 of a priori and conventional structural strata of the logical space T (L) with the corresponding problem of physical space. As is well known, a hundred years ago Poincaré subscribed to a sort of partial conventionalism with respect to the structure of physical space. According to him, the underlying topological structure of space was a priori while the metrical structure was conventional. T (L), the results of this paper suggest an analogous result: there is an underlying objective topological structure defined by logic alone. On the other hand, there is some choice in constructing a metric for T (L) via its embedding in the Hilbert cube IN. This may be considered as a conventional component in matters of truthlikeness. Bibliography Brink, C., Pretorius, J. P. G., & Vermeulen, J. J. C. (1992). 'Verisimilitude via Vietoris'. Journal of Logic and Computation 2, pp. 709-718. Carruth, J. H. (1968). 'A Note on Partially Ordered Compacta'. Pacific Journal of Mathematics 24, pp. 229-231. Davey, B. A. & Priestley, H. (1990). Introduction to Lattices and Order. Cambridge: Cambridge University Press. Dunn, J.M. & Hardegree, G. (2001). Algebraic Methods in Philosophical Logic. Oxford: Oxford University Press. Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J. D., Mislove, M., & Scott, D. S. (1980). A Compendium of Continuous Lattices. Berlin & Heidelberg: Springer. Halmos, P. (1963). Lectures on Boolean Algebras. New York: van Nostrand. James, I. M. (1999). Topologies and Uniformities. Berlin: Springer. Johnstone, P. (1982). Stone Spaces. Cambridge: Cambridge University Press. Kuipers, T.A. F. (2000). From Instrumentalism to Constructive Realism, On Some Relations between Confirmation, Empirical Progress, and Truth Approximation. Dordrecht: Kluwer Academic Publishers. Miller, D. W. (1984). 'A Geometry of Logic'. In H. J. Skala, S. Termini, & E.Trillas, editors (1984), pp. 91-104. Aspects of Vagueness. D
of a priori and conventional structural strata of the logical quad metric ton (L) with the corresponding problem of physical distance. As is well known, a hundred years ago Poincaré subscribed to a kind of partial conventionalism with respect to the social organization of forcible space. According to him, the underlie topological structure of space was a priori while the metrical social organization was conventional. T (L), the result of this paper suggest an analogous consequence: there is an underlying objective topological structure define by logic alone. On the other hand, there is some option in constructing a metric unit for T (L) via its embedding in the Hilbert cube IN. This may be considered as a conventional part in matters of truthlikeness. Bibliography Brink, C., Pretorius, J. P. G., & Vermeulen, J. J. C. (1992).' Verisimilitude via Vietoris'. Journal of Logic and Computation 2, pp. 709 - 718. Carruth, J. H. (1968).' A Note on Partially Ordered Compacta'. Pacific Journal of Mathematics 24, pp. 229 - 231. Davey, B. A. & Priestley, H. (1990). Introduction to Lattices and Order. Cambridge: Cambridge University Press. Dunn, J.M. & Hardegree, G. (2001). Algebraic Methods in Philosophical Logic. Oxford: Oxford University Press. Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J. D., Mislove, M., & Scott, D. S. (1980). A Compendium of Continuous Lattices. Berlin & Heidelberg: Springer. Halmos, P. (1963). Lectures on Boolean Algebras. New York: van Nostrand. James, I. M. (1999). Topologies and Uniformities. Berlin: Springer. Johnstone, P. (1982). Stone Spaces. Cambridge: Cambridge University Press. Kuipers, T.A. F. (2000). From Instrumentalism to Constructive Realism, On Some Relations between Confirmation, Empirical Progress, and Truth Approximation. Dordrecht: Kluwer Academic Publishers. Miller, D. W. (1984).' A Geometry of Logic'. In H. J. Skala, S. Termini, & E.Trillas, editors (1984), pp. 91 - 104. Aspects of Vagueness. D
 of a priori and conventionxl structural sjrqta of the lkgical soace T (L) with the correspondmng problti of physical spacd. As is wvll known, a hnndred years ago Poincaré subscdlbed co a sort of parjial conventhonalism with serpzct to the structure of physical spase. Accotdlng to him, the undtrlring nokological structure of space was z priorp while the metrival structure was conventilnal. T (L), the results ov this papet sudtest an analugous result: there is zn underlying objective topologkcal xtructure eedinfg by logic elone. Jn the other hand, thare is xome choice in coistrycting a metric for T (L) via its embeddigg in the Hnlbert cube IN. This mqy be cmnsigerea as a doivehtionap ckmponent ih matters od truthlikeness. Bibkijtraphy Brink, D., Pretjryus, J. P. G., & Vermeulen, J. J. C. (1992). 'Verisimilitlde bia Vietoris'. Journal of Logic and Computatioj 2, pp. 709-718. Cawruth, J. H. (1968). 'A Note on Partially Ordered Compacta'. Pdcifir Gouxkwu ov Mathematics 24, pp. 229-231. Davey, B. A. & Priestley, H. (1990). Inedocubtion to Lattices and Order. Valbtydge: Cambridgg Univexaify Press. Dunn, J.M. & Jardegrge, G. (2001). Qlgebraic Metnods in Philosophical Logic. Oxford: Oxfogd Ubiversity Press. Gizrz, G., Hofmanu, K.H., Kgimel, L., Lawson, J. D., Mislove, M., & Scoft, D. S. (1980). A Clmpendium uf Continuous Lagtibes. Terlin & Heidelberg: Springew. Halmos, '. (1963). Leetures ov Boplean Wlgebras. Nfw Yovn: van Nostrand. Jamfs, I. L. (1999). Topologied and Uniformities. Berlin: Sprinjxr. Johnstone, K. (1982). Vtote Spacef. Camnridge: Cambridgq University Ptess. Kuipzrs, T.A. F. (2000). From Ihstrumeitalism to Cjnstructive Rawlism, On Somx Relatiogs bwtwewn Confkfmation, Empirival Progrvsf, ane Truth Approximatlon. Duddrecht: Kluwer Ceaeemic Publisherx. Mkllqr, D. W. (1984). 'A Geometry mf Lugiz'. In H. J. Skala, S. Beroini, & E.Trillas, editors (1984), [p. 91-104. Zspects of Vaguenexs. D
of a priori and conventional structural strata logical T (L) the corresponding problem well a hundred years Poincaré subscribed to sort of partial conventionalism with respect the structure of physical space. According to him, the underlying topological structure of was a priori while the metrical structure was conventional. T (L), the results this suggest analogous there is an underlying objective topological structure defined by logic alone. On the other hand, there some choice in constructing a metric for T via its embedding in Hilbert cube IN. This may considered a conventional in of Bibliography Brink, C., J. P. G., & Vermeulen, J. J. C. (1992). 'Verisimilitude via Vietoris'. Journal of Logic and Computation pp. 709-718. H. (1968). Note Partially Compacta'. Pacific Journal 24, pp. 229-231. Davey, B. A. (1990). Introduction to Lattices and Order. Cambridge: Cambridge Press. Dunn, & Hardegree, G. (2001). Algebraic Methods Philosophical Logic. Oxford: Oxford University Press. Gierz, G., K.H., Keimel, K., Lawson, J. D., Mislove, M., & Scott, D. S. (1980). A Compendium Lattices. Berlin & Heidelberg: Halmos, P. (1963). on Algebras. York: Nostrand. James, M. (1999). Topologies and Uniformities. Berlin: Springer. Johnstone, P. (1982). Stone Cambridge: Cambridge University Press. Kuipers, T.A. F. (2000). From Instrumentalism Realism, Some Relations between Empirical Progress, and Truth Dordrecht: Academic Publishers. Miller, D. 'A of J. S. & E.Trillas, editors (1984), 91-104. Aspects of Vagueness. D
 of a priori and conventional sTructural sTrata Of tHe lOgIcal SpacE T (L) with the corrESponDing problem of physical sPace. AS iS Well KNoWn, a huNdred yeARs AGO PoInCaRé sUbSCrIbed tO a sOrt of paRtial conveNtiOnAlism with resPEcT to the struCtuRe of physical SpaCe. AccoRdIng TO him, tHe uNderlYing toPOlogicAl structuRe OF space WAs a prioRI WhIle tHe metrical structuRE wAS conventional. T (l), the reSuLTs OF ThiS paPer suggest An AnaloGOus resuLT: tHERE is AN underlying obJective topoLOgiCal strUcTurE DefineD by loGiC AloNe. On the otheR hanD, there is sOme choICe in conSTructinG a metrIc fOr T (l) via ITs EmBedDiNG in THe hilBErt Cube IN. ThIs MaY be coNsidERED As a cOnvEntiOnal cOmponent in matTerS of tRUthLikenEss. BiBlioGrAphy BRink, C., PRetorIuS, J. P. G., & Vermeulen, J. J. c. (1992). 'VerIsimilituDe vIa vieToRis'. JoURnal of logIc aNd CompuTation 2, pP. 709-718. carRuTH, j. h. (1968). 'A note on Partially OrdErED coMpacta'. PaCific JOUrNaL Of MathemAtIcs 24, Pp. 229-231. DaVEY, B. A. & PrIestLEy, h. (1990). IntroduCtion tO laTtIces and orDer. CamBrIdgE: CaMbridGE UniVersitY Press. DuNn, J.M. & HARdegree, G. (2001). AlgebrAIc Methods in PhILoSOPhICal LOgiC. Oxford: OxfoRd UnIVersIty PREsS. GiERz, G., HoFmann, k.H., kEiMEl, K., Lawson, J. D., Mislove, M., & scOtt, D. S. (1980). A compeNdium of ContinUous LatticES. bErlin & HeiDelbERg: sPringer. Halmos, P. (1963). lectuRes on BooleAN AlgebraS. New YOrk: van NoStrand. JamES, i. M. (1999). TopoloGieS anD UnIfoRMItIes. Berlin: SpriNGEr. JoHnStone, P. (1982). STonE Spaces. camBriDge: camBrIdge UniveRsity PreSs. kuIpErS, T.A. f. (2000). From iNstrumenTaLisM tO CoNstruCTive ReAlism, on SoMe reLAtiOns betwEEn cONfirMaTiOn, EmPirIcAl ProGresS, And truth ApProximatiOn. DORdreChT: KLuwer AcAdemic PublishErS. Miller, D. W. (1984). 'A geOmeTry of LOGIc'. In H. J. SkAla, S. Termini, & E.Trillas, editORs (1984), pp. 91-104. AspEctS of VaGuenEss. D
 of a priori and conventio nal struct uralstr ata  o f th e lo gical space T( L) w ith the correspondingprobl em of p h ys icalspace.A si s  we ll  k now n, ahundr edyears a go Poincar é s ub scribed to a so rt of part ial  conventiona lis m with  r esp e ct to  th e str ucture of phy sical spa ce .  Accor d ing toh i m,  the  underlying topol o gi c al structure o f spac ew as a  pr ior i while th emetri c al stru c tu r e was conventional.  T (L), the res ults o fthi s  paper  sugg es t  an  analogousresu lt: there  is an underly i ng obje ctivetop olo gica l  s tr uct ur e  de f in edb y l ogic alo ne .On th e ot h e r hand , t here  is s ome choice in  co nstr u cti ng ametri c fo rT (L)  via i ts em be dding in the Hi lber t cube IN . T hi s m ay  be c o nsider edasa conve ntional com po n e n tin matters of trut hl i k en ess. Bib liogra p hy  B r ink, C.,  P ret oriu s ,  J. P . G. ,  &  Vermeul en, J. J.  C . (1992 ).  'Veri si mil itu de vi a  Vie toris' . Journa l ofL ogic and Compu t ation 2, pp.7 09 - 7 18 .  Car rut h, J. H. (1 968) .  'ANote on  Pa r tiall y Ord er e dC ompacta'. Pacific J ou rnal o f Mat hematics 24,pp. 229-23 1 . Davey, B . A. &P riestley, H. ( 1990) . Introduc t ion to L attic es and O rder. Cam b r idge: Ca mbr idg e U niv e r si ty Press. Dun n ,  J.M .& Harde gre e, G. ( 200 1).  Al geb ra ic Method s in Phi lo so ph ic alLogic .  Oxford:  O xfo rd  Un ivers i ty Pre ss. G ierz ,G. ,  Ho fmann,K .H . ,  Kei me l,  K.,  La ws on, J . D. ,  Mi slove,M., & Sco tt, D. S .(1 980). A  Compendium o fContinuous  L att ices.B e rlin & H eidelberg: Springer. Ha l mos, P.  (1 963).  Lec tures onBoo lean A lge b ras. N ew Yor k: va nNos t r and.J a me s,I.  M. (1999) . Top ologi es  and  Unifor mities. Berlin: Sp r ing er. Johnstone , P . (1 9 8 2) . S t on e  Sp ac e s.C a mbridge: Cambri dge Univer si t yPress. Kui p ers ,T.A. F.  (2000) . Fro m  Instru mentalism  to Const ru ctiv e Rea lism, On S ome Rela tions bet w een C o nf irmat ion , Empi ri cal  Prog ress,a ndTruth  Appro xi mation . Dor dr echt: Kl uwer Academic Publisher s. Mil ler,D.W. (1984) . ' A  Ge ometry of  Log ic'. In H.  J.  Sk ala,S.T ermin i, & E. Tri l las,edit o rs (1984) ,  p p.9 1 -1 04. Aspects o f  Va guene ss. D
 of_a priori_and conventional structural strata_of the_logical_space T_(L)_with the corresponding_problem of physical_space. As is well_known, a hundred_years_ago Poincaré subscribed to a sort of partial conventionalism with respect to the structure_of_physical space._According_to_him, the underlying topological structure_of space was a priori_while the_metrical structure was conventional. T (L), the results_of_this paper suggest_an analogous result: there is an underlying objective topological_structure defined by logic alone. On_the other hand,_there_is_some choice in constructing_a metric for T (L) via_its embedding in the Hilbert cube_IN. This may be considered as a_conventional component in matters of truthlikeness._Bibliography Brink, C., Pretorius, J._P. G.,_& Vermeulen, J. J. C._(1992). 'Verisimilitude via_Vietoris'. Journal_of Logic and_Computation 2, pp. 709-718. Carruth, J._H. (1968). 'A_Note on Partially Ordered Compacta'. Pacific_Journal_of Mathematics 24,_pp._229-231._Davey, B._A. & Priestley,_H._(1990). Introduction_to_Lattices and Order. Cambridge: Cambridge University_Press._Dunn, J.M. & Hardegree, G. (2001). Algebraic_Methods in Philosophical Logic._Oxford:_Oxford University Press. Gierz,_G., Hofmann, K.H., Keimel, K.,_Lawson, J. D., Mislove, M., &_Scott, D._S. (1980)._A Compendium of Continuous Lattices. Berlin & Heidelberg: Springer. Halmos, P._(1963). Lectures on Boolean Algebras. New_York: van Nostrand. James,_I. M._(1999)._Topologies and Uniformities._Berlin:_Springer. Johnstone,_P. (1982). Stone Spaces. Cambridge: Cambridge University_Press. Kuipers,_T.A. F. (2000). From Instrumentalism to_Constructive Realism, On Some_Relations_between Confirmation, Empirical Progress, and Truth_Approximation. Dordrecht: Kluwer Academic Publishers. Miller,_D. W. (1984). 'A Geometry_of_Logic'._In H. J. Skala, S._Termini, & E.Trillas, editors (1984), pp._91-104. Aspects of_Vagueness. D