Frege: Kaiser’s chariot is drawn by four horses What does the number 4 belong to? None of the horses “is four”. Concept “horse” is instantiated by 4 objects. Mars has two satellites. The concept “satellite of Mars” is instantiated by 2 objects. IN each case, the object functions as a “concept” and the numbers tell us how much it is instantiated. Since the numbers refer to the object as a whole, numbers are a second order concept. Venus has no moons. Nothing falls under the concept “moon of venus”. It is not instantiated.

Existence not a predicate, because 2nd order concept. Venus has no moons. Nothing falls under the concept “moon of venus”. It is not instantiated. “moons of Venus” do not exist. So non-existence is a way of saying “there are none” – and existence is a way of saying “there are some”. So existence is a second order concept, like numbers. It is asserted of concepts as a whole (not one predicate alongside others). Another reason why existence can be shown NOT to be a 1st order predicate, is that it is meaningless to say: “There is Julius Caesar”. (While the subj-predicate sentence “Julius Caesar is a man” makes perfect sense.)

To say “God exists” is to say that all the predicates of the description (ie the concept) are instantiated. It is to posit the concept as a whole. ∃x [x(p)] There is such a x such that x has all the properties of p. To say “God does not exist” is to say that the whole concept God, with all its predicates, is not instantiated. ~∃x [x(p)] It is not the case that [there is such an x such that x has all the properties of p] It is incorrect to think of existence as a first order concept, as a property alongside other properties x(p & ∃) “There is God” also makes not sense. This was Kant’s point – that to talk of something existing was simply to posit the concept with all its predicates – no extra “is” needed. Aristotle: to exist, is just to have a particular essence. BUT..Frege agrees that it does make sense to say “Julius Caesar exists”.. so existence can be a predicate, when asserted of individual entities? And God may be sucn an entity. Aquinas said that you can distinguish concept vs existence – you can have a concept of a phoenix without knowing if it exists. ie existence is a separate property – objects can be thought of separately from their existing.

Russell Theory of Descriptions analysis of names as descriptions shows there is no subject/ entity –the name is simply the sum of properties that find extension in the world. This is a matter of synthetic judgement sentences with empty terms like “God exists” are meaningful. It gets rid of negative existentials “God does not exist” which seem to suggest God exists in order not to exist. It means that existence is not a predicate, so OA based on existence as perfection fails. Frege Statements of existence, like statements of number, are second level concepts: - they assert whether the concept is instantiated or not (Venus has 0 moons). - Also sentences like “there is Julius Caesar” are meaningless. So existence is not a predicate as in OA and OA fails. Trying to prove existence is not a predicate, in order to reject the OA is inconclusive. - still seems to make sense that objects exist independently of our concepts - Phrases like “JC exists” are meaningful.

Explain Russell and Frege’s objections to the OA.

Necessary Existence. Descartes’ clear and distinct idea: of God as supreme being lacking no perfection, must exist. agnostic: reject that there is any such being. Hume/ Kant: can reject whole idea of God, including property of necessary existence.

Malcolm – modal argument for God’s necessary existence. 1. PREMISE If it is possible that there is a maximal being, such a being cannot depend on anything else for its existence – since it is itself maximal. So a maximal being, if it exists, exists necessarily. if it does not exist, nothing can make it come into existence, so its existence is impossible. 2. So a maximal being either necessarily exists, or his existence is impossible. 3. But God’s existence is not impossible, since the idea of God is not a contradictory concept. Hence God must exist. An agnostic would reject the premise – that it is possible for there to be such maximal and necessary being Is the concept of a maximal and necessary being coherent? But can it be shown to be incoherent? The argument takes place within the definition of God as maximal being. - How God is characterised (as necessarily existing) does not lead to a claim of existence – that a being so-characterised, exists (since definitions are not claims of existence – DAVIES)

Decision Tree You will need 3 presentations of the OA: Anselm’s 1st (definitional) Anselm’s 2nd (necessary being) Descartes (existence) Choices along each presentation may include: Hume Kant Russell Frege Malcolm Davies