St. Anselm ’ s ontological arguments

1. St. Anselm’s ontologicalarguments Marie Duží The talk given in the 1stWorld Congress on Logic and ReligionBrazil, JoaoPesoa

2. Saint Anselm of Canterbury (1033–1109) • was the outstanding Christian philosopher and theologian of the eleventh century. He is best known for the celebrated “ontological argument” for the existence of God in the Proslogion, but his contributions to philosophical theology (and indeed to philosophy more generally) go well beyond the ontological argument. • The Proslogion (Latin Proslogium; English translation, Discourse on the Existence of God), written in 1077–1078, was written as a prayer, or meditation. It reflectson the attributes of God and endeavours to explain how God can have qualities which often seem contradictory. • In the course of this meditation, the first known formulations of the ontological argument for the existence of God was set out.

3. Dennis Jowers (1999). Anselm's Proslogion: One Simple Proof? Quodlibet Journal, 1. Careful analysis of Anselm’s Proslogion and his Reply to Gaunilo, however, will show that Anselm proposes not one, but six ontological arguments which, while relying on common premises about the nature of thought and the identity of God, differ in their contents, sometimes markedly. These six arguments may be conveniently divided into four classes: the arguments from God’s perfection, the argument from His necessity, the argument from His eternity, and the arguments from His simplicity. […] Anselm proposes in the Proslogion and the Reply not merely a simple argument, but a whole method of reasoning about God fertile in its implications for His nature and existence.

4. St. Anselm’s Proslogion II Anselm’s axioms(derived from Christian Revelation): • that, than which nothing greater can be conceived is God. • it is possible to conceive God • God is conceived • God exists in our minds

5. St. Anselm’s Proslogion II • The argument from God’s perfectness • The argument from His necessity • The argument from His eternity • The argument from His compactness Duží, M. (2011): St. Anselm’s Ontological Arguments. Polish Journal of Philosophy, vol. V, No. 1, Springer 2011, pp. 7-37. The variant ad (1) in Proslogion III: Pavel Tichý: Existence and GodJournal of Philosophy, 1979

6. The content of this talk • Existence (in general) • PWS intensions; intensional essentialism  requisites • Higher-order offices • Descart’s proof: two flaws • Anselm’s argument in Chapter III: logically valid;if it were also sound, then … Background theory: Transparent Intensional Logic

7. Non-trivial existence • Barack Obama has black eyes • How to evaluate: take the individual and examine whether it has the property of having black eyes • Barack Obama exists • Is existence just another feature that can be ascribed to individuals? • How should we evaluate such an existential statement? • Take the individual  but then it trivially exists! • The set of individuals is given a priori (a „pre-concept“ of TIL) • Hence every sentence claiming the existence of an individual is necessarily true • (as many philosophers and logicians observed;Hinttika, Kant, …)

8. “Existence is not a property of things”(?) • Aristoteles, Kant, Russell, … • But: Existence is non-trivially predicted and coherently denied … • True and informative sentences: • The President of the USA exists • The King of France does not exist • Do these sentences ascribe existence to any individual? • But Barack Obama does not receive mention here; and which individual would be mentioned by the second sentence?

9. The King of France does not exist • In TIL we don’t deal with possibilia (Parmenides) • The subject to which non-existence is ascribed is an individual office, role, ‘thing to be’: • Properly partial function (mapping):  - modal parameter (possible worldsw);  - temporal parameter (timest);  - universe of discourse (individuals) <w1, t1> Ind1 <w2, t2>  Ind2 <wi, ti>  nothing (value gap) <wk, tl>  Ind3 …

10. Offices, roles, things to be • Occupied – there is an individual playing the role (President of Zimbabwe, Pope, the first man who ran 100 m under 10 seconds, …) • Vacant– no individual playing the role(the King of France, the first man who ran 100 m under 9 seconds, …)

11. Existence is a property • of intensions: the property of being occupied (instantiated) in a given w(orld)/w at t(ime)/t • Exist/() • The President of USA exists: • wt [0Existwt wt [0Presidentwt0USA]] ()  o otw

12. Existence talks about an intension wt [0Existwt wt [0Presidentwt0USA]] intensionally: de dicto wt [0Blue-eyedwt wt [0Presidentwt0USA]wt ] extensionally: de re

13. Requisites of an office • Property R is a requisite of an office O: • Necessarily, if an individual a occupies the office O , then a has the property R () • [0Req R O] = wt[[0ExistwtO]  [0Truewt wt [RwtOwt]]] • Example. Requisites of the President of USA: to be a human being, elected, inaugurated, US citizenship, ...

14. Valid/invalid argument • Invalid: (+) Ris a requisite of Othe holder ofOhas the propertyR [0Req R O]  wt[RwtOwt]: the so-constructed proposition is not true if Owtfails – truth-value gap !! Yet the requisite relation obtains between intensions independently of contingent empirical facts • Valid: (++) the officeOis occupied;Ris a requisite of Othe holder ofOhas the propertyR [0Req R O] & wt[0ExistwtO]  wt [RwtOwt]

15. Inference rule (++) • [0Req R O] = wt [[0Existwt O]  [0Truewt wt [Rwt Owt]]] [0Req R O], [0Existwt O] de dicto (++)  [Rwt Owt] de re [0Req 0Politician 0Queen_of_Poland] The Queen of Poland is a politician (provided the Queen exists!)

16. Higher-degree offices • The President of USA /  • occupied by individuals; degree 1 • The highest executive office of USA • occupied by individualoffices: currently and actually by the President (rather than the King) of the USA • Type ()  degree 2

17. What does ‘God’ denote ? • If ‘God’ denoted an individual ( ), then it’d be purely contingent matter whether He is omnipotent, omniscient, benevolent, ..., because any individual might have been malevolent • ‘God’denotes a thing to be: an individual office, God_office/  • Question: “Does God exist?” is legitimate; we ask whether God-office is occupied

18. Descartes’ (ontological) proof • Invalid scenario (+): God has all the positives; existence is a positive. Hence, God exists. Moreover, Confusing intensional and extensional level of abstraction: Existence is a requisite of the God-office. • But: requisites of an individual office are properties of individuals existence would have to be such a property (which is not the case)

19. Proslogion III: That, than which nothing greater can be conceived, exists so truly that it cannot be conceived not to exist. _______________________________________________ For, it is possible to conceive of a being which cannot be conceived not to exist; And this is greater than one which can be conceived not to exist. Hence, if that, than which nothing greater can be conceived, can be conceived not to exist, it is not that, than which nothing greater can be conceived. But this is an irreconcilable contradiction.

20. ‘That, than which nothing greater can be conceived’ • Descartes presupposes that he knows the essence of God • St. Anselm is far from such arrogance • He addresses God by in a modest way: • That, than which nothing greater can be conceived • Let’s analyze this expression

21. ‘That, than which nothing greater can be conceived’ ‘greater than’ binary relation (-in intension) between what ? • The office of the President of USA is greater thanthe office of the richest peanut farmer in Georgia, but • Jimmy Carter is not greater than Jimmy Carter Hence: the concepts of both offices in (A) occur with supposition de dicto Greater than () the relation-in-intension between offices

22. ‘That, than which nothing greater can be conceived’ • ‘That, than which nothing greater can be conceived’abbr. NG () • NGis the second-order office • God-office occupiesNG • Anselm (even a fool) understandNG, they have (in mind) a concept of God; they know what it amounts for an individual office to occupy NG • But they do not know what it amounts for an individual to occupy God-office • (God is a secret !)

23. ‘That, than which nothing greater can be conceived’(NG) • Requisites of NGare properties of individual offices • Existence is a property of individual offices • Hence – existence can be a requisite of the office NG • Legitimate question: does God’s office have the property of existence? • Necessary existence: to be occupied in all possible worlds (and times)

24. Anselm’s principles • Individual office that has the property of necessary existence isgreater thanany other office lacking this property • Necessary existence is a requisite of NG

25. Anselm’s assumptions (i)There is an individual office with necessary existence (Anselm considered to be trivially valid; Tichý proved) (ii)An office with necessary existence is greater than the office without

26. The assumption thatNG is occupied Anselm proves it by reductio ad absurdum: • There are maximal offices to which greater are not conceivable • 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 Anselm does not apply the invalid inference (+)

27. Anselm’s valid argument (++) • OfficeNGhas necessary existence among its requisites, • OfficeNGis occupied, • Hence, God’s office that occupies NGhas the property of necessary existence • God exists, necessarily.

28. Gaunilo’s objection • By the same line of reasoning it is possible to prove the existence of the most perfect island • The office NGI – the greatest island office – does not have the requisite of necessary existence • Even 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

29. Anselm’s key assumption • the office with necessary existence is greater than any other office • Is necessarily occupied officeeo ipsogreater than any other office which is conceivably vacant? • The greater (more important) office, the more difficult and demanding it is to occupy it; • The first man who ran 100 m under 9 s is greater than (i.e. less occupied) • The first man who ran 100 m under10 s

30. Anselm’s key assumption: weaker one • (A’) to any office that is not necessarily occupied there is a greater necessarily occupied office • (A’) and (Occ) suffice to prove Anslem’s conclusion • The first man to run 100 m under 9 s • It does not have necessary existence • Let us extend the office: in each w,t where the office is vacantlet’s assign someindividual as the value • But: 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

31. Necessary existence and greatness • Contra Anselm • (Logically) necessary occupancy is contra greatness • L*: the office of the greatest occupied office • L* is not particularly great: among its requisites there is no perfect quality; its essence is actually poor • The more frequently occupied office, the smaller its essence • There 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

32. Proposition and truth • The more generally (in more w,t)a proposition is true, thelessinformative it is • Necessarily true proposition is informationally valueless • Necessarily occupied individual office is boring and poor; it does not demand much of an individual to occupy it

33. This analogy is even more accurate than it might seem. Individual office has the property of necessary existence iff the proposition that this office is occupied is true in all worlds and times. If God existed necessarily than the proposition that God exists were a tautology. It is difficult and hardly acceptable to suppose that a believer differs from an atheist by the fact that the believer assents to a tautology

34. Conclusion • Anselm’s argument in Proslogion III is logically valid but not sound • If God exists necessarily, then it cannot be logical/analytical necessity. • If ‘meta-physical’ has any sense then God’s existence is metaphysically necessary • But this is another story …

35. References • Charlesworth, M.J. (1965): St. Anselm’s Proslogion with ‘A Reply on Behalf of the Fool’ by Gaunilo and ‘The Author’s Reply to Gaunilo’. London: Oxford University Press. • Duží, M. (2011): St. Anselm’s Ontological Arguments. Polish Journal of Philosophy, vol. V, No. 1, Springer 2011, pp. 7-37. • Jowers, D. (1999): Anselm's Proslogion: One Simple Proof? Quodlibet Journal, vol. 1, No. 4. • Tichý, P. (1979): Existence and God. Journal of Philosophy 76: 403-420. Reprinted in (Tichý 2004: 353-372). • Tichý, P. (2004): Collected Papers in Logic and Philosophy, eds. V. Svoboda, B. Jespersen, C. Cheyne. Prague: Filosofia, Czech Academy of Sciences, and Dunedin: University of Otago Press.

36. Thank you for your attention