The classical (set-theoretic) concept of structure has become essential for every contemporary account of a scientific theory, but also for the metatheoretical accounts dealing with the adequacy of such theories and their methods. In the latter category of accounts, and in particular, the structural metamodels designed for the applicability of mathematics have struggled over the last decade to justify the use of mathematical models in sciences beyond their 'indispensability' in terms of either method or concepts/entities. In this paper, I argue (...) that these metamodels employ structures of different natures and epistemologies, and this diversity does pose a serious problem to the intended justification. (shrink)

This open access monograph offers a detailed study and a systematic defense of a key intuition we typically have, as human beings, with respect to the nature of time: the intuition that the future is open, whereas the past is fixed. For example, whereas it seems unsettled whether there will be a fourth world war, it is settled that there was a first world war. -/- The book contributes, in particular, three major and original insights. First, it provides a (...) coherent, non-metaphorical, and metaphysically illuminating elucidation of the intuition. Second, it determines which model of the temporal structure of the world is most appropriate to accommodate the intuition, and settles on a specific version of the Growing Block Theory of time (GBT). Third, it puts forward a naturalistic foundation for GBT, by exploiting recent results of our best physics (viz. General Relativity, Quantum Mechanics, and Quantum Gravity). Three main challenges are addressed: the dismissal of temporal asymmetries as non-fundamental phenomena only (e.g., thermodynamic or causal phenomena), the epistemic objection against GBT, and the apparent tension between GBT and relativistic physics. It is argued that the asymmetry between the open future and the fixed past must be grounded in the temporal structure of the world, and that this is neither precluded by our epistemic device, nor by the latest approaches to Quantum Gravity (​e.g., the Causal Set Theory). -/- Aiming at reconciling time as we find it in ordinary experience and time as physics describes it, this ​innovative book ​will raise the interest of both academic researchers and ​graduate students working on the philosophy of time. More generally, it ​presents contents of interest for all metaphysicians and non-dogmatic philosophers of physics. (shrink)

Once it is appreciated that it is not possible for an all-powerful, all-knowing, all-loving God to exist, the important question arises: What does exist that is closest to, and captures the best of what is in, the traditional conception of God? In this paper I set out to answer that question. The first step that needs to be taken is to sever the God-of-cosmic-power from the God-of-cosmic-value. The first is Einstein’s God, the underlying dynamic unity in the physical universe which (...) physics seeks to depict by means of a true, unified, physical “theory of everything”. Science has already achieved some theoretical knowledge of this God-of-cosmic-power. The second is what is of most value in our human world, and in the world of sentient life more generally. Having cut God in half in this way, our fundamental problem, intellectual and practical, becomes: How can the God-of-cosmic-value (as it is represented on earth at least) exist and best flourish within the God-of-cosmic-power? Or, in other words: How can what is of value associated with human life – and sentient life more generally – exist and best flourish within the physical universe? Clearly acknowledging that this is our fundamental problem, in academic inquiry, and in all that we do, might help what is of value in life to flourish rather better than it does at present. (shrink)

When natural selection theory was presented, much active philosophical debate, in which Darwin himself participated, centered on its hypothetical nature, its explanatory power, and Darwin's methodology. Upon first examination, Darwin's support of his theory seems to consist of a set of claims pertaining to various aspects of explanatory success. I analyze the support of his method and theory given in the Origin of Species and private correspondence, and conclude that an interpretation focusing on the explanatory strengths of natural selection (...) theory accurately reflects neither Darwin's own self-consciously held views, nor the nature of his support. Darwin's methodological and philosophical arguments were at once consistently empiricist and more sophisticated than such interpretations credit to him. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...) to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. (shrink)

In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.

Nussbaum’s theory of the emotions draws heavily on the Stoic account. In her theory, emotions are a kind of value judgment or thought. This is in stark contrast to the well-known proposal from William James, who took emotions to be bodily feelings. There are various motivations for taking emotions as judgments. One main reason is that emotions are intentional mental states. They are always about something, directed at particular objects or state of affairs. For example, fear seems to involve the (...) anticipation of danger. To grief for the passing of a loved one involves the thought that someone dear to us is now gone. In Upheavals of Thought and also in her Hochelaga Lecture, Nussbaum analyzed compassion as a set of judgments, including for example the judgment that someone is experiencing serious suffering, and that the person in question does not deserve the suffering. (shrink)

This paper explores the connection between two philosophical debates concerning the nature of properties. The first metaethical debate is about whether normative properties are ordinary natural properties or some unique kind of non-natural properties. The second metaphysical debate is about whether properties are sets of objects, transcendent or immanent universals, or sets of tropes. I argue that nominalism, transcendent realism, and immanent realism are not neutral frameworks for the metaethical debate but instead lead to either metaethical naturalism (...) or non-naturalism. We can therefore investigate the metaethical question on its own terms only within the framework of trope theory. (shrink)

Causation is a macroscopic phenomenon. The temporal asymmetry displayed by causation must somehow emerge along with other asymmetric macroscopic phenomena like entropy increase and the arrow of radiation. I shall approach this issue by considering ‘causal inference’ techniques that allow causal relations to be inferred from sets of observed correlations. I shall show that these techniques are best explained by a reduction of causation to structures of equations with probabilistically independent exogenous terms. This exogenous probabilistic independence imposes a recursive (...) order on these equations and a consequent distinction between dependent and independent variables that lines up with the temporal asymmetry of causation. (shrink)

The paper delves into manuscript sources connected with various disputations held at Prague University from around 1390 to 1420 and singles out a set of hitherto unknown quaestiones dealing with the nature of the human intellect and its relation to the body. Prague disputations from around 1400 arguably offer a unique vantage point on late medieval anthropological issues, since they encompass an entanglement of numerous doctrinal influences from Buridanian De anima commentaries to John Wyclif’s theories. The paper delineates several (...) conceptual tensions regarding the nature of the intellect, e.g., between materialism (entailed by the emphasis on the intellect’s inherence in the body) and personal immortality. It presents several strategies Prague masters employed to overcome these tensions. For example, an anonymous participant of the 1409 quodlibet develops the Buridanian distinction between the rationally demonstrable materialist tendency and the indemonstrable “catholic truth” about the intellect both inhering in and separable from the body. On the other hand, Wyclif’s adherents (Jacob of Mies and another anonymous master) postulate an immortal spirit hypostatically united to each human being beside the human soul educed from the potency of the matter. Yet, the boundaries between the doctrinal standpoints in question seem permeable, whereby a rigid definition of antagonistic groups in late medieval Prague intellectual milieu (e.g., Buridanians vs Wycliffites) is rendered ineffective. (shrink)

The horror genre (in film, literature etc.) has, for its seemingly paradoxical aesthetic appeal, been the subject of much debate in contemporary, analytic philosophy of art. At the same time, however, the nature of horror as an affective phenomenon has been largely neglected by both aestheticians and philosophers of mind. The standard view of the affective nature of horror in contemporary philosophy follows Noël Carroll in holding that horror in art (or “art-horror”) is an emotion resulting from the (...) combination of disgust and fear. The view is also often accompanied by the view that horror in art is a distinct affect from horror in real life. This raises the question of what the relationship between horror in art and in real life might be. By looking within and outside art and the horror genre, and using a combination of historical, philosophical and empirical arguments, I argue for a departure from such standard views on the affective nature of horror. In alternative, I outline a novel view, on which horror is common to both real life and art and is primarily, typically individuated by a set of (output) affective reactions. (shrink)

While Autonomous Weapons Systems have obvious military advantages, there are prima facie moral objections to using them. By way of general reply to these objections, I point out similarities between the structure of law and morality on the one hand and of automata on the other. I argue that these, plus the fact that automata can be designed to lack the biases and other failings of humans, require us to automate the formulation, administration, and enforcement of law as much as (...) possible, including the elements of law and morality that are operated by combatants in war. I suggest that, ethically speaking, deploying a legally competent robot in some legally regulated realm is not much different from deploying a more or less well-armed, vulnerable, obedient, or morally discerning soldier or general into battle, a police officer onto patrol, or a lawyer or judge into a trial. All feature automaticity in the sense of deputation to an agent we do not then directly control. Such relations are well understood and well-regulated in morality and law; so there is not much challenging philosophically in having robots be some of these agents — excepting the implications of the limits of robot technology at a given time for responsible deputation. I then consider this proposal in light of the differences between two conceptions of law. These are distinguished by whether each conception sees law as unambiguous rules inherently uncontroversial in each application; and I consider the prospects for robotizing law on each. Likewise for the prospects of robotizing moral theorizing and moral decision-making. Finally I identify certain elements of law and morality, noted by the philosopher Immanuel Kant, which robots can participate in only upon being able to set ends and emotionally invest in their attainment. One conclusion is that while affectless autonomous devices might be fit to rule us, they would not be fit to vote with us. For voting is a process for summing felt preferences, and affectless devices would have none to weigh into the sum. Since they don't care which outcomes obtain, they don't get to vote on which ones to bring about. (shrink)

While we typically think of culture as defined by geography or ethnicity (e.g., American culture, Mayan culture), the term also applies to the practices and expectations of smaller groups of people. Though embedded in the larger culture surrounding them, such subcultures have their own sets of rules like those that scientists do. Philosophy of science has as its main object of studio the scientific activity. A way in which we have tried to explain these scientific practices is from the (...) actual ontological commitments that scientists do through their scientific theories. Certainly, we know scientific theories through some specific scientific language, which is, in its turn, a subset of the natural language developed by a particular culture. This study is conducted to explore and evaluate some of the most important epistemological consequences of these ontological commitments, specially the so-called ‘truth-commitment’ and its relation with a linguistic-cultural framework. There is an interesting debate between advocates and opponents of scientific realistic view of the natural world. Some lines of scientific realism argumentation assure that: (i) Mature scientific theories are approximately true. (ii) There are entities and organisms in the world that correspond with the ontology presupposed by the best scientific theories within a specific domain of scientific research and (iii) The new acceptable scientific theories should explain why past theories were successful predecessors (Colyvan 2008, Cocchiarella 2007 & Laudan 1981). Contrary, anti- realist positions ensure against the realist’s true - claim that is a semantic commitment - that the purpose of scientific theories to found the truth it is simple an unattainable goal, especially if the kind of truth they are looking for is a corresponding relation between scientific theories and the ontology of the world. Anti-realist positions held that this relation could be circular and unknowable. I do believe that there is a deep confusion between the way in which we accede to the knowledge of the constitutive structures, entities and organisms of the world (which is an epistemological matter) and the way these structures, entities and organisms are (which is an ontological matter). It seems that there is a bridge between the epistemological and ontological aspect in need for conceptual clarification. I do propose that the type of link between the two extremes have to be linguistic in nature. (shrink)

One well-known objection to the traditional Lewis-Stalnaker semantics of counterfactuals is that it delivers counterintuitive semantic verdicts for many counterpossibles (counterfactuals with necessarily false antecedents). To remedy this problem, several authors have proposed extending the set of possible worlds by impossible worlds at which necessary falsehoods may be true. Linguistic ersatz theorists often construe impossible worlds as maximal, inconsistent sets of sentences in some sufficiently expressive language. However, in a recent paper, Bjerring (2014) argues that the “extended” Lewis-Stalnaker semantics (...) delivers the wrong truth-values for many counterpossibles if impossible worlds are required to be maximal. To make room for non-maximal or partial impossible worlds, Bjerring considers two alternative world-ontologies: either (i) we construe impossible worlds as arbitrary (maximal or partial) inconsistent sets of sentences, or (ii) we construe them as (maximal or partial) inconsistent sets of sentences that are closed and consistent with respect to some non-classical logic. Bjerring raises an objection against (i), and suggests that we opt for (ii). In this paper, I argue, first, that Bjerring’s objection against (i) conflates two different conceptions of what it means for a logic to be true at a world. Second, I argue that (ii) imposes too strong constraints on what counts as an impossible world. I conclude that linguistic ersatzists should construe impossible worlds as arbitrary (maximal or partial) inconsistent sets of sentences. (shrink)

A set of visual search experiments tested the proposal that focused attention is needed to detect change. Displays were arrays of rectangles, with the target being the item that continually changed its orientation or contrast polarity. Five aspects of performance were examined: linearity of response, processing time, capacity, selectivity, and memory trace. Detection of change was found to be a self-terminating process requiring a time that increased linearly with the number of items in the display. Capacity for orientation was found (...) to be about 5 items, a value comparable to estimates of attentional capacity. Observers were able to filter out both static and dynamic variations in irrelevant properties. Analysis also indicated a memory for previously-attended locations. These results support the hypothesis that the process needed to detect change is much the same as the attentional process needed to detect complex static patterns. Interestingly, the features of orientation and polarity were found to be handled in somewhat different ways. Taken together, these results not only provide evidence that focused attention is needed to see change, but also show that change detection itself can provide new insights into the nature of attentional processing. (shrink)

There are many important dimensions of epistemic evaluation, one of which is justification. We don’t just evaluate beliefs for truth, reliability, accuracy, and knowledge, but also for justification. However, in the epistemological literature, there is much disagreement about the nature of justification and how it should be understood. One of the controversies that has separated the contemporary epistemological discourse into two opposing camps has to do with the internalism-externalism distinction. Whereas internalists defend certain core assumptions about justification from the (...) pre-Gettier tradition, externalists generally think that the traditional conception is untenable and should be replaced. In this compilation thesis, I argue for, defend, and develop a particular brand of internalism, both in general and with respect to specific sources of justification. In papers 1 and 2, I defend a couple of well-known arguments for mentalism and accessibilism. Moreover, I also point out how prominent versions of these theses are vulnerable to serious problems (e.g., about over-intellectualization and vicious regresses). Part of my goal in the first couple of papers is to figure out what commitments the internalist should take on in order to avoid the externalist's objections, while at the same time receiving support from considerations that have motivated internalism in the past. In papers 3 and 4, I start from the assumption that mentalism is true and attempt to answer the following questions: 1) which non-factive mental states can play a justification-conferring role with respect to empirical belief? And 2) why does this set of states play the epistemic role it does? In response to question 1, I argue that all and only one's beliefs and perceptual experiences have justificatory relevance. In response to question 2, I argue that one's beliefs and perceptual experiences are one's strongly representational states, and that strongly representational states necessarily provide support to certain empirical propositions. Having done so, I then defend mentalism about scientific evidence from a couple of prominent objections in the recent literature. Lastly, in papers 5 and 6, I argue for a particular brand of internalism about testimonial and memorial justification and show how that position has a dialectical advantage over its main competitors. (shrink)

On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surreal numbers; and (...) a natural extension of BLT is definitionally equivalent with ZF. (shrink)

Although a substantial number of papers is published on the topic of consciousness, there is still little consensus on what its nature is and how the physical and phenomenal worlds are connected. Most published research establishes a causal relation between the brain and the mind, but it lacks a cogent theory of how this relation comes to be. In contrast, this paper uses a set of thought experiments grounded in quantum information theory to derive a framework for resolving the (...) hard problem of consciousness. Despite the common tendency to treat the problem purely philosophically, in this paper, consciousness and qualia are analyzed through established formal theory deriving conclusions regarding their relation which provide counter-arguments for the commonly held dualist view. Through the informational monism framework, a case is made for a fundamentally phenomenal nature of information. (shrink)

Marya Schechtman has given us reasons to think that there are different questions that compose personal identity. On the one hand, there is the question of reidentification, which concerns what makes a person the same person through different time-slices. On the other hand, there is the question of characterization, which concerns the actions, experiences, beliefs, values, desires, character traits, etc. that we take to be attributable to a person over time. While leaving the former question for another work, Schechtman answers (...) the latter question by proposing what she terms the narrative self-constitution view, whereby Schechtman claims that we account for intuitive features (moral responsibility, survival, compensation, and self-interested concern) of characterization through narratives. Still, merely having a narrative is not enough. In order to live the life of a person, an agent’s narrative must sync with the narrative told about him/her in community. This paper, while in full agreement with Schechtman’s claim regarding narratives and their ability to explain the intuitive features that regard the question of characterization, puts pressure on the latter claim. I argue that a person’s narrative is not merely one that synchs with the narrative told in community, but one that is determined by the person’s community. In focusing on Schechtman’s second claim, I appeal to the Akan conception of personhood, showing that the community sets the parameters of personal identity, and by body politics and conferring social recognition, determines the traits that we take to be attributed to a given person over time. (shrink)

1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for improvement (...) of mathematical education. The present article presupposes the previous one. Herein we develop our ideas of the purposes of a theory of proof and the criterion of success to be applied to such theories. In addition we speculate at length concerning the specific kinds of uses to which a successful theory of proof may be put vis-a-vis improvement of various aspects of mathematical education. The final article will deal with the construction of such a theory. The 1st is the 1971. Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and Stratification of Language, Journal of Structural Learning 3, #1, 55–74. https://www.academia.edu/s/fb081b1886?source=link . (shrink)

Introduction There are some exceptions, which we shall see below, but virtually all theories in psychology and cognitive science make use of the notion of representation. Arguably, folk psychology also traffics in representations, or is at least strongly suggestive of their existence. There are many different types of things discussed in the psychological and philosophical literature that are candidates for representation-hood. First, there are the propositional attitudes – beliefs, judgments, desires, hopes etc. (see Chapters 9 and 17 of this volume). (...) If the propositional attitudes are representations, they are person-level representations – the judgment that the sun is bright pertains to John, not a subpersonal part of John. By contrast, the representations of edges in V1 of the cerebral cortex that neuroscientists talk about and David Marr’s symbolic representations of “zero-crossings” in early vision (Marr 1982) are at the “sub-personal” level – they apply to parts or states of a person (e.g. neural parts or computational states of the visual system). Another important distinction is often made among perceptual, cognitive, and action-oriented representations (e.g. motor commands). Another contrast lies between “stored representations” (e.g. memories) and “active representations” (e.g. a current perceptual state). Related to this is the distinction between “dispositional representations” and “occurrent representations.” Beliefs that are not currently being entertained are dispositional, e.g. your belief that the United States is in North America - no doubt you had this belief two minutes ago, but you were not consciously accessing it until you read this sentence. Occurrent representations, by contrast, are active, conscious thoughts or perceptions. Which leads us to another important distinction: 1 between conscious and non-conscious mental representations, once a bizarre-sounding distinction that has become familiar since Freud (see Chapter 4 of this volume). I mention these distinctions at the outset to give you some idea of the range of phenomena we will be considering, and to set the stage for our central “problem of representation”: what is a mental representation, exactly, and how do we go about deciding whether there are any? We know there are public representations of various kinds: words, maps, and pictures, among others.. (shrink)

In “Is semantics possible?” Putnam connected two themes: the very possibility of semantics (as opposed to formal model theory) for natural languages and the proper semantic treatment of common nouns. Putnam observed that abstract semantic accounts are modeled on formal languages model theory: the substantial contribution is rules for logical connectives (given outside the models), whereas the lexicon (individual constants and predicates) is treated merely schematically by the models. This schematic treatment may be all that is needed for an account (...) of validity in a formal setting, but it does not help to understand how proper and common nouns function in reality (not in models). Putnam then initiated the empirical study of such nouns to indicate, (i), that the popular Frege-Carnap account of them as (“disguised” compound) predicates is empirically incorrect, and, (ii), that they offer a new paradigm for a naturalistic semantics of natural languages. We take Putnam’s program a couple of steps further. First, we investigate the semantics of common nouns and argue that they refer (to kinds), rather than apply by satisfaction/truth to a designation/denotation. Second, we point to general results about semantics as a theory whose fulcrum is the reference relation rather than satisfaction in models and validity across them. (shrink)

In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction system (...) of Wansing's bi-intuitionistic logic 2Int, which I will turn into a term-annotated form. Therefore, we need a type theory that extends to a two-sorted typed lambda-calculus. I will present such a term-annotated proof system for 2Int and prove a Dualization Theorem relating proofs and refutations in this system. On the basis of these formal results I will argue that this gives us interesting insights into questions about sense and denotation as well as synonymy and identity of proofs from a bilateralist point of view. (shrink)

A prominent argument for moral realism notes that we are inclined to accept realism in science because scientific inquiry supports a robust set of critical practices—error, improvement, explanation, and the like. It then argues that because morality displays a comparable set of critical practices, a claim to moral realism is just as warranted as a claim to scientific realism. But the argument is only as strong as its central analogy—and here there is trouble. If the analogy between the critical practices (...) of science and morality is loosely interpreted, the argument does not support moral realism—for paradigmatically constructivist discourses like fashion display the relevant critical practices just as well. So if the argument is to have force, the realist must say more about why the critical practices of morality are sufficiently like those of science to warrant realism. But this cannot be done—moral inquiry differs from scientific inquiry in too many important ways. So the analogy with the critical practices of science fails to vindicate moral realism. But there are further lessons: in looking closely at the critical practices of our moral discourse—and in comparing them to the critical practices of science and fashion—we gain insight into what is distinctive about morality objectivity and moral metaphysics. (shrink)

Scientists cannot devise theories, construct models, propose explanations, make predictions, or even carry out observations, without first classifying their subject matter. The goal of scientific taxonomy is to come up with classification schemes that conform to nature's own. Another way of putting this is that science aims to devise categories that correspond to 'natural kinds.' The interest in ascertaining the real kinds of things in nature is as old as philosophy itself, but it takes on a different guise (...) when one adopts a naturalist stance in philosophy, that is when one looks closely at scientific practice and takes it as a guide for identifying natural kinds and investigating their general features. This Element surveys existing philosophical accounts of natural kinds, defends a naturalist alternative, and applies it to case studies in a diverse set of sciences. This title is also available as Open Access on Cambridge Core. (shrink)

Suppose that the members of a group each hold a rational set of judgments on some interconnected questions, and imagine that the group itself has to form a collective, rational set of judgments on those questions. How should it go about dealing with this task? We argue that the question raised is subject to a difficulty that has recently been noticed in discussion of the doctrinal paradox in jurisprudence. And we show that there is a general impossibility theorem that that (...) difficulty illustrates. Our paper describes this impossibility result and provides an exploration of its significance. The result naturally invites comparison with Kenneth Arrow's famous theorem (Arrow, 1963 and 1984; Sen, 1970) and we elaborate that comparison in a companion paper (List and Pettit, 2002). The paper is in four sections. The first section documents the need for various groups to aggregate its members' judgments; the second presents the discursive paradox; the third gives an informal statement of the more general impossibility result; the formal proof is presented in an appendix. The fourth section, finally, discusses some escape routes from that impossibility. (shrink)

Today, there are many natural sciences, one of which is physics, but there is no science in the sense of a Theory of Nature. In our everyday life, the opinion is rightly held that there is only one nature, but whether this opinion stands up to reflection is questionable. When we apply the speculation that Aristotle developed in Metaphysics Λ to his Physics, we will see, that Aristotle has developed a Theory of Nature that consists in posing (...) the question of the being of the natural being (Frage nach dem Sein des Naturseienden). The standardinterpretation wants us to believe that Aristotle founded a substance metaphysics with a corresponding theology, and that he practised natural science. But, our hermeneutical situation could lead us to an "Aristotle today" and free us from old beliefs so that we, like Thomas Aquinas and others, could learn from a contemporary Aristotle as an immediate interlocutor. One of the learning points, for example, would be that questions are more crucial than new assertions, even if they are sophisticated, and that unassertive thinking (unbehauptendes Denken) in a topical attitude can lead us to insight into the multiplicity of worlds. This insight would have immediate consequences for our behaviour towards our co-inhabitants of our planet and towards our environment. (shrink)

It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of these equivalences lies in the set existence principles that are necessary and sufficient to prove those theorems. In this article I analyse the role of set existence principles in reverse mathematics, and argue that they are best understood as closure conditions on the powerset of (...) the natural numbers. (shrink)

According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes (...) do exist. However we do not understand this logical truth so well as we understand, for example, the logical truth $${\forall x \, x = x}$$ . In this paper we formulate a logical truth which we call the productivity principle. Rusell (Proc Lond Math Soc 4(2):29–53, 1906 ) was the first one to formulate this principle, but in a restricted form and with a different purpose. The principle explicates a logical mechanism that lies behind paradoxical multitudes, and is understandable as well as any simple logical truth. However, it does not explain the concept of set. It only sets logical bounds of the concept within the framework of the classical two valued $${\in}$$ -language. The principle behaves as a logical regulator of any theory we formulate to explain and describe sets. It provides tools to identify paradoxical classes inside the theory. We show how the known paradoxical classes follow from the productivity principle and how the principle gives us a uniform way to generate new paradoxical classes. In the case of ZFC set theory the productivity principle shows that the limitation of size principles are of a restrictive nature and that they do not explain which classes are sets. The productivity principle, as a logical regulator, can have a definite heuristic role in the development of a consistent set theory. We sketch such a theory—the cumulative cardinal theory of sets. The theory is based on the idea of cardinality of collecting objects into sets. Its development is guided by means of the productivity principle in such a way that its consistency seems plausible. Moreover, the theory inherits good properties from cardinal conception and from cumulative conception of sets. Because of the cardinality principle it can easily justify the replacement axiom, and because of the cumulative property it can easily justify the power set axiom and the union axiom. It would be possible to prove that the cumulative cardinal theory of sets is equivalent to the Morse–Kelley set theory. In this way we provide a natural and plausibly consistent axiomatization for the Morse–Kelley set theory. (shrink)

The article considers the problem of images and the role they play in our reflection turning to evidence provided by two seemingly very distant theories of mind together with two sorts of corresponding visions: dreams as analyzed by Freud who claimed that they are pictures of our thoughts, and their mechanical counterparts produced by neural networks designed for object recognition and classification. Freud’s theory of dreams has largely been ignored by philosophers interested in cognition, most of whom focused solely on (...) the linguistic incarnation of thoughts, but even though commonly neglected by respectable theories of thinking, dream images may prove to be the key to the black box of thought. As argued in this article, when seen from the right perspective and approached with the right set of questions, oneiric visions yield groundbreaking insights into the mechanism of how concepts and judgments are formed. Support for this conclusion comes from a tradition seemingly remote, if not opposed to psychoanalysis: the mechanical model of the mind conceived by information sciences and embodied in the form of artificial neural nets which mirror the activity of human visual cortex producing visions strikingly similar to those created by the sleeping mind. These purely mechanical, artificial ‘dreams’ constitute byproducts of algorithms designed for object recognition and classification, which, as I shall argue, reveals the true purpose of our own oneiric visual formations. Just like their mechanical counterparts produced by neural networks, condensations and displacements encountered in dreams are in fact visual universals. (shrink)

Julius Kovesi was a moral philosopher contemporary with Alasdair MacIntyre, and dealing with many of the same questions as MacIntyre. In our view, Kovesi’s moral philosophy is rich in ideas and worth revisiting. MacIntyre agrees: Kovesi’s Moral Notions, he has said, is ‘a minor classic in moral philosophy that has not yet received its due’. Kovesi was not a thinker whose work fits readily into any one tradition. Unlike the later MacIntyre, he was not a Thomistic Aristotelian, nor even an (...) Aristotelian. He saw his viewpoint as Platonic, or perhaps more accurately as Socratic. His writings, unlike MacIntyre’s, have little to say about justice. However, Kovesi did offfer a theory of practical reason. His main contention was that all human social life embodies a set of concepts that govern and guide that life, concepts without which that life would be impossible. These include our moral concepts. For Kovesi, moral concepts are not external to, but constitutive of social life in any of its possible forms. But in the course of his argument he also developed a way of thinking about how concepts work, which we term ‘conceptual functionalism’, and which we will elucidate. (shrink)

This paper addresses philosophical issues concerning whether mental disorders are natural kinds and how the DSM should classify mental disorders. I argue that some mental disorders (e.g., schizophrenia, depression) are natural kinds in the sense that they are natural classes constituted by a set of stable biological mechanisms. I subsequently argue that a theoretical and causal approach to classification would provide a superior method for classifying natural kinds than the purely descriptive approach adopted by the DSM since DSM-III. My argument (...) suggests that the DSM should classify natural kinds in order to provide predictively useful (i.e., projectable) diagnostic categories and that a causal approach to classification would provide a more promising method for formulating valid diagnostic categories. (shrink)

The performance of natural behavior is commonly used as a criterion in the determination of animal welfare. This is still true, despite many authors having demonstrated that it is not a necessary component of welfare – some natural behaviors may decrease welfare, while some unnatural behaviors increase it. Here I analyze why this idea persists, and what effects it may have. I argue that the disagreement underlying this debate on natural behavior is not one about which conditions affect welfare, but (...) a deeper conceptual disagreement about what the state of welfare actually consists of. Those advocating natural behavior typically take a “teleological” view of welfare, in which naturalness is fundamental to welfare, while opponents to the criterion usually take a “subjective” welfare concept, in which welfare consists of the subjective experience of life by the animal. I argue that as natural functioning is neither necessary nor sufficient for understanding welfare, we should move away from the natural behavior criterion to an alternative such as behavioral preferences or enjoyment. This will have effects in the way we understand and measure welfare, and particularly in how we provide for the welfare of animals in a captive setting. (shrink)

The term ‘human nature’ can refer to different things in the world and fulfil different epistemic roles. Human nature can refer to a classificatory nature (classificatory criteria that determine the boundaries of, and membership in, a biological or social group called ‘human’), a descriptive nature (a bundle of properties describing the respective group’s life form), or an explanatory nature (a set of factors explaining that life form). This chapter will first introduce these three kinds of (...) ‘human nature’, together with seven reasons why we disagree about human nature. In the main, this chapter focuses on the explanatory concept of human nature, which is related to one of the seven reasons for disagreement, namely, the scientific authority inherent in the term ‘nature’. I will examine why, in a number of historical contexts, it was attractive to refer to ‘nature’ as an explanatory category, and why this usage has led to the continual contestation of the term within the sciences. The claim is that even if the contents of talk about ‘nature’ varied historically, the term’s pragmatic function of demarcation stayed the same. The term ‘nature’ conveys scientific authority over a territory; ‘human nature’ is a concept used to divide causes, as well as experts, and thereby conquer others who threaten to invade one’s epistemic territory. Analysing this demarcation, which has social as well as epistemic aspects, will help us to understand why the explanatory role has been important and why it is unlikely that people will ever agree on either the meaning or the importance of ‘human nature’ as an explanatory category. (shrink)

From a moral point of view we think of ourselves as capable of responsible actions. From a scientific point of view we think of ourselves as animals whose behaviour, however highly evolved, conforms to natural scientific laws. Natural Agency argues that these different perspectives can be reconciled, despite the scepticism of many philosophers who have argued that 'free will' is impossible under 'scientific determinism'. This scepticism is best overcome, according to the author, by defending a causal theory of action, that (...) is by establishing that actions are constituted by behavourial events with the appropriate kind of mental causal history. He sets out a rich and subtle argument for such a theory and defends it against its critics. Thus the book demonstrates the importance of philosophical work in action theory for the central metaphysical task of understanding our place in nature. (shrink)

DEFINING OUR TERMS A “paradox" is an argumentation that appears to deduce a conclusion believed to be false from premises believed to be true. An “inconsistency proof for a theory" is an argumentation that actually deduces a negation of a theorem of the theory from premises that are all theorems of the theory. An “indirect proof of the negation of a hypothesis" is an argumentation that actually deduces a conclusion known to be false from the hypothesis alone or, more commonly, (...) from the hypothesis augmented by a set of premises known to be true. A “direct proof of a hypothesis" is an argumentation that actually deduces the hypothesis itself from premises known to be true. Since `appears', `believes' and `knows' all make elliptical reference to a participant, it is clear that `paradox', `indirect proof' and `direct proof' are all participant-relative. PARTICIPANT RELATIVITY In normal mathematical writing the participant is presumed to be “the community of mathematicians" or some more or less well-defined subcommunity and, therefore, omission of explicit reference to the participant is often warranted. However, in historical, critical, or philosophical writing focused on emerging branches of mathematics such omission often invites confusion. One and the same argumentation has been a paradox for one mathematician, an inconsistency proof for another, and an indirect proof to a third. One and the same argumentation-text can appear to one mathematician to express an indirect proof while appearing to another mathematician to express a direct proof. WHAT IS A PARADOX’S SOLUTION? Of the above four sorts of argumentation only the paradox invites “solution" or “resolution", and ordinarily this is to be accomplished either by discovering a logical fallacy in the “reasoning" of the argumentation or by discovering that the conclusion is not really false or by discovering that one of the premises is not really true. Resolution of a paradox by a participant amounts to reclassifying a formerly paradoxical argumentation either as a “fallacy", as a direct proof of its conclusion, as an indirect proof of the negation of one of its premises, as an inconsistency proof, or as something else depending on the participant's state of knowledge or belief. This illustrates why an argumentation which is a paradox to a given mathematician at a given time may well not be a paradox to the same mathematician at a later time. -/- The present article considers several set-theoretic argumentations that appeared in the period 1903-1908. The year 1903 saw the publication of B. Russell's Principles of mathematics, [Cambridge Univ. Press, Cambridge, 1903; Jbuch 34, 62]. The year 1908 saw the publication of Russell's article on type theory as well as Ernst Zermelo's two watershed articles on the axiom of choice and the foundations of set theory. The argumentations discussed concern “the largest cardinal", “the largest ordinal", the well-ordering principle, “the well-ordering of the continuum", denumerability of ordinals and denumerability of reals. The article shows that these argumentations were variously classified by various mathematicians and that the surrounding atmosphere was one of confusion and misunderstanding, partly as a result of failure to make or to heed distinctions similar to those made above. The article implies that historians have made the situation worse by not observing or not analysing the nature of the confusion. -/- RECOMMENDATION This well-written and well-documented article exemplifies the fact that clarification of history can be achieved through articulation of distinctions that had not been articulated (or were not being heeded) at the time. The article presupposes extensive knowledge of the history of mathematics, of mathematics itself (especially set theory) and of philosophy. It is therefore not to be recommended for casual reading. AFTERWORD: This review was written at the same time Corcoran was writing his signature “Argumentations and logic”[249] that covers much of the same ground in much more detail. https://www.academia.edu/14089432/Argumentations_and_Logic . (shrink)

In this paper I will show the problems that are encountered when dealing with uniqueness of connectives in a bilateralist setting within the larger framework of proof-theoretic semantics and suggest a solution. Therefore, the logic 2Int is suitable, for which I introduce a sequent calculus system, displaying - just like the corresponding natural deduction system - a consequence relation for provability as well as one dual to provability. I will propose a modified characterization of uniqueness incorporating such a duality of (...) consequence relations, with which we can maintain uniqueness in a bilateralist setting. (shrink)

The incompleteness of set theory ZF C leads one to look for natural nonconservative extensions of ZF C in which one can prove statements independent of ZF C which appear to be “true”. One approach has been to add large cardinal axioms.Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski-Grothendieck set theory T G or It is a nonconservative extension of ZF C and is obtained from other axiomatic set theories by the inclusion of Tarski’s axiom (...) which implies the existence of inaccessible cardinals. See also related set theory with a filter quantifier ZF (aa). In this paper we look at a set theory NC# ∞# , based on bivalent gyper infinitary logic with restricted Modus Ponens Rule In this paper we deal with set theory NC# ∞# based on bivalent gyper infinitary logic with Restricted Modus Ponens Rule. Nonconservative extensions of the canonical internal set theories IST and HST are proposed. (shrink)

The performance of natural behavior is commonly used as a criterion in the determination of animal welfare. This is still true, despite many authors having demonstrated that it is not a necessary component of welfare –some natural behaviors may decrease welfare, while some unnatural behaviors increase it. Here I analyze why this idea persists, and what effects it may have. I argue that the disagreement underlying this debate on natural behavior is not one about which conditions affect welfare, but a (...) deeper conceptual disagreement about what the state of welfare actually consists of. Those advocating natural behavior typically take a “teleological” view of welfare, in which naturalness is fundamental to welfare, while opponents to the criterion usually take a “subjective” welfare concept, in which welfare consists of the subjective experience of life by the animal. I argue that as natural functioning is neither necessary nor sufficient for understanding welfare, we should move away from the natural behavior criterion to an alternative such as behavioral preferences or enjoyment. This will have effects in the way we understand and measure welfare, and particularly in how we provide for the welfare of animals in a captive setting. (shrink)

The theory of plithogeny developed by Smarandache is described as a more generalized form of representing sets of different nature such as crisp, fuzzy, intuitionistic and neutrosophic. Plithogenic set comprises degree of appurtenance and contradiction degree with respect only to the dominant attribute. This paper introduces extended plithogenic sets comprising degrees of appurtenance and contradiction with respect to both dominant and recessive attributes. The extension of the 5-tuple Plithogenic sets to a 7- tuple plithogenic sets (...) helps in developing a more comprehensive kind of Plithogenic sociogram. The newly developed plithogenic sets and its implications in Plithogenic sociogram is validated by the decision making problem on food processing industries. The obtained results using extended plithogenic sets are more promising in comparison to the conventional plithogenic sets. The proposed kind of plithogenic sets will benefit the decision makers to make optimal decisions based on both optimistic and pessimistic approaches. (shrink)

A theistic science would have to represent the integration of all kinds of knowledge intent on explaining the whole of reality. These would include, at least, history, metaphysics, theology, formal logic, mathematics, and experimental sciences. However, what is the whole of reality that one wants to explain? :.

Certain results, most famously in classical statistical mechanics and complex systems, but also in quantum mechanics and high-energy physics, yield a coarse-grained stable statistical pattern in the long run. The explanation of these results shares a common structure: the results hold for a ‘typical’ dynamics, that is, for most of the underlying dynamics. In this paper I argue that the structure of the explanation of these results might shed some light—a different light—on philosophical debates on the laws of nature. (...) In the explanation of such patterns, the specific form of the underlying dynamics is almost irrelevant. The constraints required, given a free state-space evolution, suffice to account for the coarse-grained lawful behaviour. An analysis of such constraints might thus provide a different account of how regular behaviour can occur. This paper focuses on drawing attention to this type of explanation, outlining it in the diverse areas of physics in which it appears, and discussing its limitations and significance in the tractable setting of classical statistical mechanics. (shrink)

To bring our topic within manageable limits, the attempt will be made to approach the philosophy of nature in a systematic manner. Borrowing the quantitative categories of one, some and all, nature will be treated as first as singular, then a whole or totality and finally discussed in terms of various distinctions which set nature apart as a part. Past philosophic treatments will be discussed when germane to this treatment, as an example of a particular view of (...) nature. I will argue that nature is not a per se being, cannot be singular or the whole and that the various distinctions that separate the natural from other—the artificial, theconventional, etc.—are inadequate. (shrink)

A possible world is a junky world if and only if each thing in it is a proper part. The possibility of junky worlds contradicts the principle of general fusion. Bohn (2009) argues for the possibility of junky worlds, Watson (2010) suggests that Bohn‘s arguments are flawed. This paper shows that the arguments of both authors leave much to be desired. First, relying on the classical results of Cantor, Zermelo, Fraenkel, and von Neumann, this paper proves the possibility of junky (...) worlds for certain weak set theories. Second, the paradox of Burali-Forti shows that according to the Zermelo-Fraenkel set theory ZF, junky worlds are possible. Finally, it is shown that set theories are not the only sources for designing plausible models of junky worlds: Topology (and possibly other "algebraic" mathematical theories) may be used to construct models of junky worlds. In sum, junkyness is a relatively widespread feature among possible worlds. (shrink)

Stephen Jay Gould argued that replaying the ‘tape of life’ would result in radically different evolutionary outcomes. Recently, biologists and philosophers of science have paid increasing attention to the theoretical importance of convergent evolution—the independent origination of similar biological forms and functions—which many interpret as evidence against Gould’s thesis. In this paper, we examine the evidentiary relevance of convergent evolution for the radical contingency debate. We show that under the right conditions, episodes of convergent evolution can constitute valid natural experiments (...) that support inferences regarding the deep counterfactual stability of macroevolutionary outcomes. However, we argue that proponents of convergence have problematically lumped causally heterogeneous phenomena into a single evidentiary basket, in effect treating all convergent events as if they are of equivalent theoretical import. As a result, the ‘critique from convergent evolution’ fails to engage with key claims of the radical contingency thesis. To remedy this, we develop ways to break down the heterogeneous set of convergent events based on the nature of the generalizations they support. Adopting this more nuanced approach to convergent evolution allows us to differentiate iterated evolutionary outcomes that are probably common among alternative evolutionary histories and subject to law-like generalizations, from those that do little to undermine and may even support, the Gouldian view of life. (shrink)

Contemporary analytic philosophy is dominated by metaphilosophical naturalism, the view that philosophy ought to be continuous with science. This naturalistic turn is for a significant part due to the work of W. V. Quine. Yet, the development and the reception of Quine’s naturalism have never been systematically studied. In this paper, I examine Quine’s evolving naturalism as well as the reception of his views. Scrutinizing a large set of unpublished notes, correspondence, drafts, papers, and lectures as well as published responses (...) to Quine’s work, I show how both internal tensions and external criticisms forced him to continuously develop, rebrand, and refine his metaphilosophy before he explicitly decided to label his view ‘naturalism’ in the late 1960s. (shrink)

Considering the axiom of infinity, then N and Peano axioms, together a list of N subsets, inclusion relation and union operation, a contradiction is obtained.

This chapter serves as an introduction to the collected volume. In the first section, we aim to provide background on important themes in social egalitarianism and to set the context for understanding which significant questions the chapters in this book pose and attempt to answer. In this section we focus especially on what could be said to characterize socially egalitarian relationships, on which relationships are of concern, and on what might make social egalitarianism distinct. In the second section, we provide (...) a brief explanation of the structure of the book and each of its chapters. (shrink)

Paul Horwich (1990) once suggested restricting the T-Schema to the maximally consistent set of its instances. But Vann McGee (1992) proved that there are multiple incompatible such sets, none of which, given minimal assumptions, is recursively axiomatizable. The analogous view for set theory---that Naïve Comprehension should be restricted according to consistency maxims---has recently been defended by Laurence Goldstein (2006; 2013). It can be traced back to W.V.O. Quine(1951), who held that Naïve Comprehension embodies the only really intuitive conception of (...) set and should be restricted as little as possible. The view might even have been held by Ernst Zermelo (1908), who,according to Penelope Maddy (1988), subscribed to a ‘one step back from disaster’ rule of thumb: if a natural principle leads to contra-diction, the principle should be weakened just enough to block the contradiction. We prove a generalization of McGee’s Theorem, anduse it to show that the situation for set theory is the same as that for truth: there are multiple incompatible sets of instances of Naïve Comprehension, none of which, given minimal assumptions, is recursively axiomatizable. This shows that the view adumbrated by Goldstein, Quine and perhaps Zermelo is untenable. (shrink)