Gonzalo Rodriguez-Pereyra

In The Parmenidean Ascent, Michael Della Rocca presents a fascinating case for what he calls Strict Monism, which is the thesis that there are no distinctions. In this paper I shall explain why I do not believe in Strict Monism. I shall first explain Strict Monism in detail, and then I shall explain why it is false. If a thesis is false, whatever arguments have been provided for it must fail in one way or another, and so I shall also explain why and how the arguments provided for Strict Monism fail. Finally, I shall comment on the significance of my conclusions and I shall point out, among other things, that we do not have any reason, at least at the moment, to think that any version of the Principle of Sufficient Reason entails Strict Monism.

The Identity of Indiscernibles is the thesis that there cannot be numerical difference without extra-numerical difference, that is, there cannot be two objects that differ only numerically, solo numero. It is an important issue in metaphysical discussions of identity, haecceitism/non-haecceitism, and theories of properties (since extra-numerical identity is often explained in terms of properties). Although it is most often referred to as a principle, its axiomatic character is not currently a topic of discussion, and the fact that it is referred to as such is simply due to Leibniz’s influence.

This chapter is a discussion of Class and Resemblance Nominalism. According to the traditional versions of these theories, properties are classes of particulars. Thus, the property of being red is the class of red particulars, and the property of being square is the class of square particulars. Several objections have been advanced against these theories, and one of the most powerful of such objections is the so-called Coextension Difficulty, according to which Class and Resemblance Nominalism have to wrongly identify distinct but coextensive properties. After discussing the nature of Class and Resemblance Nominalism, some problems of these theories and how they can be deal with, the superiority of Class and Resemblance Nominalism over other theories of properties and the superiority of Resemblance Nominalism over Class Nominalism, I concentrate on the Coextension Difficulty. With respect to this I argue that Class and Resemblance Nominalism can be developed in such a way that they admit properties without identifying them with classes, and this allows them to avoid the Coextension Difficulty, since such versions of these theories are not forced to wrongly identify distinct but coextensive properties. Thus the Coextension Difficulty is not a lethal problem for Class and Resemblance Nominalism.

The resemblance nominalist says that the truthmaker of 〈Socrates is white〉 ultimately involves only concrete particulars that resemble each other. Furthermore he also says that Socrates and Plato are the truthmakers of 〈Socrates resembles Plato〉, and Socrates and Aristotle those of 〈Socrates resembles Aristotle〉. But this, combined with a principle about the truthmakers of conjunctions, leads to the apparently implausible conclusion that 〈Socrates resembles Plato and Socrates resembles Aristotle〉 and 〈Socrates resembles Plato and Plato resembles Aristotle〉 have the same truthmakers, namely, Socrates, Plato and Aristotle. I shall argue that the resemblance nominalist can say that those conjunctions have the same truthmakers but these truthmakers make them true in different ways. I shall also use this view to account for the truthmakers of propositions like 〈Socrates is white〉, and respond to previous objections by Cian Dorr and Jessica Wilson.

Jamin Asay’s A Theory of Truthmaking is one of the most important books on truthmaking, full of important ideas from beginning to end. One of the most interesting parts of the book is Asay's attack on the explanation-first truthmaking. Explanation-first truthmaking is the explanatory project of explaining why truths are true. This is in contrast with ontology-first truthmaking, the project defended by Asay, and which is the project of answering the fundamental ontological question “What is there?”. Asay thinks explanation-first truthmaking should be abandoned because it is problematic and it offers no benefits over those of ontology-first truthmaking. In this brief paper, I argue that he has not established the problematicity of explanation-first truthmaking, and that explanation-first truthmaking offers benefits over ontology-first truthmaking.

Consider a certain red rose. The proposition that the rose is red is true because the rose is red. One might say as well that the proposition that the rose is red is made true by the rose’s being red. This, it has been thought, does not commit one to a truthmaker of the proposition that the rose is red. For there is no entity that makes the proposition true. What makes it true is how the rose is, and how the rose is is not an entity over and above the rose. It is against this view that I shall argue in this paper. I shall argue that a significant class of true propositions, including inessential predications like the proposition that the rose is red, are made true by entities. "No truthmaking without truthmakers" is my slogan. Although I have my view about what kinds of entities are truthmakers, I shall not argue for or presuppose that view here. All I shall argue for here is that if a proposition is made true by something, it is made true by some thing, but my argument will leave it open what kind of thing that thing is: it could be a fact or state of affairs, a trope, or any other sort of entity.

Universals have traditionally thought to obey the identity of indiscernibles, that is, it has traditionally been thought that there can be no perfectly similar universals. But at least in the conception of universals as immanent, there is nothing that rules out there being indiscernible universals. In this paper, I shall argue that there is useful work indiscernible universals can do, and so there might be reason to postulate indiscernible universals. In particular, I shall argue that postulating indiscernible universals can allow a theory of universals to identify particulars with bundles of universals, and that postulating indiscernible universals can allow a theory of universals to develop an account of the resemblance of quantitative universals that avoids the objections that Armstrong’s account faces. Finally, I shall respond to some objections and I shall undermine the criterion of distinction between particulars and universals that says that the distinction between particulars and universals lies in that while there can be indiscernible particulars, there cannot be indiscernible universals.

Universals have traditionally thought to obey the identity of indiscernibles, that is, it has traditionally been thought that there can be no perfectly similar universals. But at least in the conception of universals as immanent, there is nothing that rules out there being indiscernible universals. In this paper, I shall argue that there is useful work indiscernible universals can do, and so there might be reason to postulate indiscernible universals. In particular, I shall argue that postulating indiscernible universals can allow a theory of universals to identify particulars with bundles of universals, and that postulating indiscernible universals can allow a theory of universals to develop an account of the resemblance of quantitative universals that avoids the objections that Armstrong’s account faces. Finally, I shall respond to some objections and I shall undermine the criterion of distinction between particulars and universals that says that the distinction between particulars and universals lies in that while there can be indiscernible particulars, there cannot be indiscernible universals.

In the 1750s Optimism, the Leibnizian doctrine that the actual world is the best possible world, popularized by Pope in 1733 in his Essay on Man, was a hot topic. In 1759 Kant wrote and published a brief essay defending Optimism, Attempt at some Reflections on Optimism. Kant’s aim in this essay is to establish that there is one and only one best possible world. In particular, he argues against the claim that, for every possible world, there is a possible world better than it and against the claim that there are two or more equally good possible worlds that are better than all the rest. Although it is not clear why, Kant was later dissatisfied with his essay. In this article I shall reconstruct, discuss, and evaluate Kant’s arguments. My evaluation will be negative, and so I think Kant had reasons to be dissatisfied with his essay.

Are the categorical laws of ontology metaphysically contingent? I do not intend to give a full answer to this question in this paper. But I shall give a partial answer to it. In particular, Gideon Rosen, in his article “The Limits of Contingency”, has distinguished a certain conception of metaphysical necessity, which he calls the Non-Standard conception, which, together with the assumption that all natures or essences are Kantian, is supposed to entail that many laws of ontology are metaphysically contingent. Now, the argument Rosen gives supports the conclusion that all categorical laws of ontology are contingent. I shall argue that the Non-Standard conception and the thesis that all natures are Kantian are incompatible with each other and that, if the Non-Standard conception is true, there must be at least one metaphysically necessary categorical law of ontology, and I shall identify such a law. Thus my contribution to the question of the title of the paper will be that not all categorical ontological laws can be contingent if the Non-Standard conception is true.

The Razor says: do not multiply entities without necessity! The Laser says: do not multiply fundamental entities without necessity! Behind the Laser lies a deep insight. This is a distinction between the costs and the commitments of a theory. According to the Razor, every commitment is a cost. Not so according to the Laser. According to the Laser, derivative entities are an ontological free lunch: that is, they are a commitment without a cost. Jonathan Schaffer (2015) has argued that the Laser should replace the Razor. In Sections 2-4 we shall discuss and argue against Schaffer’s arguments for replacing the Razor with the Laser. Schaffer considers several objections to his views, and in Sections 5-7 we shall argue that Schaffer does not deal successfully with two of them. In Section 8 we shall present a probabilistic argument for the Laser. However, the argument has a limitation and does not support the replacement of the Razor with the Laser. Indeed, it supports only the claim that, given certain assumptions, the multiplication of explanatorily relevant derivative entities does not matter; but, as we argue in the same section, there is an argument that multiplying explanatorily superfluous derivative entities does makes a theory less rationally acceptable. Our conclusion is that the Laser cannot replace the Razor and that derivative entities are not an ontological free lunch.

In the 1750s Optimism, the Leibnizian doctrine that the actual world is the best possible world, popularised by Pope in 1733 in his Essay on Man, was a hot topic. In 1759 Kant wrote and published a brief essay defending Optimism, Attempt at some Reflections on Optimism. Kant’s aim in this essay is to establish that there is one and only one best possible world. In particular, he argues against the claim that, for every possible world, there is a possible world better than it and against the claim that there are two or more equally good possible worlds that are better than all the rest. Although it is not clear why, Kant was later dissatisfied with his essay. In this article I shall reconstruct, discuss, and evaluate Kant’s arguments. My evaluation will be negative, and so I think Kant had reasons to be dissatisfied with his essay.

Leibniz’s short letter to the mathematician and physicist Ludovico Casati of 1689 is a short but interesting text on the Principle of Identity of Indiscernibles, to which it is entirely dedicated. Since there is no watermark in the paper of the letter, the letter is difficult to date, but it is likely that it was written during Leibniz’s stay in Rome, sometime between April and November of 1689 (A 2 2 287–8). When addressing the letter, Leibniz wrote ‘Casani’, but this seems to be a mistake and the real addressee is thought to be Ludovico Casati, nephew of Paolo Casati, the Jesuit mathematician. The letter, reproduced in the Berlin’s Academy edition of Leibniz’s works, was first published by Gerhardt in the Archiv für Geschichte der Philosophie in 1892 (Gerhardt 1892: 53–54). It also appears in Robinet’s Iter Italicum (Robinet 1988: 134–35). But neither Gerhardt nor Robinet provide a philosophical discussion of the letter, and I am not aware of any other philosophical discussion of it. Furthermore, as far as I know, the letter has never been translated into any language. Thus I shall here provide a transcription (from A 2 2 288–89) and a translation of the letter into English, and a philosophical discussion of its treatment of the Identity of Indiscernibles.

In this note we shall argue that Milne’s new effort does not refute Truthmaker Maximalism. According to Truthmaker Maximalism, every truth has a truthmaker. Milne has attempted to refute it using the following self-referential sentence M: This sentence has no truthmaker. Essential to his refutation is that M is like the Gödel sentence and unlike the Liar, and one way in which Milne supports this assimilation is through the claim that his proof is essentially object-level and not semantic. In Section 2, we shall argue that Milne is still begging the question against Truthmaker Maximalism. In Section 3, we shall argue that even assimilating M to the Liar does not force the truthmaker maximalist to maintain the ‘dull option’ that M does not express a proposition. There are other options open and, though they imply revising the logic in Milne’s reasoning, this is not one of the possible revisions he considers. In Section 4, we shall suggest that Milne’s proof requires an implicit appeal to semantic principles and notions. In Section 5, we shall point out that there are two important dissimilarities between M and the Gödel sentence. Section 6 is a brief summary and conclusion

1. The Bundle Theory I shall discuss is a theory about the nature of substances or concrete particulars, like apples, chairs, atoms, stars and people. The point of the Bundle Theory is to avoid undesirable entities like substrata that allegedly constitute particulars. The version of the Bundle Theory I shall discuss takes particulars to be entirely constituted by the universals they instantiate.' Thus particulars are said to be just bundles of universals. Together with the claim that it is necessary that particulars have constituents, the fundamental claim of the Bundle Theory is: (BT) Necessarily, for every particular x and every entity y, y constitutes x if and only ify is a universal and x instantiates y. 2 The standard and supposedly devastating objection to the Bundle Theory is that it entails or is committed to a false version of the Principle of Identity of Indiscernibles (Armstrong 1978: 91, Loux 1998: 107), namely: (Pll) Necessarily, for all particulars x and y and every universal z, if z is instantiated by x if and only if z is instantiated byy, then x is numerically identical with y. The most famous counterexample to the Identity of Indiscernibles is that put forward by Max Black, consisting of a world where there are only two iron spheres two miles apart from each other, having the same diameter, temperature, colour, shape, size, etc (Black 1952: 156). Let us from now on think of the properties of the spheres in this world as universals. The possibility of this world, which I shall hereafter refer to as 'Black's world', makes (Pll) false.' And according to common philosophical opinion this means that the Bundle Theory is false..