Mutability and Relationality: Towards an African Four-Dimensionalist Pan-Psychism

This article challenges a certain Theist conception of God as immutable. I argue that the idea that God is immutable can be challenged on the grounds of its metaphysical groundwork. More precisely, I contend that the idea that God is immutable entails endurantism, which I demonstrate to be mistaken. This view cannot be right because it potentially involves three absurd implications: (a) a violation of the principle of the Indiscernibility of Identicals (b) the idea that God becomes a different God with any change that occurs (c) the view that only the present is real and there is no future and past. As these solutions are absurd, the endurantist view ought to be abandoned. I then suggest an alternative theory that does not meet the same problems, which I call African four-dimensionalist Pan-Psychism. This theory I advance maintains that God is the sum of His spatial and temporal parts, is mutable and has relational properties (e.g., He changes with the occurrence of evil or good in the world). I uphold that this view does not have the absurd implications of its competitors.

Collocation and Constitution

Many philosophers accept the view that, when one object constitutes a second (say a tree and an aggregate of wood molecules), the two objects can be entirely in the same place at the same time (collocated). But what of two objects such that neither constitutes the other (a non-constituting pair)? Can they be collocated? If there can be such a pair of objects, they would have to share the same material constituents. To show that there are two collocated objects and not just one object at a specific time and place, one has to show that one of the objects has some property that the other fails to have. I claim that the properties I use in my example are legitimate substitution instances in the Law of the Indiscernibility of Identicals. I offer a metaphysically possible example that illustrates such collocation, a possible case from ‘raw nature’, two trees.

The Indiscernibility of Identicals and the Transitivity of Identity in Spinoza’s Logic of the Attributes

Puzzlingly, Spinoza appears to reject two principles that are central to our understanding of numerical identity: the Indiscernibility of Identicals and the Transitivity of Identity. For each principle, this chapter does three things. First, it explains where and how Spinoza appears to reject it. Second, it examines and argues against two proposals for resolving the puzzle that results from the apparent rejection: one proposal that appeals to Michael Della Rocca’s conception of “intensional properties” and one that denies, as Colin Marshall does, that Spinoza really means numerical identity by his phrase “one and the same” (“una, eademque”). Third, it offers and defends an original proposal for resolving the puzzle that appeals to two Spinozistic doctrines that it calls “Strong Ontological Pluralism of Attributes” and the “Adequate-Idea Conception of Truth.”

Propositional attitude statements

Propositional attitude statements – statements about our beliefs, desires, hopes and fears – exhibit certain logical peculiarities. For example, in apparent violation of Leibniz’s law of the indiscernibility of identicals, we cannot freely substitute expressions which designate the same object within such statements. According to Leibniz’s law, every instance of the following scheme is valid: - a = b - F(a) - Therefore, F(b) The validity of Leibniz’s law seems beyond question. It says, in effect, that if an object has a certain property, then anything identical to that object also has that property. Valid instances abound. But consider the following apparently invalid instance: - Hesperus is Phosphorus - Hammurabi believed that Hesperus often rose in the evening - Therefore, Hammurabi believed that ‘Phosphorus’ often rose in the evening. If we take ‘Hammurabi believed that…often rose in the evening’ to serve as the predicate F and ‘Hesperus’ and ‘Phosphorus’ to be a and b respectively, this argument appears to be an instance of Leibniz’s law. Yet (3) apparently fails to follow from (1) and (2). Hammurabi believed that Hesperus and Phosphorus were two heavenly bodies not one. And he believed that Hesperus did, but that Phosphorus did not rise in the evening. We have derived a false conclusion from true premises and an apparently valid law. If that law is really valid, then our argument had better not be a genuine instance of the law. The tempting conclusion, widely accepted, is that we were wrong to construe propositional attitude statements as simple predications. We should not, that is, construe ‘Hammurabi believed that…often rose in the evening’ to be just a long predicate with the semantic function of attributing some property to the object commonly denoted by ‘Hesperus’ and ‘Phosphorus’. But then the question arises: if attitude reports are not simple predications, what are they? Philosophers have disagreed sharply in their answers. Moreover, their disagreements are intimately connected to a wide range of deep issues about the nature of meaning and reference.

Identity of indiscernibles

The principle of the identity of indiscernibles states that objects which are alike in all respects are identical. It is sometimes called Leibniz’s Law. This name is also frequently used for the converse principle, the indiscernibility of identicals, that objects which are identical are alike in all respects. Both principles together are sometimes taken to define the concept of identity. Unlike the indiscernibility of identicals, which is widely accepted as a logical truth, the identity of indiscernibles principle has frequently been doubted and rejected. The principle is susceptible of more precise formulation in a number of ways, some more dubitable than others.

Philosophy of Logic

Logic may be characterized as the science aiming at revealing the deep logical structure of statements and, correlatively, at evaluating the arguments involving such statements. This chapter focuses on the content of different categories of expression of ordinary language, a question that arises typically in the analysis of singular terms and propositional attitudes. It starts from the paradoxes of the “indiscernibility of identicals” and goes through two main solutions to these paradoxes: a “logic of sense and denotation” (à la Frege) and a “logic of meaning” (à la Russell). A logic halfway between the two is also discussed. In the closing section, a comparative appraisal of these solutions is proposed.

On a Misguided Argument for the Necessity of Identity

There is a certain popular argument, deriving from Ruth Barcan and Saul Kripke, from the conjunction of the Principle of the Indiscernibility of Identicals (PInI, for short) and the Principle of the Necessity of Self-Identity to the Thesis of the Necessity of Identity. My purpose is to show that this argument does not work, at least not in the form it is often presented. I also give a correct formulation of the argument and point out that PInI is not even needed in the argument for the necessity of identity.

The logical contingency of identity

I show that intuitive and logical considerations do not justify introducing Leibniz’s Law of the Indiscernibility of Identicals in more than a limited form, as applying to atomic formulas. Once this is accepted, it follows that Leibniz’s Law generalises to all formulas of the first-order Predicate Calculus but not to modal formulas. Among other things, identity turns out to be logically contingent.