A s emantic argument against the existence of universally held real properties

1. A semantic argument against the existence of universally held real properties Emanuel Rutten Faculty of Philosophy VU University

2. Preliminaries • Asemantic argument is a deductive argument fromsometheory of meaning. So, the argument’sconclusion is entailedbyone or more premisesaboutmeaning • I proposea semantic argument for the ontological claim thatthere are nouniversally held realproperties • A property is universally held ifandonlyifeverything has it • Thus the ontological claim canbephrased as: ∀P(Real(P) → ∃x¬P(x)) • A property is realifitaddssomethingto(or is a modification of) itsbearer. Propertiesthat are not real are calledCambridge properties • Someexamples of realproperties: being red, beingtriangular, being a man, being a table, beingmaterial, being contingent, being in love, knowingthat 1+1=2 • Someexamples of Cambridgeproperties: being the onlything in the world, being to the south of Paris, beinglovedby Brigitte, beingthought of by Mark, beingself-identical, beingsuchthat 1+1=2

3. A theory of meaning • The class of linguisticexpressionsincludesterms. There are two types of terms • So, in (neo-)Fregeanlinguistics, terms have a meaning (intension, content, mode of presentation) and a reference (extension, designation). A term expressesitsmeaning and designatesitsreference • Singularterms (e.g., proper namessuch as Johnanddefinite descriptions such as the president of the United States) • General terms (e.g, man, table, red and gold) • As Fregefamouslypointed out, evening star and morning star refer to the samething without having the samemeaning. The sameholdsformanyother cases, such as Obamaand president of the United States • As a special case, consider Jo. Jo decides to assignabc and xyz as proper namesforhisiPhone. In these cases of (Kripkean) ostensivedefinition, the meaning of abc is (the singleton set containing) Jo’siPhone. And the sameholdsforxyz • In all above cases, the meaning of a term fixesitsreference

4. A theory of meaning (cont.) • Considertermsthat are either • Singular (e.g., Jo, Kim, king of the Netherlands, president of the United States), • Genericand stand for a real property (e.g., red, material, unicorn, triangular), or • Generic and stand foreverything (e.g, being, existent, thing, object,entity) • Plausibly, these termsexpress a positivedeterminatemeaning • Moreover, these positivedeterminatemeanings are, plausibly, composed of positivedeterminatemeaningelements Examples The meaningelements of king of the Netherlands are kingandthe Netherlands (More precisely:the meaningelementsof the meaningexpressedby the term king of the Netherlands are the meaningsexpressedby the termskingandthe Netherlands) The meaningelements of unicornare a.o. horn, forehead, tailandhorseshoe

5. A theory of meaning (cont.) • Considertermsthat are either • Singular (e.g., Jo, Kim, king of the Netherlands, president of the United States), • Genericand stand for a real property (e.g., red, material, unicorn, triangular), or • Generic and stand foreverything (e.g, being, existent, thing, object,entity) • Plausibly, these termsexpress a positivedeterminatemeaning • Moreover, these positivedeterminatemeanings are, plausibly, composed of positivedeterminatemeaningelements Examples The meaningelements of evening star are eveningandstar The meaningelements of Alvin Plantinga are AlvinandPlantinga The meaningelements of being, red, abc and Kim arebeing, red, abc andKim

6. A theory of meaning (cont.) • Eachpositivedeterminatemeaning element has a reference set (e.g., the reference set of red is the set of all red things, the reference set of John is the set of all John’s) • More generally, eachpositivedeterminatemeaning has a reference set • The reference set RefSet(M) of a positivedeterminatemeaningM is the union of the reference sets of M’s meaningelements RefSet(M) = ∪ { RefSet(Mi) | Mi is a meaning element of M } Examples Take the meaningexpressedbyunicorn. The reference set of thatmeaning is the set of allhorns, allforeheads, alltails, allhorseshoe’s, etc. Take the meaningexpressedbypresident of the United States. The reference set of thatmeaning is the set of allpresidentsand the United States Take the meaningexpressedbyevening star. The reference set of thatmeaning is the set of alleveningsandall stars Take the meaningexpressedbyabc. The reference set of thatmeaning is Jo’siPhone

7. A theory of meaning (cont.) • Althoughmeaning and referencesurely do notcoincide, meaningandreference are plausiblycloselyrelated. For, the things ‘out there’ is whatmeaning is allabout • So, meanings are devicesforreferring – and thusanalysable in terms of reference • I positthistheory of meaning: M1= M2ifandonlyifRefSet(M1) = RefSet(M2) Example 1 Meaning(Obama)≠Meaning(president of the United States) RefSet(Meaning(Obama)) ≠RefSet(Meaning(president of the United States)) RefSet(Obama) ≠RefSet(president of the United States) Example 2 Meaning(morning star)≠Meaning(evening star) RefSet(morning star)≠RefSet(evening star)

8. A theory of meaning (cont.) • Althoughmeaning and referencesurelydo notcoincide, meaningandreference are plausiblycloselyrelated. For, the things ‘out there’ is whatmeaning is allabout • So, meanings are devicesforreferring – and thusanalysable in terms of reference • I positthistheory of meaning: M1= M2ifandonlyifRefSet(M1) = RefSet(M2) Example 3 Meaning(abc) = Meaning(xyz) RefSet(abc)=RefSet(xyz) Yet, “Brigitte knowsthatJo’siPhone is calledabc” does notentail “Brigitte knowsthatJo’siPhone is calledxyz”. Wouldthatrefuteabcandxyzhaving the samemeaning? No, abcandxyz are mentionedandnotused in these sentences (use-mentiondistinction)

9. The semantic argument Needto show thatthere are no universally held real properties:∀P(Real(P) → ∃x¬P(x)) Supposefor reductio ad absurdum thatthere is a real property that is universally held That property is either complex or simple(e.g., red is simpleandunicorn is complex) Ifit is simple call itP. Ifit is complex, it has a simple property as constituent. Call thatP It followsthatP is a simpleuniversally held real property SinceP is simple, RefSet(Meaning(P)) is the set of allP’s SinceP is universally held, everybeing is P. Hence, RefSet(Meaning(P)) is everything ThusRefSet(Meaning(P)) = RefSet(Meaning(being)) But then, Meaning(P) = Meaning(being)

10. The semantic argument (cont.) SinceP means beingandP is a real property, itfollowsthatbeing is also a real property ( Onecould even arguethat [Meaning(P) = Meaning(being)] entails [P = being]. For [Everybeing is P] canonlybean a priori conceptualtruth in case [P = being] ) But being is not a realproperty Realproperties, such as red, addsomething to thingsthatalreadyexist. So, ifbeing is a realproperty, itshouldaddexistence to alreadyexistingthings, which is impossible Ifbeingwouldbe a realproperty, thenitshouldaddbeing to itsbearer. Butthis is impossiblesincebearers are prior to theirrealproperties in respect of existence Indeed, if the bearer is notalready a being, there is nothingforbeing to attachitself to, i.e., there is nothingforbeing to be a property of. Thereforebeingcannotaddexistence We arrive at acontradiction. Therefore, there are no universally held real properties

11. Somecorollaries of the argument’sconclusion • Noteverything is physical. There is at leastonenon-physicalthing • Noteverything is contingent. There is at leastonenecessarything • Noteverything is caused. There is at leastoneuncausedthing • Noteverything is composite. There is at leastonesimplething • Noteverything is finite. There is at leastoneinfinitething

12. Someobjections • So[Noteverything is not-unicorn] is trueas well? But thenthere are unicorns? Not-unicornisn’t a term withpositivedeterminatemeaning. RefSet(Meaning(not-unicorn)) is thusnotdefinedand [Noteverything is not-unicorn] does not follow • But is [Noteverything is self-identical]true? Is there a thingnotidenticaltoitself? Thisdoesn’t follow either, sinceself-identical is a relational property andthus a Cambridgeinstead of a real property. It doesn’taddto (or modify)itsbearer • Is then [Noteverything is knowable?] true? Is theresomethingthat is unknowable? Ifknowable is a real property, thenthis is indeed a corollaryof the conclusion of the argument. But ifknowable is a Cambridge property, itdoesn’t follow. I do in factthinkthatknowable is a Cambridge property But whatifthere are unknowablethings? Wouldn’tthatreject the first premise of mymodal-epistemic argument for the existence of God? No, forthe refinedversionof the modal-epistemic argument is compatible withtherepossiblybeingunknowablefacts, such as John left Amsterdam andnobodyknowsit

13. ThankYou • Slidesavailable at gjerutten.nl