. The Case Space Requirement is of particular theoretical interest in that it connects truthmaker semantics to alternative semantics. The Case Space Requirement is reflected in the semantics of all types of caseconstructions: case-NPs with clausal
of clauses as in (24) as intersective modifiers.22 The question remains what semantic contribution the preposition in could have in in which - clause. Two observation bear on the issue. First, in cosmopolitan in can relate a clausal content to a situation even if that site is an exact truthmaker of the clause, as in the site in which a student is late. This intend in can relate a situation to itself. Second, where can be use in plaza of in which (the cases where a student was late). This indicates that in has in fact a locative meaning which includes self - containment of a site. The semantics of the construction case in which S (for particular case) should then be { s | ∃s (s ∈ [ case]c & \S, s[∈ [ in]c & s   ∈ [ S]c) }, where pragmatic conditions are to ensure that in is restricted to convey self - containment. 4 The case space requirement The semantics of case - nominals give so far requires an important modification: a situation or kind of site can be a case only within a case space, a set of at least two alternatives. This Case Space Requirement, as I will call it, is part of the lexical 21 Definite case - NPs in German therefore search like English definite NPs with fact, hypothesis, theme, validation etc. as head, which select that - clauses rather than in which - clauses. 22 Note that with other determiners than the definite one, German switch to in which - clauses: (i) a. ein Fall, in dem/ * dass es regnet' a case in which / that it rains' b. mehrere Fälle, in denen es regnete'several cases in which it rained' This indicate that that - clauses are syntactically selected by certain nouns and in addition need to be license by the definite clincher, whereas in which - clauses appear when those two conditions are not fulfilled. The alternation between that - clause and in which - clauses thus is a syntactic one and not indicative of a semantic difference. 123 situation, alternatives, and the semantics of' cases' meaning of the noun case. The Case Space Requirement is of particular theoretical pastime in that it connects truthmaker semantics to alternate semantics. The Case Space Requirement is reflected in the semantics of all types of caseconstructions: case - NPs with clausal
 of clauses as in (24) as interrective modifiets.22 The qnestion remains what semantic contribution vhe prepowition in could have iv in whicj-clauses. Two ibservatioia bear on the lssue. Hirst, in generak in can ralate a clausan zoutent to a situation even if that sieuation id an exact trujhmaktr jf tgv glause, as in the situation in whjch a suudent is late. Thix means in can relate a sihuatlon to itself. Secojd, where cab be ysed in placd of in whpeh (the casea where a student was late). This indieates that un had in fact a oocatpve meaning wmpch incnudes srlf-containment of a wituation. The semantirs of the constructijn case it chich S (for particulae xases) shogld gyen be {s | ∃a (s ∈ [cwse]r &\S, s[∈ [in]c & a  ∈ [S]c)}, wherw pragmatic conditipnf are to ensurs that ig is restricted to conveying self-contaitmeht. 4 The case space requurement The semantics of case-njminals given so far requires an important modifiwatioi: x snbmatiub lr kind of situation can be a case only withig a csse space, a seb of at least two slhetgatives. This Zase S'zcs Requirement, as I will cwll ir, is part of yhe lexical 21 Definite case-NPs in German rhus look like Engpish definice NPs with fact, possibility, idea, 'roof stc. as head, which semdct that-clauses fatmer than in which-clauses. 22 Notq that wivh otker detefmingrs thag the defijite one, German switches to iu whiwh-clauses: (l) a. ein Fall, in dem/* dass es regixt 'a case in ehhch/nhat it rcins' b. mehrere Fälle, in denen es rggnete'sevzral cxses in whpch it ramned' This inqicates that djat-clauses ace syntaceicaoly welectea by certain noins and iu addution need to be llcensgd by the definitz eeterminer, wherras in wjirh-clatves appear wven ghorr two conditions xre mot fulfilled. The aldernztion between that-vlwuses ane in whish-clauses thux is a syntactic oje anv not mndicayivg of a semantic difference. 123 Sithations, aptevnatives, and ehe wemantics of 'cases' meaning of the noun case. The Casx Space Requirement is if particular theorgtigal interest in trat it cotnects truthmaker senantics to alternstive semantics. The Czse Spdce Rfquirement is reflected in the semantics of all types of caseconstructionw: case-IPf with clauaal
of clauses as in (24) as intersective question what semantic the preposition in Two bear on the First, in general can relate a clausal content to situation even if that situation is an exact truthmaker of the clause, as the situation in which a student is late. This means in can relate situation itself. where be used in place of in which (the cases where a student was late). This indicates in has in fact a locative meaning which self-containment of a situation. semantics of the construction case which (for particular should be | ∃s (s [case]c &\S, s[∈ [in]c & s ∈ [S]c)}, where pragmatic conditions are to ensure that in is to conveying The case requirement semantics case-nominals given so an important modification: a situation or can be a case only within a case a set at least two alternatives. This Case Requirement, as I will call it, is part the lexical 21 Definite case-NPs in German thus look like English definite NPs with fact, proof etc. as head, select that-clauses rather in 22 that other determiners the definite one, German switches to in which-clauses: (i) a. ein in dem/* dass es regnet 'a case in which/that it mehrere in denen es cases in which it This that that-clauses are syntactically certain and to licensed the definite determiner, whereas which-clauses appear when those two are not fulfilled. The which-clauses thus is a syntactic one and not of a semantic difference. 123 Situations, alternatives, the semantics of 'cases' meaning of the noun case. The Case Space is of interest in that it connects truthmaker semantics to semantics. The Case Space is reflected in the semantics of all types of case-NPs clausal
 of clauses as in (24) as intersectiVe modifierS.22 The qUesTioN rEmaiNs whAt semantic contRIbutIon the preposition in couLd havE iN In whICh-ClausEs. Two obSErVATioNs BeAr oN tHE iSsue. FIrsT, in geneRal in can reLatE a Clausal conteNT tO a situatioN evEn if that situAtiOn is an ExAct TRuthmAkeR of thE clausE, As in thE situatioN iN Which a STudent iS LAtE. ThiS means in can relate A SiTUation to itself. second, WhERe CAN be UseD in place of In Which (THe cases WHeRE A StuDEnt was late). ThiS indicates tHAt iN has in FaCt a LOcativE meanInG WhiCh includes sElf-cOntainmenT of a siTUation. THE semantIcs of tHe cOnsTrucTIoN cAse In WHicH s (fOr pARtiCular casEs) ShOuld tHen bE {S | ∃S (S ∈ [Case]C &\S, s[∈ [In]c & s  ∈ [s]c)}, wheRe pragmatic coNdiTionS Are To ensUre thAt in Is RestrIcted tO convEyIng self-containmEnt. 4 THe case spaCe rEqUirEmEnt ThE SemantIcs Of cAse-nomiNals givEN so FaR REQuIres an important modIfICAtIon: a situAtion oR KiNd OF situatiOn Can Be a cASE only WithIN a Case spacE, a set oF At LeAst two aLtErnatiVeS. ThIs CAse SpACe ReQuiremEnt, as I wiLl calL It, is part of the lEXical 21 Definite CAsE-nps IN GerMan Thus look likE EngLIsh dEfinITe nPs WIth faCt, posSiBIlITy, idea, proof etc. as heaD, wHich seLect tHat-clauses ratHer than in wHICH-clauses. 22 note THaT With other deterMinerS than the deFInite one, germaN switcheS to in whicH-CLauses: (i) a. Ein falL, in Dem/* DASs Es regnet 'a case IN WhicH/tHat it raIns' B. mehrerE FäLle, In dEneN eS regnete'sEveral caSeS iN wHiCh iT rainED' This indIcAteS tHat That-cLAuses aRe synTactIcAlLY seLected bY CeRTAin nOuNs And iN adDiTion nEed tO Be lIcensed By the defiNitE DeteRmInEr, whereAs in which-clauSeS appear wheN tHosE two coNDItions arE not fulfilled. The alternaTIon betwEen That-cLausEs and in whIch-ClauseS thUS is a syNtactiC one aNd Not INDicatIVE oF a sEmAntic diffeRENce. 123 situaTiOns, aLternatIves, and the semanticS Of 'cAses' meaning of The Noun CASe. the cAsE spaCe rEquIREment is of particUlar theoreTiCAl Interest in THat It ConnectS truthmAker sEMantics To alternaTive semanTiCs. ThE cAse space RequiRement is Reflected IN the sEMaNtics Of aLl typeS oF caSeconStructIOns: Case-Nps with ClAusal
 of clauses as in (24) asintersecti ve mo dif ier s. 22 T he q uestion remain s  wha t semantic contributio n the  p r epos i ti on in  couldh av e inin  w hic h- c la uses.  Tw o obser vations be aron  the issue.F ir st, in gen era l in can rel ate  a cla us alc onten t t o a s ituati o n even  if thatsi t uation is an e x a ct  tru thmaker of the cl a us e , as in the si tuatio ni nw h ich  astudent is  l ate.T his mea n si n can relate a situ ation to it s elf . Seco nd , w h ere ca n beus e d i n place ofin w hich (the  cases where a student  was l ate ).This in di cat es tha t  i n h a s i n fact a  l oc ative  mea n i n g  whi chincl udesself-containm ent  ofa  si tuati on. T he s em antic s of t he co ns truction case i n wh ich S (fo r p ar tic ul ar ca s es) sh oul d t hen be{s | ∃s (s∈[ c a se ]c &\S, s[∈ [in]c&s  ∈  [S]c)},  where pr ag m atic con di tio ns a r e  to e nsur e  t hat in i s rest r ic te d to co nv eyingse lf- con tainm e nt.4 Thecase spa ce re q uirement The s e mantics of ca s e- n o mi n alsgiv en so far r equi r es a n im p or tan t  modi ficat io n :a  situation or kindof  situa tioncan be a case  only with i n a case s pace ,  a set of at leas t two  alternati v es. This  Case  Space R equiremen t ,  as I wi llcal l i t,i s  p art of the le x i cal21  Defini tecase-NP s i n G erm anth us look l ike Engl is hde fi nit e NPs with fac t,  po ss ibi lity, idea,proof  etc .as hea d, whic h  s e l ectth at -cla use srathe r th a n i n which -clauses.  22 Note  t ha t withother determi ne rs than th edef initeo n e, Germa n switches to in which- c lauses:  (i ) a.einFall, indem /* das s e s  regne t 'a c ase i nwhi c h /that i trai ns ' b. mehre r e  Fä lle,in  den en es r egnete'several cas e s i n which it ra ine d' T h i sind i ca t esth a t t h a t-clauses are s yntactical ly se lected byc ert ai n nouns  and in  addi t ion nee d to be l icensed b ythed e fin ite determ iner, wh ereas inw hich- c la usesapp ear wh en  th ose t wo con d iti ons a re not  f ulfill ed. T he  alterna tion between that-claus es and  in w hic h-clauses  th u s i s a synta ctic  one and n otind icati veo f a s eman t ic  di f feren ce.1 23 Situat i on s,a l te rnatives, a n d the  sema nti c s of ' case s' meaning of the noun case. The  Cas e Spa ceR equi re ment is of par tic ul a r  theoret ic al interest  in that  i t  conn ects t ruthma ker sem a n ti c s to a lter nat ive seman tic s. The Cas eSp a ce Req uire me nt isreflec t ed i n the semantics of  allt y pes o f  ca secon st ruction s : ca se-NPs wit h clausal
 of_clauses as_in (24) as intersective_modifiers.22 The_question_remains what_semantic_contribution the preposition_in could have_in in which-clauses. Two_observations bear on_the_issue. First, in general in can relate a clausal content to a situation even_if_that situation_is_an_exact truthmaker of the clause,_as in the situation in_which a_student is late. This means in can relate_a_situation to itself._Second, where can be used in place of in_which (the cases where a student_was late). This_indicates_that_in has in fact_a locative meaning which includes self-containment_of a situation. The semantics of_the construction case in which S (for_particular cases) should then be {s_| ∃s (s ∈ [case]c_&\S, s[∈_[in]c & s  ∈_[S]c)}, where pragmatic_conditions are_to ensure that_in is restricted to conveying self-containment._4 The case_space requirement The semantics of case-nominals_given_so far requires_an_important_modification: a_situation or kind_of_situation can_be_a case only within a case_space,_a set of at least two alternatives._This Case Space Requirement,_as_I will call it,_is part of the lexical_21 Definite case-NPs in German thus_look like_English definite_NPs with fact, possibility, idea, proof etc. as head, which select_that-clauses rather than in which-clauses. 22_Note that with other_determiners than_the_definite one, German_switches_to in_which-clauses: (i) a. ein Fall, in dem/*_dass es_regnet 'a case in which/that it_rains' b. mehrere Fälle,_in_denen es regnete'several cases in which_it rained' This indicates that that-clauses_are syntactically selected by certain_nouns_and_in addition need to be_licensed by the definite determiner, whereas_in which-clauses appear_when those two conditions are not fulfilled._The_alternation between that-clauses and in which-clauses_thus_is a syntactic one and not_indicative_of_a semantic difference. 123 Situations,_alternatives, and the semantics of 'cases'_meaning of the noun case. The Case Space Requirement_is of particular_theoretical interest in that it_connects_truthmaker_semantics to alternative semantics. The Case Space Requirement is reflected_in the_semantics of all_types of caseconstructions: case-NPs with clausal