•1 Existence and God Pavel Tichý Journal of Philosophy, 1979 Marie Duží VSB-Technical University Ostrava marie.duzi@vsb.cz •2 Prof. Dr. Pavel Tichý n1954 – 1959: Charles University nPhilosophy and Mathematics n1968: left for England (Exeter) n1971: emigrated to New Zealand, Otago, Prof. University of Dunedin nOctober 26, 1994: died in Dunedin •3 The contents 1.Denotation and existence (in general) 2.Extensions vs. intensions; intensional essentialism à requisites 3.Descart’s proof: two errors 4.Anselm’s argument: logically correct, (doubts about the validity of a premise) n •4 Denotation and existence nJimmy Carter has blue eyes nHow to evaluate: take the individual and examine whether he has the property of having blue eyes nJimmy Carter exists nIs existence just another feature that can be ascribed to individuals? nHow should we evaluate such an existential statement? nTake the individual à but then it trivially exists! nThe set of individuals is given a priori (a „pre-concept“ of the universe in TIL) nHence every sentence claiming the existence of an individual is necessarily true n(as many philosophers and logicians observed; Hinttika, Kant, …) •5 “Existence is not a property of things” nAristoteles, Kant, Russell, … nBut: Existence is non-trivially predicted and coherently denied of something nTrue and informative sentences: nThe President of the USA exists nThe King of France does not exist nDo these sentences ascribe existence to any individual? nBut Obama, or Trump, or whoever, is not mentioned here; and which individual would be mentioned by the second sentence? •6 The King of France does not exist nWhat does it predict the non-existence about? nAbout “non-existing individual”? nWe don’t deal with possibilia (Parmenides) nThe subject to which non-existence is ascribed is an individual office, role, ‘thing to be’: nProperly partial function (mapping): w ® (t ® i); itw ; w - modal parameter (possible worlds); t - temporal parameter (times); i - universe of discourse (individuals) n à Ind1 n à Ind2 n à nothing (value gap) n à Ind3 n… •7 Offices, roles, things to be n nOccupied – there is an individual playing the role (President of Zimbabwe, the Pope, the first man who run 100 m under 10 seconds, …) n nVacant – no individual playing the role (the King of France, the first man to run 100 m under 9 seconds, …) •8 Existence is a property nNot of individuals, but nof intensions (or functions, in general): the property of being occupied, instanciated, having a value, in a given w(orld) at t(ime) nExist/(oitw)tw nThe President of USA exists: nlwlt [0Existwt lwlt [0Presidentwt 0USA]] n (ii) i n i n (oitw) itw •9 Existence concerns intensions nlwlt [0Existwt lwlt [0Presidentwt 0USA]] n n de dicto n nlwlt [0Blue-eyedwt lwlt [0Presidentwt 0USA]wt ] n n de re • • •10 Definition of existence n0Exist1 = lwlt lp [0$lx [pwt x]], p ® (oa)tw n0Exist2 = lwlt lu [0$lx [uwt = x]], u ® atw n nlwlt [0Exist2wt lwlt [0Presidentwt 0USA]] =df nlwlt [lwlt lu [0$lx [uwt = x]]wt lwlt [0Presidentwt 0USA]] =b nlwlt [0$lx [lwlt [0Presidentwt 0USA]wt = x]] n (b-reduction) •11 Requisites of an office nProperty R is a requisite of an office U: nNecessarily, if a occupies the office U à itw, then a has the property R à (oi)tw n[0Req R U] = "w"t [[0Existwt U] É [0Truewt lwlt [Rwt Uwt]]] n nExample. Requisites of the President of USA: to be a human being, properly elected, inaugurated, US citizenship, ... •12 Valid/invalid argument nInvalid: n(+) R is a requisite of U Þ the holder of U has the property R n [0Req R U] Þ lwlt [Rwt Uwt]: the so-constructed proposition is not true if Uwt fails – truth-value gap !! nYet the requisite relation obtains between intensions independently of contingent empirical facts nValid: n(++) the office U is occupied; R is a requisite of U Þ the holder of U has the property R n[0Req R U] & lwlt [0Existwt U] Þ lwlt [Rwt Uwt] •13 Valid inference rule (++) n[0Req R U] = "w"t [[0Existwt U] É [0Truewt lwlt [Rwt Uwt]]] n n [0Req R U], [0Existwt U] n(++) ¾¾¾¾¾¾¾¾¾¾¾ n [Rwt Uwt] n nExample: n[0Req 0Politician lwlt [0Presidentwt 0USA]] •14 Higher-level offices nThe President of USA / itw n occupied by individuals; level 1 nThe highest executive office of USA n occupied by offices: currently and actually by the President (rather than the King) of the USA nEntity / (itw)tw ¾ level 2 nThe most favourite proposition of A. Eistein / (otw)tw •15 What does ‘knowing an office’ amount for? nWe can never know the uncountable infinite mapping nOnly that we do understand an instruction: n‘the Mayor of Dunedin’; knowing the meaning amounts for knowing the instruction how to evaluate in any possible world w (lw) at any time t (lt) the procedure n [0Mayor-ofwt 0Dunedin] nIt does not mean to be able to execute, nor to know the holder! nWe can never know the actual world •16 What does ‘God’ denote ? nIf ‘God’ denoted an individual (® i), than it’d be purely contingent matter whether he is omnipotent, omniscient, benevolent, ..., because any individual might have been malevolent n‘God’ denotes a thing to be: individual office (® itw) nRequisites of the office: all positives nQuestion: “Does God exist?” is reasonable; we ask whether the God-office is occupied •17 Descartes’ (ontological) proof nRené Descartes (1596 – 1650) n nThe essence of the God-office are all the positive properties n nInvalid scenario: n God has all the positives; existence is a positive. Hence, God exists. nWhat is wrong here? •18 Descartes’ proof: two problems 1.Existence is a requisite of the God-office. nBut: requisites of an individual office are properties of individuals Þ existence would have to be such a property (which is not the case) 2.He applies the invalid inference rule (+): nExistence is a requisite of the God-office Þ the holder of the office has the property of existence (missing assumption: if the office is occupied) •19 Schema of modal ontological proofs nEssence of God G = {P1,…,Pn}, where Pi / (oi)tw are all the positives nHence, (analytically) necesssarily (ex definitione) God has all the positive properties (if he can have them, if they do not contradict each other): Pi(G) ® ( Pi(G) ® Pi(G)) = ( Pi(G) ® Pi(G)) nExistence E is positive, and it is possible that God exists (the concept of God does not involve a contradiction): E(G). nHence, E(G) nGod exists, necessarily. • • • • • • • • •20 What is wrong here? n(regardless of the problem of existence ascribed to individuals) nInvalid inference (+) nfrom necessary intensional (de dicto) truth (ex definitione) to extensional (de re) truth nIt is necessary that the King of France is a king (de dicto) nPossibly the King of France is a king. (de dicto) nÞ The King of France is necessarily a king. (de re) •21 Modality de dicto / de re nThe King of France might not be a king n“Almost” (analytically) true: nNo individual is necessarily a king! nIf FK exists, then FK might not be a king: FK® itw, x ® i. nlwlt [lx [$w*$t* Ø[FKw*t* = x]] FKwt] de re nIt is possible that the King of France is not a king nAnalytically false nlwlt [$w*$t* Ø[FKw*t* FKw*t*]] de dicto •22 Modality de dicto / de re nAnalogicky nDřevěné stoly jsou nutně dřevěné nNepravda! nNutně, dřevěné stoly jsou dřevěné nPravda! n(analyzujte) •23 Anselm’s ontological arguments nSt. Anselm of Canterbury (1033 – 1109) n nProslogion II – complicated argument following in principle the flawed schema of modal ontological proofs n nProslogion III (prayer) – simple, elegant and transparent argument which had been neglected •24 Anselm’s ontological argument: n‘Thy to whom nothing greater is conceivable’, exist so truly and actually that it is not thinkable that you would not exist. nFor it is thinkable that there is something the non-existence of which is not thinkable; nAnd this thing is greater than anything the non-existence of which is thinkable. nHence, if it were thinkable that ‘Thy to whom nothing greater is conceivable’ might not exist, then ‘Thy to whom nothing greater is conceivable’ would not be ‘Thy to whom nothing greater is conceivable’ – contradiction •25 ‘Thy to whom nothing greater is conceivable’ nDescartes assumes that he knows the essence of God nSt. Anselm is far from such arogance nHe addresses God by the modest: n‘Thy to whom nothing greater is conceivable’ n nLet’s analyze this description •26 ‘Thy to whom nothing greater is conceivable’ n‘greater than’ ® binary relation (-in intension) between what ? nCharles is greater than Peter: „greater what“ ??? A.The office of the President of USA is greater than the office of the richest peanut farmer in Georgia, but B.Jimmy Carter is not greater than Jimmy Carter nHence: the concepts of both offices in (A) de dicto (substitution test, not in B !) nGreater than ® (oitwitw)tw the relation-in-intension between offices •27 ‘Thy to whom nothing greater is conceivable’ n‘Thy to whom nothing greater is conceivable’ – abbr. NV ® (itw)tw nNV is the second-level office nGod-office occupies NV nAnselm (even a fool) understand NV, they have a concept of NV; what does it amount for an individual office to occupy NV nBut they do not know what does it amount for an individual to occupy God-office •28 ‘Thy to whom nothing greater is conceivable’ (NV) nRequisites of NV are properties of individual offices nExistence is a property of individual offices nHence – existence can be a requisite of the office NV nNecessary existence: to be occupied in all possible worlds (and times) •29 Anselm’s principles (A)Individual office that has the property of necessary existence is greater than any other office lacking this property (B)Necessary existence is a requisite of NV nAnselm did not apply the invalid inference (+) – slide 11 •30 Anselm’s assumptions n(i) There is an individual office with necessary existence (Anselm considered to be trivially valid; Tichý proved) n(ii) An office with necessary existence is greater than the office without n(iii) The office NV is occupied (O): n (Anselm proves it) •31 ad i) – there is a necessarily occupied office n nTichý: nDefined the second-level office L, which has the property of necessary existence: nOffice L of the smallest occupied individual office •32 Anselm’s valid argument nOffice NV has necessary existence among its requisites, nOffice NV is occupied, ÞHence God-office that occupies NV has the property of necessary existence ÞGod exists, necessarily. •33 The assumption that NV is occupied nThere are maximal offices to which greater are not conceivable nReductio ad absurdum: if there were two such things, then these things would have to be greater via different things; but then it would be conceivable that there is a thing that has both the things via which it is greater n nConclusion: God necessarily exists, hence also actually? •34 Gaunilo’s objection nBy the same line of reasoning it is possible to prove the existence of the most perfect island nThe office NVI – the greatest island office – does not have the requisite of necessary existence nEven if it were true that in the actual world islands always existed and will exist, there is nothing impossible in conceiving a world void of islands n •35 Anselm’s key assumption n(slide 25): the office with necessary existence is greater than any other office nIs necessarily occupied office eo ipso greater than any other office which is conceivably vacant? nThe greater (more important) office, the more difficult it is to occupy it; •36 Anselm’s key assumption nThe first man to run 100 m under 9 s n is greater than (i.e. less occupied) nThe first man who run 100 m under 10 s (Carl Lewis, 9.86, Usain Bolt 9.58) nTichý – necessarily occupied office L: the smallest ... nIs the office of the most rotten apple core in Chicago litter basket greater than the office of the Pope ??? •37 Anselm’s key assumption: weaker one n(A’) to any office that is not necessarily occupied there is a greater necessarily occupied office n(A’) and (O) suffice to prove God’s existence nThe first man who run 100 m under 9 s nIt does not have necessary existence nLet us extend the office: in each w,t where the office is vacant let’s assign some individual as the value nBut: in this way we weaken the office – it will not have the desirable requisites – we obtain necessarily occupied office, but the price is too high. We lose the greatness; lacking better candidates it will be occupied by lower-quality individuals •38 Necessary existence and greatness nContra Anselm nNecessarily occupied is contra greatness nL* (the opposite of L): the office of the greatest occupied office nL* is not particularly great: among its requisites there is no perfect quality; its essence is really poor nThe more frequently occupied office, the smaller its essence nThere are worlds in which everybody is ignorant of this or that fact: in this world L* must be occupied by a low-quality individual; simply because there are no better candidates •39 Proposition and truth nThe more generally (in more w,t) a proposition is true, the less informative it is nNecessarily true proposition is informationally valueless (concerning an empirical information) nNecessarily occupied individual office is boring and grey; it does not demand much of an individual to occupy it •40 Tichý: nThis analogy is even more accurate than it might seem. nIndividual office has the property of necessary existence iff the proposition that this office is occupied is true in all worlds and times. nIf God existed necessarily than the proposition that God exists were a tautology. nIt is difficult and hardly acceptable to suppose that a believer differs from an atheist by the fact that the believer assents to a tautology