We show the existence of Lorentz invariant Berry phases generated, in the Stueckelberg–Horwitz–Piron manifestly covariant quantum theory (SHP), by a perturbed four dimensional harmonic oscillator. These phases are associated with a fractional perturbation of the azimuthal symmetry of the oscillator. They are computed numerically by using time independent perturbation theory and the definition of the Berry phase generalized to the framework of SHP relativistic quantum theory.
A recent group of social scientists have argued that counterfactual questions play an essential role in their disciplines, and that it is possible to have rigorous methods to investigate them. Unfortunately, there has been little (if any) interaction between these social scientists and the philosophers who have long held that rigorous counterfactual reasoning is possible. In this paper, I hope to encourage some fresh thinking on both sides by creating new connections between them. I describe what I term "problem of (...) selecting antecedent scenarios," and show that this is an essential challenge in real-life counterfactual reasoning. Then, I demonstrate that the major extant theories of counterfactuals (especially the Lewis/Stalnaker theory and Igal Kvart's rival account) are unable to solve this problem. I show that there are instances of real-life counterfactual reasoning in the social sciences that are counterexamples to both of these accounts. And finally, I develop a new theory of how to select antecedent scenarios that overcomes these difficulties, and so would be part of a more adequate theory of counterfactuals (and counterfactual reasoning). (shrink)
Igal Kvart A Coding Conception in Action-Directed-Pragmatics -/- I present formal Pragmatics for a domain in Pragmatics that I call Action-Directed Pragmatics, which focuses on the Pragmatic riddle of how implicit contents are conveyed and understood, by adopting a coding model, in which the speaker and addressee simulate each other iteratively in a deliberative context (an ‘action-pregnant’ one). The implicit content, conveyed by a speaker and decoded by her addressee, in such cases, consists in the specified steered-to action, plus (...) modulations on the action-polarity (pro or con) and the degree of the so-called Steering Thrust that accompanies such assertions and is conveyed by verbal locutions, intonation, and/or bodily and facial gestures. There are two main tasks to model (in a given setup and conversational context): First, how is the speaker, with a steered-to action in mind (and Steering Thrust), to select an assertion so as to (say) optimize the successful transmission and decoding of its implicit pragmatic content by her and her addressee? Second, how does the addressee, given an assertion by the speaker, decipher the implicit pragmatic content conveyed via it? Both will invoke pertinent information they have about each other and the setup/context in order to best encode and best decode the implicit pragmatic content. (This coding mechanism proposed here is not offered for the ubiquitous ‘frozen’, ‘trivial’ or ‘routinized’ pragmatic messages.) A prelude to this formal Pragmatics is a general formal Pragmatic account of Assertibility in contexts that are multi-normative (which is the common case). I focus here only on Epistemic/Semantic and Instrumental Norms. A linear representation of degrees of Overall Assertibility (i.e., taking into account various operative norms) will be an n-dimensional qualitative vector space with a function that computes them given different degrees of sub-normative Assertibility on each axis. (shrink)
Igal Kvart RATIONAL ASSERTIBILITY, THE STEERING ROLE OF KNOWLEDGE, AND PRAGMATIC ENCROACHMENT Abstract In the past couple of decades, there were a few major attempts to establish the thesis of pragmatic encroachment – that there is a significant pragmatic ingredient in the truth-conditions for knowledge-ascriptions. Epistemic contextualism has flaunted the notion of a conversational standard, and Stanley's subject-sensitive invariantism (SSI) promoted stakes, each of which, according to their proponents, play a major role as pragmatic components in the truth conditions (...) of knowledge ascriptions. These conceptions were propelled first and foremost by examples of knowledge ascriptions with obvious pragmatic aspects that seemed to require a pragmatic component in the truth-conditions of knowledge ascriptions in order to be accounted for. However, if such examples can be adequately explained not by pragmatic encroachment purely pragmatically, the central role that such examples play in supporting these accounts will be undermined. I lay out here a new pragmatic account, offering a different, purely pragmatic picture that explains such examples, and much more. If such an account and its associated explanations are adequate, then much of a need or a motivation for pragmatic encroachment is undermined. Specifically, I will develop the notion of rational assertibility, appealing to rational norms (which are not Gricean) as interfacing with semantic and epistemic (and other) norms to yield assertibility simpliciter. More importantly, I will argue for a well-entrenched pragmatic profile of knowledge, the so-called steering role of knowledge. Knowledge ascriptions, or simple assertions (that don't invoke the notion of knowledge), it will be argued, play a pragmatic role of steering audiences in joint deliberational setups to the speaker's preferred action by invoking an impending practical inference leading to that preferred action, and of ignoring incompatible alternatives. The recognition of rational forces as affecting, sometimes strongly and predominantly, intuitions associated with knowledge ascriptions, has important implications to philosophical methodology regarding what count as evidence for semantic features. One such lesson calls for securing examples with no significant rational forces at play in order to establish semantic features. Another calls attention to the ill-suitability of employing assertibility by figures in examples featuring deliberational setups for such a purpose in view of the role that such assertibility plays in reflecting rational aspects of such figures, in addition to their epistemic and semantic characteristics. Still another lesson points to a specific role that audiences play in such deliberational setups. (shrink)
In this paper, I provide a probabilistic account of factual knowledge, based on the notion of chance, which is a function of an event given a prior history. This account has some affinity with my chance account of token causation, but it neither relies on it nor presupposes it. Here, I concentrate on the core cases of perceptual knowledge and of knowledge by memory. The analysis of knowledge presented below is externalist. The underlying intuition guiding the treatment of knowledge in (...) this paper is that knowledge boils down to high token discriminative indicativeness. Type indicativeness or type discriminability are neither necessary nor sufficient for knowledge: the token aspect comes out in the strong dependence on the specific circumstances and chances of the case. The main condition of the first section, the indicativity condition, properly refined, yields pertinent indicativity as a main constituent. Very roughly, it involves the chance of the content clause p being higher given the subject's believing that p than otherwise. The discriminability condition in question captures the sense of discriminability appropriate for knowledge and yield the indicativity condition: it is an extension of the indicativity condition KI. Roughly, the subject’s ability to discriminate the object in front of her being red from its being green is captured by holding fixed, in the indicativity condition, the condition “the object in front of her is red or green.” A major element in the analysis is the so-called Contrast Class, which governs the scope of discriminability. This is the class of features that have to be taken into account in the discriminability condition, and it is characterized by two constraints. Very roughly, according to the first constraint, for a feature to be in the contrast class, it must not represent a sub-type of the predicate in the content clause. According to the second constraint, which is a central condition with many implications, the chance that the object specified in the content clause has a feature represented in the contrast class must not under the circumstances be too low. This constraint, within the framework of the discriminability condition, brings out a major constitutive aspect of knowledge: knowledge amounts to a limited vulnerability to mistakes of the belief in question under the circumstances at hand. The contrast class plays a major role in my treatment of skepticism. The second constraint on the Contrast Class together with the VHP condition below bring out precisely the way in which perceptual knowledge is fallible. (shrink)
Philosophers have long been fascinated by the connection between cause and effect: are 'causes' things we can experience, or are they concepts provided by our minds? The study of causation goes back to Aristotle, but resurged with David Hume and Immanuel Kant, and is now one of the most important topics in metaphysics. Most of the recent work done in this area has attempted to place causation in a deterministic, scientific, worldview. But what about the unpredictable and chancey world we (...) actually live in: can one theory of causation cover all instances of cause and effect? _Cause and Chance: Causation in an Indeterministic World _is a collection of specially written papers by world-class metaphysicians. Its focus is the problem facing the 'reductionist' approach to causation: the attempt to cover all types of causation, deterministic and indeterministic, with one basic theory. Contributors: Stephen Barker, Helen Beebee, Phil Dowe, Dorothy Edgington, Doug Ehring, Chris Hitchcock, Igal Kwart, Paul Noordhof, Murali Ramachandran and Michael Tooley. (shrink)
The relationship between physics and mathematics is reviewed upgrading the common in physics classes’ perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge (...) important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning. (shrink)
David Lewis’s counterfactual analysis of cause consisted of the counterfactual conditional closed under transitivity.2 Namely, a sufﬁcient condition for A’s being a cause of C is that ∼A > ∼C be true; and a necessary as well as sufﬁcient condition is that there be a series of true counterfactuals ∼A > ∼E1, ∼E1 > ∼E2, . . . , ∼En >∼C (n > 0).
In the past couple of decades, there were a few major attempts to establish the thesis of pragmatic infringement – that a significant pragmatic ingredient figures significantly in the truth-conditions for knowledge-ascriptions. As candidates, epistemic contextualism and Relativism flaunted conversational standards, and Stanley's SSI promoted stakes. These conceptions were propelled first and foremost by obviously pragmatic examples of knowledge ascriptions that seem to require a pragmatic component in the truth-conditions of knowledge ascriptions in order to be accounted for. However, if (...) such examples can be adequately explained purely pragmatically, the need that such examples seem to invoke in such a pragmatic component is undermined. Here I lay out a new pragmatic account – of action-directed pragmatics, offering a different account of such examples and their pragmatic flavor. If adequate, it obviates the above need for pragmatic enrichment. Specifically, I develop and I argue for a well-entrenched pragmatic feature – that of a steering role. The assertions of knowledge ascriptions and their denials as well as of simple assertions (that don't invoke knowledge) play a pragmatic role of steering audiences in joint deliberational setups toward, or away from, the speaker's preferred action (as well as in assertions of 'I am sure', of epistemic modals, taste assertions, causal assertions, and more.) Various features and consequences of this account are drawn. Specifically, I explain why in the bank example (and related ones) the husband, in denying the knowledge ascription, neither lies nor misleads. (shrink)
In this paper I provide a probabilistic account of factual knowledge, based on the notion of chance. This account has some affinity with my chance account of token causation, but it neither relies on it nor presupposes it. Here I concentrate on the core cases of perceptual knowledge and of knowledge by memory (based on perception). The analysis of knowledge presented below is externalist; but pursuing such an analysis need not detract from the significance of attempts to flesh out justificational (...) analyses knowledge; indeed, I have pursued such an analysis in great detail myself. (shrink)
In Kvart (1991a), I discussed the analysis of causal relevance presented in A Theory of Counterfactuals (1986) (and first in 1975). I explained there in what respect the notion captured by the analysis of Kvart (1986) is a mere approximation to the requisite notion of causal relevance. In this paper I present another analysis of causal relevance, devoid of the shortcoming of its predecessor. The present analysis of causal relevance is, again, grounded in a chancelike notion of objective probability. The (...) correlative notion of causal independence is analyzed as holding in case there is a so-called causal impact series, which is defined here. The basic notions used for this analysis are the notion of a differentiator, which upsets an equiprobability case, and that of a blocker, which restores it. (shrink)
Abstract In this paper I consider an easier-to-read and improved to a certain extent version of the causal chance-based analysis of counterfactuals that I proposed and argued for in my A Theory of Counterfactuals. Sections 2, 3 and 4 form Part I: In it, I survey the analysis of the core counterfactuals (in which, very roughly, the antecedent is compatible with history prior to it). In section 2 I go through the three main aspects of this analysis, which are the (...) following. First, it is a causal analysis, in that it requires that intermediate events to which the antecedent event is not a cause be preserved in the main truth-condition schema. Second, it highlights the central notion to the semantics of counterfactuals on the account presented here -- the notion of the counterfactual probability of a given counterfactual, which is the probability of the consequent given the following: the antecedent, the prior history, and the preserved intermediate events. Third, it considers the truth conditions for counterfactuals of this sort as consisting in this counterfactual probability being higher than a threshold. In section 3, I re-formulate the analysis of preservational counterfactuals in terms of the notion of being a cause, which ends up being quite compact. In section 4 I illustrate this analysis by showing how it handles two examples that have been considered puzzling – Morgenbesser's counterfactual and Edgington's counterfactual. Sections 5 and on constitute Part II: Its main initial thrust is provided in section 5, where I present the main lines of the extension of the theory from the core counterfactuals (analyzed in part I) to counterfactuals (roughly) whose antecedents are not compatible with their prior history. In this part II, I elaborate on counterfactuals that don't belong to the core, and more specifically on so-called reconstructional counterfactuals (as opposed to the preservational counterfactuals, which constitute the core counterfactual-type). The heart of the analysis is formulated in terms of processes leading to the antecedent (event/state), and more specifically in terms of processes likely to have led to the antecedent, a notion which is analyzed entirely in terms of chance. It covers so-called reconstructional counterfactuals as opposed to the core, so-called preservational counterfactuals, which are analyzed in sections 2 and 3 of part I. The counterfactual probability of such reconstructional counterfactuals is determined via the probability of possible processes leading to the antecedent weighed, primarily and roughly, by the conditional probability of the antecedent given such process: The counterfactual probability is thus, very roughly, a weighted sum for all processes most likely to have led to the antecedent, diverging at a fixed time. In section 6 I explain and elaborate further on the main points in section 5. In section 7 I illustrate the reconstructional analysis. I specify counterfactuals which are so-called process-pointers, since their consequent specifies stages in processes likely to have led to their antecedent. I argue that so-called backtracking counterfactuals are process-pointers counterfactuals, which fit into the reconstructional analysis, and do not call for a separate reading. I then illustrate cases where a speaker unwittingly employs a certain counterfactual while charitably construable as intending to assert (or ‘having in mind’) another. Here I also cover the issue of how to construe what one can take as back-tracking counterfactuals, or counterfactuals of the reconstructional sort, and more specifically, which divergence point they should be taken as alluding to (prior to which the history is held fixed). Some such cases also give rise to what one can take as a dual reading of a counterfactual between preservational and reconstructional readings. Such cases may yield an ambiguity, where in many cases one construal is dominant. In section 8 I illustrate the analysis by applying it to the famous Bizet-Verdi counterfactuals. This detailed analysis of counterfactuals (designed for the indeterministic case) has three main distinctive elements: its being chance-based, its causal aspect, and the use it makes of processes most likely to have led to the antecedent-event. This analysis is couched in a very different conceptual base from, and is an alternative account to, analyses in terms of the standard notion of closeness or distance of possible worlds, which is the main feature of the Stalnaker-Lewis-type analyses of counterfactuals. This notion of closeness or distance plays no role whatsoever in the analysis presented here. (This notion of closeness has been left open by Stalnaker, and to significant extent also by Lewis's second account.) . (shrink)
In this article I offer an approach to counterfactuals based on a notion of objective probability. It is in the spirit of, though it does not fall squarely under, the metalinguistic model. Thus, it is not developed in terms of possible worlds, or notions parasitic on them (e.g., similarity). Its dominant features are rooted in objective probability and causal relevance (analyzed probabilistically), and thus it is not close in spirit to a maximal similarity or a minimal change approach.
In this paper I explore the ambiguity that arises between two readings of the counterfactual construction, then–d and thel–p, analyzed in my bookA Theory of Counterfactuals. I then extend the analysis I offered there to counterfactuals with true antecedents, and offer a more precise formulation of the conception of temporal divergence points used in thel–p interpretation. Finally, I discuss some ramifications of these issues for counterfactual analyses of knowledge.
I argue that 'know' is only partly, though considerably, gradable. Its being only partly gradable is explained by its multi-parametrical character. That is, its truth-conditions involve different parameters, which are scalar in character, each of which is fully gradable. Robustness of knowledge may be higher or lower along different dimensions and different modes. This has little to do with whether 'know' is context-dependent, but it undermines Stanley's argument that the non-gradability of 'know' renders it non-context-dependent.
In this paper, I present a counter-example to the two most prominent theories of pragmatic encroachment (regarding knowledge ascriptions): Contextualism (specifically, DeRose's version), and Stanley's Subject-Sensitive Invariantism (SSI). The example is a variation on DeRose's bank case. -/- Key words: Knowledge, knowledge ascriptions, pragmatic encroachment, Stanley, DeRose, bank case, standards, stakes.
This study considers the short list of Nature of Science features frequently published and widely known in the science education discourse. It is argued that these features were oversimplified and a refinement of the claims may enrich or sometimes reverse them. The analysis shows the need to address the range of variation in each particular aspect of NOS and to illustrate these variations with actual events from the history of science in order to adequately present the subject. Another implication of (...) the proposal is the highlighting of the central role of science educators who, facing various strong claims of researchers in education and philosophy of science, often have difficulty in making a choice of what to teach about NOS. It is suggested that a representative variation with regard to the traditional NOS claims may be appropriate for a genuine understanding of the subject. In that, using the discipline-culture structure of the fundamental theories of physics and addressing the plurality of scientific methods may be helpful in the actual teaching and learning of NOS. (shrink)
Abstract In this paper I present a short outline of an Indicativity Theory of Knowledge, for the cases of Perceptual Knowledge and Knowledge by Memory. I explain the main rationale for a token-indicativity approach, and how it is fleshed out precisely in terms of chances. I elaborate on the account of the value of knowledge it provides, and what that value is. I explain why, given the rationale of conceiving Knowledge as token indicativity, separate sub-accounts in terms of chances should (...) be extracted for the different modes of Knowledge, elaborating on the common core of high token-indicativity. In the main section that outlines the account of Perceptual Knowledge, the main Indicativity condition is presented, as are the main condition of in what sense high token indicativity should yields high chance, the important Discriminability condition, and its associated Contrast Class. (shrink)
The problem facing us in this paper is that of how to analyze the notion of causal relevance. This is the inverse relation of causal dependence: A is causally irrelevant to C iff C is causally independent of A. As an example of causal relevance, consider: Example 1: A - The American astronaut on Mir scratched his left ear exactly an hour ago B - I am writing this paper right now. Intuitively, A was not causally relevant to B. It (...) is this kind of intuition that I’ll mostly be relying on when analyzing the notion of causal relevance. (shrink)
In this paper I start by briefly presenting an analysis of token cause and of token causal relevance that I developed elsewhere, and then apply it to the famous thirsty traveler riddle. One general outcome of the analysis of causal relevance employed here is that in preemption cases (early or late) the preempted cause is not a cause since it is causally irrelevant to the effect. I consider several variations of the thirsty traveler riddle. In the first variation the first (...) enemy emptied the canteen and the second enemy threw it away. On this variation, the act of neither enemy comes out, on the analysis employed here, as causally relevant to, and thus not as a cause of, the fact that the traveler died, but the conjunction of the two acts is a cause of it. This version is a case of mutual preemption. I argue that it has the same structure as the voting paradox, which thus has an analogous solution. In the standard version, in which the first enemy added poison to the water in the traveler's canteen, the act of the second enemy (who threw the canteen away) comes out, on the analysis used here, as causally relevant to and as a cause of the fact that the traveler died, but the act of the first enemy comes out as neither. I also make a comparison with Lewis' accounts, and discuss alternative treatments of the puzzle such as those of Hart and Honore and of Gavison, Margalit, and Ullmann-Margalit. (shrink)