The Maximal Contingent Fact in Leibniz’s Cosmological Arguments

Leibnizovski kozmologijski argumenti razred su kozmologijskih argumenata za opstojnost metafizički prvoga uzroka, kojih je definirajuće obilježje primjena nekoga širokoga eksplanacijskog načela ili pak ne‑lokalnoga načela kauzalnosti na tzv. maksimalnu kontingentnu činjenicu, tj. kontingentnu činjenicu koja sadržava ili povlači svaku kontingentnu činjenicu relevantne vrste. Jedna je od strategija za napad na leibnizovski argument stoga argumentirati da odgovarajuća maksimalna kontingentna činjenica ne postoji. Rad opisuje dva načelna načina na koja se to može pokušati učiniti. Prvi je zanijekati da je maksimalna kontingentna činjenica legitimna cjelina činjenica, drugi je zanijekati opstojnost kontingentnih činjenica općenito. Iznosi se nekoliko alternativnih formulacija tvrdnje o postojanju maksimalne kontingentne činjenice, njihova pozadinska teorijska motivacija i načini na koje pojedine formulacije izbjegavaju prigovore. Argumentira se da prigovori koji se odnose na maksimalnu kontingentnu činjenicu nisu ozbiljna prijetnja leibnizovskim argumentima za opstojnost prvoga uzroka.Leibniz’s cosmological arguments are a class of cosmological arguments for existence of the metaphysical first cause, whose defining characteristic is application of some wider explanatory principle or non‑local principle of causality on so‑called maximal contingent fact, i.e., contingent fact that contains or implies every contingent fact of the relevant kind. One of the strategies of attack on Leibniz’s argument is, therefore, to argue that the respective maximal contingent fact does not exist. The article describes two principal ways in which one might try to carry out this critique. The first is to deny that the maximal contingent fact is the legitimate sum of facts, the second is to deny the existence of contingent facts in general. The article presents a few alternative formulations of the claim of existence of maximal contingent fact, their background theoretical motivation, and manners in which specific formulations avoid critique. The author argues that the forms of critique that are related to the maximal contingent fact are not a serious threat to Leibniz’s arguments for the existence of the first cause

A Universe from Nothing and Cosmological Arguments

Cilj je rada opisati konceptualni odnos između pojma spontana nastanka svemira ni iz čega i kozmologijskih argumenata. Svaka inačica kozmologijskoga argumenta počiva na tri središnje tvrdnje, uključujući one koje se u radu nazivaju načelom objašnjenja i načelom utemeljenja. Tvrdi se da obrana metafizičke mogućnosti spontana nastanka svemira ni iz čega obvezuje na odbacivanje barem jednoga od tih načela, no da odbacivanje bilo kojega od njih povlači neplauzibilne metafizičke posljedice.The aim of the paper is to analyse some conceptual and logical relations between the notion of the spontaneous arising ex nihilo of the Universe and the so-called cosmological arguments for the existence of the First Cause. In the first section, it is argued that no scientific theory could in principle describe the Universe\u27s coming into being from nothing. In the second, three standard classes of cosmological arguments are analysed, and it is demonstrated that the first phase of every cosmological argument is based on three central premises, including what is termed in the paper ʻthe principle of explanationʼ and ʻthe principle of foundationʼ. The role of the principle of explanation is to exclude, as metaphysically impossible, some relevant kinds of brute facts, and the role of the principle of foundation is to deny the explanatory completeness of certain non-well-founded explanatory chains. In the final section of the paper the notion of coming into being from nothing is given a more precise meaning. It is then argued that the conjunction of the two metaphysical principles in any variant of the cosmological argument excludes the metaphysical possibility that the Universe spontaneously came into being from nothing and that defending the metaphysical possibility of the Universe\u27s arising from nothing therefore commits one to reject either the explanatory principle or the foundation principle. Finally, it is suggested that either option comes at a high metaphysical price

RAMIFIED TYPE THEORY AS INTENSIONAL LOGIC

Ovaj doktorski rad sastoji se od dva glavna dijela. Prvi se dio bavi pitanjem što sustava čine funkcije u razgranatoj teoriji tipova Bertranda Russella, kako ju je izložio u filozofijskome uvodu prvoga izdanja Principia Mathematica.U tome se dijelu rada brani eliminativističko tumačenje i pokušava pokazati da Russell sam stavačne funkcije u Principia razumije samo kao izraze, kao tzv. nepotpune simbole, koji ne označavaju nikakve izvanjezične predmete poput pojmova ili atributa.This doctoral thesis consists of two main sections. The first section addresses the background ontology of Bertrand Russell’s ramified type theory as described in Principia Mathematica. More precisely, it deals with the question of the ontological status of propositional functions. The concept of a propositional function is one of the central concepts of Russell’s theory of types, both in the first draft of the theory in “Appendix B” of The Principles of Mathematics andinitsmatureformulationinthefirsteditionofPrincipia.However,howtounderstandwhat Russell meant by “propositional functions” remains controversial. What are propositional functions? Are they some sort of intensional abstract entities, like properties and relations, or just expressionsofthelanguageoftypetheory,i.e.openformulas?Aneliminativistinterpretationis proposedandclaimedthatRussell’spropositionalfunctionsaretobeunderstoodonlyasexpressions,astheso-called“incompletesymbols”,whichdonotdenoteanyextra-linguisticobjects, such as attributes, whether in realist or constructivist sense. It is argued that the ramified type theory of Principia should not be understood as an abandonment of Russell’s earlier substitutional theory, but rather as its continuation. The ramified type hierarchy is a consequence of Russell’s belief that the paradoxes of propositions that plagued the substitutional theory can only be avoided by some kind of a type differentiation of propositions. On the other hand, the elimination of propositional functions (as well as propositions) from the ontology of Principia is a consequence of Russell’s conception of logic as universal science, which must contain only one type of genuine variables – viz., completely unrestricted entity variables, with everything that exists as their values. The doctrine of the unrestricted variable has been formulated by Russell in The Principles of Mathematics and is an inseparable part of his understanding of logic. The theory of denoting phrases he developed in “On Denoting” provided the tool for the elimination of higher-order entities from the background ontology of his logic. This way, Russell managed to retain a complex type hierarchy of expressions needed to avoid the paradoxes and at the same time preserve the doctrine of the unrestricted variable. At the end of the first section, certain advantages of rejecting the doctrine of the unrestricted variable and Russell’s understanding of propositional functions as incomplete symbols are recognized, and suggested that the interpretation of the ramified hierarchy as an ontological hierarchy of concepts might be philosophically justified. Inthesecondsection,aformalsystemofcumulativeintensionalramifiedtypetheory(KIRTT) is presented, guided by a realist interpretation of a ramified type hierarchy and with semantics based on an intensional generalization of Henkin models. The aim was to formalize certain metaphysical intuitions concerning the nature of intensional entities and to sketch one possible formal theory of concept

RAMIFIED TYPE THEORY AS INTENSIONAL LOGIC

Ovaj doktorski rad sastoji se od dva glavna dijela. Prvi se dio bavi pitanjem što sustava čine funkcije u razgranatoj teoriji tipova Bertranda Russella, kako ju je izložio u filozofijskome uvodu prvoga izdanja Principia Mathematica.U tome se dijelu rada brani eliminativističko tumačenje i pokušava pokazati da Russell sam stavačne funkcije u Principia razumije samo kao izraze, kao tzv. nepotpune simbole, koji ne označavaju nikakve izvanjezične predmete poput pojmova ili atributa.This doctoral thesis consists of two main sections. The first section addresses the background ontology of Bertrand Russell’s ramified type theory as described in Principia Mathematica. More precisely, it deals with the question of the ontological status of propositional functions. The concept of a propositional function is one of the central concepts of Russell’s theory of types, both in the first draft of the theory in “Appendix B” of The Principles of Mathematics andinitsmatureformulationinthefirsteditionofPrincipia.However,howtounderstandwhat Russell meant by “propositional functions” remains controversial. What are propositional functions? Are they some sort of intensional abstract entities, like properties and relations, or just expressionsofthelanguageoftypetheory,i.e.openformulas?Aneliminativistinterpretationis proposedandclaimedthatRussell’spropositionalfunctionsaretobeunderstoodonlyasexpressions,astheso-called“incompletesymbols”,whichdonotdenoteanyextra-linguisticobjects, such as attributes, whether in realist or constructivist sense. It is argued that the ramified type theory of Principia should not be understood as an abandonment of Russell’s earlier substitutional theory, but rather as its continuation. The ramified type hierarchy is a consequence of Russell’s belief that the paradoxes of propositions that plagued the substitutional theory can only be avoided by some kind of a type differentiation of propositions. On the other hand, the elimination of propositional functions (as well as propositions) from the ontology of Principia is a consequence of Russell’s conception of logic as universal science, which must contain only one type of genuine variables – viz., completely unrestricted entity variables, with everything that exists as their values. The doctrine of the unrestricted variable has been formulated by Russell in The Principles of Mathematics and is an inseparable part of his understanding of logic. The theory of denoting phrases he developed in “On Denoting” provided the tool for the elimination of higher-order entities from the background ontology of his logic. This way, Russell managed to retain a complex type hierarchy of expressions needed to avoid the paradoxes and at the same time preserve the doctrine of the unrestricted variable. At the end of the first section, certain advantages of rejecting the doctrine of the unrestricted variable and Russell’s understanding of propositional functions as incomplete symbols are recognized, and suggested that the interpretation of the ramified hierarchy as an ontological hierarchy of concepts might be philosophically justified. Inthesecondsection,aformalsystemofcumulativeintensionalramifiedtypetheory(KIRTT) is presented, guided by a realist interpretation of a ramified type hierarchy and with semantics based on an intensional generalization of Henkin models. The aim was to formalize certain metaphysical intuitions concerning the nature of intensional entities and to sketch one possible formal theory of concept

METAFIZIČKI KRAJOBRAZ ATEIZMA

Dva su glavna cilja ovoga rada predložiti klasifikaciju ateističkih teorija na temelju načina na koje odgovaraju na tzv. problem kontingentnosti i procijeniti njihovu filozofijsku održivost kao metafizičkih teorija. Klasificiramo ateističke teorije u tri široke kategorije koje nazivamo “naivni necesitizam”, “brutizam” i “fundacionalizam” i sugeriramo da načelno samo fundacionalističke teorije mogu biti branjive alternative teizmu

Filogenetska analiza hrvatskih izolata virusa virusnog proljeva goveda.

Between 2007 and 2011, a total of 1937 sera samples and five spleen samples from nine Croatian dairy herds were tested for the bovine viral diarrhea virus (BVDV) using virus isolation and the immunoperoxidase test. BVDV was detected in 13 persistently infected (PI) cattle with a non-cytopathogenic biotype, while in five animals with fatal mucosal disease, isolates from spleen samples were of the cytopathogenic biotype. To reveal the genetic typing of Croatian BVDV isolates, viral RNA was extracted from infected cell cultures and amplified by RT-PCR, with primers targeting the 5’-UTR and the Npro gene, followed by direct sequencing of purified PCR products. Sequence and phylogenetic analysis of the 5’-UTR genome region determined that all Croatian isolates belonged to BVDV genotype 1; 11 isolates were grouped with BVDV-1b and 7 with BVDV- 1f viruses. The phylogenetic tree inferred by the Bayesian approach, using combined 5’-UTR/Npro, supported clustering of Croatian isolates in two subgroups. The deduced aminoacid sequence of the Npro region revealed 5 sites unique for four domestic BVDV-1f isolates.Od 2007. do 2011. godine na virus virusnog proljeva goveda (VPG) pretraženi su uzorci pet slezena i 1937 uzoraka seruma podrijetlom iz 9 stada mliječnih goveda. Imunoperoksidaznim testom (IP) u 13 je uzoraka dokazan necitopatogeni biotip virusa VPG te je potvrđena perzistentna zaraza. Iz svih pet uzoraka slezena izdvojen je citopatogeni virus VPG. U svrhu genotipizacije vlastitih izolata virusa VPG, iz nadtaloga inficiranih staničnih kultura izdvojena je virusna RNK i umnožena lančanom reakcijom polimerazom uz prethodnu reverznu transkripciju (RT-PCR). Umnoženi odsječci 5’-UTR i gena Npro su potom sekvencirani. Filogenetska analiza hrvatskih izolata virusa VPG pokazala je da svi pretraženi izolati pripadaju genotipu 1; 11 izolata svrstano je u podtip 1b, a 7 u 1f. Filogenetska analiza na temelju spojene 5’-UTR/Npro genske sekvencije potvrdila je rezultate genotipizacije pretraženih izolata. Na Npro dijelu genoma utvrđeno je pet aminokiselinskih promjena osebujnih za hrvatske izolate iz podtipa 1f