Fara and Williamson (Mind, 2005) argue that counterpart theory is unable to account for modal claims that use an actuality operator. This paper argues otherwise. Rather than provide a different counterpart translation of the actuality operator itself, the solution presented here starts out with a quantified modal logic in which the actuality operator is redundant, and then translates the sentences of this logic into claims of counterpart theory.

In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing "actually" operators, Journal of Philosophical Logic 30(1): 57-78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an "actually" operator with the work of Arthur Prior now known (...) under the name of hybrid logic. This analysis relates the "actually" axioms to standard hybrid axioms, yields the decidability results in [8], and provides a number of complexity results. Finally, we use a bisimulation argument to show that the hybrid language is strictly more expressive than Gregory's language. (shrink)

I argue that ‘actually’ does not have a reading according to which it is synonymous with the actuality operator of modal logic, and propose an alternative account of ‘actually’. The cases that have been thought to show that ‘actually’ is synonymous with the actuality operator are modal and counterfactual sentences in which an embedded clause's evaluation is held fixed at the world of the context. In these cases, though, this embedded clause's evaluation is not due to (...) the presence of ‘actually’. As an alternative, I propose that ‘actually’ is a presupposition trigger along the lines of ‘even’ or ‘too’, and it signals that presupposed information states in the discourse are evolving in a non-standard way. (shrink)

In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing “actually” operators, Journal of Philosophical Logic 30(1): 57–78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an “actually” operator with the work of Arthur Prior now known (...) under the name of hybrid logic. This analysis relates the “actually” axioms to standard hybrid axioms, yields the decidability results in [8], and provides a number of complexity results. Finally, we use a bisimulation argument to show that the hybrid language is strictly more expressive than Gregory's language. (shrink)

The addition of "actually" operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing "actually" operators has concentrated entirely upon extensions of KT5 and has employed a particular modeltheoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing "actually" operators, the weakest of which are conservative extensions of K, (...) using a novel generalisation of the standard semantics. (shrink)

In this paper the language of first-order modal logic is enriched with an operator @ ('actually') such that, in any model, the evaluation of a formula @A at a possible world depends on the evaluation of A at the actual world. The models have world-variable domains. All the logics that are discussed extend the classical predicate calculus, with or without identity, and conform to the philosophical principle known as serious actualism. The basic logic relies on the system K, whereas (...) others correspond to various properties that the actual world may have. All the logics are axiomatized. (shrink)

In this paper, I claim that two ways of defining validity for modal languages (“real-world” and “general” validity), corresponding to distinction between a correct and an incorrect way of defining modal valid- ity, correspond instead to two substantive ways of conceiving modal truth. At the same time, I claim that the major logical manifestation of the real- world/general validity distinction in modal propositional languages with the actuality operator should not be taken seriously, but simply as a by-product of (...) the way in which the semantics of such an operator is usually given. (shrink)

The view that actually has a reading on which it is a two-dimensional indexical modal operator has some problems.

We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula ${\phi}$ in the propositional modal language with A, there is a formula ${\psi}$ not containing A such that ${\phi}$ and ${\psi}$ are materially equivalent at the actual world in every Kripke model (respectively, neighborhood model). Inspection of the proofs leads to corresponding proof-theoretic results concerning the eliminability of (...) the actuality operator in the actuality extension of any normal propositional modal logic and of any “classical” modal logic. As an application, we provide an alternative proof of a result of Williamson’s to the effect that the compound operator A□ behaves, in any normal logic between T and S5, like the simple necessity operator □ in S5. (shrink)

In this paper, I motivate the addition of an actuality operator to relevant logics. Straightforward ways of doing this are in tension with standard motivations for relevant logics, but I show how to add the operator in a way that permits one to maintain the intuitions behind relevant logics. I close by exploring some of the philosophical consequences of the addition.

The counterpart theorist has a problem: there is no obvious way to understand talk about actuality in terms of counterparts. Fara and Williamson have charged that this obstacle cannot be overcome. Here I defend the counterpart theorist by offering systematic interpretations of a quantified modal language that includes an actuality operator. Centrally, I disentangle the counterpart relation from a related notion, a ‘representation relation’. The relation of possible things to the actual things they represent is variable, and (...) an adequate account of modal language must keep track of the way it is systematically shifted by modal operators. I apply my account to resolve several puzzles about counterparts and actuality. In technical appendices, I prove some important logical results about this ‘representational’ counterpart system and its relationship to other modal systems. (shrink)

Decision theory is founded on the principle that we ought to take the action that has the maximum expected value from among actions we are in a position to take. But prior to the notion of expected value is the notion of the actual value of that action: roughly, a measure of the good outcomes you would in fact procure if you were to take it. Surprisingly many decision theories operate without an analysis of actual value. I offer a definition (...) of actual value, and show that a form of decision theory due to Stalnaker can be reformulated so as to be in line with the edict to maximize expected value. By contrast, I show that there is no quantity — given by my definition or otherwise — that plays the role of actual value in Jeffrey's decision theory. (shrink)

The word 'actually' often refers to what is in fact the case, but it also often points to what would have been the case in a possible situation that is being envisaged. To capture such nuances, the formal languages discussed in the paper add subscripts to modal operators; in the model theory the subscripts allow an actuality operator to turn the evaluation of a formula to a world introduced by a preceding possibility or necessity operator having the (...) same subscript. The paper covers both propositional and predicate logic and proves the completeness of axiomatizations that extend standard modal systems beginning with K. (shrink)

The well-known argument of Frederick Fitch, purporting to show that verificationism (= Truth implies knowability) entails the absurd conclusion that all the truths are known, has been disarmed by Dorothy Edgington''s suggestion that the proper formulation of verificationism presupposes that we make use of anactuality operator along with the standardly invoked epistemic and modal operators. According to her interpretation of verificationism, the actual truth of a proposition implies that it could be known in some possible situation that the proposition (...) holds in theactual situation. Thus, suppose that our object language contains the operatorA — it is actually the case that ... — with the following truth condition: vA iff w0, wherew 0 stands for the designated world of the model — the actual world. Then we can formalize the verificationist claim as follows. (shrink)

“There is no longer any world,” wrote the late philosopher Jean-Luc Nancy in 1993, and in this paper, the sense of this loss of world is analysed in terms of the modal notions of necessity, impossibility, and possibility. Modal differentiation can illuminate what constitutes the sense of actuality in a world, and hence, what it is that has been lost regarding this actuality of being in a world. Modal thinking does not rely on knowledge of the true state (...) of affairs, nor on having a constant grasp on necessity: modal thinking enables us to discern the actual by way of the relations between necessity, possibility, and impossibility. It is on the basis of these relations that a mode of rethinking actuality is suggested. In order to pursue this line of thought, I rely on Jacques Lacan’s understanding of modalities as writing operations, concentrating mostly on certain sections from his Seminar XXI, wherein he refers to Aristotelian modal logic and mentions the analytic philosopher Jaakko Hintikka. This ternary relation between Aristotle, Hintikka, and Lacan suggests a different outlook on the actual being-such of a world. The being-such of a world, its actuality, is understood as a contingency, a possibility emerging from the relation between what is declared necessary and what is impossible. The paper shows the implications of such a modal understanding of actuality, as demonstrated in Lacan’s view of human sexuality and sexual difference. (shrink)

In this paper we present tableau methods for two-dimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain first-order quantifiers with identity, and all the formulas in the language are doubly-indexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux modulate (...) over different notions of validity such as local, general, and diagonal, besides being general enough for several two-dimensional logics proposed in the literature. We also motivate the introduction of a new operator into two-dimensional languages and explore some of the philosophical questions raised by it concerning the relations there are between actuality, necessity, and the a priori, that seem to undermine traditional intuitive interpretations of two-dimensional operators. (shrink)

The actually-operator, understood as a rigidifier, has been employed for a range of purposes in natural language semantics. In this article I argue that the properties of the operator do not correspond to any feature of natural language or feature natural language users have access to. Nor is it needed to provide a formal representation of natural language sentences—the examples usually provided to illustrate the indispensability of the operator are much more plausibly interpreted using plural quantifiers. This (...) lack of connection to natural language is a serious worry for accounts that appeal to rigidifying operations to explain natural language phenomena, as well as a challenge to theories that appeal to the operator to capture the difference between different kinds of necessity expressed in natural language. (shrink)

William Lane Craig has argued that there cannot be actual infinities because inverse operations are not well-defined for infinities. I point out that, in fact, there are mathematical systems in which inverse operations for infinities are well-defined. In particular, the theory introduced in John Conway's *On Numbers and Games* yields a well-defined field that includes all of Cantor's transfinite numbers.

The aim of this article is to propose a novel supervaluationist theory of ‘actually’ in the open future. First, I will argue that any adequate theory of actuality in a branching setting must comply with three main desiderata. Second, I will prove that none of the actuality operators that have been proposed in the literature is up to the task. Finally, I will propose a novel theory of actuality in the open future combining one of the existing (...) definitions of the actuality operator with a new definition of the historical possibility operator, and argue for its adequacy. The central feature of the theory I will advance is the introduction of an actuality parameter capable of being shifted by the historical possibility operator. I will argue that this account appears to not only be consistent with the idea that the future is genuinely open, but also with the general idea that ‘actually’ is, in a relevant sense, a ‘rigid’ operator. (shrink)

Actualists of a certain stripe—dispositionalists—hold that metaphysical modality is grounded in the powers of actual things. Roughly: p is possible iff something has, or some things have, the power to bring it about that p. Extant critiques of dispositionalism focus on its material adequacy, and question whether there are enough powers to account for all the possibilities we intuitively want to countenance. For instance, it seems possible that none of the actual contingent particulars ever existed, but it is impossible to (...) explain this by appealing to the powers of some actual thing or things to bring it about. I argue instead that dispositionalism, in the simple form championed by its proponents, is formally inadequate. Dispositionalists interpret the modal operators as simple existential claims about powers, but if we interpret the operators that way, the resulting system of modal logic is too weak to capture metaphysical modality. I argue that we can modify the standard dispositionalist interpretations of the operators to secure formal adequacy, but at the cost of accepting that not all modality is grounded in powers. This, I shall suggest, is not a bad thing—the resulting theory still has powers at its core and has certain attractive features, in addition to formal adequacy, that the standard theory lacks. (shrink)

We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal (...) possibility quantifies over some point on the diagonal. Thus, they are just like the epistemic operators for apriority and its dual. We take this extension of Fitch’s familiar derivation system to be a very natural one, since the new rules and labeled lines hereby introduced preserve the structure of Fitch’s own rules for the modal case. (shrink)

A series of representations must be semantics-driven if the members of that series are to combine into a single thought: where semantics is not operative, there is at most a series of disjoint representations that add up to nothing true or false, and therefore do not constitute a thought at all. A consequence is that there is necessarily a gulf between simulating thought, on the one hand, and actually thinking, on the other. A related point is that a popular doctrine (...) - the so-called 'computational theory of mind' (CTM) - is based on a confusion. CTM is the view that thought-processes consist in 'computations', where a computation is defined as a 'form-driven' operation on symbols. The expression 'form-driven operation' is ambiguous, as it may refer either to syntax-driven operations or to morphology-driven operations. Syntax-driven operations presuppose the existence of operations that are driven by semantic and extra-semantic knowledge. So CTM is false if the terms 'computation' and 'form-driven operation' are taken to refer to syntax-driven operations. Thus, if CTM is to work, those expressions must be taken to refer to morphology-driven operations. CTM therefore fails, given that an operation must be semantics-driven if it is to qualify as a thought. CTM therefore fails on each possible disambiguation of the expressions 'formal operation' and 'computation,' and it is therefore false. (shrink)

Political interaction among citizens who hold opposing moral views commonly requires reaching beyond toleration, toward actual co‐operation with policies one opposes. On the more personal level, however, regarding (e.g.) interactions between healthcare providers and patients, several authors emphasise the importance of preserving integrity. But those who oppose any ‘complicity in evil’ often wrongly conflate instances in which the other's position is (and should be) totally rejected with instances of legitimate, although deep, disagreement. Starting with a striking example from the context (...) of a particular tradition, I argue generally that in the latter sort of disagreements, talk of ‘complicity’ should be largely replaced with a more co‐operative moral stance, grounded in a pluralistic framework. Co‐operation Despite Disagreement (CDD) should be sought either for institutional reasons – akin to the political – or for relational reasons. CDD involves sharing another's perspective and sometimes calls for adopting another's moral judgements in preference to one's own. I seek to identify some of the conditions and circumstances that would justify such a shift, particularly in scenarios involving assistance, such as physician‐assisted suicide (PAS) or the role of an anaesthesiologist in abortion. This discussion is meant to provide examples of the kind of second‐order reasons appropriate for determining the terms for CDD – in distinction from first‐order considerations (e.g., the much‐contested ‘active/passive’ distinction) which are likely to be the subject of the initial disagreement and hence cannot serve to resolve it. (shrink)

We ponder about the kind of problems and perspectives of a “formalized epistemology”, by considering the advantages than one can get from a concern with the “formal”, with its structural orientation, that would favour comprehensive, unifying and synthetic, intelligibility. We confront this perspective with that of the changes in knowledge, considering the relation between form and meaning for knowledge contents, and examine the notion of “epistemic operation” as instrumental for creating new forms, at the theoretical and meta-theoretical levels. Actually, the (...) notions of form, of formal and of object are not independent of the problem of a subject that decides on conventions and choices. “Epistemic operations” might suggest a link with “algorithmic functions” for knowledge statements, that themselves entail the risk of reductionism in a naturalistic conception of representation. (shrink)

Dr. Vukov analyzing patients with disorders of consciousness, proposed that medical well-regarded policy recommendations cannot be justified by looking solely to patients’ actual levels of consciousness (minimally conscious state – MCS versus vegetative state – VS), but that they can be justified by looking to patients’ potential for consciousness. One objective way to estimate this potential (actual physical possibility) is to consider a neurophysiologically informed strategy. Ideally such strategy would utilize objective brain activity markers of consciousness/unconsciousness. The Operational Architectonics (OA) (...) theory of brain-mind functioning is an example of such a strategy. Besides being mathematically simple, neurophysiologically accurate, and compatible with the cognitive/phenomenal perspectives on consciousness, application of OA strategy to quantitative EEG analysis of patients in VS and MCS revealed that the absence of consciousness in VS is paralleled by impairment of overall EEG operational architecture. Specifically, neuronal assemblies become smaller, their life span shortened, and they became highly unstable and functionally disconnected (desynchronized). At the same time, fluctuating (minimal) awareness in patients in MCS was paralleled by partial restoration of EEG operational architecture (increased size, life span, and stability of neuronal assemblies, together with an increased number and strength of functional connections among them), approaching the level found in healthy fully conscious participants. Moreover OA strategy to EEG analysis allowed predicting the emergence of consciousness in VS patients after six years following the brain trauma. Therefore, the OA methodology could reliably predict which patients may regain consciousness, and thus determine which patients may have the potential for consciousness. (shrink)

In March 2003, President Bush declared the start of Operation Iraqi Freedom, the anticipated commencement of intensive American-led military operations in Iraq. With this declaration, the media began intense coverage of military operations from the field. For the first time, viewers were able to see images of actual events. This was due to three developments: the advancement of technology allowing immediate transmission of text and images, the actual presence of journalists identified as "embedded journalists" at military sites, and the fierce (...) competition among networks for viewers. One result of this constant coverage was significant pressure on decision makers within the television and cable news networks to decide within a matter of seconds which images to air. In particular, producers and broadcasters of competing networks experienced this pressure. Though the radio and broadcasting industry has a published code of standards, it is "general and advisory rather than specific and restrictive." Therefore, it did not address the unique time sensitive decision-making required within this new environment. Issues such as the security of soldiers, confidentiality of troop maneuvers, and the safety of the embedded journalists were critically important. Equally serious were the concerns about the impact of the immediate airing of information and violent images to the public. This research used Patrick Primeaux's ' mind-heart-sou¾ model of decision-making as its theoretical framework. The study investigated the gender and industry experience of selected professionals in a cable news network, MSNBC, to explore how ethical codes of behavior are integrated when people make decisions. Decision-making in both their professional and personal lives was examined. It is from this perspective that their professional decisions to air/not to air material from Operation Iraqi Freedom were studied. The findings on decisions about airing/not airing material from Operation Iraqi Freedom yielded both expected and unexpected results. There was no clear gender difference regarding ethical decision-making, but there was a difference when analyzed by industry experience. When the study focused on questions regarding the respondents' personal lives, the original hypothesis that there was a gender difference was validated. (shrink)

In response to Kripke's modal argument contemporary descriptivists suggest that referring terms, e.g., ‘water’, are synonymous with actually-rigidified definite descriptions, e.g., ‘the actual watery stuff’. Following Scott Soames, this strategy has the counterintuitive consequence that possible speakers on Perfect Earth cannot be ascribed water-beliefs without beliefs about the actual world. Co-indexing the actuality and possibility operators has the equally untoward result that possible speakers on Twin Earth are ascribed water-beliefs. So, Soames's dilemma is that the descriptivist can account for (...) either Twin Earth or Perfect Earth but not both. In response, this paper argues that since ‘actual’ is an indexical, the content of water-beliefs is egocentric, and so if the descriptivist avails herself of relativized propositions as the content of such beliefs, she is able to account for both Twin Earth and Perfect Earth. The lesson is that we have to tread carefully when making inferences about the contents of beliefs from the semantics of belief-reporting sentences that contain actually-rigidified expressions. (shrink)

The actual/virtual distinction is used to give an alternative account of quantum interference by way of a new theory of probability. The new theory is obtained by changing one of the axioms of the canonical theory of probability while keeping the other axioms fixed. It is used to give an alternative account of constructive quantum interference in the two-slit experiment. The account crucially involves a distinction between actual and virtual probabilities. Although actual probabilities are operational and virtual probabilities are not, (...) there is a substantial connection between them. Virtual probabilities may be obtained indirectly from actual probabilities. In showing this, interpretive considerations are brought to bear including some having to do with quantum non-locality. Directions for future research are discussed in closing.La distinción actual/virtual se utiliza para dar una explicación alternativa de la interferencia cuántica a través de una nueva teoría de la probabilidad. La nueva teoría se ha obtenido cambiando uno de los axiomas de la teoría canónica de la probabilidad y manteniendo los otros axiomas fijos. Se usa para dar una explicación alternativa de la interferencia cuántica constructiva en el experimento de la doble rendija. El informe fundamentalmente implica una distinción entre las probabilidades actuales y virtuales. Aunque las probabilidades actuales son operativas y las probabilidades virtuales no, hay una relación sustancial entre ellas. Probabilidades virtuales pueden obtenerse indirectamente a partir de las probabilidades reales. Para demostrar esta interpretación hay que tener en cuenta las consideraciones de interpretación que se ejercen entre ellos y que tienen relación con la no-localidad cuántica. Directrices para futuras investigaciones se abordan al final del artículo. (shrink)

Ratio, Volume 35, Issue 2, Page 104-111, June 2022.

It is known that indicative and subjunctive conditionals interact differently with a rigidifying "actually" operator. The paper studies this difference in an abstract setting. It does not assume the framework of possible world semantics, characterizing "actually" instead by the type of logically valid formulas to which it gives rise. It is proved that in a language with such features all sentential contexts that are congruential (in the sense that they preserve logical equivalence) are extensional (in the sense that they (...) preserve material equivalence). For a subjunctive conditional, the natural conclusion to draw is that it is non-congruential. It is much harder to defend the claim that an indicative conditional is non-congruential. The pressure to treat the indicative conditional as truth-functional is correspondingly greater. The implications of these results for attempts to interpret the indicative conditional as an epistemic or doxastic operator are assessed. (shrink)

This is a philosophical `position paper' (html and pdf versions), starting from the observation that we have an intuitive grasp of a family of related concepts of ``possibility'', ``causation'' and ``constraint'' which we often use in thinking about complex mechanisms, and perhaps also in perceptual processes, which according to Gibson are primarily concerned with detecting positive and negative affordances, such as support, obstruction, graspability, etc. We are able to talk about, think about, and perceive possibilities, such as possible shapes, possible (...) pressures, possible motions, and also risks, opportunities and dangers. We can also think about constraints linking such possibilities. If such abilities are useful to us (and perhaps other animals) they may be equally useful to intelligent artefacts. All this bears on a collection of different more technical topics, including modal logic, constraint analysis, qualitative reasoning, naive physics, the analysis of functionality, and the modelling design processes. The paper suggests that our ability to use knowledge about ``de-re'' modality is more primitive than the ability to use ``de-dicto'' modalities, in which modal operators are applied to sentences. The paper explores these ideas, links them to notions of ``causation'' and ``machine'', suggests that they are applicable to virtual or abstract machines as well as physical machines. Some conclusions are drawn regarding the nature of mind and consciousness. (shrink)

Lewis (The Journal of Philosophy, 65(5), 113–126, 1968) attempts to provide an account of modal talk in terms of the resources of counterpart theory, a first-order theory that eschews transworld identity. First, a regimentation of natural language modal claims into sentences of a formal first-order modal language L is assumed. Second, a translation scheme from L-sentences to sentences of the language of the theory is provided. According to Hazen (The Journal of Philosophy, 76(6), 319–338, 1979) and Fara & Williamson (Mind, (...) 114(453), 1–30, 2005), the account cannot handle certain natural language modal claims involving a notion of actuality. The challenge has two parts. First, in order to handle such claims, the initial formal modal language that natural language modal claims are regimented into must extend L with something like an actuality operator. Second, certain ways that Lewis’ translation scheme for L might be extended to accommodate an actuality operator are unacceptable. Meyer (Mind, 122(485), 27–42, 2013) attempts to defend Lewis’ approach. First, Meyer holds that in order to handle such claims, the formal modal language L$$^*$$ ∗ that we initially regiment our natural language claims into need not contain an actuality operator. Instead, we can make do with other resources. Next, Meyer provides an alternative translation scheme from L$$^*$$ ∗ -sentences to sentences of an enriched language of counterpart theory. Unfortunately, Meyer’s approach fails to provide an appropriate counterpart theoretic account of natural language modal claims. In this paper, I demonstrate that failure. (shrink)

This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines (...) of two arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. (shrink)

In this paper a possible interpretative value of Aristotle’s fundamental ontological doctrine of potentiality and actuality is considered in the context of operationally undoubtedly the most successful but interpretatively still controversial theory of modern physics – quantum mechanics – especially regarding understanding the nature of the world, the phenomena of which it describes and predicts so successfully. In particular, beings of the atomic world are interpreted as real potential beings actualized by the measurement process in appropriate experimental arrangement, and (...) the problem of actual beings of the atomic world is considered in the context of Aristotle’s threefold requirement for the priority of actuality over potentiality – in time , definition or knowledge , and substantiality .Dieser Artikel setzt sich mit der interpretativen Relevanz der ontologischen Theorie Aristoteles’ über die Möglichkeit und die Wirklichkeit für die Quantenmechanik auseinander, also für die auf der empirischen Ebene erfolgreichste Theorie innerhalb der modernen Physik, die jedoch noch immer kontrovers interpretiert wird. Dies gilt insbesondere im Hinblick auf das Verständnis der Natur der Atomwelt, deren Phänomene sie erfolgreich beschreibt. Die W esen der Atomwelt werden als reale Möglichkeitswesen begriffen , die in der experimentellen Situation aktualisiert werden, während das Problem der W irklichkeitswesen der Atomwelt im Kontext des von Aristoteles dreifach begründeten Vorrangs der W irklichkeit vor der Möglichkeit betrachtet wird – nämlich auf der Ebene der Zeit , auf der Ebene desBegriffs und auf der Ebene des Seins .U članku se promišlja možebitna interpretativna vrijednost Aristotelova temeljnog ontološkog nauka o možnosti i zbiljnosti  u kontekstu izračunski nesumnjivo najuspješnije, ali interpretativno još uvijek dvojbene teorije suvremene fizike – kvantne mehanike, posebno kada je riječ o razumijevanju naravi samoga atomnoga svijeta čije pojavnosti tako uspješno opisuje i predviđa. Poglavito, bića atomnoga svijeta poimaju se kao realna možna bića koja bivaju ozbiljena prema prigotku eksperimentalne situacije, a problem zbiljskih bića atomnoga svijeta promišljen je u kontekstu Aristotelova trojnog zahtjeva o prvotnosti zbiljnosti nad možnošću – prema vremenu , prema pojmu i prema bivstvu. (shrink)

The notion of validity for modal languages could be defined in two slightly different ways. The first is the original definition given by S. Kripke, for which a formula φ of a modal language L is valid if and only if it is true in every actual world of every interpretation of L. The second is the definition that has become standard in most textbook presentations of modal logic, for which a formula φ of L is valid if and only (...) if it is true in every world in every interpretation of L. For simple modal languages, “Kripkean validity” and “Textbook validity” are extensionally equivalent. According to E. Zalta, however, Textbook validity is an “incorrect” definition of validity, because: (i) it is not in full compliance with Tarski’s notion of truth; (ii) in expressively richer languages, enriched by the actuality operator, some obviously true formulas count as valid only if the Kripkean notion is used. The purpose of this paper is to show that (i) and (ii) are not good reasons to favor Kripkean valid- ity over Textbook validity. On the one hand, I will claim that the difference between the two should rather be seen as the result of two different conceptions on how a modal logic should be built from a non-modal basis; on the other, I will show the advantages, for the question at issue, of seeing the actuality operator as belonging to the family of two-dimensional operators. (shrink)

Consider two standard quantified modal languages A and P whose vocabularies comprise the identity predicate and the existence predicate, each endowed with a standard S5 Kripke semantics where the models have a distinguished actual world, which differ only in that the quantifiers of A are actualist while those of P are possibilist. Is it possible to enrich these languages in the same manner, in a non-trivial way, so that the two resulting languages are equally expressive-i.e., so that for each sentence (...) of one language there is a sentence of the other language such that given any model, the former sentence is true at the actual world of the model iff the latter is? Forbes (1989) shows that this can be done by adding to both languages a pair of sentential operators called Vlach-operators, and imposing a syntactic restriction on their occurrences in formulas. As Forbes himself recognizes, this restriction is somewhat artificial. The first result I establish in this paper is that one gets sameness of expressivity by introducing infinitely many distinct pairs of indexed Vlach-operators. I then study the effect of adding to our enriched modal languages a rigid actuality operator. Finally, I discuss another means of enriching both languages which makes them expressively equivalent, one that exploits devices introduced in Peacocke (1978). Forbes himself mentions that option but does not prove that the resulting languages are equally expressive. I do, and I also compare the Peacockian and the Vlachian methods. In due course, I introduce an alternative notion of expressivity and I compare the Peacockian and the Vlachian languages in terms of that other notion. (shrink)

The doctrine of the communication of natures has played a primarily descriptive role in the history of Christology, and so it is perhaps unsurprising that it has largely gone missing from contemporary theology. This is a serious oversight. But Karl Barth is a noteworthy exception to the reductionist trend, and he provides the Reformed tradition's most complete and substantive engagement with the communication of natures and its implications for dogmatic theology. Through a close reading of volume IV/2 of the Church (...) Dogmatics , this essay considers Karl Barth's vital emphasis upon the communicatio naturarum and the role it plays in his actualist Christology. Barth demonstrates that the traditional threefold communication (of attributes, graces, and operations) has material as well as formal importance. According to Barth, we see in Christ not the mere coincidence of two natures, nor an interpenetration, nor the transformation of one into the other – but mutual operation and interpretation, where divinity and humanity each acquires and has its determination in the other. (shrink)

Modal Meinongianism provides the semantics of sentences involving intentional verbs Priest. To that end, Modal Meinongianism employs a pointed non-normal quantified modal logic model. Like earlier Meinongian views Modal Meinongianism has a characterisation principle, that claims that any condition whatsoever is satisfied by some object in some world. Recently, Everett has proposed an argument against QCP that, if successful, gives rise to problems identical to those Russell raised for Naïve Meinongianism, namely that it allows for true contradictions, and allows us (...) to define anything into existence. Everett claims that the ordinary meanings of “actual” license an inference pattern, such that if an object satisfies Actual A at some world, then that object satisfies A in the actual world. Given that actual world is the designated point of evaluation for truth simpliciter, QCP would fall prey to Russell’s criticisms. As opposed to Everett, I argue that, even if we grant Everett the assumption that “actual” is a modal indexical that rigidly refers to the actual world, it does not conform to the inference pattern above. This is because when an object satisfies Actual A at some world, this alters the assertoric force of “actual”, because “actual” is interpreted in the scope of some modal or intentional operator. I also explain that Everett’s proposed example carries existential commitment because the problematic noun-phrase occurs outside the scope of a modal or intentional operator. (shrink)

As argued in Hellman (1993), the theorem of Pour-El and Richards (1983) can be seen by the classicist as limiting constructivist efforts to recover the mathematics for quantum mechanics. Although Bridges (1995) may be right that the constructivist would work with a different definition of 'closed operator', this does not affect my point that neither the classical unbounded operators standardly recognized in quantum mechanics nor their restrictions to constructive arguments are recognizable as objects by the constructivist. Constructive substitutes that (...) may still be possible necessarily involve additional 'incompleteness' in the mathematical representation of quantum phenomena. Concerning a second line of reasoning in Hellman (1993), its import is that constructivist practice is consistent with a 'liberal' stance but not with a 'radical', verificationist philosophical position. Whether such a position is actually espoused by certain leading constructivists, they are invited to clarify. (shrink)

Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these extensions are often justified (...) only by example rather than by rigorous proof. In this paper, we provide proofs of many of these claims and present a more complete picture of the expressive landscape for such languages. (shrink)

An actual cause of some token effect is itself a token event that helped to bring about that effect. The notion of an actual cause is different from that of a potential cause – for example a pre-empted backup – which had the capacity to bring about the effect, but which wasn't in fact operative on the occasion in question. Sometimes actual causes are also distinguished from mere background conditions: as when we judge that the struck match was a cause (...) of the fire, while the presence of oxygen was merely part of the relevant background against which the struck match operated. Actual causation is also to be distinguished from type causation: actual causation holds between token events in a particular, concrete scenario; type causation, by contrast, holds between event kinds in scenario kinds. (shrink)

A set of parameters for classifying composition operations is introduced. These parameters determine whether a composition operation is 1) universal, 2) determinate, 3) whether there is a difference between possible and actual compositions, 4) whether there can be singleton compositions, 5) whether they give rise to a hierarchy, and 6) whether components of compositions can be repeated. Philosophical implications of these parameters (in particular in relation to set theory) and mereology are discussed.

A time operator, which incorporates the idea of time as a dynamical variable, was first introduced in the context of a theory of irreversible evolution. The existence of a time operator has interesting implications in several areas of physics. Here we demonstrate a close link between the existence of the time operator for relativistic particles and the existence of an indivisible time interval or chronons for dynamical evolution. More explicitly, we consider a Klein-Gordon particle and require the (...) existence of a time operator for its evolution. We also make a natural choice of the form of the time operator which expresses it in terms of the generators of the Poincaré group. These then imply that the physical time evolution group must be the discrete subgroup Unτ (n integers) of the originally given evolution group Ut of the Klein-Gordon particle and the constant τ is given by τ=h/2mc2. This means that the requirement of the existence of a time operator implies that the time evolution cannot be followed to time intervals smaller than τ and, as such, τ emerges as a chronon for the dynamical evolution. Expecting that the same results hold for a Dirac particle also, we conclude that the so-called Zitterbewegungdoes not occur in reality. Thus, possible confirmation of the existence of chronons would result if no observableconsequence of Zitterbewegungis actually realized in nature. This calls for a search of observable consequences of the Zitterbewegungand a re-examination of their agreement (if any) with experiments. A possible consequence of Zitterbewegung,the so-called Darwin term present in the Dirac Hamiltonian in an electric field, is briefly considered. (shrink)

Natural language provides motivation for studying modal backwards-looking operators such as “now”, “then” and “actually” that evaluate their argument formula at some previously considered point instead of the current one. This paper investigates the expressive power over models of both propositional and first-order basic modal language enriched with such operators. Having defined an appropriate notion of bisimulation for first-order modal logic, I show that backwards-looking operators increase its expressive power quite mildly, contrary to beliefs widespread among philosophers of language and (...) formal semanticists. That in turn presents a strong argument for the use of operator-based systems in the semantics of natural language, instead of systems with explicit quantification over worlds and times that have become a de-facto standard for such applications. The popularity of such explicit-quantification systems is shown to be based on the misinterpretation of a claim by Cresswell, which led many philosophers and linguists to assume that introducing “now” and “then” is expressively equivalent to explicitly quantifying over worlds and times. (shrink)

The supervaluationist approach to branching time (‘SBT-theory’) appears to be threatened by the puzzle of retrospective determinacy: if yesterday I uttered the sentence ‘It will be sunny tomorrow’ and only in some worlds overlapping at the context of utterance it is sunny the next day, my utterance is to be assessed as neither true nor false even if today is indeed a sunny day. John MacFarlane (“Truth in the Garden of Forking Paths” 81) has recently criticized a promising solution to (...) this puzzle for falling short of an adequate account of ‘actually’. In this paper, I aim to rebut MacFarlane's criticism. To this effect, I argue that: (i) ‘actually’ can be construed either as an indexical or as a nonindexical operator; (ii) if ‘actually’ is nonindexical, MacFarlane's criticism is invalid; (iii) there appear to be independent reasons for SBT-theorists to claim that ‘actually’ is a nonindexical expression. (shrink)

In [2] a semantics for implication is offered that makes use of stories — sets of sentences assembled under various constraints. Sentences are evaluated at an actual world and in each member of a set of stories. A sentence B is true in a story s just when B s. A implies B iff for all stories and the actual world, whenever A is true, B is true. In this article the first-order language of [2] is extended by the addition (...) of the operator the story... says that..., as in The story Flashman among the Redskins says that Flashman met Sitting Bull. The resulting language is shown to be sound and complete. (shrink)

T. M. Scanlon posits a universal moral relationship in response to the worry that his relational approach to blame cannot answer the question of how strangers can fittingly blame one another. However, commentators have noted that appealing to universal moral standards seems to explicitly deviate from a relational approach’s basis in actual relationship norms. This paper argues that Scanlon’s idea of a moral relationship can nevertheless provide a basis for response to the problem of strangers if we recognize that actual (...) and ideal moral relationships both play a role within the relational approach. An interesting consequence of this recognition is that it seems to undermine the moral relationship’s universality. However, a presumptive case for assuming the relationship exists even between strangers can be found in seeing our blaming practices as akin to public policy nudges, where blame operates like an opt-out choice architecture with respect to the moral relationship. On this understanding, though the moral relationship is escapable, individuals are naturally encouraged to participate through the expression of interpersonal attitudes that communicate relational norms and expectations. (shrink)

While the theory of belief change has attracted a lot of interest from researchers, work on implementing belief change and actually putting it to use in real-world problems is still scarce. In this paper, we present an implementation of propositional belief change using Binary Decision Diagrams. Upper complexity bounds for the algorithm are presented and discussed. The approach is presented both in the general case, as well as on specific belief change operators from the literature. In an effort to gain (...) a better understanding of the empirical efficiency of the algorithms involved, a fault diagnosis problem on combinational circuits is presented, implemented and evaluated. (shrink)