The paper rst lays out a non-congurational approach to scope ambiguities in which scope dependencies are treated as dependencies between evaluation indices of variables. The notions of dependent and domain variables are dened naturally in this framework. These concepts are then used to account for the distribution and interpretation of determiner reduplication in Hungarian, a phenomenon that has not received much attention so far.1 1. Introduction This paper contributes to the study of the semantics of indenites in natural language (...) by introducing on the scene a new type of indenite, called dependent. We meet it in Hungarian, where one may reduplicate certain determiners, as illustrated in [1]-[3]. (shrink)

The paper proposes a novel solution to the problem of scope posed by natural language indefinites that captures both the difference in scopal freedom between indefinites and bona fide quantifiers and the syntactic sensitivity that the scope of indefinites does nevertheless exhibit. Following the main insight of choice functional approaches, we connect the special scopal properties of indefinites to the fact that their semantics can be stated in terms of choosing a suitable witness. This is in (...) contrast to bona fide quantifiers, the semantics of which crucially involves relations between sets of entities. We provide empirical arguments that this insight should not be captured by adding choice/Skolem functions to classical first-order logic, but in a semantics that follows Independence-Friendly Logic, in which scopal relations involving existentials are part of the recursive definition of truth and satisfaction. These scopal relations are resolved automatically as part of the interpretation of existentials. Additional support for this approach is provided by dependent indefinites, a cross-linguistically common class of special indefinites that can be straightforwardly analyzed in our semantic framework. (shrink)

According to Madhyamaka Buddhist philosophers, everything depends for its existence on something else. But what would a world devoid of fundamentalia look like? In this paper, I argue that the anti-foundationalist “neither-one-nor-many argument” of the Indian Mādhyamika Śrīgupta commits him to a position I call “metaphysical indefinitism.” I demonstrate how this view follows from Śrīgupta’s rejection of mereological simples and ontologically independent being, when understood in light of his account of conventional reality. Contra recent claims in the secondary literature, I (...) clarify how the Madhyamaka metaphysical dependence structure is not a straightforward infinitism since it does not honor strict asymmetry or transitivity. Instead, its dependence relations are irreflexive and extendable, admitting of dependence chains of indefinite (though not actually infinite) length and dependence loops of non-zero length. Yet, the flexible ontology of Śrīgupta's Madhyamaka can accommodate a contextualist account of asymmetry and support a revisable theory of conventional truth, delivering significant payoffs for the view, including the capacity to accommodate developments in scientific explanation. (shrink)

Of all the cases made against classical logic, Michael Dummett's is the most deeply considered. Issuing from a systematic and original conception of the discipline, it constitutes one of the most distinctive achievements of twentieth century British philosophy. Although Dummett builds on the work of Brouwer and Heyting, he provides the case against classical logic with a new, explicit and general foundation in the philosophy of language. Dummett's central arguments, widely celebrated if not widely endorsed, concern the implications of the (...) relation between meaning and use for both the inference rules that govern logical connectives and the relation between truth and its recognition. It is less often noted that Dummett has a further argument against classical logic, one based on the semantic and set-theoretic paradoxes. That is the topic of this paper. (shrink)

It is widely assumed that the scope of indefinites is island insensitive, i.e., that, generally, an indefinite inside of a syntactic island, such as an adjunct clause, is capable of taking scope outside of that island. This paper challenges this assumption by studying the scope behaviour of the Spanish plural indefinite algunos ’). It presents an experimental study that shows that the scope of algunos is not free and depends on its syntactic environment, at least in the dialect of (...) Spanish studied here. The paper discusses some of the implications of the study for current theories of indefinite scope: it points out the problems that choice functions and singleton indefinites have with the Spanish data, and it also discusses the implications for Schwarzschild's solution to the so-called ‘Donald Duck’ problem. (shrink)

Quantum mechanics has recently indicated that, at the fundamental level, temporal order is not fixed. This phenomenon, termed Indefinite Causal Order, is yet to receive metaphysical or theological engagement. We examine Indefinite Causal Order, particularly as it emerges in a 2018 photonic experiment. In this experiment, two operations A and B were shown to be in a superposition with regard to their causal order. Essentially, time, intuitively understood as fixed, flowing, and fundamental, becomes fuzzy. We argue that if Indefinite Causal (...) Order is true, this is good evidence in favor of a B‐theory of time, though such a B‐theory requires modification. We then turn to theology, suggesting that a B‐theoretic temporal ontology invites serious reconsideration of the doctrine of salvation. This paper concludes that the best explanation for salvation given a B‐theory is mind‐dependent salvific becoming, a type of psychological soteriological change that occurs through downward causation. (shrink)

Some patients who are dependent on extracorporeal membrane oxygenation (ECMO) are alert and retain capacity to participate in decision-making, including decisions regarding whether to continue life...

Patrick Grim has put forward a set theoretical argument purporting to prove that omniscience is an inconsistent concept and a model theoretical argument for the claim that we cannot even consistently define omniscience. The former relies on the fact that the class of all truths seems to be an inconsistent multiplicity (or a proper class, a class that is not a set); the latter is based on the difficulty of quantifying over classes that are not sets. We first address the (...) set theoretical argument and make explicit some ways in which it depends on mathematical Platonism. Then we sketch a non Platonistic account of inconsistent multiplicities, based on the notion of indefinite extensibility, and show how Grim’s set theoretical argument could fail to be conclusive in such a context. Finally, we confront Grim’s model theoretical argument suggesting a way to define a being as omniscient without quantifying over any inconsistent multiplicity. (shrink)

According to the so-called “Folk Theorem” for repeated games, stable cooperative relations can be sustained in a Prisoner’s Dilemma if the game is repeated an indefinite number of times. This result depends on the possibility of applying strategies that are based on reciprocity, i.e., strategies that reward cooperation with subsequent cooperation and punish defectionwith subsequent defection. If future interactions are sufficiently important, i.e., if the discount rate is relatively small, each agent may be motivated to cooperate by fear of retaliation (...) in the future. For finite games, however, where the number of plays is known beforehand, there is a backward induction argument showing that rational agents will not be able to achieve cooperation. On behalf of the Hobbesian “Foole”, who cannot see any advantage in cooperation, Gregory Kavka (1983, 1986) has presented an argument that significantly extends the range of the backward induction argument. He shows that, for the backward induction argument to be effective, it is not necessary that the precise number of future interactions be known. It is sufficient that there is a known definite upper bound on the number of interactions. A similar argument is developed by John W. Carroll (1987). We will here question the assumption of a known upper bound. When the assumption is made precise in the way needed for the argument to go through, its apparent plausibility evaporates. We then offer a reformulation of the argument, based on weaker, and more plausible, assumptions. (shrink)

This paper argues that, given a simple [DP VP] sentence, the availability of a collective interpretation crucially depends on the syntactic and semantic properties of the subject DP, specifically the presence versus absence of a pluralizing function that makes the collective interpretation available. In support of my claim, I present Lebanese Arabic and Western Armenian examples in which an indefinite DP contains a cardinal numeral and there is no overt distributivity operator but the interpretation of the sentence is nevertheless obligatorily (...) distributive, regardless of the predicate. I show that neither a distributivity operator within the DP nor one on the predicate can explain this strictly distributive interpretation. Instead, I argue that in order to allow a collective interpretation, an indefinite DP must denote a quantifier over pluralities, a condition that is not always met in numeral-containing indefinite DPs. While the claims in this paper are based primarily on observations from Lebanese Arabic and Western Armenian, because both are morphologically rich languages, the fact that this constraint is operative in these two unrelated languages, in addition to striking similarities to the Russian gender system, suggest that it is an inherent property of DPs crosslinguistically. (shrink)

This paper deals with the exceptions-tolerance property of generic sentences with indefinite singular and bare plural subjects (IS and BP generics, respectively) and with the way this property is connected to some well-known observations about felicity differences between the two types of generics (e.g. Lawler's 1973, Madrigals are popular vs. #A madrigal is popular). I show that whereas both IS and BP generics tolerate exceptional and contextually irrelevant individuals and situations in a strikingly similar way, which indicates the existence of (...) a basically equivalent tolerance mechanism, there is also a difference between them, unnoticed so far, which concerns the degree to which the properties of the legitimate exceptions can be characterized in advance. Following claims in Greenberg (2003), I argue that both this newly observed difference as well as the traditional felicity differences result from an underlying contrast in the type of ‘non-accidentalness’ expressed by the two types of generic sentences, and more formally, in the accessibility relations that their generic quantifier (Gen) is compatible with. To capture the new difference in tolerance of exceptions, I develop an improved version of the exceptions-tolerance mechanism for generic sentences suggested in Kadmon & Landman (1993), namely, a restriction on the set of individuals and situations quantified by Gen, which is partially vague to two different degrees using supervaluationist methods. The different degrees of vagueness in this restriction are shown to be systematically dependent on the two types of accessibility relations that IS and BP generics are compatible with, which are redefined as precise and vague restrictions on the generic quantification over worlds. (shrink)

The paper proposes a novel account to the problem of exceptional scope (ES) of (in)definites, e.g. the widest and intermediate scope readings of the sentence Every student of mine read every poem that a famous Romanian poet wrote before World War II. We propose that ES readings are available when the sentence is interpreted as anaphoric to quantificational domains and quantificational dependencies introduced in the previous discourse. For example, the two every quantifiers and the indefinite elaborate on the sets of (...) individuals and the correlations between them introduced by a previous sentence like Every student chose a poet and read every poem written by him (for the intermediate scope reading) or a sentence like Every student chose a poet - the same poet - and read every poem written by him (for the widest scope reading). Our account, formulated within a compositional dynamic system couched in classical type logic, relies on two independently motivated assumptions: (a) the discourse context stores not only (sets of) individuals, but also quantificational dependencies between them, and (b) quantifier domains are always contextually restricted. Under this analysis, (in)definites are unambiguous and we do not resort to movement or special storage mechanisms, nor do weposit special choice-functional variables. (shrink)

A study on minimalist syntax develops an empirical argument for a crash-proof computational system. A crash-proof system is obtained if syntactic dependencies are strictly local (i.e. there is no long-distance Agree). Apparent long-distance dependencies turn out to be the outcome of a recursive chain on local complex dependencies. This framework allows for novel analyses of quirky subjects in Icelandic and Spanish, indefinite SE in Spanish and different types of expletive constructions in English, French, German, Spanish, Italian, and Icelandic.

This paper contributes to the semantic typology of dependent indefinites, by accounting for the distribution and interpretation of the Romanian indefinite vreun. It is shown that its occurrences are restricted to negative polarity and a subset of modal contexts. More specifically, the study of its behavior in intensional environments reveals that vreun is systematically incompatible with non-epistemic operators, a restriction we capture by proposing a novel empirical generalization (‘the epistemic constraint’). To account for the observed pattern, we adopt (...) the unitary approach to polarity in Chierchia (Logic in Grammar: polarity, free choice and intervention, 2013a; in: Fălăuş (ed.) Alternatives in semantics, 2013b) and derive the properties of vreun from its obligatory association with alternatives. Its distributional restrictions are argued to follow from the interplay between the types of alternatives it activates (scalar and subdomain alternatives), the way these alternatives are factored into meaning (via an independently motivated mechanism of exhaustification) and the lexical semantics of the operators in the context of occurrence. We propose that the epistemic constraint arises from the lexicalization of an inference (anti-total variation) that non-epistemic operators can never satisfy. (shrink)

The paper proposes the first unified account of deictic/sentence-external and sentence-internal readings of singular different . The empirical motivation for such an account is provided by a cross-linguistic survey and an analysis of the differences in distribution and interpretation between singular different , plural different and same (singular or plural) in English. The main proposal is that distributive quantification temporarily makes available two discourse referents within its nuclear scope, the values of which are required by sentence-internal uses of singular different (...) to be distinct, much as its deictic uses require the values of two discourse referents to be distinct. Thus, we take sentence-internal readings to be a form of ‘association with distributivity’ that is similar to association with focus. The contrast between singular different , plural different and same is explained in terms of several kinds of quantificational distributors that license their internal readings. The analysis is executed in a stack-based dynamic system couched in type logic, so we get compositionality in the usual Montagovian way. Quantificational subordination and dependent indefinites in various languages provide additional motivation for the account. Investigating the connections between items with sentence-internal readings and the quantificational licensors of these readings opens up a larger project of formally investigating (i) the typology of quantificational distributors and distributivity-dependent items and (ii) the fine-grained contexts of evaluation needed to capture this typological variation. (shrink)

Crosslinguistically, questions frequently make crucial use of morphosyntactic elements which also occur outside of questions. Chief among these are focus, disjunctions, and wh-words with indefinite semantics. This paper provides a compositional account of the semantics of wh-, alternative, and polar questions in Yucatec Maya (YM), which are composed primarily of these elements. Key to the account is a theory of disjunctions and indefinites (extending work by others) which recognizes the inherently inquisitive nature of these elements. While disjunctions and (...) class='Hi'>indefinites are inquisitive, they differ from questions since they are also truth-conditionally informative. Compositionally, then, the role of focus in YM questions is to presuppose the informative component of an indefinite wh-word or disjunction, rendering the inquisitive component the question’s only new contribution to the discourse. In addition to deriving question denotations compositionally, the account also captures a potentially surprising fact: focused disjunctions in YM can function as either questions or assertions, depending solely on the discourse context. (shrink)

Bare plurals (dogs) behave in ways that quantified plurals (some dogs) do not. For instance, while the sentence John owns dogs implies that John owns more than one dog, its negation John does not own dogs does not mean “John does not own more than one dog”, but rather “John does not own a dog”. A second puzzling behavior is known as the dependent plural reading; when in the scope of another plural, the ‘more than one’ meaning of the (...) plural is not distributed over, but the existential force of the plural is. For example, My friends attend good schools requires that each of my friends attend one good school, not more, while at the same time being inappropriate if all my friends attend the same school. This paper shows that both these phenomena, and others, arise from the same cause. Namely, the plural noun itself does not assert ‘more than one’, but rather the plural denotes a predicate that is number neutral (unspecified for cardinality). The ‘more than one’ meaning arises as an scalar implicature, relying on the scalar relationship between the bare plural and its singular alternative, and calculated in a sub-sentential domain; namely, before existential closure of the event variable. Finally, implications of this analysis will be discussed for the analysis of the quantified noun phrases that interact with bare plurals, such as indefinite numeral DPs (three boys), and singular universals (every boy). (shrink)

In The Dynamics of Meaning , Gennaro Chierchia tackles central issues in dynamic semantics and extends the general framework. Chapter 1 introduces the notion of dynamic semantics and discusses in detail the phenomena that have been used to motivate it, such as "donkey" sentences and adverbs of quantification. The second chapter explores in greater depth the interpretation of indefinites and issues related to presuppositions of uniqueness and the "E-type strategy." In Chapter 3, Chierchia extends the dynamic approach to the (...) domain of syntactic theory, considering a range of empirical problems that includes backwards anaphora, reconstruction effects, and weak crossover. The final chapter develops the formal system of dynamic semantics to deal with central issues of definites and presupposition. Chierchia shows that an approach based on a principled enrichment of the mechanisms dealing with meaning is to be preferred on empirical grounds over approaches that depend on an enrichment of the syntactic apparatus. Dynamics of Meaning illustrates how seemingly abstract stances on the nature of meaning can have significant and far-reaching linguistic consequences, leading to the detection of new facts and influencing our understanding of the syntax/semantics/pragmatics interface. (shrink)

Introduction The mainstream view in philosophy of language is that sentence meaning determines truth-conditions. A corollary is that the truth or falsity of an utterance depends only on what words mean and how the world is arranged. Although several prominent philosophers (Searle, Travis, Recanati, Moravcsik) have challenged this view, it has proven hard to dislodge. The alternative view holds that meaning underdetermines truth-conditions. What is expressed by the utterance of a sentence in a context goes beyond what is encoded in (...) the sentence itself. Truth-conditional content depends on an indefinite number of unstated background assumptions, not all of which can be made explicit. A change in background assumptions can change truth-conditions, even bracketing disambiguation and reference assignment. That is, even after disambiguating any ambiguous words in a sentence and assigning semantic values to any indexical expressions in the sentence, truth-conditions may vary with variations in the background. (shrink)

Consideration of the counting and reidentification of particulars leads naturally enough to the orthodox doctrine that, “on pain of indefiniteness,” an identity statement in some way involves or presupposes a general term or “covering concept”: i.e., that the principium individuationis or criterion of identity implied depends upon the kind of thing in question. Thus it is said that an auditor understands the question whether A is the same as B only in so far as he knows, however informally or implicitly, (...) the answer to the supplementary question, “The same what?”. (shrink)

The received view about meteorological predicates like ‘rain’ is that they carry an argument slot for a location which can be filled explicitly or implicitly. The view assumes that ‘rain’, in the absence of an explicit location, demands that the context provide a specific location. In an earlier article in this journal, I provided a counter-example, viz. a context in which ‘it is raining’ receives a location-indefinite interpretation. On the basis of that example, I argued that when there is tacit (...) references to a location, it takes place for pragmatic reasons and casts no light on the semantics of meteorological predicates. Since then, several authors have reanalysed the counter-example, so as to make it compatible with the standard view. I discuss those attempts and argue that my account is superior. (shrink)

This paper revisits some foundational questions concerning the abstract representation of a discourse context. The context of a conversation is represented by a body of information that is presumed to be shared by the participants in the conversation – the information that the speaker presupposes a point at which a speech act is interpreted. This notion is designed to represent both the information on which context-dependent speech acts depend, and the situation that speech acts are designed to affect, and (...) so to be a representation of context that is appropriate for explaining the interaction of context and the contents expressed in them. After reviewing the motivating ideas and the outlines of the apparatus, the paper responds to a criticism of the framework, and considers the way it can help to clarify some phenomena concerning pronouns with indefinite antecedents. (shrink)

In the first section of the chapter, I scrutinize Howard Stein’s 1991 definition of a transitive becoming relation that is Lorentz invariant. I argue first that Stein’s analysis gives few clues regarding the required characteristics of the relation complementary to his becoming—i.e. the relation of indefiniteness. It turns out that this relation cannot satisfy the condition of transitivity, and this fact can force us to reconsider the transitivity requirement as applied to the relation of becoming. I argue that the relation (...) of becoming need not be transitive, as long as it satisfies the weaker condition of “cumulativity”: for a given observer the area of the events that have become real should not diminish as time progresses. I show that there are actually two relations of becoming that meet this weakened condition: Stein’s (transitive) relation of causal past connectibility and the (non-transitive) relation that is the logical complement of the future causal connectibility. In the second part of the chapter I defend Stein’s notion of temporal becoming against the attack that appeals to quantum-mechanical non-locality. I critically evaluate the argument given by Mauro Dorato (1996) that purports to show that space-like separated measurements done on the EPR system have to be mutually determinate. Finally, in order to account for the truth of counterfactual statements that link the space-like separated outcomes, I propose a dynamic conception of becoming, according to which the sphere of determinate events as of a given point may depend on the physical phenomena transpiring at this point. (shrink)

In this article, we take into consideration two semantics of the future tense: linearism, according to which future-tense sentences are interpreted on a single history, and universalism, according to which they are evaluated by universally quantifying on the plurality of future histories that radiate from the present instant. Specifically, we focus on a objection advanced against universalism: if universalism were correct semantics of will, negated future-tense sentences of natural language should have two readings, depending on the scope of negation with (...) respect to the universal quantifier on histories. However, since natural language does not show this difference, one may conclude that there is no universal quantifier in the interpretation of these sentences. We show that this conclusion is premature. First, will has clear scope interactions with indefinite nouns phrases, contrary to what linearism predicts. Second, it is possible to extend the treatment of vague predicates as partial predicates to will: Since partial predicates have no scope interactions with negation, this can account for the scopelessness of will. The partiality of truth conditions is not restricted to will but also pertains to counterfactuals and generics and probably is part of a general tendency to maximize contraries. (shrink)

The paper sketches the place of dynamic semantics within a broader picture of developments in philosophical and linguistic theories of meaning. Some basic concepts of dynamic semantics are illustrated by means of a detailed analysis of anaphoric definite and indefinite descriptions, which are treated as contextually dependent quantificational expressions. It is shown how a dynamic view sheds new light on the contextual nature of interpretation, on the difference between monologue and dialogue, and on the interplay between direct and indirect (...) information. (shrink)

Relativists about knowledge ascriptions think that whether a particular use of a knowledge-ascribing sentence, e.g., “Keith knows that the bank is open” is true depends on the epistemic standards at play in the assessor’s context—viz., the context in which the knowledge ascription is being as- sessed for truth or falsity. Given that the very same knowledge-ascription can be assessed for truth or falsity from indefinitely many perspectives, relativism has a striking consequence. When I ascribe knowledge to someone (e.g., when I (...) say that, at a particular time, “Keith knows that the bank is open”), what I’ve said does not get a truth-value absolutely, but only relatively. If this semantic thesis about the word “knows” and its cognates is true, what implications would this have for epistemology, the philosophical theory of knowledge? e present aim will be to engage with this mostly unexplored question, and then to consider how the epistemological conclusions drawn might bear on the plausibility of a relativist semantics for “knows”. (shrink)

Metaphysical foundationalists argue that without fundamental facts, we cannot explain why there exist any dependent facts at all. Thus, metaphysical infinitism, the view that chains of ground can descend indefinitely without ever terminating in a level of fundamental facts, allegedly exhibits a kind of explanatory failure. I examine this argument and conclude that foundationalists have failed to show that infinitism exhibits explanatory failure. I argue that explaining the existence of dependent facts in terms of further dependent facts (...) ad infinitum is unproblematic by arguing for the plausibility of a ground-theoretic version of the Hume-Edwards Principle, which states that if each fact in a plurality of facts has a ground, then the plurality itself has a ground. (shrink)

The exclusive component of unembedded disjunctions is standardly derived as a conversational implicature by assuming that or forms a lexical scale with and. It is well known, however, that this assumption does not suffice to determine the required scalar competitors of disjunctions with more than two atomic disjuncts (McCawley, Everything that linguists have always wanted to know about logic* (But were ashamed to ask). Chicago University Press, Chicago, 1993, p. 324; Simons, “Or”: Issues in the semantics and pragmatics of disjunction. (...) Ph.D. thesis, Cornell University, Ithaca, NY, 1998). To solve this, Sauerland (Linguist Philos 27(3): 367–391, 2004) assumes that or forms a lexical scale with two otherwise unattested silent connectives ( ${\mathbb{L}}$ and ${\mathbb{R}}$ ) that retrieve the left and right terms of a disjunction. A number of recent works have proposed an Alternative Semantics for indefinites and disjunction to account for their interaction with modals and other propositional operators (Kratzer and Shimoyama, In: Otsu Y (ed) The Proceedings of the Third Tokyo Conference on Psycholinguistics. Hituzi Syobo, Tokyo, pp. 1–25, 2002; Aloni, In: Weisgerber M (ed) Proceedings of the Conference “SuB7—Sinn und Bedeutung”. Arbeitspapier Nr. 114. Konstanz, pp. 28–37, 2003; Simons, Nat Lang Semantics 13: 271–316, 2005; Alonso-Ovalle, Disjunction in alternative semantics. Ph.D. thesis, University of Massachusetts, Amherst, MA, 2006). We note that the McCawley–Simons problem does not arise in an Alternative Semantics, if we assume that the set of pragmatic competitors to a disjunction is the closure under intersection of the set of propositions that it denotes. An adaptation of the strengthening mechanism presented in Fox (In: Sauerland U, Stateva P (eds) Presupposition and implicature in compositional semantics. MacMillan, Palgrave, pp. 71–120, 2007) allows for the derivation of the exclusive component of disjunctions with more than two atomic disjuncts without having to rely on the ${\mathbb{L}}$ and ${\mathbb{R}}$ operators. The proposal extends to the case of disjunctions with logically dependent disjuncts. (shrink)

The science of operations research is one of the modern sciences that have made a great revolution in all areas of life through the methods provided by it, suitable and appropriate to solve most of the problems that were facing researchers, scholars and those interested in the development of societies, and the most beneficiaries of this science were companies and institutions that are looking for scientific methods that help them manage their work so that they achieve the greatest profit and (...) the lowest cost, and one of the important methods that have been used in the management of companies we offer in this research two methods, Dynamic programming method. This method has been used in many practical matters and helped decision-makers in companies to achieve a maximum profit and less cost by formulating the reality of the state of the company and the data provided by decision-makers with a dynamic mathematical model that is solved using methods of solving dynamic models and we will provide in this research an example of this through the issue of choosing the optimal investment for the budget of a company so that it achieves a maximum profit, and the method of programming with integers: the method that provided these companies with solutions with integer values suitable for the nature of its work, through the use of the binary integer in the formulation of the appropriate mathematical model on the one hand, and on the other hand, the use of the binary integer variable helped to convert some nonlinear models that lead to some practical problems into linear models, and it should be noted here that in the previous two methods there is something indeterminable because we must make a decision in choosing or not choosing something, but the optimal solution that we will get remains A specific value because we are building the mathematical model for any realistic issue through the data provided by those responsible for the work and these data are calculated quantities and therefore they are uncertain values because their validity depends on the circumstances surrounding the work environment, they may be exposed to increase or decrease, and therefore the optimal solution on which the company will base its decision is suitable for specific values and any change in them can cause the company an uncalculated loss, so in this research we will use the concepts of neutrosophic science, the branch of science founded by the American scientist Florentin Smarandache in 1995 based on his belief that there is no absolute truth, a science that is interested in the study of ideas and concepts that are neither true nor false, but just in between, and we will take the data (calculated quantities) neutrosophic values that are specified or unspecified values are any set close to the calculated quantities, then the resulting mathematical model is a neutrosophic model and the optimal solution has neutrosophic values and thanks to the indefinite uncertainty that these values have, companies from the development of appropriate plans for all circumstances and thus achieve the greatest profit and the lowest cost, and we will clarify the above through two issues, the issue of optimal designation of a warehouse site, which we will formulate the mathematical model of using the neutrosophic integer programming method - and the issue of capital budget, which we will present in two different forms, we use in the first form the neutrosophic integer programming method and in the second the neutrosophic dynamic programming method. (shrink)

A prominent Thomistic cosmological argument maintains that an infinite regress of causes, which exhibits a certain pattern of ontological dependence among its members, would be vicious and so must terminate in a first member. Interestingly, Jonathan Schaffer offers a similar argument in the contemporary grounding literature for the view called metaphysical foundationalism. I consider the striking similarities between both arguments and conclude that both are unsuccessful for the same reason. I argue this negative result gives us indirect reason to consider (...) metaphysical infinitism as a genuine possibility, the view that chains of ontological dependence or ground can descend indefinitely. (shrink)

Weight systems on chord diagrams play a central role in knot theory and Chern-Simons theory; and more recently in stringy quantum gravity. We highlight that the noncommutative algebra of horizontal chord diagrams is canonically a star-algebra, and ask which weight systems are positive with respect to this structure; hence we ask: Which weight systems are quantum states, if horizontal chord diagrams are quantum observables? We observe that the fundamental gl(n)-weight systems on horizontal chord diagrams with N strands may be identified (...) with the Cayley distance kernel at inverse temperature beta=ln(n) on the symmetric group on N elements. In contrast to related kernels like the Mallows kernel, the positivity of the Cayley distance kernel had remained open. We characterize its phases of indefinite, semi-definite and definite positivity, in dependence of the inverse temperature beta; and we prove that the Cayley distance kernel is positive (semi-)definite at beta=ln(n) for all n=1,2,3,... In particular, this proves that all fundamental gl(n)-weight systems are quantum states, and hence so are all their convex combinations. We close with briefly recalling how, under our "Hypothesis H", this result impacts on the identification of bound states of multiple M5-branes. (shrink)

It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive diagnoses of (...) the breakdown than do others. The paper concludes with some morals about the nature of validity and about a possible alternative to the idea that mathematical theories are indefinitely extensible. (shrink)

Summary Verbs of creation (create, make, paint) are not transparent. The object created does not exist during the event time but only thereafter. We may call this type of opacity temporal opacity. I is to be distinguished from modal opacity, which is found in verbs like owe or seek. (Dowty, 1979) offers two analyses of creation verbs. One analysis predicts that no object of the sort created exists before the time of the creation. The other analysis says that the object (...) exists throughout the act of creation. I investigate three theories: Theory I says that no object of the sort created and which is caused by the very act of creation exists before the creation. In this theory, verbs of creation must embed a property. Theory II can regard the indefinite object of a creation verb as a quantifier and gives it wide scope with respect to the verb. The theory has to make sure that the objects quantified over exist only after the event. While Theory I and II start from the assumption that the extension of all nouns depend on time, Theory III says that Individual Level predicates do not depend on time. This ontology will enable us to treat verbs of creation as first order relations. The theory will entail that a picture does not mean the same as there is a picture. The paper discusses various approaches to the problem: Krifka, Parsons, Landman, Kratzer and Zucchi. (shrink)

Perception purports to help you gain knowledge of the world even if the world is not the way you expected it to be. Perception also purports to be an independent tribunal against which you can test your beliefs. It is natural to think that in order to serve these and other central functions, perceptual representations must not causally depend on your prior beliefs and expectations. In this paper, I clarify and then argue against the natural thought above. All perceptual systems (...) must solve an under-determination problem: the sensory data they receive could be caused by indefinitely many arrangements of distal objects and properties. Using a Bayesian approach to perceptual processing, I argue that in order to solve the under-determination problem, perceptual capacities must rely on prior beliefs or expectations of some kind. I then argue that perceptual states or processes can help ground knowledge of the world whether the ‘beliefs’ necessary for perceptual processing are encoded as sub-personal states within a perceptual system or cognitive states, such as person-level beliefs. My argument has two main parts. First, I give a preliminary argument that cognitive influence on perception can be appropriate, and I respond to three lines of objection. Second, I argue that cognitively influenced perceptual states can be instances of seeing that p, which makes the relevant states well suited to help ground knowledge that p. I conclude that a cognitively penetrated perceptual state or process can help ground knowledge under some circumstances. (shrink)

Everything around us is made of 'stuff', from planets, to books, to our own bodies. Whatever it is, we call it matter or material substance. It is solid; it has mass. But what is matter, exactly? We are taught in school that matter is not continuous, but discrete. As a few of the philosophers of ancient Greece once speculated, nearly two and a half thousand years ago, matter comes in 'lumps', and science has relentlessly peeled away successive layers of matter (...) to reveal its ultimate constituents.Surely, we can't keep doing this indefinitely. We imagine that we should eventually run up against some kind of ultimately fundamental, indivisible type of stuff, the building blocks from which everything in the Universe is made. The English physicist Paul Dirac called this 'the dream of philosophers'. But science has discovered that the foundations of our Universe are not as solid or as certain and dependable as we might have once imagined. They are instead built from ghosts and phantoms, of a peculiar quantum kind. And, at some point on this exciting journey of scientific discovery, we lost our grip on the reassuringly familiar concept of mass.How did this happen? How did the answers to our questions become so complicated and so difficult to comprehend? In Mass Jim Baggott explains how we come to find ourselves here, confronted by a very different understanding of the nature of matter, the origin of mass, and its implications for our understanding of the material world. Ranging from the Greek philosophers Leucippus and Democritus, and their theories of atoms and void, to the development of quantum field theory and the discovery of a Higgs boson-like particle, he explores our changing understanding of the nature of matter, and the fundamental related concept of mass. (shrink)

After an undergraduate degree with a major in mathematics, I turned to philosophy—in part because philosophy had all the interest of math (and logic) plus an indefinitely wide range of subject matter. I began philosophy at an intersection of metaphysics and philosophy of science. My dissertation, Ontological and Linguistic Aspects of Temporal Becoming, was on the philosophy of time. A convinced physicalist, I defended the idea that past, present and future (the A-series) are merely “mind-dependent.” I spent a year (...) as a Mellon postdoctoral fellow at the University of Pittsburgh, working mainly with Adolf Grünbaum, who was very generous to me with his time. Other members of the philosophical community in Pittsburgh suggested that there was no philosophical interest in nowness; the word ‘now’ exhausted whatever there was of real interest concerning the status of the present. I therefore turned my attention from the status of the present (nowness) to the word ‘now’. (shrink)

The goal of synthetic biology is to create artificial organisms. To achieve this it is essential to understand what life is. Metabolism-replacement systems, or (M, R)-systems, constitute a theory of life developed by Robert Rosen, characterized in the statement that organisms are closed to efficient causation, which means that they must themselves produce all the catalysts they need. This theory overlaps in part with other current theories, including autopoiesis, the chemoton, and autocatalytic sets, all of them invoking some idea of (...) closure. A simple model of an (M, R)-system has been implemented in the computer, and behaves in ways that may shed light on the requirements for a prebiotic self-organizing system. In addition to a trivial steady state in which nothing happens, it can establish a non-trivial steady state in which all intermediates have finite concentrations, with their rates of degradation balanced by their rates of synthesis. The system can be regenerated from the set of food components plus a single intermediate, and maintain itself in that state indefinitely, despite continuous degradation. At the very low compartment volumes that may have existed in prebiotic conditions, for example in cavities in minerals, or in micelles formed by simple amphiphiles, statistical fluctuations in the numbers of molecules need to be taken into account. With the stochastic approach there is no non-trivial steady state in strict mathematical terms, because the system will always collapse to the trivial state after sufficient time. However, the average time before collapse is so long for volumes greater than $10^{-19}\;{\textsc{l}}$ (much smaller than the volume of the order of $10^{-15}\;{\textsc{l}}$ for a typical bacterial cell) that for practical purposes the self-maintaining state of non-null concentrations becomes significant, recalling the situation of bistability that is observed in deterministic analysis. In turn, there exists a minimum size below which the self-organizing system cannot maintain itself on chemically relevant time scales. The value of the critical volume depends on the particular concentrations and rate constants assumed, but the principle could apply generally. (shrink)

ASL can express plurals by repeating a noun, in an unpunctuated fashion, in different parts of signing space. We argue that this construction may come with a rich iconic component: the geometric arrangement of the repetitions provides information about the arrangement of the denoted plurality; in addition, the number and speed of the repetitions provide information about the size of the denoted plurality. Interestingly, the shape of the repetitions may introduce a new singular discourse referent when a vertex can be (...) inferred to denote a singular object. Thus one may point towards the first or last iteration of a horizontal repetition of BOOK to denote the left- or right-edge of the corresponding row. This yields a remarkable interaction between iconic semantics and standard logical semantics. We show that our analysis extends to ‘punctuated’ repetitions, which involve clearly individuated iterations of a singular noun. While these may initially look like coordinated indefinites, they are better handled by the same iconic framework as plural, unpunctuated repetitions. Some repetition-based mass terms also give rise to iconic effects, and to different readings depending on whether the repetition is continuous, unpunctuated, or punctuated. Our analysis highlights the need for a formal semantics with iconicity to study the integration of such iconic and logical conditions. It also raises a question: can similar facts be found in spoken language when gestures are taken into account? We suggest that several effects can be replicated, especially when one considers examples involving ‘pro-speech gestures’. (shrink)

Socrates’ claim that pleasure is a γένεσις unifies the Philebus’ conception of pleasure. Close examination of the passage reveals an emphasis on metaphysical-normative dependency in γένεσις. Seeds for such an emphasis were sown in the dialogue’s earlier discussion of μεικτά, thus linking the γένεσις claim to Philebus’ description of pleasure as ἄπειρον. False pleasures illustrate the radical dependency of pleasure on outside determinants. I end tying together the Philebus’ three descriptions of pleasure: restoration, indefinite, and γένεσις.

How do-or how should-we parse the world into kinds of things? Going back at least to Plato, most philosophers have done so with respect to some notion or other of natural kinds. And many analyses of natural kinds have been essentialistic-that is defining those kinds with respect to universals, or some set of intrinsic properties, or necessary and sufficient conditions. And there's a long-standing dispute between thinkers who regard scientific categories as natural kinds with essential properties fixed by nature-those that (...) "cut nature at its joints"-and thinkers who maintain that our classifications and categories have no essence and instead merely reflect human interests and values. A typical example of the former would be "having a mass of 1.7 × 10-27," and examples of the latter would be the categories of "ADHD," "race," or "child abuse." Khalidi aims for an epistemic, naturalistic, non-essentialist, account of natural kinds, one which comfortably embraces not only the usual candidates favored by essentialists (e.g., elementary particles, chemical elements, biological species), but also categories in the social and behavioral sciences. Drawing on cases from many scientific fields, from fluid mechanics and polymer science to virology and psychiatry, Khalidi argues that "natural kinds are investigative or epistemic kinds, in the sense that they are the categories revealed by our systematic attempts to gain knowledge of nature" (p. 43). Moreover, he claims that natural kinds can be "fuzzy" (i.e. have indefinite boundaries), satisfy epistemic virtues to varying degrees, and be mind-dependent in a way that doesn't detract from their reality or objectivity. Although the book is pitched for a sophisticated and philosophically informed audience (and, needless to say, too complex to be adequately summarized in a brief notice such as this), it's clearly written, nuanced, compellingly argued, and worth the effort for JSE readers curious about the unavoidable metaphysical dimensions of doing science of any kind. (shrink)

Speculation concerning the age of the earth begins with civilisation itself. The creation myths of ancient Egypt and other early cultures were soon expanded into elaborate cosmologies by Indian, Persian and Greek philosophers. Jewish and, more insistently, Christian scholars long believed that the Bible provided an exact chronology beginning with the Creation . Such truncated apocalyptic chronologies were opposed first by Aristotelian advocates of an eternal earth and then by deistic freethinkers who regarded the earth's age as indefinite but immense. (...) As textual scholarship cast doubt upon the literal reliability of Genesis, alternative chronologies arose which depended increasingly upon geological evidence. James Hutton's assertions about the earth's age reflect his awareness of this broader context and define his own important contribution to it. (shrink)

In the future, human destiny may depend on our ethics. In particular, biotechnology and expansion in space can transform life, raising profound questions. Guidance may be found in Life-centered ethics, as biotic ethics that value the basic patterns of organic gene/protein life, and as panbiotic ethics that always seek to expand life. These life-centered principles can be based on scientific insights into the unique place of life in nature, and the biological unity of all life. Belonging to life then implies (...) a human purpose: to safeguard and propagate life. Expansion in space will advance this purpose but will also raise basic questions. Should we expand all life or only intelligent life? Should we aim to create populations of trillions? Should we seed other solar systems? How far can we change but still preserve the human species, and life itself? The future of all life may be in our hands, and it can depend on our guiding ethics whether life will fulfil its full potentials. Given such profound powers, life-centered ethics can best secure future generations. Our descendants may then understand nature more deeply, and seek to extend life indefinitely. In that future, our human existence can find a cosmic purpose. (shrink)

In this paper I present two reasons why generalized skill-selection--a policy whereby skill, education, and economic independence are indefinitely prioritized in immigration decisions--is pro tanto unjust. First, such policies feed into existing biases, exacerbating status harms for low-SES citizens. The claim that we prefer the skilled to the unskilled, the educated to the uneducated, and the financially secure to the insecure is also heard by citizens. And there is considerable overlap between this message and the stereotypes and biases that set (...) their social status. Skill-selection can reinforce these biases, offering state support for the claim that they are less desirable as members of the society. -/- Second, the need for skilled immigrants ordinarily depends upon and reinforces failures of fair equality of opportunity (FEO). According to the dependency thesis, the need for skilled migrants stems from a failure to ensure domestic FEO. Many low-SES residents would desire to work, for example, as doctors or nurses. However, unequal education, as well as poverty and debt, have made such opportunities largely inaccessible. According to the reinforcement thesis, skill-selection disincentivizes the pursuit of FEO. A state that can meet domestic labor needs through less costly immigration policies will be disinclined to pursue programs designed to equalize opportunities for low-SES residents. -/- Generalized skill-selection in high-income countries like the US is, therefore, pro tanto unjust. However, this is not an argument for excluding the skilled. Skilled immigrants can be admitted through other policies—open borders, family-reunification, or a lottery—without the state signaling that the skilled are more desirable or perpetuating failures of FEO. And states can, responding to local emergencies, temporarily select for particular professions without contributing to these injustices. These concerns only arise when skill is generally and indefinitely prioritized. (shrink)

This article contributes to the debate among just war theorists about the ethics of using armed drones in the war on terror. If violence of this kind is to be effectively restrained, it is necessary first to establish an understanding of its nature. Because it is difficult to conceptualize drone-based violence as war, there is concern that such violence is thus not captured by the traditional jus ad bellum framework. Drone strikes probably do not constitute a law enforcement practice, so (...) the peacetime ethics of criminal justice do not apply either. One possible solution is to develop and apply a legitimization framework of jus ad vim in which vim is “force short of war,” although this depends upon a vim–bellum distinction being a sustainable one. Moving beyond discussion of these three alternative concepts of drone-based violence, the article suggests a fourth—vis perpetua —and explores the ethical implications thereof. As a form of violence that presents no physical risk to individual users of force, a program of drone strikes poses a moral problem if it is intended to continue indefinitely, leading to the systematic endangerment of innocents without the eventual promise of peace. (shrink)

Whether God has a knowledge is a controversial issue both philosophy and theology. Does God have a knowledge? If He has, does He know the particulars? When we assume that God knows particulars, is there any change in God’s essence? In the theistic tradition, it is accepted that God is wholly perfect, omniscience, omnipotent and wholly good. Therefore, it is not possible to say that there is a change in God. Because changing is a kind of imperfection. On God’s knowledge, (...) another controversial issue is whether God knows particulars or not. Most of theist thinkers argued that God is wholly perfect; because of perfectness, He must have perfect attributes. Knowing and goodness are a kind of perfect attributes. Ignoring and evil are a kind of imperfectness. If God is perfect being, He should have the perfect attributes and must know the particulars. For me in this subject, there are some similarities between al-Ghazālī and Maimonides. In this study I took into consideration the idea of al-Ghazālī and Maimonides on this subject. Based on Griffel and Stroumsa’s argument, I tried to show similarity between al-Ghazālī and Maimonides on God’s knowledge. Summary: Whether God has a knowledge is a controversial issue both philosophy and theology. Does God have a knowledge? If He has, does He know the particulars? When we assume that God knows particulars, is there any change in God’s essence? In this study I took into consideration the idea of al-Ghazālī and Maimonides on this subject. Based on Griffel’s and Stroumsa’s arguments, I tried to show similarity between al-Ghazālī and Maimonides on God’s knowledge.In the theistic tradition, it is accepted that God is wholly perfect, omniscience, omnipotent and wholly good. Therefore, it is not possible to say that there is a change in God because changing is a kind of imperfection. On God’s knowledge, another controversial issue is whether God knows particulars or not. Most of theist thinkers argued that God is wholly perfect; because of perfectness, He must have perfect attributes. Knowing and goodness are a kind of perfect attributes. Ignoring and evil are kinds of imperfectness. If God is perfect being, He should have the perfect attributes and must know the particulars. Based on God’s immutability, some thinkers argued that God does not knows particulars. Particulars occurs due to the matter. Matter and its functions are continually changing. Therefore, to know the particulars requires changing in God’s essence. If God is the most perfect being, it is impossible that He is subject to affection. Thus, God does not know the particulars. Other thinkers, like Avicenna, argued that God knows the particulars as a universal way. For example, God knows only humanity and He cannot know Zayd as a particular person. al-Ghazālī criticizes Avicenna’s idea in Tahafut al-Falasifa (The Incoherence of the Philosophers) and argues that God is a perfect being and He should know particulars as a particulars. For al-Ghazālī, God should know everything, and His knowledge is different from our knowledge. In order to explain this matter, he says in Ninety-Nine Names of God;“But this can be understood only through an example. Perhaps you have seen the clock which informs one of the hour of worship. If you have not seen it, then, generally speaking, (it is constructed in this manner). There must be a mechanism in the form of a cylinder which contains a known amount of water. There must also be another hollow mechanism which is placed within the cylinder (but) above the water, and a string which has one of its ends tied to this hollow mechanism. The other end is tied to the part of a small container which is placed above the hollow cylinder. In (this container) there is a ball. Under the ball there is another bowl (placed) in such a manner that if the ball drops will fall into the bowl, and its jingle will be heard. Then the bottom of the cylindrical mechanism must be pierced to a determined extent so that the water can escape through it little by little…. All of this can be determined by a determination of the extent of cause which neither increases nor decreases. It is possible to make the falling of the ball into the bowl a cause of another action and this other action a cause of a third action, and to continue this process indefinitely so that from it are generated remarkable and predetermined movements (actions) of circumscribed extent. The first cause was the falling of the water in a determined quantity…. All of that happens in a determined quantity and to a determined extent which causes the determination of all of it by (adding at this point) the determination of the first movement which is the movement of the water. When you understand that these mechanisms are the principles from which movements must result, and that the movement must be determined if the result is to be regulated, then certainly that which has been determined must proceed from them….Even as the movement of the mechanism, the string, and the ball are not external to the will of the inventor of the mechanism -on the contrary, that is what He willed when He invented the mechanism- so also all the events which occur in the world, both the evil and the good and the beneficial and harmful, are not external to the will of God Most High. Rather (all of) that is the intention of God Most High for the sake of which He has planned its causes.” For Maimonides, as in al-Ghazālī, God is a perfect being and He must have the perfect attributes. Because of knowing is a perfect attribute, He should know everything, and His knowledge is different from human knowledge. In order to explain the difference between God’s knowledge and human knowledge Maimonides gives a parable in The Guide of the Perplexed. “Suppose a thing is produced in accordance with the knowledge of the producer, the producer was then guided by his knowledge in the act of producing the thing. Other people, however, who examine this work and acquire a knowledge of the whole of it, depend for that knowledge on the work itself. An artisan makes a box in which weights move with the running of the water, and thus indicate how many hours have passed of the day and of the night. The whole quantity of the water that is to run out, the different ways in which it runs, every thread that is drawn, and every little ball that descends -all this is fully perceived by him who makes the clock; and his knowledge is not the result of observing the movements as they are actually going on; but, on the contrary, the movements are produced in accordance with his knowledge. But another person who looks at that instrument will receive fresh knowledge at every movement he perceives; the longer he looks on, the more knowledge does he acquire; he will gradually increase his knowledge till he fully understands the machinery…Our knowledge is acquired and increased in proportion to the things known by us. This is not the case with God. His knowledge of things is not derived from the things themselves; if this were the case, there would be change and plurality in His knowledge…” As can be seen from above, when Maimonides is explaining the difference of God’s and human knowledge, he uses the same example what al-Ghazālī used. Even though Maimonides does not mention al-Ghazālī’s name in his works, it could be seen that there are a lot of similarities between al-Ghazālī’s and Maimonides’s ideas. Based on Griffel and Stroumsa’s argument, in this paper, I tried to show that there is a similarity between al-Ghazālī’s and Maimonides’s ideas on God’s knowledge. In my opinion, therefore, in the formation of Maimonides’s thought, as he thanks to Muslim philosophers like al-Farābī, Avicenna and Averroes, he also thanks to al-Ghazālī. (shrink)

The two Heisenberg Uncertainties (UR) entail an incompatibility between the two pairs of conjugated variables E, t and p, q. But incompatibility comes in two kinds, exclusive of one another. There is incompatibility defineable as: (p → − q) & (q→ − p) or defineable as [(p →− q) & (q →− p)] ↔ r. The former kind is unconditional, the latter conditional. The former, in accordance, is fact independent, and thus a matter of logic, the latter fact dependent, (...) and thus a matter of fact. The two types are therefore diametrically opposed. In spite of this, however, the existing derivations of the Uncertainties are shown here to entail both types of incompatibility simultaneously. Δ E Δ t ≥ h is known to derive from the quantum relation E = hν plus the Fourier relation Δ ν Δ t ≥ 1. And the Fourier relation assigns a logical incompatibility between Δ ν = 0, Δ t = 0. (Defining a repetitive phenomenon at an instant t → 0 is a self contradictory notion.) An incompatibility, therefore, which is fact independent and unconditional. How can one reconcile this with the fact that Δ EΔ t exists if and only if h > 0, which latter supposition is a factual truth, entailing that a Δ E = 0, Δ t = 0 incompatibility should itself be fact dependent? Are we to say that E and t are unconditionally incompatible (via Δ ν Δ t ≥ 1) on condition that E = hν is at all true? Hence, as presently standing, the UR express a self-contradicting type of incompatibility. To circumvent this undesirable result, I reinterpret E = hν as relating the energy with a period. Though only one such period. And not with frequency literally. (It is false that E = ν. It is true that E = ν times the quantum.) In this way, the literal concept of frequency does not enter as before, rendering Δ ν Δ t ≥ 1 inapplicable. So the above noted contradiction disappears. Nevertheless, the Uncertainties are derived. If energy is only to be defined over a period, momentum only over a distance (formerly a wavelength) resulting during such period, thus yielding quantized action of dimensions Et = pq, then energies will become indefinite at instants, momenta indefinite at points, leading, as demanded, to (symmetric!) Δ E Δ t = Δ p Δ q ≥ h’s. (shrink)

_ Source: _Volume 29, Issue 1, pp 9 - 38 Hobbes tried to develop a strict version of the mechanical philosophy, in which all physical phenomena were explained only in terms of bodies in motion, and the only forces allowed were forces of collision or impact. This ambition puts Hobbes into a select group of original thinkers, alongside Galileo, Isaac Beeckman, and Descartes. No other early modern thinkers developed a strict version of the mechanical philosophy. Natural philosophies relying solely on (...) bodies in motion require a concept of inertial motion. Beeckman and Descartes assumed rectilinear motions were rectilinear, but Galileo adopted a theory which has been referred to as circular inertia. Hobbes’s natural philosophy depended to a large extent on what he called “simple circular motions.” In this paper, I argue that Hobbes’s simple circular motions derived from Galileo’s belief in circular inertia. The paper opens with a section outlining Galileo’s concept, the following section shows how Hobbes’s physics depended upon circular motions, which are held to continue indefinitely. A third section shows the difficulty Hobbes had in maintaining a strictly mechanistic philosophy, and the conclusion offers some speculations as to why Galileo’s circular inertia was never entertained as a serious rival to rectilinear inertia, except by Hobbes. (shrink)

The two Heisenberg Uncertainties (UR) entail an incompatibility between the two pairs of conjugated variables E, t and p, q. But incompatibility comes in two kinds, exclusive of one another. There is incompatibility defineable as: (p → -q) & (q → -p) or defineable as [(p → -q) & (q → -p)] ↔ r. The former kind is unconditional, the latter conditional. The former, in accordance, is fact independent, and thus a matter of logic, the latter fact dependent, and (...) thus a matter of fact. The two types are therefore diametrically opposed. In spite of this, however, the existing derivations of the Uncertainties are shown here to entail both types of incompatibility simultaneously. ΔEΔt ≥ h is known to derive from the quantum relation E = hv plus the Fourier relation ΔvΔt ≥ 1. And the Fourier relation assigns a logical incompatibility between Δv = 0, Δt = 0. (Defining a repetitive phenomenon at an instant t → 0 is a self contradictory notion.) An incompatibility, therefore, which is fact independent and unconditional. How can one reconcile this with the fact that ΔEΔt exists if and only if h > 0, which latter supposition is a factual truth, entailing that a ΔE = 0, Δt = 0 incompatibility should itself be fact dependent? Are we to say that E and t are unconditionally incompatible (via ΔvΔt ≥ 1) on condition that E = hv is at all true? Hence, as presently standing, the UR express a self-contradicting type of incompatibility. To circumvent this undesirable result, I reinterpret E = hv as relating the energy with a period. Though only one such period. And not with frequency literally. (It is false that E = v. It is true that E = v times the quantum.) In this way, the literal concept of frequency does not enter as before, rendering ΔvΔt ≥ 1 inapplicable. So the above noted contradiction disappears. Nevertheless, the Uncertainties are derived. If energy is only to be defined over a period, momentum only over a distance (formerly a wavelength) resulting during such period, thus yielding quantized action of dimensions Et = pq, then energies will become indefinite at instants, momenta indefinite at points, leading, as demanded, to (symmetric!) ΔEΔt = ΔpΔq ≥ h's. (shrink)