I critically examine the claim that modal collapse arguments against the traditional doctrine of divine simplicity (DDS) are in general fallacious. In a recent paper, Christopher Tomaszewski alleges that modal collapse arguments against DDS are invalid, owing to illicit substitutions of nonrigid singular terms into intensional contexts. I show that this is not, in general, the case. I show, further, that where existing modal collapse arguments are vulnerable to this charge the arguments can be (...) repaired without any apparent dialectical impropriety. I conclude that the genuine debate over modal collapse and divine simplicity and modal collapse is substantially a controversy over the metaphysics of divine action, and that this constitutes a fruitful direction in which to take future discussions of the subject. (shrink)

The modal collapse objection to classical theism has received significant attention among philosophers as of late. My aim in this paper is to advance this blossoming debate. First, I briefly survey the modal collapse literature and argue that classical theists avoid modal collapse if and only if they embrace an indeterministic link between God and his effects. Second, I argue that this indeterminism poses two challenges to classical theism. The first challenge is that it (...) collapses God’s status as an intentional agent who knows and intends what he is bringing about in advance. The second challenge is that it collapses God’s providential control over which creation obtains. (shrink)

After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of (...) the lapse of time. As a result, modal collapse should not be conceived in Gödel so much as a deficit, but rather as a kind of the rise of modalities to the “perfect” being. We further show that, in accordance with Gödel’s ontology, the concepts of modality and time should be derived in terms of the “fundamental philosophical concept” of cause. To give an example of how a formalization of such causative Gödelian ontology and ontological proof might look, we propose the transformation of GO into a kind of causally re-interpreted justification logic. (shrink)

On one classical conception of God, God has no parts, not even metaphysical parts. God is not composed of form and matter, act and potency, and he is not composed of existence and essence. God is absolutely simple. This is the doctrine of Absolute Divine Simplicity. It is claimed that ADS implies a modal collapse, i.e. that God’s creation is absolutely necessary. I argue that a proper way of understanding the modal collapse argument naturally leads the (...) proponent of ADS to reject a particular premise of the argument: namely, “the same identical cause brings about the same effect.” However, I argue that the rejection of that premise leads to a deeper problem for ADS. It leads to an explanatory gap: how can we explain the relevant type of indeterminism in an absolutely simple God? (shrink)

Modal collapse arguments are all the rage in certain philosophical circles as of late. The arguments purport to show that classical theism entails the absurdly fatalistic conclusion that everything exists necessarily. My first aim in this paper is bold: to put an end to action-based modal collapse arguments against classical theism. To accomplish this, I first articulate the ‘Simple Modal Collapse Argument’ and then characterize and defend Tomaszewski’s criticism thereof. Second, I critically examine Mullins’ (...) new modal collapse argument formulated in response to the aforementioned criticism. I argue that Mullins’ new argument does not succeed. Third, I critically examine a powers-based modal collapse argument against classical theism that has received much less attention in the literature. Fourth, I show why God’s being purely actual, as well God’s being identical to each of God’s acts, simply cannot entail modal collapse given indeterministic causation. This, I take it, signals the death of modal collapse arguments. But not all hope is lost for proponents of modal collapse arguments—for the death is a fruitful one insofar as it paves the way for new inquiry into at least two new potential problems for classical theism. Showing this is my paper’s second aim. (shrink)

One of the most pressing objections against Divine simplicity is that it entails what is commonly termed a ‘modal collapse’, wherein all contingency is eliminated and every true proposition is rendered necessarily true. In this paper, I show that a common form of this argument is in fact famously invalid and examine three ways in which the opponent of Divine simplicity might try to repair the argument. I conclude that there is no clear way of repairing the argument (...) that does not beg the question against the doctrine of Divine simplicity. (shrink)

In recent years the doctrine of divine simplicity has become a topic of interest in the philosophical theological community. In particular, the modal collapse argument against divine simplicity has garnered various responses from proponents of divine simplicity. Some even claiming that the modal collapse argument is invalid. It is our contention that these responses have either misunderstood or misstated the argument, and have thus missed the force of the objection. Our main aim is to clarify what (...) the modal collapse argument in fact says, and explain why the recent responses do not succeed. In order to argue our case, we will proceed in several steps. First, we aim to systematically articulate the doctrine of divine simplicity. Second, articulate the Christian conviction that God is free to create any feasible world or no world at all. Third, argue that divine simplicity suffers a modal collapse and thus undermines God's freedom. Fourth, respond to potential objections to modal collapse. Fifth, we offer some concluding remarks. (shrink)

God is traditionally taken to be a necessarily existing being who is unsurpassably powerful, knowledgeable, and good. The familiar problem of actual evil claims that the presence of gratuitous suffering in the actual world constitutes evidence against the existence of such a being. In contrast, the problem of possible evil claims that the possibility of bad worlds constitutes evidence against theism. How? It seems plausible to suppose that there are very bad possible worlds. But if God exists in every world, (...) then God exists in those, too. And if God exists in very bad worlds, some say, God is culpable for not ensuring that they are better. In what follows, I consider this argument, survey some responses, and offer a novel solution. Along the way, I argue that theists should maintain that the actual world is a multiverse featuring all and only universes worthy of being created and sustained by God, and – more controversially – I suggest that theists should embrace modal collapse: the claim that this multiverse is the only possible world. (shrink)

Either a ‘best world’ scenario is true or a ‘no best world’ scenario is true. In a ‘best world’ scenario, God actualizes a world that is unsurpassable. In a ‘no best world’ scenario, for any possible world God actualizes, God could have actualized a better world. A ‘no best world’ scenario precludes theism, so the theist should endorse a ‘best world’ scenario. However, a ‘best world’ scenario leads to the highly counter-intuitive conclusion of modal collapse: the position that (...) nothing could have turned out differently than it did. A tentative solution to modal collapse is if the ‘best world’ scenario turns out to be the theistic multiverse containing many universes. (shrink)

Theistic modal realism argues for an extension of Lewis's modal realism capable of accommodating a theistic God. By affording elegant solutions to many atheistic challenges, the view is of great theoretical utility for the theist. However, it has been objected that within a Lewisian framework God cannot be causally efficacious on pain of collapsing intuitively distinct modal notions. In this article I explain why these worries are ill-founded and show how God's existence and causal power over the (...) pluriverse can be consistently understood. If successful, the proposal offers a congenial theistic way to adopt modal realism and address the atheological problems. (shrink)

Three variants of Kurt Gödel's ontological argument, proposed by Dana Scott, C. Anthony Anderson and Melvin Fitting, are encoded and rigorously assessed on the computer. In contrast to Scott's version of Gödel's argument the two variants contributed by Anderson and Fitting avoid modal collapse. Although they appear quite different on a cursory reading they are in fact closely related. This has been revealed in the computer-supported formal analysis presented in this article. Key to our formal analysis is the (...) utilization of suitably adapted notions of ultrafilters, and a careful distinction between extensions and intensions of positive properties. (shrink)

On Jaakko Hintikka’s understanding of Aristotle’s modal thought, Aristotle is committed to a version of the Principle of Plenitude, which is the thesis that no genuine possibility will go unactualized in an infinity of time. If in fact Aristotle endorses the Principle of Plenitude, everything becomes necessary. Despite the strong evidence that Aristotle indeed accepts that Principle of Plenitude, there are key texts in which Aristotle seems to contradict it. On Hintikka’s final word on the matter, Aristotle either endorses (...) the Principle of Plenitude or Aristotle is simply inconsistent. Without challenging Hintikka’s interpretation of the relevant texts, I show how Aristotle may accept a form of the Principle of Plenitude that allows for genuine unactualized possibilities in the world. What allows me to reconcile the seemingly inconsistent data is to show how Aristotle is only committed to a de re version of the Principle of Plenitude. After I lay out my proposal, I show how it opens up new ways in which we might understand Aristotle’s attempt to reject fatalism in his De interpretatione 9. (shrink)

Føllesdal (1966 and 1969) claims that modal distinctions collapse, that is that p and Necessarily p are equivalent, in any system of modal logic that incorporates a standard theory of definite descriptions, like the one proposed by Carnap in M&N. I argue that his argument fails.

Sections 1 and 2 respectively raise and settle the question of whether, if an affirmative modality collapses (reduces to the null modality, that is) in a normal modal logic, then all modalities of the same length collapse in that logic, while Section 3 considers some special cases of an analogous phenomenon for congruential modal logics, closing with a general question about collapsing modalities in this broader range of logics.

Marton ( 2019 ) argues that that it follows from the standard antirealist theory of truth, which states that truth and possible knowledge are equivalent, that knowing possibilities is equivalent to the possibility of knowing, whereas these notions should be distinct. Moreover, he argues that the usual strategies of dealing with the Church–Fitch paradox of knowability are either not able to deal with his modal-epistemic collapse result or they only do so at a high price. Against this, I (...) argue that Marton’s paper does not present any seriously novel challenge to anti-realism not already found in the Church–Fitch result. Furthermore, Edgington ( 1985 ) reformulated antirealist theory of truth can deal with his modal-epistemic collapse argument at no cost. (shrink)

The conjunction of Schrodinger dynamics and the usual way of thinking about the conditions under which quantum systems exhibit determinate values implies that measurements don't have outcomes. The orthodox fix to this quantum measurement problem is von Neumann's postulate of measurement collapse, which suspends Schrodinger dynamics in measurement contexts. Contending that the fundamental dynamical law of quantum theory breaks down every time we test the theory empirically, the collapse postulate is unsatisfactory. Recently philosophers and physicists have proposed a (...) less violent solution to the measurement problem. Their modal interpretations of quantum mechanics advocate unusual ways of thinking about the situations under which quantum systems exhibit determinate observable values, semantics which reconcile determinate measurement outcomes with universal Schrodinger dynamics. Thus modal interpretations hold out hope that quantum theory is complete and exceptionless. ;This dissertation tempers that hope. I consider the modal approach to the neglected problem of state preparation. A promising modal account exploits standard quantum transition probabilities. But, I claim, modal interpretations must subject these transition probabilities to a consistency constraint which they can be shown to violate. Non-standard transition probabilities might avoid this inconsistency, but they would also introduce novel dynamics, and so undo the modal triumph of taking Schrodinger dynamics to be complete and universal. Next I consider Albert and Loewer's assault on modal accounts of "error-prone" measurements. I argue that the Albert-Loewer problem is more general than Albert, Loewer, or their critics appreciate, and that the Araki-Yanase theorem implies the existence of a class of observables whose error-free measurements succumb to the Albert-Loewer problem. I review modal responses to Albert and Loewer which appeal to the palliative effects of a decohering environment and find them incomplete. Finally, based on the physicist Anthony Leggett's work with SQUIDs, I present a system concerning which the empirical commitments of modal interpretations contradict those of the quantum statistical algorithm, minimally interpreted. I conclude that these modal difficulties can be resolved only by taking the quantum formalism to be incomplete. (shrink)

This paper examines and discusses an argument for the collapse of modal distincions offered by Quine in "Reference and Modality" and in Word and Object that relies exclusively on a version of the Principle of Substitution. It is argued that the argument does not affect its historical targets: Carnap's treatment of modality, presented in Meaning and Necessity, and Church's Logic of Sense and Denotation, developed by Kaplan; nor does it affect a treatment of modality inspired in Frege's treatment (...) of oblique contexts. It is argued, nevertheless, that the immunity of those systems to Quine's argument depends on the success of their rejection of the Principle of Substitution presupposed by Quine. (shrink)

This paper analyzes Mally’s system of deontic logic, introduced in his The Basic Laws of Ought: Elements of the Logic of Willing (1926). We discuss Mally’s text against the background of some contributions in the literature which show that Mally’s axiomatic system for deontic logic is flawed, in so far as it derives, for an arbitrary A, the theorem “A ought to be the case if and only if A is the case”, which represents a collapse of obligation. We (...) then try to sort out and understand which axioms are responsible for the collapse and consider two ways of amending Mally’s system: (i) by changing its original underlying logical basis, that is classical logic, and (ii) by modifying Mally’s axioms. (shrink)

In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the simple observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-theoretic pluralist’ claims that (...) the search for the true axioms of set theory is. We show that the obvious responses to this argument fail. However, a new response has emerged that purports to prove, from higher-order logical principles, that metaphysical possibility is the broadest kind of possibility applying to propositions, and is to that extent special. We distill two lines of reasoning from the literature, and argue that their import depends on premises that any ‘modal pluralist’ should deny. Both presuppose that there is a unique typed hierarchy, which is what the modal pluralist, in the context of higher-order logic, should disavow. In other words, both presupposes that there is a unique candidate for what higher-order claims could mean. We consider the worry that, in a higher-order setting, modal pluralism faces an insuperable problem of articulation, collapses into modal monism, is vulnerable to the Russell-Myhill paradox, or even contravenes the truism that there is a unique actual world, and argue that these worries are misplaced. We also sketch the bearing of the resulting ‘Higher-Order Pluralism’ on the theory of content. One theme of the discussion is that, if Higher-Order Pluralism is correct, then there is no fixed metatheory from which to characterize higher-order reality. (shrink)

Data involving epistemic modals suggest that some classically valid argument forms, such as _reductio_, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a _de re–de dicto_ collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms that (...) govern the use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic. (shrink)

Structural realism has been suggested as the best compromise in the debate on scientific realism. It proposes that we should be realist about the relational structure of the world, not its nature. However, it faces an important objection, first raised by Newman against Russell: if relations are not qualified, then the position is either trivial or collapses into empiricism, but if relations are too strongly qualified, then it is no longer SR. A way to overcome this difficulty is to talk (...) about modal, or nomological relations instead of purely extensional relations. I argue that this is insufficient, for then, SR collapses into modal empiricism. I suggest, however, that ME could be the best position in the debate on scientific realism. 1Introduction2Objections to Structural Realism3How to Escape Newman’s Objection4Which Modal Relations Are Retained in Theory Change?5Are Modal Relations Real?6Relativity and Fundamentality7Is Modal Empiricism Really Empiricism?8Could Modal Empiricism Be the Best of Both Worlds? (shrink)

The subject of the first section is Carnapian modal logic. One of the things I will do there is to prove that certain description principles, viz. the ''self-predication principles'', i.e. the principles according to which a descriptive term satisfies its own descriptive condition, are theorems and that others are not. The second section will be devoted to Carnapian modal arithmetic. I will prove that, if the arithmetical theory contains the standard weak principle of induction, modal truth collapses (...) to truth. Then I will propose a different formulation of Carnapian modal arithmetic and establish that it is free of collapse. Noteworthy is that one can retain the standard strong principle of induction. I will occupy myself in the third section with Carnapian epistemic logic and arithmetic. Here too it is claimed that the standard weak principle of induction is invalid and that the alternative principle is valid. In the fourth and last section I will get back to the self-predication principles and I will point to some of the consequences if one adds them to Carnapian Epistemic arithmetic. The interaction of self-predication principles and the strong principle of induction results in a collapse of de re knowability. (shrink)

Modal interpretations are hidden-variable, no-collapse interpretations of quantum mechanics that were designed to solve the measurement problem and reconcile this theory with relativity. Yet, as no-go theorems by Dickson and Clifton, Arntzenius and Myrvold demonstrate, current modal interpretations are incompatible with relativity. In the mainstream modal interpretations, properties of composite systems are generally unrelated to the properties of their subsystems. We propose holistic and relational interpretations of properties to explain this failure of property composition. Based on (...) these interpretations, we consider strategies for circumventing Myrvold's theorem, which are also effective against the other two theorems. (shrink)

Reinhardt’s conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond the first epsilon number. We prove a weaker version of the conjecture, by elementary methods and transfinite induction up to a smaller ordinal.

We show that the modal µ-calculus over GL collapses to the modal fragment by showing that the fixpoint formula is reached after two iterations and answer to a question posed by van Benthem in [4]. Further, we introduce the modal µ~-calculus by allowing fixpoint constructors for any formula where the fixpoint variable appears guarded but not necessarily positive and show that this calculus over GL collapses to the modal fragment, too. The latter result allows us a (...) new proof of the de Jongh, Sambin Theorem and provides a simple algorithm to construct the fixpoint formula. (shrink)

We shall try to defend two non-standard views that run counter to two well-entrenched familiar views. The standard views are the universal and existential quantifiers of first-order logic are not modal operators, and the quantifiers are extensional. If that is correct then the counterclaims create genuine problems for some traditional philosophical doctrines.

We show that the modal µ-calculus over GL collapses to the modal fragment by showing that the fixpoint formula is reached after two iterations and answer to a question posed by van Benthem in [4]. Further, we introduce the modal µ~-calculus by allowing fixpoint constructors for any formula where the fixpoint variable appears guarded but not necessarily positive and show that this calculus over GL collapses to the modal fragment, too. The latter result allows us a (...) new proof of the de Jongh, Sambin Theorem and provides a simple algorithm to construct the fixpoint formula. (shrink)

We study the strictness of the modal μ-calculus hierarchy over some restricted classes of transition systems. First, we prove that over transitive systems the hierarchy collapses to the alternationfree fragment. In order to do this the finite model theorem for transitive transition systems is proved. Further, we verify that if symmetry is added to transitivity the hierarchy collapses to the purely modal fragment. Finally, we show that the hierarchy is strict over reflexive frames. By proving the finite model (...) theorem for reflexive systems the same results holds for finite models. (shrink)

Rumfitt has given two arguments that in unilateralist verificationist theories of meaning, truth collapses into correct assertibility. In the present paper I give similar arguments that show that in unilateral falsificationist theories of meaning, falsehood collapses into correct deniability. According to bilateralism, meanings are determined by assertion and denial conditions, so the question arises whether it succumbs to similar arguments. I show that this is not the case. The final section considers the question whether a principle central to Rumfitt's first (...) argument, ‘It is assertible that if and only if it is assertible that it is assertible that ’, is one that bilateralists can reject, and concludes that they cannot. It follows that the logic of assertibility and deniability, according to a result by Williamson, is the little known modal logic K4 studied by Sobociński. The paper ends with a plaidoyer for bilateralists to adopt this logic. (shrink)

Two EPR arguments are reviewed, for their own sake, and for the purpose of clarifying the status of "stochastic" hidden variables. The first is a streamlined version of the EPR argument for the incompleteness of quantum mechanics. The role of an anti-instrumentalist ("realist") interpretation of certain probability statements is emphasized. The second traces out one horn of a central foundational dilemma, the collapse dilemma; complex modal reasoning, similar to the original EPR, is used to derive determinateness (of all (...) spin components of two spin- 1 / 2 particles in the singlet state) from just (a form of) weak locality, result definiteness, and an assumption on propensities based on conservation. Theories meeting these conditions are therefore constrained by the Bell inequalities. Neither controversial assumptions of "strong locality" ("factorability") nor of determinism are employed in the derivation. The categories of "stochastic hidden variables" are then analyzed; one can focus on "quasi-definite" theories, without loss of generality. A means of excluding these is proposed, based on a demand that certain ideal cases be accurately treated. Theorems from quantum measurement theory, sometimes cited as showing that such cases are not physically possible, are found inapplicable. (shrink)

In the first chapter I have introduced Carnapian intensional logic against the background of Frege's and Quine's puzzles. The main body of the dissertation consists of two parts. In the first part I discussed Carnapian modal logic and arithmetic with descriptions. In the second chapter, I have described three Carnapian theories, CCL, CFL, and CNL. All three theories have three things in common. First, they are formulated in languages containing description terms. Second, they contain a system of modal (...) logic. Third, they do not contain the unrestricted classical substitution principle, but they do contain the classical substitution principle restricted to non-modal formulas and the Carnapian substitution principle, which says that two terms can be substituted salva veritate if they are necessarily coreferential. There are two major differences between the three theories. First, CCL and CFL allow universal instantiation with description terms, whereas CNL does not. Moreover, the quantificational theory of the CCL is classical, whereas the quantificational theory of CFL is a free logic. Another difference is that CCL and CFL contain different description principles. Most importantly, the description principle of CCL ensures that even improper descriptions have a denotation, whereas the description principle of CFL does not guarantee this. CNL does not have a description principle. In the third chapter, I have studied collapse arguments for CCL, CFL, and CNL. A collapse argument is an argument for the following statement: if p is true, then it is necessarily true. A crucial role in the proofs of these collapse results was played by so-called self-predication principles, which say that under certain conditions the predicate that expresses the descriptive condition can be combined by the description term formed out of that predicate with the result being a true sentence. In this chapter I have discussed a collapse argument for the extension of CCL with a self-predication principle, I have given a collapse argument for a similarly extended CFL, and most importantly, I have given a collapse argument for the extension of CNL with a self- predication principle. Finally, I have argued that the relevant self-predication principles are unsound under a Carnapian interpretation. In the fourth chapter, I have studied the extension of Peano Arithmetic with a Carnapian modal logic C, which is a dummy letter standing for either CCL or CFL. One can prove that the principle of the necessity of identity is a theorem of CPA. This implies that one gets a collapse result for CPA. The standard principle of weak induction was crucial for the proof. One can also prove that, if one assumes a particular self-predication principle, and if one assumes the principle of strong induction or, equivalently, the least-number principle, then one gets a partial collapse of de re modal truths in de dicto modal truths. I have argued that, if the box operator is interpreted as a metaphysical necessity operator, then Platonists would not be inimical to the collapse result. But if CPA is extended with a physical theory, then there is a threat that physical truths become physical necessiti es. It was shown that, under a Carnapian interpretation, the standard principle of weak induction is unsound, and that it can be replaced by a Carnapian principle of weak induction that is sound. The problem of logical and mathematical omniscience prevents ordinary Carnapian intensional logic from being taken seriously as a logic adequate for describing the principles of demonstrability. Yet many of the proof-theoretic results of the first part carry over to the part on Carnapian epistemic arithmetic with descriptions, since proof-theoretic results are independent of the informal reading of the operators. In the fifth chapter, I looked at extensions of arithmetic with a modal logic in which the box operator is interpreted as a demonstrability operator. A first extension in that sense is Shapiro s Epistemic Arithmetic. Shapiro himself offered the problem of mathematical omniscience as a reason why it is difficult to find a model theory for EA. Horsten attempted to provide a model theory via the detour of Modal-Epistemic Arithmetic. The attention of the reader was drawn to an incoherence in the model theory of. Two alternative solutions were presented and, after a short discussion of the problem of de re demonstrability one of those alternatives was chosen. The discussion of the problem of de re demonstrability made it clear that it would be interesting to study the epistemic properties of notation systems. Horsten himself provided a framework for this, viz. Carnapian Epistemic Arithmetic, and he started a systematic study of the epistemic properties of notation systems within that framework. However, he did not provide non-trivial but adequate models. To make a start with solving the problem of finding good models for CEA, I introduced Carnapian Modal-Epistemic Arithmetic In constructing CMEA I incorporated the lesson about the principle of weak induction learnt in the fourth chapter. In the sixth chapter, I gave a critical assessment of an argument concerning the limits of de re demonstrability about the natural numbers. The conclusion of the Description Argument is that it is undemonstrable that there is a natural number that has a certain property but of which it is undemonstrable that it has that property. A crucial step in the Description Argument involved a self-predication principle. Making good use of one of the results obtained in the third chapter, I proved a collapse result for the background theory against which the Description Argument was formulated. I concluded that either the either the Description Argument is sound but its conclusion is trivial, o r the Description Argument is unsound, or it is a cheapshot. As an appendix I included an article co-authored by prof. dr. Leon Horsten and me. The topic of the article is indirectly related to some other topics investigated in my dissertation. Also, it backs up one of the addition al theses I might be asked to publicly defend during my doctoral exam. T he topic of the appendix is the set of the so-called paradoxes of strict implication. Jonathan Lowe has argued that a particular variation on C.I. Lewis notion of strict implication avoids the paradoxes of strict implication. Pace Lowe, it is argued that Lowe s notion of implication does not achieve this aim. Moreover, a general argument is offered to the effect that no other variation on Lewis notion of constantly strict implication describes the logical behaviour of natural language conditional s in a satisfactory way. (shrink)

Two of the main interpretative problems in quantum mechanics are the so-called measurement problem and the question of the compatibility of quantum mechanics with relativity theory. Modal interpretations of quantum mechanics were designed to solve both of these problems. They are no-collapse (typically) indeterministic interpretations of quantum mechanics that supplement the orthodox state description of physical systems by a set of possessed properties that is supposed to be rich enough to account for the classical-like behavior of macroscopic systems, (...) but sufficiently restricted so as to avoid the no-hidden-variables theorems. But, as recent no-go theorems suggest, current modal interpretations are incompatible with relativity. In this paper, we suggest a strategy for circumventing these theorems. We then show how this strategy could naturally be integrated in a relational version of the modal interpretation, where quantum-mechanical states assign relational rather than intrinsic properties. (shrink)

Buchholz’s Ω μ+1-rules provide a major tool for the proof-theoretic analysis of arithmetical inductive definitions. The aim of this paper is to put this approach into the new context of modal fixed point logic. We introduce a deductive system based on an Ω-rule tailored for modal fixed point logic and develop the basic techniques for establishing soundness and completeness of the corresponding system. In the concluding section we prove a cut elimination and collapsing result similar to that of (...) Buchholz (Iterated inductive definitions and subsystems of analysis: recent proof theoretic studies. Lecture notes in mathematics, vol. 897, pp. 189–233, Springer, Berlin, 1981). (shrink)

In the fifth of his John Locke Lectures, Robert Brandom takes up the challenge to define a formal semantics for modelling conceptual contents according to his normative analysis of linguistic practices. The project is to exploit the notion of incompatibility in order to directly define a modally robust relation of entailment. Unfortunately, it can be proved that, in the original definition, the modal system represented by Incompatibility Semantics (IS) collapses into propositional calculus. In this paper I show how IS (...) can be technically amended so to overcome this failure: the required modifications are already known and consist in adapting and including the main notions of Kripke's standard framework of possible worlds. I also show that the modifications do not jeopardize Brandom's original project. (shrink)

Classical theism is often said to suffer from the problem of modal collapse: if God is necessary and simple then all of his effects (creatures) are also necessary. Many classical theists have turned to extrinsic predication in response: God’s simple and necessary act is compatible with any number of possible effects or no effects, and is only said to be an act of creating in virtue of the existence of the universe itself. Leftow and Schmid criticize this solution (...) for leading to “providential collapse”: God would not have control over which creation obtains if all his intrinsic features are compatible with any possible universe. Thomistic classical theism avoids both modal collapse and providential collapse by utilizing the metaphysics of relations. With no differences within his simple essence/act, God can relate himself differently to his possible effects, willing some and not willing others. These relations determine whether or not the effects will exist. Thomistic classical theism’s version of divine simplicity is not incompatible with God having a multiplicity of relations, for the three divine persons are distinct relations within God. Divine simplicity is only incompatible with a multiplicity of absolute items within God. Furthermore, not all differences of relation are grounded in the different absolute characteristics of their relata. Rather, sometimes differences of relation themselves ground differences in the absolute characteristics of their relata. God’s divine act is thus said to be an act of willing this creation rather than that in virtue of his chosen, contingent relation to possible creatures, rather than in virtue of the creatures themselves. (shrink)

There are logics where necessity is defined by means of a given identity connective: \ is a tautology). On the other hand, in many standard modal logics the concept of propositional identity \ can be defined by strict equivalence \}\). All these approaches to modality involve a principle that we call the Collapse Axiom : “There is only one necessary proposition.” In this paper, we consider a notion of PI which relies on the identity axioms of Suszko’s non-Fregean (...) logic SCI. Then S3 proves to be the smallest Lewis modal system where PI can be defined as SE. We extend S3 to a non-Fregean logic with propositional quantifiers such that necessity and PI are integrated as non-interdefinable concepts. CA is not valid and PI refines SE. Models are expansions of SCI-models. We show that SCI-models are Boolean prealgebras, and vice-versa. This associates non-Fregean logic with research on Hyperintensional Semantics. PI equals SE iff models are Boolean algebras and CA holds. A representation result establishes a connection to Fine’s approach to propositional quantifiers and shows that our theories are conservative extensions of S3–S5, respectively. If we exclude the Barcan formula and a related axiom, then the resulting systems are still complete w.r.t. a simpler denotational semantics. (shrink)

In this paper we attempt to physically interpret the Modal Kochen–Specker theorem. In order to do so, we analyze the features of the possible properties of quantum systems arising from the elements in an orthomodular lattice and distinguish the use of “possibility” in the classical and quantum formalisms. Taking into account the modal and many worlds non-collapse interpretation of the projection postulate, we discuss how the MKS theorem rules the constraints to actualization, and thus, the relation between (...) actual and possible realms. (shrink)

On Anselmian theism, God is, amongst other things, a necessary being. On genuine modal realism, possible worlds are maximal mereological sums of spatiotemporally connected individuals. I argue in this paper that AT and GMR are either incompatible or their conjunction leads to—amongst other things—modal collapse. Specifically, I argue: regardless of whether God is concrete or abstract, His necessary existence either is inconsistent with AT-GMR or it leads to, amongst other things, modal collapse for AT-GMR. I (...) conclude the paper by contending that, if I am correct, the ATist will have an argument against the truth of GMR, and the GMRist will have an argument against the truth of AT. (shrink)

An appraisal of the current status of the modalities and of quine's arguments against them. The author accepts "quine's thesis," that one cannot quantify into referentially opaque contexts, And argues that nobody has succeeded in making sense of such quantification. However, It is shown that modal constructions, Being constructions on general terms and sentences, Can be referentially transparent and extensionally opaque and that consequently the collapse of modal distinctions warned against by quine in "word and object" can (...) be avoided. This combination of referential transparency and extensional opacity is just what quine means by essentialism, And the author therefore agrees with quine that quantified modal logic commits one to essentialism. (shrink)

How are we to understand the talk about properties of structures the existence of which is conditional upon the assumption of the reality of those structures? Mathematics is not about abstract objects, yet unlike fictionalism, modal-structuralism respects the truth of theorems and proofs. But it is nominalistic with respect to possibilia. The problem is that, for fear of reducing possibilia to actualities, the second-order modal logic that claims to axiomatise modal existence has no real semantics. There is (...) no cross-identification of higher-order mathematical entities and thus we cannot know what those entities are. I suggest that a scholastic notion of realism, interspersed with cross-identification of higher-order entities, can deliver the semantics without collapse. This semantics of modalities is related to Peirce's logic and his pragmaticist philosophy of mathematics. (shrink)

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes but leaves the theory’s basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory permits assuming that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture (...) of states and Hilbert-space trajectories to the more realistic case of open quantum systems despite the generic development of entanglement. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure—which we call subsystem space—that we believe merits further study. We conclude with a summary, a list of criteria for future work on quantum foundations, and further research directions. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text. (shrink)

We prove a uniqueness theorem showing that, subject to certain natural constraints, all 'no collapse' interpretations of quantum mechanics can be uniquely characterized and reduced to the choice of a particular preferred observable as determine (definite, sharp). We show how certain versions of the modal interpretation, Bohm's 'causal' interpretation, Bohr's complementarity interpretation, and the orthodox (Dirac-von Neumann) interpretation without the projection postulate can be recovered from the theorem. Bohr's complementarity and Einstein's realism appear as two quite different proposals (...) for selecting the preferred determinate observable--either settled pragmatically by what we choose to observe, or fixed once and for all, as the Einsteinian realist would require, in which case the preferred observable is a 'beable' in Bell's sense, as in Bohm's interpretation (where the preferred observable is position in configuration space). (shrink)

Resumen El lamento por el fin de la utopía que expresa la novela futurista, Cría terminal (2014), expone la crisis de un ideal ético: la pérdida de la posibilidad de un mundo mejor. Las bases del contrato moral implícitas en la amenaza de su disolución en un futuro cercano serán el objeto de indagación de este trabajo, que toma a la filosofía de Hans Jonas como principal referencia teórica. Se buscará, por consiguiente, precisar la relación entre la barbarización de la (...) cultura (con sus comportamientos y personajes modélicos) y los procesos económico-políticos tendientes a la dominación biotecnológica del medio humano. La perspectiva modalizadora de la acción y la intriga narrativas y su adecuación a un interés de tipo ético por establecer un modelo de vida óptimo para la sociedad, defraudado por la civilización técnica del futuro, serán motivo de análisis. Abstract The lament for the end of utopia which expresses the futuristic novel, Cría Terminal (2014), exposes the crisis of an ethical ideal: the loss of the possibility of a better world. The bases of the moral contract implicit in the threat of its dissolution in the near future will be the object of investigation of this work, which considers the philosophy of Hans Jonas as the main theoretical reference. Therefore, it will be sought to specify the relationship between the barbarization of culture (with its exemplary behaviors and characters) and the economic-political processes tending to the biotechnological domination of the human environment. The modalizing perspective of the narrative action and intrigue and its adaptation to an ethical interest in establishing an optimal life model for society, disappointed by the technical civilization of the future, will be the subject of analysis. (shrink)

How are we to understand the talk about properties of structures the existence of which is conditional upon the assumption of the reality of those structures? Mathematics is not about abstract objects, yet unlike fictionalism, modal-structuralism respects the truth of theorems and proofs. But it is nominalistic with respect to possibilia. The problem is that, for fear of reducing possibilia to actualities, the second-order modal logic that claims to axiomatise modal existence has no real semantics. There is (...) no cross-identification of higher-order mathematical entities and thus we cannot know what those entities are. I suggest that a scholastic notion of realism, interspersed with cross-identification of higher-order entities, can deliver the semantics without collapse. This semantics of modalities is related to Peirce's logic and his pragmaticist philosophy of mathematics. (shrink)

Proposed derivations of the Born rule for Everettian theory are controversial. I argue that they are unnecessary but may provide justification for a simplified version of the Principal Principle. It’s also unnecessary to replace Everett’s idea that a subject splits in measurement contexts with the idea that subjects have linear histories which partition Many worlds? Everett, quantum theory, and reality, Oxford University Press, Oxford, pp 181–205, 2010; Wallace in The emergent multiverse, Oxford University Press, Oxford, 2012, Chapter 7; Wilson in (...) Br J Philos Sci 64:709–737, 2013; The nature of contingency: quantum physics as modal realism, Oxford University Press, Oxford, forthcoming). Linear histories were introduced to provide a concept of pre-measurement uncertainty and I explain why pre-measurement uncertainty for splitting subjects is after all coherent, though not necessary because Everett’s original fission interpretation of branching can arguably be rendered coherent without it, via reference to Vaidman, Tappenden, Sebens and Carroll and McQueen and Vaidman. A deterministic and probabilistic quantum mechanics can be made intelligible by replacing the standard collapse postulate with a no-collapse postulate which identifies objective probability with relative branch weight, supplemented by the simplified Principal Principle and some revisionary metaphysics. (shrink)

Contextuality is trivially pervasive: all human experience takes place in endlessly changing environments and inexorably moving time frames. In order to have any meaning, the changing items must be placed within a more stable setting, a framework that is not subject to the same kind of contextual change. Total contextuality collapses into chaos, or becomes ineffable. While basic learning is highly contextual (one learns by example), what is learned transcends the examples used in the learning. Perhaps, in a similar manner, (...) artistic expression transcends context by fully embracing it. In any case, a philosophical account of contextuality is itself stated in a more absolute mode, not necessarily a picture from an “eternal” view point, but at least one that avoids the contextuality which it describes. (shrink)

Any realist interpretation of quantum theory must grapple with the measurement problem and the status of state-vector collapse. In a no-collapse approach, measurement is typically modeled as a dynamical process involving decoherence. We describe how the minimal modal interpretation closes a gap in this dynamical description, leading to a complete and consistent resolution to the measurement problem and an effective form of state collapse. Our interpretation also provides insight into the indivisible nature of measurement—the fact that (...) you can't stop a measurement part-way through and uncover the underlying 'ontic' dynamics of the system in question. Having discussed the hidden dynamics of a system's ontic state during measurement, we turn to more general forms of open-system dynamics and explore the extent to which the details of the underlying ontic behavior of a system can be described. We construct a space of ontic trajectories and describe obstructions to defining a probability measure on this space. (shrink)

Modal interpretations of quantum mechanics admit two kinds of state: physical states, which specify the values of observables on a system, and theoretical states, which specify a probability distribution over possible physical states. They appear to use this distinction to deny the projection postulate, claiming that collapse corresponds only to a change from discussing the theoretical state to discussing the physical state. I argue that modal interpretations should adopt a projection postulate at the level of the theoretical (...) state. However, other features of modal interpretations might render the projection postulate immune from the usual objections. (shrink)