The ontological foundation of Russell's theory of modality

Prominent thinkers such as Kripke and Rescher hold that Russell has no modal logic, even that Russell was indisposed toward modal logic. In Part I, I show that Russell had a modal logic which he repeatedly described and that Russell repeatedly endorsed Leibniz's multiplicity of possible worlds. In Part II, I describe Russell's theory as having three ontological levels. In Part III, I describe six Parmenidean theories of being Russell held, including: literal in 1903; universal in 1912; timeless in 1914; transcendental in 1918–1948. The transcendental theory underlies the primary level of Russell's modal logic. In Part IV, I examine Rescher's view that Russell and modal logic did not mix.The United States Naval Academy Research Council kindly provided a summer 1988 research grant for work on this essay. This essay was presented at the Bertrand Russell Society Meeting during the December 1988 Eastern Division Meeting of the American Philosophical Association in Washington, D.C.     

ESSENTIALISM AND RIGIDITY

Michael Della Rocca has recently argued that Kripkean essentialism is subtly self-defeating: to defend it, certain modal intuitions must be reconstrued in terms of similarity, but reconstruing them in this way threatens the principled rejection of similarity comparisons on which Kripke's essentialism depends. Della Rocca holds that Kripke's strategy must assume the necessity of identity, and that the necessity of identity already presupposes essentialism, which renders the defence circular. Against this, I argue that the necessity of identity may be accepted independently; therefore no circularity need arise. I also argue that Della Rocca fails to rebut an objection raised by Stephen Yablo.     

Actuality and the amodal perspective

In this paper, I examine our intuitive understanding of metaphysical contingency, and ask what features a metaphysical picture must possess in order to satisfy our intuitions about modal matters. After spelling out what I think are the central intuitions in this domain, I examine the debate between the two most widely held views on the nature of modality, namely, modal realism and modal actualism. I argue that while each of these views is able to accommodate some of our intuitions, it leaves others unsatisfied. I then present an alternative metaphysical picture, which I argue can accommodate our intuitions in a way that the traditional views cannot. More specifically, I argue that our intuitions about modality call for a pluralist view of the structure of reality—a view on which there is more than one ultimate ‘shape’ to the fundamental facts, each corresponding to a distinct metaphysically privileged perspective on reality.     

The Context of Essence

I address two related questions: first, what is the best theory of how objects have de re modal properties? Second, what is the best defence of essentialism given the variability of our modal intuitions? I critically discuss several theories of how objects have their de re modal properties and address the most threatening antiessentialist objection to essentialism: the variability of our modal intuitions. Drawing on linguistic treatments of vagueness and ambiguity, I show how essentialists can accommodate the variability of modal intuitions while holding that objects have their modal properties independently of contexts.     

Logic and contingent existence

It is argued here that Prior's non-standard modal system Q, and the Parry–Dunn system of analytic implication, though entirely independent and independently motivated systems, together provide a rationale for explicating the concept of validity in a non-standard way; their implications are explored for the theory of natural deduction as well as for modal logic and the concept of entailment. I give an account of formal logic from this non-standard viewpoint, together with an informal presentation of the system that unites the insights of Prior (drawing on Russell) and, Parry (drawing on Kant), and the motivations for both in the concept of the contingent existence – as opposed to the contingent truth or falsehood – of a proposition.     

Bilattices and the theory of truth

Conclusion While Kripke's original paper on the theory of truth used a three-valued logic, we believe a four-valued version is more natural. Its use allows for possible inconsistencies in information about the world, yet contains Kripke's development within it. Moreover, using a four-valued logic makes it possible to work with complete lattices rather than complete semi-lattices, and thus the mathematics is somewhat simplified. But more strikingly, the four-valued version has a wide, natural generalization to the family of interlaced bilattices. Thus, with little more work, the theory is extended to a broad class of settings. Indeed, a result like Theorem 6.2 would not even be possible to state without the interlaced bilattice machinery. We hope the notion of interlaced bilattice will make apparent further such connections.     

Not All Worlds Are Stages

The stage theory is a four-dimensional account of persistence motivatedby the worm theory's inability to account for our intuitions in thecases involving coinciding objects. Like the worm theory, it claimsthat there are objects spread out in time, but unlike the worm theory,it argues that these spacetime worms are not familiar particulars liketables and chairs. Rather, familiar particulars are the instantaneoustemporal slices of worms. In order to explain our intuitions that particulars persist for more than an instant, the stage theory drawson the counterpart theory of modal possibilism, which it is supposedto parallel. In this paper I show how the stage theory presupposes thattime can be divided into instants, which I call the atomistic view oftime. I do this by laying out an alternative theory of the nature oftime, the gunky view, and show that if time is gunky the stage theorycollapses into the worm theory. The deeper problem is that the merepossibility of gunky time would cause the stage theory's parallels topossibilism to break down. I therefore conclude that the stage theoryis committed to the view that time is necessarily atomistic. Finally,in the last section I argue that the fact that the stage theory rulesout a priori the possibility of time being gunky gives us reason toreject it as an account of persistence.     

Reply to Dr. Lambert

Psychologism in logic holds that logic is a branch of psychology. This view has been vigorously defended by John Stuart Mill and by a number of German philosophers of logic, notably Erdmann. Its chief critics have been Husserl and Frege and, to a lesser extent, Russell. Husserl set forth a profound and detailed critique of psychologism in Logical Investigations. This paper examines this critique. First, I explain why the psychologistic theory is attractive. Then I show that Husserl's critique is not convincing, partly because he does not take the theory in its most plausible form and partly because he ignores certain important distinctions (for example, between what a statement is about and what it is true in virtue of). Then I raise two new objections to the psychologistic theory. The purpose of this paper is to suggest that the psychologistic theory remains an important and serious position from which we can learn much about the status of logic.     

The Liar, the Strengthened Liar, and Bivalence

A view often expressed is that to classify the liar sentence as neither true nor false is satisfactory for the simple liar but not for the strengthened liar. I argue that in fact it is equally unsatisfactory for both liars. I go on to discuss whether, nevertheless, Kripke's theory of truth represents an advance on that of Tarski.     

Beltrami's model and the independence of the parallel postulate

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell's Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege's extant logical system, if Frege's system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege's logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therin. therein.     

Counting Stages

This paper defends stage theory against the argument from diachronic counting. It argues that stage theorists can appeal to quantifier domain restriction in order to accommodate intuitions about diachronic counting sentences. Two approaches involving domain restriction are discussed. According to the first, domains of counting are usually restricted to stages at the time of utterance. This approach explains intuitions in many cases, but is theoretically costly and delivers wrong counts if diachronic counting is combined with fission or fusion. On the second approach, domains of counting are usually restricted in an indeterminate way, so as to include at most one member of any maximal class of counterpart-interrelated stages (with respect to a certain utterance). This view can accommodate all the relevant intuitions about counting sentences, and it fits well with a new stage-theoretic view of reference that allows speakers to refer to both present and past stages.     

On the philosophy of psi

In Naming and Necessity, Kripke argues that intuitions about what is possible play a limited, but important, role in challenging philosophical theses, counting as evidence against them only if they cannot be reconstrued as intuitions about something else, compatible with the thesis in question. But he doesn't provide clear guidelines for determining when such intuitions have been successfully reconstrued, leading some to question their status as evidence for modal claims. In this paper I focus on some worries, articulated by Michael Della Rocca, about whether modal intuitions can be evidence for claims about essential properties, and argue that there is a way of viewing the role of modal intuition in philosophical argument that can preserve their evidential force.     

Semantic intuitions,conceptual analysis,and cross-cultural variation

While philosophers of language have traditionally relied upon their intuitions about cases when developing theories of reference, this methodology has recently been attacked on the grounds that intuitions about reference, far from being universal, show significant cultural variation, thus undermining their relevance for semantic theory. I’ll attempt to demonstrate that (1) such criticisms do not, in fact, undermine the traditional philosophical methodology, and (2) our underlying intuitions about the nature of reference may be more universal than these critics suppose.     

Ethical Naturalism and Moral Twin Earth

In order to rebut G. E. Moore’s open question argument, ethical naturalists adopt a theory of direct reference for our moral terms. T. Horgan and M. Timmons have argued that this theory cannot be applied to moral terms, on the ground that it clashes with competent speakers’ linguistic intuitions. While Putnam’s Twin Earth thought experiment shows that our linguistic intuitions confirm the theory of direct reference, as applied to ‘water’, Horgan and Timmons devise a parallel thought experiment about moral terms, in order to show that this theory runs against our linguistic intuitions about such terms. My claim is that the Horgan–Timmons argument does not work. I concede that their thought experiment is a good way to test the applicability of the theory of direct reference to moral terms, and argue that the upshot of their experiment is not what they claim it is: our linguistic intuitions about Moral Twin Earth are parallel to, not different from, our intuitions about Twin Earth.

How to Lewis a Kripke–Hintikka

It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issues in possible-world semantics.     

Pessimism About Motivating Modal Personism

In ‘What's Wrong with Speciesism?’, Shelly Kagan sketches an account on which both actually being a person and possibly being a person are relevant to one's moral status, labelling this view ‘modal personism’ and supporting its conclusions with appeals to intuitions about a range of marginal cases. I tender a pessimistic response to Kagan's concern about motivating modal personism: that is, of being able to ‘go beyond the mere appeal to brute intuition, eventually offering an account of why modal personhood should matter in the ways we may intuitively think that it does.’