Standard rigid designator accounts of a name’s meaning have trouble accommodating what I will call a descriptive name’s “shifty” character -- its tendency to shift its referent over time in response to a discovery that the conventional referent of that name does not satisfy the description with which that name was introduced. I offer a variant of Kripke’s historical semantic theory of how names function, a variant that can accommodate the character of descriptive names while maintaining rigidity for proper names. (...) A descriptive name’s shiftiness calls for a semantic account of names that makes their semantic values bipartite, containing both traditional semantic contents and what I call "modes of introduction." Both parts of a name's semantic value are derived from the way a name gets introduced into discourse -- from what I refer to as its "context of introduction." Making a name's semantic value bipartite in this way allows for a definite description to be a part of proper name's meaning without thereby sacrificing that name’s status as a rigid designator. On my view, a definite description is part of descriptive name’s mode of introduction. That is, it is part of what determines the content assigned to that name. As it turns out, making a definite description part of a descriptive name’s mode of introduction allows for that definite description to play the role of a mere reference-fixer regarding that name’s content, as Kripke would have it. However, my account allows a definite description to fix a descriptive name’s content actively over time, thereby explaining its inherent shiftiness. (shrink)

Empty names vary in their referential features. Some of them, as Kripke argues, are necessarily empty -- those that are used to create works of fiction. Others appear to be contingently empty -- those which fail to refer at this world, but which do uniquely identify particular objects in other possible worlds. I argue against Kripke's metaphysical and semantic reasons for thinking that either some or all empty names are necessarily non-referring, because these reasons are either not the right reasons (...) for thinking that a name necessarily must fail to refer, or they are too broad -- they make every empty name necessarily non-referential. Plausibly, the explanation for the necessary non-reference of fictional names should be semantic, yet the explanation should not rule out a priori the contingent non-reference of certain other empty names. In light of this, I argue that a name's semantic value needs to carry information about its referential potential. I claim that names do so by encoding information about the way they were introduced into discourse. Names that are fictional will be marked as being non-referential -- they will fail to refer as a matter of their semantics. In contrast, names that are contingently empty will be marked as referential, but they will be failed referential names that could have been successful. The reason, then, for the non-referential status of a fictional name, will be semantic, as our intuitions suggest it should be. Likewise, the reason for the non-referential status of other empty names, those created by acts of failed attempts to refer, will be metaphysical, again, in keeping with our intuitions. (shrink)

This is what I hope is an illuminating, and to a certain degree, novel exposition of Montague Grammar. It is against many standard interpretations, and perhaps even against things Montague himself says at times. However, it makes more sense of how his various commitments fit together in a systematic way. Why, for instance, is it called "Montague Grammar" rather than "Montague Semantics," and what role does his commitment to Fregeanism plays in his conception of language? It is clear that he (...) is committed to the idea that function application is the fundamental mode of semantic composition, and that he is committed to an intensional framework. However, intensions have, since Carnap, been understood as nearly conceptually equivalent to functions from possible worlds to sets of individuals. But, in truth, possible worlds semantics is just dressed up extensional semantics. There are just more objects to go around to serve as inputs for functions, whatever we think of their ontological status. That is, possible worlds semantics is really a semantic reduction of intensional semantics achieved by expanding our ontological commitments. It would be difficult to make sense of Montague's strong commitment to Fregean semantics, if his notion of intension was that of Carnap's. According to my interpretation, Montague's notion of intension must be distinct from the version adopted by possible world semantics. Montague took seriously the idea that intensional semantics was something quite different from extensionalist semantics. The first was not reducible to the second semantically speaking. Just as Frege believed that meaning consisted of both sense and reference, so too did Montague. However, just as Frege also believed, Montague thought that sense and reference were systematically related. As I illustrate, interpreting Montague as adopting a different notion of intension can also resolve the apparent problem of distinguishing the difference in meaning between intensional equivalents. It might also enable us to draw a distinction in epistemic logic between an agent having contradictory beliefs and believing contradictions. (shrink)

Observable consequences of the hypothesis that the observed universe is a numerical simulation performed on a cubic space-time lattice or grid are explored. The simulation scenario is first motivated by extrapolating current trends in computational resource requirements for lattice QCD into the future. Using the historical development of lattice gauge theory technology as a guide, we assume that our universe is an early numerical simulation with unimproved Wilson fermion discretization and investigate potentially-observable consequences. Among the observables that are considered are (...) the muon g-2 and the current differences between determinations of alpha, but the most stringent bound on the inverse lattice spacing of the universe, b−1 > ~ 10^11 GeV, is derived from the high-energy cut off of the cosmic ray spectrum. The numerical simulation scenario could reveal itself in the distributions of the highest energy cosmic rays exhibiting a degree of rotational symmetry breaking that reflects the structure of the underlying lattice. (shrink)

In “Semantics of Fictional Terms,” Garcia-Carpintero critically surveys the most recent literature on the topic of fictional names. One of his targets is realism about fictional discourse. Realists about fictional discourse believe that: (a) it contains true sentences that have fictional names as their subjects; (b) sentences containing names can be true only if those names have referents; (c) fictional names have fictional characters – abstract objects – as their referents. The fundamental problem that arises for realists is that not (...) all true sentences containing fictional names are plausibly about abstract objects. This leads to the need to introduce disjunctive conceptions of property attribution that Garcia-Carpintero claims are implausible, and that realism should therefore be rejected. He also maintains, however, that (a) is correct. I agree. Furthermore, I am also committed to anti-realism about fictional discourse – that fictional names have no referents. Garcia-Carpintero claims that my view is simply a notational variant of realism. I argue that this is false – that my view could not possibly be a notational variant of any extant realist theory. (shrink)

Abstract: Many, if not most philosophers, deny that a sentence like ‘Sherlock Holmes smokes’ could be true. However, this attitude conflicts with the assignment of true to that sentence by natural language speakers. Furthermore, this process of assigning truth values to sentences like ‘Sherlock Holes smokes’ seems indistinguishable from the process that leads speakers to assign true to other sentences, those like ‘Bertrand Russell smokes’. I will explore the idea that when speakers assign the value true to the first sentence, (...) they are not mistaken or confused — that we ought to take these assignments at face value. I show how the most popular alternative to this idea is inadequate for explaining various sentences involving fictional names. In addition, I offer evidence that these truth value assignments to sentences are tracking semantic content rather than pragmatic effects. (shrink)

There are many examples offered as evidence that proper names are predicates. Not all of these cases speak to a name’s semantic content, but many of them do. Some of these include attributive, quantifier, and ambiguity cases. We will explore those cases here, and we will see that none of them conclusively show that names are predicates. In fact, all of these constructions can be given alternative analyses that eliminate the predicative characteristics of names they feature. These analyses do not (...) involve having names functioning as predicates in any way at all. In attributive cases, the names within them are to be understood as occurring in a comparative construction, not an attributive construction. In the last two sorts of cases, the names that occur are analyzed as part of a more complex referring device for a specific domain, rather than functioning as predicates. Both paraphrases can be given plausible semantic treatments that have significant advantages over their competitors. For this reason, there is less motivation to focus on predicative views of proper names. (shrink)

Recently, and rather startlingly, given the history of the debate about a name's semantic content, some claim that names are in fact predicates -- predicativism. Some of predicativists claim that a name's semantic content involves the concept of being called -- calling accounts that have been traditionally meta-linguistic. However, these accounts fail to be informative. Inspired by Burge's claim that proper names are literally true of the individuals that have them, Fara develops a non-meta-linguistic concept of being called analysed in (...) terms of property attributions. I offer seven separate reasons for rejecting the account, one of which is that Fara's development of the view, at least, has implausible consequences for a theory of name acquisition. I sketch an alternative account of name acquisition that is meta-linguistic in nature, but because it is not offered as a theory of name's content, the standard worries fail to apply. In fact, I argue that an account of name acquisition must be meta-linguistic, and therefore a more nuanced conception of meta-linguistic speech acts is required. The account invokes Austin's performative-constative distinction. It analyses name acquisition as due to performative meta-linguistic speech acts. (shrink)

This was a public talk given in the spring of 2013 during sexual assault awareness week. I believe roughly 800 attended. The philosophy dept was NOT expecting that but at any rate, this is the gist: While there are many different motivations for raising questions about the Sexual Assault Awareness Movement, at least one motivation comes from feminist controversies about what counts as consensual sex. Historically, this controversy arose between those known as "anti-pornography feminists", and "sex positive feminists" whose proponents (...) had very different understandings of what counts as sexual autonomy for women. It is important to understand that questioning the current definitions of what counts as an instance of sexual assault does not entail an anti-feminist agenda. There is not a unified feminist front on this topic. To assume otherwise is to risk silencing victims of sexual assault even further by imposing a particular conception of sexual assault upon them that they might themselves reject. If we are to properly address sexual assault as feminists we must listen to victims of sexual assault and develop a theory of consent in tandem with victims' own understanding of that concept. (shrink)

My aim in this paper is to show that the existence of empty names raise problems for the Millian that go beyond the traditional problems of accounting for their meanings. Specifically, they have implications for Millian strategies for dealing with puzzles about belief. The standard move of positing a referent for a fictional name to avoid the problem of meaning, because of its distinctly Millian motivation, implies that solving puzzles about belief, when they involve empty names, do in fact hang (...) on Millian assumptions after all. (shrink)

According to EJ Lowe, diachronic necessity and synchronic necessity are logically independent. Diachronic possibility concerns what could happen to an object over time and therefore concerns future possibilities for that object given its past history. Synchronic possibility concerns what is possible for an object in the present or at a past present moment. These are logically independent, given certain assumptions. While it may true that because I am 38, it is impossible diachronically for me to be 30 (at least once (...) we restrict the degree of relevant possibility), it is possible, given that at some point in the past, I may have been conceived slightly earlier than I was, that I am now 37. Likewise, it is possible diachronically for me to be somewhere other than where I am, but given that one object cannot be in different places at the same time, it is impossible for me now to be somewhere other than where I am, and this is true at each past point in my history too. There are, then, two axis upon which to distinguish what is and is not possible: tensed possibilities and possibilities of degree, which include nomic, metaphysical, and logical necessities, among others. I examine the interactions between these possibilities and I come to the conclusion that logical necessity is not in fact logical necessity simpliciter. Whether something is logically necessary depends upon tensed possibilities. I argue that while synchronic logical necessity entails diachronic logical necessity, the reverse entailment does not hold. I explore the consequences of this for certain philosophical debates in semantics including the concept of rigid designation, and descriptive names. (shrink)

This book is about whether reference to an individual is the essential feature of a proper name -- a widely held view -- or whether referring to an individual is simply a contingent feature. Three questions need resolving, then. First, whether all names in particular contexts are themselves referring devices. Second, whether recognizing names types and the consequent issue of their ambiguity can be resolved simply by distinguishing between name types and tokens thereof. Last, whether names are ever referential in (...) the way Kripke and others have convincingly argued. The answer to first two questions is negative. The answer to third is a qualified "yes." I explain the theory that allows for these answers in the manuscript, as well as addressing other issues such as: the problem of fictional names; descriptive names; empty names; what an act of naming consists of; an account of ontological commitment; and the data that suggests that names are predicates. (shrink)

In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation (...) that satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems -- without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of “idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent. (shrink)

Savage's framework of subjective preference among acts provides a paradigmatic derivation of rational subjective probabilities within a more general theory of rational decisions. The system is based on a set of possible states of the world, and on acts, which are functions that assign to each state a consequence€. The representation theorem states that the given preference between acts is determined by their expected utilities, based on uniquely determined probabilities (assigned to sets of states), and numeric utilities assigned to (...) consequences. Savage's derivation, however, is based on a highly problematic well-known assumption not included among his postulates: for any consequence of an act in some state, there is a "constant act" which has that consequence in all states. This ability to transfer consequences from state to state is, in many cases, miraculous -- including simple scenarios suggested by Savage as natural cases for applying his theory. We propose a simplification of the system, which yields the representation theorem without the constant act assumption. We need only postulates P1-P6. This is done at the cost of reducing the set of acts included in the setup. The reduction excludes certain theoretical infinitary scenarios, but includes the scenarios that should be handled by a system that models human decisions. (shrink)

The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to (...) a dominance condition; that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe- Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance. (shrink)

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To (...) fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework. (shrink)

This paper offers a fine analysis of different versions of the well known sure-thing principle. We show that Savage's formal formulation of the principle, i.e., his second postulate (P2), is strictly stronger than what is intended originally.

Sir James Frazer’s The Golden Bough presents a puzzle regarding how primitive peoples believe they can control something which civilized people regard as beyond their control: the weather. I clarify the puzzle and consider Frazer’s solution to it, as well as other solutions.

I argue that (i) even though Adam Smith’s four stages theory has been criticized with good reasons as both vitiated by undue generalization from modern Europe to the first stage and made bottom-heavy by assumptions of modern episteme, yet, in his writings an alternative view emerges where the savage is not just crushed under the weight of want and isolation but is endowed with imagination and sympathy; (ii) his picture of the fourth stage is, far from a triumphal apology (...) of Capitalism, a tragic diagnosis of an inner tension between ambition and greed and their unintended beneficial effects; (iii) the tensions in the picture are not just a report of tensions out there, but also depend on Smith’s pre-comprehension of the phenomena he tries to account for; (iv) and yet, the tragic character of this picture is to be credited to his integrity; I summarize peculiarities of Smith’s peculiar outlook, post-empiricism, as well as its potentialities (sect 2). I then reconstruct his view of development of language and science, suggesting that his theory of association of ideas and imagination provides a consistent account of both science and lore, yielding a comparatively less ethnocentric evaluation of the savage mind (sect. 3). I reconstruct his virtually twofold reconstruction of subsistence in the rude and early state, arguing that he tends to ascribe inability to evolve to want and isolation and describes his own view of evolution as a necessary path but also that in several passages imagination and sympathy do play a role also for the savage (sect. 4). I compare Smith’s view of the first stage with his diagnosis of commercial society arguing that his reconstruction is burdened by eighteenth-century ideology as well as by modern episteme and I conclude with an ambivalent appraisal of Smith’s comparison between the polished man and the savage. -/- . (shrink)

An opinion piece on the history of the black man and the prisoner which assimilates them, their history, their politics, their geography and status. The fiction associated with them, the psychology and general authors opinion on their futures.

In this paper, I investigate the betting behavior of a decision-maker who can influence the likelihood of the events upon which she is betting. In decision theory, this is best known as a situation of moral hazard. Focusing on a particularly simple case, I sketch the first systematic analysis of moral hazard in the canonical Savage framework. From the results of this analysis, I draw two philosophical conclusions. First, from an observational and a descriptive point of view, there need (...) to be no incompatibility between moral hazard and the Savage framework. This qualifies the incompatibility view, that is ubiquitous in decision theory. Second, in general, moral hazard is not sufficient to overcome the challenges posed by state-dependent utility to the behavioral identification of beliefs. This qualifies the sufficiency view, that is influential in decision theory. These two philosophical conclusions are the main contributions of my paper. (shrink)

In this paper I argue that Kant would have endorsed Clifford’s principle. The paper is divided into four sections. In the first, I review Kant’s argument for the practical postulates. In the second, I discuss a traditional objection to the style of argument Kant employs. In the third, I explain how Kant would respond to this objection and how this renders the practical postulates consistent with Clifford’s principle. In the fourth, I introduce positive grounds for thinking that Kant (...) would have endorsed this principle. (shrink)

This essay is titled "Critique the Postulation of the Historical Law Theory and relate it to African Law. The postulation of the historical law school that law emanates from customs through an ordered pattern of systematized progress into a codified system in relation to African law forms the crust of this essay. To achieve this task, this essay adopts a critical method in exposing c postulation of the historical law school and the African Law (keeping in mind the Ukelle communal (...) Law System). This essay questions whether there can be an independent law made or promulgated without targeting a given people or that there can be a people-free law? This essay claims that like the historical law school, laws emanate from their ground norms but insists that unlike the historical law school, laws in Ukelle Traditional System do not necessarily have to submit to through the rigor of systematic and strict evolutionary pattern of progress. Like Herder, this essay avers that there is a unique character with each culture, and as such Ukelle Traditional Law does not have to submit to any universal character of law. (shrink)

I summarize, in this informal interview, the main approaches to the ‘Past Hypothesis’, the postulation of a low-entropy initial state of the universe. I’ve chosen this as an open problem in the philosophical foundations of physics. I hope that this brief overview helps readers in gaining perspective and in appreciating the diverse range of approaches in this fascinating unresolved debate.

In the Critique of Practical Reason, Kant grounds his postulate for the immortality of the soul on the presupposed practical necessity of the will’s endless progress toward complete conformity with the moral law. Given the important role that this postulate plays in Kant’s ethical and political philosophy, it is hard to understand why it has received relatively little attention. It is even more surprising considering the attention given to his other postulates of practical reason: the existence of God and (...) freedom. The project of this paper is to examine Kant’s postulate of the immortality of the soul, examine critiques of this argument, and show why the argument succeeds in showing that belief in the moral law also obligates one to believe in the soul’s immortality. (shrink)

In the article, I consider seven metaphysical postulates that lie in the foundations of modern physics. These are postulates: about the nature of space-time, about the existence, about the direction of time, about the causality, about the elementary event, about the nature of information and about the immutability of laws. The directions of critical analysis and possible radical revision of these postulates are briefly presented. It is supposed that this revision can indirectly contribute to the development of (...) a theory that will be able to generalize quantum phenomena, gravity and the evolution of the universe. (shrink)

One of the most well-known and defining characteristics of indigenous Andean thought is its adherence to a “complementary dualism” in which the “opposites” of existence are viewed as interdependent parts of a harmonious whole. This is in many ways in stark contrast to Western philosophical models, which have historically tended towards an “antagonistic dualism,” the view that the opposites are engaged in an eternal struggle for dominance. This paper considers how a culture’s relationship to the opposites—whether seen as a “war” (...) or a “dance”—influences the way an individual creates psychological meaning. The results of my research into Andean complementary dualism are first presented. I then consider how this cultural-philosophical worldview compares to other complementary models, specifically that of G.W. Hegel and C. G. Jung. The paper concludes with a consideration of how the similar ideals of these complementary worldviews might inform the work of transpersonal researchers and practitioners. (shrink)

Moritz Geiger (1880–1937) in Phänomenologische Ästhetik paper postulates aesthetics to become an autonomous science. The new science is intended to analyze aesthetic values and to discover the rules of their regulations. It tends to be separated from aesthetics as the sub-discipline of philosophy (especially under the influence of metaphysics) and aesthetics as a field of applying other sciences (mainly psychology). It may be achieved by the usage of a phenomenological method.

In this paper I trace the arc of Kant’s critical stance on the belief in God, beginning with the Critique of Pure Reason (1781) and culminating in the final chapter of the Metaphysics of Morals (1797). I argue that toward the end of his life, Kant changed his views on two important topics. First, despite his stinging criticism of it in the Critique of Pure Reason, by the time of the Metaphysics of Morals, Kant seems to endorse the physico-theological argument. (...) Second, some time around the publication of the Metaphysics of Morals, Kant seems to move away from the argument for the practical postulates. (shrink)

Is vision merely a state of the beholder’s sensory organ which can be explained as an immediate effect caused by external sensible objects? Or is it rather a successive process in which the observer actively scanning the surrounding environment plays a major part? These two general attitudes towards visual perception were both developed already by ancient thinkers. The former is embraced by natural philosophers (e.g., atomists and Aristotelians) and is often labelled “intromissionist”, based on their assumption that vision is an (...) outcome of the causal influence exerted by an external object upon a sensory organ receiving an entity from the object. The latter attitude to vision as a successive process is rather linked to the “extramissionist” theories of the proponents of geometrical optics (such as Euclid or Ptolemy) who suggest that an entity – a visual ray – is sent forth from the eyes to the object. The present paper focuses on the contributions to this ancient controversy proposed by some 13th-century Latin thinkers. [...]. (shrink)

Wenn überhaupt in einem Gebiet Wahrheit und Existenz unabhängig von unseren Erkenntnisfähigkeiten sind, dann in der Metaphysik – etwa bei der Frage, ob es Gott gibt oder eine Seele, die unseren Tod überdauert. Die metaphysica specialis schreit geradezu nach metaphysischem Realismus und dem zugehörigen Wahrheitsbegriff. Von diesem Ausgangspunkt gerät man allerdings schnell in Verlegenheit, wenn man fragt: Nach welchen Kriterien sollen wir uns richten, wenn wir uns über Gott oder Unsterblichkeit ein Urteil bilden wollen? Mit den Mitteln der Naturwissenschaft und (...) deren rationaler Methodologie (in der es um Empirie, Einfachheit, Sparsamkeit usw. geht) kommen wir bei Themen wie Gott oder Unsterblichkeit immer nur bis zum Patt. Genauso steht es bei der Frage, ob wir in unseren Entscheidungen frei sind. Urteilsenthaltung können wir uns nicht erlauben, dafür sind die metaphysischen Fragen zu wichtig; Auslosen kommt auch nicht infrage. Statt erkenntnistheoretisch zu kapitulieren, schlage ich programmatisch vor, die Erkenntnislehre auf weichere Weise weiterzubetreiben. Emotion, Intuition, Moral – das sind einige der zusätzlichen außerrationalen Hilfsmittel, mit deren Hilfe wir weiterkommen können. Ich zeige, dass diese Hilfsmittel respektabler und gewichtiger sind, als kühle, rationale Erkenntnistheoretiker zugeben wollen. Diese Hilfsmittel führen zu guten Postulaten aus Unvernunft (und zwar nicht nur in der Metaphysik). Wie schlimm es für den Realismus ist, dass diese Postulate immer noch falsch sein könnten, diese Frage werde ich im vorliegenden Aufsatz nicht mehr klären. (shrink)

This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the thinking of one of the greatest modern logicians as late as 1831. Today it is difficult to accept the proposition that Aristotle was blind to the fact that, (...) for example, incommensurability is a relation and not a property: that the proposition “In every square, the diagonals are incommensurable with the sides” is relational and not categorical. This paper asks the reader to do something more difficult: to accept the proposition that as late as 1831 De Morgan was blind to the same fact. This paper shows conclusively that in 1831, De Morgan was still in the grips of the allegedly Aristotelian paradigm. (shrink)

In the paper, certain rational postulates for protocols describing real communicating are introduced.These rational postulates, on the one hand, allow assigning a certain typology of real systems of interactions, which is consistent with the reality of epistemic argumentation in systems of communicating, and on the other one – defining rules of using argumentation in real situations. Moreover, the presented postulates for protocols characterize information networks and administering knowledge in real interactivity systems. Due to the epistemic character of (...) the considerations, the problem undertaken in the paper concerns working out fundamental assumptions that refer to building of epistemic logics. They allow establishing the correctness of the discourse defined by rational postulates of protocols of real communication. In the context of the presented problem there are the following two research questions distinguished: 1) How do we determine the rule of building of real dynamic epistemic logics? and 2) How should we define semantics for these logics? Within the framework of considerations relating to the research questions asked, certain epistemic operators, relativized to types of communicating, are introduced. Basic logical relations between using these operators are established for these operators. The relations are presented by a diagram called the square of epis temic operators. On the basis of these logical relations some axioms for real dynamic epistemic logics are presented. The semantics of real dynamic epistem ic logics is extended by the methods of lower and upper approximation of formula evaluating. This allows defining ‘approximation Kripke models’. The results of conceptualization of knowledge on real premises of epistemic argum entation presented in this paper can be applied to rhetoric in real systems of interaction. (shrink)

The notion of so-called "postulated ontology" appears in the context of a well- -known thesis of the underdetermination of scientific theories by empirical data. It is argued in the paper, that the conviction of the existence of some kind of relation between a given theory and ontological ideas can be derived from this thesis, regardless of its particular form. Therefore, certain solutions to classical philosophical questions can be obtained, in principle, by careful inspection of scientific achievements. However, if the thesis (...) of underdetermination holds, such philosophical solutions are not imposed by science itself. In order to arrive at some kind of ontology based on science, it seems necessary to accept certain philosophical presuppositions in the first place. This, and the fact that scientific theories change in time show that although such a kind of ontology is possible, and perhaps desirable, it can never be ultimate. (shrink)

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail (...) not only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory. (shrink)

The mathematical structure of realist quantum theories has given rise to a debate about how our ordinary 3-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined. Which of the two spaces is our (more) fundamental physical space? I review the debate between 3N-Fundamentalists and 3D-Fundamentalists and evaluate it based on three criteria. I argue that when we consider which view leads to a deeper understanding of the physical world, especially given the deeper topological (...) explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons in favor of 3D-Fundamentalism. I conclude that our evidence favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I outline lines of future research where the evidential balance can be restored or reversed. Finally, I draw lessons from this case study to the debate about theoretical equivalence. (shrink)

As timely renovation of artificial ideology about authenticity of nature in proportion to contemporaneous historical background of remarkable highlight of microcosmic configuration of matter, “Homogenous Cosmos Originated from Unique Genesis” is innovative cosmos redefinition and thoroughly coherent PNT dynamics about universal existence & motion as spontaneous occurrence in the nature of essence of matter in a class by itself, which is radically extended from newly highlighted factuality that “discretionary particles in cosmos are mutually convertible” as lineal logic system based on (...) unique assumable precondition of Homogenous cosmos originated from unique genesis postulate. (shrink)

The article gives a short characterization of Russell's solution to Hume's problem: empirical postulates.

Russell's a priori postulates of empirist theories of knowledge. Kurze Darstellung von Russells Postulaten als Ermöglichung einer empiristischen Erkenntnistheorie.

The measurement problem concerns an apparent conflict between the two fundamental principles of quantum mechanics, namely the Schrödinger equation and the measurement postulate. These principles describe inconsistent behavior for quantum systems in so-called "measurement contexts." Many theorists have thought that the measurement problem can only be resolved by proposing a mechanistic explanation of (genuine or apparent) wavefunction collapse that avoids explicit reference to "measurement." However, I argue here that the measurement problem dissolves if we accept Humeanism about laws of nature. (...) On a Humean metaphysics, there is no conflict between the two principles, nor is there any inherent problem with the concept of "measurement" figuring into the account of collapse. (shrink)

There are two traditional ways to read Kant's claim that every event necessarily has a cause: the weaker every-event some-cause and the stronger same-cause same-effect causal principles. The focus of the debate about whether and where he subscribes to the SCP has been in the Analogies in the Critique of Pure Reason and in the Metaphysical Foundations of Natural Science. By analysing the arguments and conclusions of both the Analogies and the Postulates as well as the two Latin principles (...) non datur casus and non datur fatum that summarise their results, I will argue for the novel thesis that the SCP is actually demonstrated in the Postulates of the First Critique. (shrink)

Science is founded on a method based on critical thinking. A prerequisite for this is not only a sufficient command of language but also the comprehension of the basic concepts underlying our understanding of reality. This constraint implies an awareness of the fact that the truth of the World is not directly accessible to us, but can only be glimpsed through the construction of mod- els designed to anticipate its behaviour. Because the relationship between models and reality rests on the (...) interpretation of founding postulates and in- stantiations of their predictions (and is therefore deeply rooted in language and culture), there can be no demarcation between science and non-science. However, critical thinking is essential to ensure that the link between models and reality is gradually made more adequate to reality, based on what has already been established, thus guaranteeing that science progresses on this basis and excluding any form of relativism. (shrink)

What is a number? Answering this will answer questions about its philosophical foundations - rational numbers, the complex numbers, imaginary numbers. If we are to write or talk about something, it is helpful to know whether it exists, how it exists, and why it exists, just from a common-sense point of view [Quine, 1948, p. 6]. Generally, there does not seem to be any disagreement among mathematicians, scientists, and logicians about numbers existing in some way, but currently, in the mainstream (...) arena only definitions, descriptions of properties, and effects are presented as evidence. Enough historical description of numbers in history provides an empirical basis of number, although a case can be made that numbers do not exist by themselves empirically. Correspondingly, numbers exist as abstractions. All the while, though, these "descriptions" beg the question of what numbers are ontologically. Advocates for numbers being the ultimate reality have the problem of wrestling with the nature of reality. I start on the road to discovering the ontology of number by looking at where people have talked about numbers as already existing: history. Of course, we need to know not only what ontology is but the problems of identifying one, leading to the selection between metaphysics and provisional approaches. While we seem to be dimensionally limited, at least we can identify a more suitable bootstrapping ontology than mere definitions, leading us to the unity of opposites. The rest of the paper details how this is done and modifies Peano's Postulates. (shrink)

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the (...) last: the parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)

The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. (...) Thus, the pair of arithmetic and set are to be similar to Euclidean and non-Euclidean geometries distinguishably only by the Fifth postulate now, i.e. after replacing it and its negation correspondingly by the axiom of finiteness (induction) versus that of finiteness being idempotent negations to each other. Indeed, the axiom of choice, as far as it is equivalent to the well-ordering “theorem”, transforms any set in a well-ordering either necessarily finite according to the axiom of induction or also optionally infinite according to the axiom of infinity. So, the Gödel incompleteness statement relies on the logical contradiction of the axiom of induction and the axiom of infinity in the final analysis. Nonetheless, both can be considered as two idempotent versions of the same axiom (analogically to the Fifth postulate) and then unified after logicism and its inherent intensionality since the opposition of finiteness and infinity can be only extensional (i.e., relevant to the elements of any set rather than to the set by itself or its characteristic property being a proposition). So, the pathway for interpreting the Gödel incompleteness statement as an axiom and the originating from that assumption for “Hilbert mathematics” accepting its negation is pioneered. A much wider context relevant to realizing the Gödel incompleteness statement as a metamathematical axiom is consistently built step by step. The horizon of Hilbert mathematics is the proper subject in the third part of the paper, and a reinterpretation of Gödel’s papers (1930; 1931) as an apology of logicism as the only consistent foundations of mathematics is the topic of the next second part. (shrink)

This paper discusses knowledge of opposites. In particular, attention is given to the linguistic notion of antonymy and how it represents oppositional relations that are commonly found in perception. The paper draws upon the long history of work on the formalisation of antonymy in linguistics and formal semantics, and also upon work on the perception of opposites in psychology, and an assessment is made of the main approaches. Treatments of these phenomena in linguistics and psychology posit that the principles of (...) minimal difference and invariance are centrally important. It will be suggested that the standard approach employing meaning postulates fails to capture the relevant notion of antonymy, in part because it is not informed by these principles, and in part due to a number of other problems with this kind of approach, many of which may be overcome by building in the central principles from the beginning. The paper also discusses the issue of whether we can know that opposites necessarily exclude each other and, if so, how. This issue is intertwined with what is known as the colour incompatibility problem that Wittgenstein wrangled with at various times during his life. The paper assesses various solutions to these problems including an approach that was first put forward by Jerrold J. Katz. The relation between this approach and the theory of determinables and determinates is also examined. A further development upon this approach is proposed and then applied to the case of the formalisation of antonymy. It is argued that this approach avoids the problems suffered by the main approaches discussed earlier in the paper. (shrink)

This paper argues that (1) Richard Swinburne’s general account of the simplicity of empirical hypotheses fails because it involves a deeply problematic notion of postulating a property, while there is a wide range of hypotheses where the assessment of simplicity rests entirely on the number and kinds of postulated properties, (2) Swinburne’s main argument in ’The Christian God’ for the simplicity of theism, the one based on considerations about pure limitless intentional power, is significantly weaker than he seems to believe. (...) The paper does not draw a conclusion about whether theism is simple. (shrink)