St. Andrews Kant Reading Party 2019: Kant and Leibniz on the Ontological Argument
Paper Session 1 (31st of July, 16:30-18:00)
Jun Young Kim (UIC)
‘A Combinatorial Theory of Compossibility in Leibniz’s Metaphysics’
Most contemporary metaphysicians think that for any two distinct things, it is always possible for them to coexist with one another. Leibniz gives a somewhat different answer: two distinct things are able to coexist with one another only when they are compossible. God cannot create all possible substances together because not all of them are compossible. But what is the basis within Leibniz’s philosophy for the incompossibility of substances? This has been one of the most hotly contested issues in the recent secondary literature. Four kinds of interpretations have been presented. Logical interpretations maintain that compossibility is ultimately nothing but logical consistency. Advocates of logical interpretations argue that two possible substances are compossible just in case their complete concepts are logically consistent. In contrast, lawful, cosmological, and packing interpretations assume that possible substances are logically independent of one another. They maintain that any two possible substances are per se compossible. However, God is precluded from actualizing all possible substances by some non-logical constraints.
The second literature has long been dominated by variations of those four approaches. In this presentation, however, I show that there is one important issue which has been largely overlooked: compossibility relation might be intransitive. Intransitivity will be problematic for all the above interpretations; for, despite their differences, they all agree that compossibility relation is transitive. According to logical interpretations, each possible substance is compossible with and only with its world-mates; thus, compossibility is an equivalence relation (reflexive, symmetric, and transitive). According to lawful, cosmological, and packing interpretations, the compossibility relation is trivially transitive since any two possible substances are per se compossible. However, there are passages where Leibniz suggests that the compossibility relation is intransitive. If compossibility is intransitive for him, then none of those four approaches is on the right track. This indicate that we need a new approach to the puzzle of compossibility. In this paper I present a novel interpretation of compossibility. My alternative has the following features: (1) It uses combinatorial principles to solve the problem of compossibility; God calculates all the possible combinations and the sum of the perfection of each combination by simple mathematical principles. But (2) the combinatorial principles I am relying on are non- Humean. Thus, I deny that everything can be combined with everything else. The intransitivity of compossibility is in fact a natural consequence of non-Humean combinatorialism. Moreover, (3) my view can provide solutions to the important puzzles of compossibilty. More specifically, it can explain both that (i) Spinozistic necessitarianism is logically impossible, and that (ii) the World-Apart scenario is logically possible for Leibniz. My work will reveal what Leibniz has in mind when he says that his metaphysics is nothing but the “Divine Mathematics” in a rigorous manner.
Paper Session 2 (1st of August, 14:00-15:30)
Nicholas Currie (UCL)
‘Distinguishing Logical from Real Predicates’
Recently, a reading of Kant’s critique of ontological arguments has emerged as standard in the anglophone literature.  It states that Kant’s objection to these arguments is that they treat existence as a determination, even though ‘Being is […] not a real predicate’ (A596/B624). The thought runs that a real predicate, in Kant’s sense, is one which can serve as determinative of the character of the subject. The concept EXISTS, however, can serve as no such a predicate, given that something’s existing is not a determination of the way that it is; it is merely that it is.
These interpreters then take Kant to be setting real predicates up in opposition to merely logical predicates. Considering a concept as a logical predicate, the thought goes, is to consider it not as the determination of a subject, but instead as a predicate in a thin syntactic or grammatical sense. More specifically, a concept is considered as a logical predicate for Kant, just in case one is concerned with
- (LS) relations of logical consistency between positive and negative (i.e. negated and non-negated) concepts,  or
- (LG) the ‘grammatical predicate position’ of a judgement. 
This then allows these interpreters to argue that, whilst in existential judgements the concept EXISTS fails to characterise the subject in a way that goes beyond the subject concept and, hence, is not real, it nonetheless still appears in predicate position, and thus counts as a logical predicate, in the sense of (LG).
In this paper, I challenge this reading, arguing that it errs in its account of
logical predicates and hence misconstrues important aspects of Kant’s challenge.
Specifically, I argue that neither (LS) nor (LG) capture what Kant means by a logical predicate. (LS) fails because, properly understood, contrariety of Kantian concepts is not a syntactic opposition (i.e. conceptual negation), but a semantic one (i.e. complementation relation which holds between conceptual content). (LG) fails insofar as it mistakenly takes Kantian logic to be formal in our modern sense.
Following this, I present an alternative reading. I urge that to consider some concept B as a logical predicate of a judgement <A is B> is to consider these concepts only insofar as
- (L) A contains/excludes B, or vice versa, where containment and exclusion are properties of a well-defined structure (technically, a meet semi-lattice) which holds of all concepts qua concepts.
I then explain why Kant can’t think that EXISTS counts as a logical predicate in the ontological judgement <God exists>. For were he to think this, <God exists> would, by his own lights, count as analytic. That is to say, either GOD would contain EXISTS, in which case it would be a priori that, if there are any Gods, they have the property of existing necessarily, or GOD would exclude EX- ISTS, meaning that it would be a priori that if there are any Gods, they have the property of not existing necessarily. Either way, existence would be being treated as a determination in the way that Kant explicitly proscribes.
 Cf. Abaci (2008, 2011), Chignell (2012), Stang (2016), Bader (forthcoming).
 Cf. esp Chignell (2012) [pp.643-4], Stang (2016) [pp.64-5]
 Gardner (1999), p.155, Abaci (2008) [p.572] and (2011) [p.450]
Abaci, U. (2008) ’Kant’s Theses on Existence’ from British Journal for the History of Philosophy, Vol. 16(3), pp.559-593
— (2011) Kant’s Critical Theory of Modality: A Basis for a Moral Metaphysics, PhD Thesis
Bader, R. (forthcoming) Kant’s Theory of Modality (Cambridge: Cambridge University Press) Chignell, A. (2012) ’Kant, Real Possibility, and the Threat of Spinoza’ from Mind, Vol. 121(483), pp.635-675
Gardner, S. (1999) Kant and the Critique of Pure Reason, (New York, NY. : Routledge)
Kant, I. (1998) Critique of Pure Reason (trans. Guyer & Wood) (Cambridge: Cambridge University Press)
Stang, N. (2016) Kant’s Modal Metaphysics (Oxford: Oxford University Press)
Paper Session 3 (2nd of August, 10:00-11:30)
Martijn Buijs (UC Santa Barbara)
‘The Need of Reason. Kant’s Transcendental Ideal and the Afterlife of Ontotheology’
Kant’s opposition to ontotheology is commonly captured in the phrase that existence is not a predicate, but positing. While the ontological argument has had its share of contemporary defenders, it is nevertheless often held by analytic and continental philosophers alike that Kant has with this insight shown once and for all the vanity of ontotheology. This, I argue, is a misreading for two reasons.
First, it marginalizes the fact that Kant in his pre-critical Nova Delucidatio (1755) and Beweisgrund-essay (1763) provides a different proof for the existence of God: the proof from possibility. It further marginalizes the fact that, despite the distance between the pre-critical and the critical works, Kant explicitly holds onto the subjective necessity for human reason of the proof from possibility, which re-emerges as the Ideal of Reason in the first Critique. Kant’s thought thus cannot be said to simply abandon ontotheology. Instead, the transcendental ideal as a genuine need of reason forms what we might call the afterlife of ontotheology.
In this paper I will first trace the development of Kant’s proof from possibility and describe its reliance on what has been called the Grounding Premise: that real possibility, as distinct from mere logical possibility, must be grounded in actuality. God thus emerges as the sum-total of actuality or omnitudo realitatis. It has recently been argued that Kant’s thought here is less innovatory than has been thought: Leibniz too, without explicitly arguing the point, is committed to the ideas that existential propositions are synthetic, and that God must be seen as the “root of possibility”. I will closely map this Leibnizian inspiration on Kant’s thought.
I will then argue that the Ideal of Reason and the afterlife of ontotheology it allows us to think remains a crucial philosophical resource today. Against readings which seek to excise the Transcendental Ideal as a mere “hangover” of dogmatic metaphysics from Kant’s critical project, and equally against deflationary readings which, while maintaining the Ideal’s structural place, marginalize the role it does or should play, I will defend both the justified need of such a thought for Kant’s overall understanding of the nature of human reason, and the fruitfulness of the Ideal as a response to that need.
Third, I will show one way in which the fruitfulness of the Ideal might be brought to light. For against both facile dismissals of ontotheology on the one hand, or the outright speculative revindication of the ontological argument such as one finds in Hegel on the other, Schelling in his late philosophy turns it into the structuring principle of his thought: that human reason is and remains constitutively in need of a grounding it cannot on its own strength achieve.