It is often argued that it does not matter morally whether biomedical interventions treat or prevent diseases or enhance nondisease traits; what matters is whether and how much they promote well-being. Therapy and enhancement both promote well-being, the argument goes, so they are not morally distinct but instead continuous. I provide three reasons why this argument should be rejected when it is applied to choices concerning the genetic makeup of future people. First, it rests on too simple a (...) conception of the badness of disease. Second, it wrongly assumes that disease avoidance and enhancement can proceed with similar accuracy. Third, it overlooks that disease avoidance tends to be more urgent than enhancement from the point of view of distributive justice. Although none of these reasons establishes a firm therapy-enhancement distinction, they show that a continuum model is not an attractive alternative. (shrink)

In this paper, I propose a logical-cognitive approach to argumentation and advocate an idea that argumentation presupposes that intelligent agents engaged in it are cognitively diverse. My approach to argumentation allows drawing distinctions between justification, conviction and persuasion as its different kinds. In justification agents seek to verify weak or strong coherency of an agent’s position in a dialogue. In conviction they argue to modify their partner’s position by means of demonstrating weak or strong cogency of their positions before a (...) ‘rational judge’. My approach to argumentation employs a ‘light’ version of Dung’s abstract argumentative frameworks. It is based on Stich’s idea of agents’ cognitive diversity the epistemic aspect of which is argued to be close to Pavilionis’s conception of meaning continuum. To illustrate my contributions I use an example based on the Kitchen Debate (1959) between Khrushchev and Nixon. (shrink)

This paper defends the Quine-Putnam mathematical indispensability argument against two objections raised by Penelope Maddy. The objections concern scientific practices regarding the development of the atomic theory and the role of applied mathematics in the continuum and infinity. I present two alternative accounts by Stephen Brush and Alan Chalmers on the atomic theory. I argue that these two theories are consistent with Quine’s theory of scientific confirmation. I advance some novel versions of the indispensability argument. I argue (...) that these new versions accommodate Maddy’s history of the atomic theory. Counter-examples are provided regarding the role of the mathematical continuum and mathematical infinity in science. (shrink)

The article deals with Cantor's argument for the non-denumerability of reals somewhat in the spirit of Lakatos' logic of mathematical discovery. At the outset Cantor's proof is compared with some other famous proofs such as Dedekind's recursion theorem, showing that rather than usual proofs they are resolutions to do things differently. Based on this I argue that there are "ontologically" safer ways of developing the diagonal argument into a full-fledged theory of continuum, concluding eventually that famous semantic (...) paradoxes based on diagonal construction are caused by superficial understanding of what a name is. (shrink)

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to (...) randomly pick out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. (shrink)

Our model of time is the classical continuum of real numbers, and our model of other measurable quantities that change over time is that of functions defined on real numbers with real numbers as values. This model is not derived from reality or from our experience of it, but imposed on reality; and the fit is very imperfect. In classical mathematics, the value of a function for any real number as argument is independent of its value for any (...) other argument: the analogue is Hume's doctrine that events are loose and separate. This makes continuity in the change of any quantity a contingent law of physica, rather than a conceptual necessity. The article explores alternatives to this classical model. (shrink)

Some philosophical accounts imply that masturbation is inferior sexual activity. Against this, Soble argues that masturbation is central. Relying on the physical-anatomical indistinguishability of sexual act-types, he derives a Zeno-style paradox about sexual activity: either all sexual activity (even ordinary coitus) is masturbatory or none of it is (not even solitary masturbation). Soble argues for the first horn of the dilemma, thus ensuring that solitary masturbation is a member of the continuum of sexual activities. Going beyond anatomy, Soble also (...) argues that the central psychological features of paired sexual activity are normally exhibited also by solitary masturbation, which further establishes that solitary masturbation is on the continuum of sexual activity. Altogether, Soble's arguments support a "unary" model of sexuality, compelling us to take seriously the genuine sexual nature of solitary masturbation, a result that is important for the philosophy of sex, the scientific study of sexuality, and the politics of human sexuality. (shrink)

The major point of contention among the philosophers and mathematicians who have written about the independence results for the continuum hypothesis (CH) and related questions in set theory has been the question of whether these results give reason to doubt that the independent statements have definite truth values. This paper concerns the views of G. Kreisel, who gives arguments based on second order logic that the CH does have a truth value. The view defended here is that although Kreisel's (...) conclusion is correct, his arguments are unsatisfactory. Later sections of the paper advance a different argument that the independence results do not show lack of truth values. (shrink)

ABSTRACT I consider paradoxical spectrum arguments involving transitive relations like ‘better than’. I argue that, despite being formally different from sorites arguments, at least some spectrum arguments arise from vagueness, and that vagueness might often be the most natural diagnosis.

The target article, in stressing the balance between neurobiological and psychological factors, makes a compelling argument in support of a continuum of perceptual and hallucinatory experience. Nevertheless, two points need to be addressed. First, the authors are probably underestimating the incidence of hallucinations in the normal population. Second, one should consider the role of absorption as a predisposing factor for hallucinations.

The Continuum Problem has inspired set theorists and philosophers since the days of Cantorian set theory. In the last 15 years, W. Hugh Woodin, a leading set theorist, has not only taken it upon himself to engage in this question, he has also changed his mind about the answer. This paper illustrates Woodin’s solutions to the problem, starting in Sect. 3 with his 1999–2004 argument that Cantor’s hypothesis about the continuum was incorrect. From 2010 onwards, Woodin presents (...) a very different argument, an argument that Cantor’s hypothesis is in fact true. This argument is still incomplete, but according to Woodin, some of the philosophical issues surrounding the Continuum Problem have been reduced to precise mathematical questions, questions that are, unlike Cantor’s hypothesis, solvable from our current theory of sets. (shrink)

Given a cardinal κ that is λ-supercompact for some regular cardinal λ⩾κ and assuming GCH, we show that one can force the continuum function to agree with any function F:[κ,λ]∩REG→CARD satisfying ∀α,β∈domα F. Our argument extends Woodinʼs technique of surgically modifying a generic filter to a new case: Woodinʼs key lemma applies when modifications are done on the range of j, whereas our argument uses a new key lemma to handle modifications done off of the range of (...) j on the ghost coordinates. This work answers a question of Friedman and Honzik [5]. We also discuss several related open questions. (shrink)

There are powerful fairness and efficiency arguments for making charitable donations to soup kitchens 100% deductible. These arguments have no purchase for donations to fund opulent church organs, yet these too are 100% deductible under the current tax code. This stark dichotomy is only the tip of the iceberg. Looking at a wider sampling of charitable gifts reveals a charitable continuum. Based on sliding scales for efficiency, multiple theories of fairness, pluralism, institutional competence and social welfare dictate that charitable (...) deductions should in most cases be fractions between zero and one. Moreover, the Central Limit Theorem strongly suggests that combining this welter of largely independent criteria with the wide variety of charitable gifts results in a classic bell-shaped normal curve of optimal deductions, with a peak at some central value and quickly decaying to zero at the extremes of 0% and 100%. Given that those are the only two options under the current tax code, the current charitable deduction regime inevitably makes large errors in most cases. Actually calculating a precise optimal percentage for each type of charitable donation is of course impractical. This Article suggests, however, that we can do much better than the systematically erroneous current charitable deduction. Granting a 100% deduction only for donations to the desperately poor, along with 50%, 25%, and 0% for gifts yielding progressively fewer efficiency, fairness, pluralism, and institutional competence benefits, promises to deliver a socially more desirable charitable deduction. (shrink)

In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In practice, this means excluding (...) as inadmissible all those real numbers whose decimal expansions cannot be calculated in as much detail as one would like by some rule. We argue against Ormell that the classical realist account of the continuum has explanatory power in mathematics and should be accepted, much in the same way that "dark matter" is posited by physicists to explain observations in cosmology. In effect, the indefinable real numbers are like the "dark matter" of real analysis. (shrink)

The essence of the argument of the beard (so-called by some logic textbooks) is the tactic used by a respondent to reply to a proponent, "The criterion you used to define a key term in your argument is vague, therefore your use of this term in your argument is illegitimate, and your argument is refuted." This familiar kind of argument tactic is similar to the much more famous heap (sorites) argument of Eubulides, closely associated (...) with the slippery slope argument. This article provides a system of classification for sorting out these three arguments, and related types of argument of interest in informal logic. (shrink)

There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be dated (...) fairly precisely, it is to be found in the margin of Brouwer's notes for his course on Pointset Theory of 1915/16. The course was repeated in 1916/17 and he must have inserted his first formulation of the continuity principle in the fall of 1916 as new material right at the beginning of the course.In modern language, the principle readswhere α and β range over choice sequences of natural numbers, m and x over natural numbers, and stands for ⟨α, α, …, α⟩, the initial segment of α of length m.An immediate consequence of WC-N is that all full functions are continuous, and, as a corollary, that the continuum is unsplittable [28]. Note that WC-N is incompatible with Church's thesis, [22], section 4.6.After Brouwer asserted WC-N, Troelstra was the first to ask in print for a conceptual motivation, but he remained an exception; most authors followed Brouwer by simply asserting it, cf. [18].Let us note first that in one particular case the principle is obvious indeed, namely in the case of the lawless sequences. The notion of lawless sequence surfaced fairly late in the history of intuitionism. Kreisel introduced it in [17] for metamathematical purposes. There is a letter from Brouwer to Heyting in which the phenomenon also occurs [7]. This is an important and interesting fact since it is the only time that Brouwer made use of a possibility expressly stipulated in, e.g., [5], see below. (shrink)

This article offers an analysis of a continuum along which interactive, participatory and emancipatory inquiries may be placed in critical qualitative research with a social justice focus. It draws on critical distinctions to make the argument that labelling research ‘participatory’ hides both interactive approaches and those that might be seen to be emancipatory in the vein of Paolo Freire and Stanley Biggs. To support the argument for a continuum of engaged research, four recent research studies from (...) South Africa, Cameroon, Nigeria and Sierra Leone that address youth marginality and views on an array of topics are discussed with a view to articulating divergences and convergences in approaches. Included are considerations around adapting research for specific audiences and participants, the location of power, research ethics, as well as the demystification and democratisation of knowledge ownership and generation, and the nature of collaboration. The article offers tentative criteria by which research may be located along the suggested continuum and argues that an emancipatory approach, whilst being key to bringing about change or freedom, is a difficult but not impossible aim to achieve in research. (shrink)

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s (...) theory of rest and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises. (shrink)

This book is about experiential content: what it is; what kind of account can be given of it. I am concerned with identifying and attacking one main view - I call it the inferentialist proposal. This account is central to the philosophy of mind, epistemology and philosophy of science and perception. I claim, however, that it needs to be recast into something far more subtle and enriched, and I attempt to provide a better alternative in these pages. The inferentialist proposal (...) holds that experiential content is necessarily under¬pinned by sophisticated cognitive influences. My alternative, the continuum theory, holds that these influences are relevant to experience only at certain levels of organisation and that at other levels there are contents which such features do not capture at all. Central to my account is that there are degrees to which cognitive influences affect experiential content; indeed, for the most part, experience is an amalgam of both inferential and non-inferential features. I claim that the inferentialist proposal is fundamentally flawed and deserves replacement, and I argue that my alternative fills the hollow that remains. The book is divided into four sections. In Part I, Chapter 1, I introduce two traditionally rival views of experiential content. In Chapter 2, I develop my continuum alternative. Chapter 3 assesses the relationship between experience and language, while Chapter 4 explores the relationship between beliefs and experience. The overall argument is that it has been a mistake to understand experience simply in inferential or non-inferential terms. In Part II, I examine the structure of mental content. Chapter 5 is concerned with the kinds of experiences which escape the inferentialist analysis. Chapter 6 considers Kant’s metaphysic of experience counterpointed to Lorenz’s reading of his work in the light of evolutionary biology. Chapter 7 treats animal experience in relation to the continuum view I am developing, while Chapter 8 reviews Fodor’s contribution to perceptual psychology. It is argued that the view of experiential content being developed is both consistent with empirical data on informationally local perceptual sub-systems, but also accords well with evolutionary theory and a naturalist interpretation of Kant’s taxonomy. Part III deals with inferentialism in the philosophy of science. In Chapter 9, I assess the theory dependence of observation thesis as it is advanced by Paul Feyerabend. I bring out of his account a subtle confusion concerning the importance of inference in the context of scientific inquiry. Part IV deals with the issue of experience in the philosophy of mind. In Chapter 10, I look at Wilfred Sellars’s attack on sense data theories. Chapter 11 confronts Paul Churchland’s treatment of ‘folk psychology’ while Chapter 12 isolates the issue of experiential qualia and the position of property dualism. I offer a critical review of Thomas Nagel’s work in this chapter and claim that his position can be read in a way which is consistent with the continuum account I am developing. I conclude the book in the usual fashion with a summary of the central claims. (shrink)

The overgeneration argument attempts to show that accepting second-order validity as a sound formal counterpart of logical truth has the unacceptable consequence that the Continuum Hypothesis is either a logical truth or a logical falsehood. The argument was presented and vigorously defended in John Etchemendy’s The Concept of Logical Consequence and it has many proponents to this day. Yet it is nothing but a seductive fallacy. I demonstrate this by considering five versions of the argument; as (...) I show, each is either unsound or lacks a troubling conclusion. (shrink)

There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be dated (...) fairly precisely, it is to be found in the margin of Brouwer's notes for his course on Pointset Theory of 1915/16. The course was repeated in 1916/17 and he must have inserted his first formulation of the continuity principle in the fall of 1916 as new material right at the beginning of the course.In modern language, the principle readswhere α and β range over choice sequences of natural numbers, m and x over natural numbers, and stands for ⟨α, α, …, α⟩, the initial segment of α of length m.An immediate consequence of WC-N is that all full functions are continuous, and, as a corollary, that the continuum is unsplittable [28]. Note that WC-N is incompatible with Church's thesis, [22], section 4.6.After Brouwer asserted WC-N, Troelstra was the first to ask in print for a conceptual motivation, but he remained an exception; most authors followed Brouwer by simply asserting it, cf. [18].Let us note first that in one particular case the principle is obvious indeed, namely in the case of the lawless sequences. The notion of lawless sequence surfaced fairly late in the history of intuitionism. Kreisel introduced it in [17] for metamathematical purposes. There is a letter from Brouwer to Heyting in which the phenomenon also occurs [7]. This is an important and interesting fact since it is the only time that Brouwer made use of a possibility expressly stipulated in, e.g., [5], see below. (shrink)

We present here an approach to the fine structure of L based solely on elementary model theoretic ideas, and illustrate its use in a proof of Global Square in L. We thereby avoid the Lévy hierarchy of formulas and the subtleties of master codes and projecta, introduced by Jensen [3] in the original form of the theory. Our theory could appropriately be called ”Hyperfine Structure Theory”, as we make use of a hierarchy of structures and hull operations which refines the (...) traditional Lα -or Jα-sequences with their Σn-hull operations.§1. Introduction. In 1938, K. Gödel defined the model L of set theory to show the relative consistency of Cantor's Continuum Hypothesis. L is defined as a unionof initial segments which satisfy: L0 = ∅, Lλ = ∪α<λLα for limit ordinals λ, and, crucially, Lα + 1 = the collection of 1st order definable subsets of Lα. Since every transitive model of set theory must be closed under 1st order definability, L turns out to be the smallest inner model of set theory. Thus it occupies the central place in the set theoretic spectrum of models.The proof of the continuum hypothesis in L is based on the very uniform hierarchical definition of the L-hierarchy. The Condensation Lemma states that if π : M → Lα is an elementary embedding, M transitive, then some ; the lemma can be proved by induction on α. If a real, i.e., a subset of ω, is definable over some Lα,then by a Löwenheim-Skolem argument it is definable over some countable M as above, and hence over some, < ω1. This allows one to list the reals in L in length ω1 and therefore proves the Continuum Hypothesis in L. (shrink)

A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely, the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective (...) on the matter. We prove a number of results establishing that the entanglement is sensitive to the kind of semantics used for second-order logic. These results provide evidence that by moving from the standard set-theoretic semantics for second-order logic to a semantics which makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic. (shrink)

Photo by Hannah Busing on Unsplash INTRODUCTION Religion has long provided guidance that has led to standards reflected in some aspects of medical practices and traditions. The recent bioethical literature addresses numerous new problems posed by advancing medical technology and demonstrates an erosion of standards rooted in religion and long widely accepted as almost axiomatic. In the deep soul-searching that pervades the publications on bioethics, several disturbing and dangerous trends neglect some basic lessons of philosophy, logic, and history. The bioethics (...) discourse on medical aid in dying emphasizes similarity over previously recognized important distinguishing features. For example, it overplays a likeness between assistance in dying and the withdrawal of life-saving technology. In many bioethics’ topics, arguments based on a logical continuum are used to question the lines demarcating important moral differences. l. The Line Between Ethical and Not: Logic Based on Continuum Careful case selection, often either end of a continuum, allows the tearing down or ridiculing of many rules and codes across most professions and fields of interest. This situation holds true for traffic laws as well as medical ethics guidelines. It is relatively simple for those who desire to attack a particular viewpoint by selecting a case that makes that position seem untenable. In the ethics realm, good and bad medicine exist at opposite ends of an ethical continuum, with many practices lying in between. For example, much of medical ethics exists between the Nazi criminal physicians and the most sainted nurse or physician. A gradual progression occurred over less than two decades from a utilitarian position that supported limited euthanasia for those with certain mental illnesses to genocide. German society embraced a utilitarian ethic in which the value of human life no longer was intrinsic but instrumental.[1] Many morally significant points on a continuum were then ignored as the misguided utilitarian policy rampantly continued. A point in the continuum to distinguish between ethically justifiable and that which is not can be difficult to identify compared to the two extremes. This continuum is not unique to ethics but can be applied to almost any other aspect of human life and endeavor. Between a severely ill schizophrenic person and a superbly well-adjusted individual, there is a continuum of mental and psychological function. The existence of a continuum should not paralyze thinking and prevent us from drawing lines and identifying moral differences based on objective criteria as well as moral philosophy. Yet, by focusing on a continuum, many bioethicists use logic to disregard dividing lines between an "ethical" and an "unethical" act. Unfortunately, sometimes bioethicists draw revolutionary conclusions that would change the scope of medical practices which is accepted as ethical. There are many examples of similar shifts on the continuum. Many authors argue for the ethical permissibility of abortion by pointing out that the human fetus is no different in various characteristics, one arguing it is as like an ape or chick as it is like a person,[2] and does not achieve unique human and individual characteristics until well into the first year of life.[3] While human fetuses arguably do not have certain distinctive qualities of personhood, most people shy away from the logical next conclusion: permitting infanticide. For example, Joshua Lederberg condemns infanticide, in the face of biological illogic, because of our emotional commitment to infants, to me, a relatively weak explanation. Sir Francis Crick suggests we might consider birth at two days of life in order to decide whether an infant is a "suitable" member of society.[4] Giublini and Minerva suggest that infanticide should be permissible since late pregnancy abortions are permissible, arguing there is no significant difference between a fetus just before birth and an infant just after birth.[5] Clearly the continuum approach would allow for subjective arguments in favor of later infanticide at other points many days post-birth. Years ago, with a cynical tone, I mentioned infanticide as a further step on the continuum beyond abortion, and I was rightly shouted down as being deliberately provocative to assert the logic would ever stretch so far. While it is not an accepted mainstream position, the movement in academic settings from widespread condemnation to limited possible acceptance of infanticide has taken place in an incredibly short time. Public opinion and medical opinion in these areas have shifted dramatically in a short time. In another area, from a biological and chemical point of view, there is a continuum from man down to a single carbon atom. Yet, it would not seem logical to ignore the emotional differences, the meaning of personhood, or the moral distinction between killing an insect and killing a person. ll. A False Continuum: Medical Aid in Dying I assert that there has been an erosion of ethical guidelines in recent years attributable to using continuums to camouflage important distinctions. James Rachels’ work on active and passive euthanasia, which contends that the two are ethically identical, exemplifies that logic.[6] He illustrates this thesis, using a continuum to compare different scenarios with like consequences as morally equivalent, by comparing the deliberate drowning of a child with a deliberate failure to rescue a drowning child when easily able to do so. The author's comparison proposes that since much of the medical profession has already made peace with withholding treatment in order to hasten death, consistency inexorably demands that we permit active euthanasia as well.[7] When permission for active euthanasia was first introduced, it was limited exclusively to patients suffering severely from an intractable, incurable, and irreversible disease. These guidelines have been continuously eroded. There is now a substantial serious consideration for permitting active euthanasia of healthy elderly individuals who feel that they have completed their lives and are "tired of living."[8] There are many moral and factual differences along the ethical continuum. In human life, there is a difference between a live baby and a fetus, between a viable fetus and one that is not, between a fetus and a zygote, and between a zygote and a sperm cell. Similarly, there is a difference between pulling a trigger to kill someone and not interfering in preventing his death, which is reprehensible though both may be. There is a difference between not resuscitating an 80-year-old man with cancer when his heart stops and injecting him with a fatal dose of potassium chloride. I argue that an overt act of taking life repels civilized human beings is to be commended and encouraged as the reverence for human life or even for just a moment of human life is one of the great contributions of our civilization. CONCLUSION As an orthodox Jew, I feel that divinely inspired guidelines that have stood the test of centuries shape my beliefs, and such guidelines contradict medical aid in dying. I cannot speak to the viewpoint of those who do not access religion in defining their moral stance, nor do I implicate them in the current bioethics' trends, as I am not aware of the personal role of religion in the lives of most such authors. While many nonreligious people have a firm philosophical grounding and oppose medical aid in dying, I suggest that in the absence of any religious or other absolute standards, developing logically defensible ethical guidelines may be challenging. At the least, religion may play a role in defining the points on the continuums that are ethically meaningful and refuting the trending beliefs that if the endpoint is the same, allowing different methods of arriving at that end are somehow ethically equal. The continuum of ways death may result does not negate analysis of whether death is brought about in ways that recognize the importance of life. The German philosopher Hans Jonas said, "It is a question whether without restoring the category of the sacred, the category most thoroughly destroyed by the scientific enlightenment, we can have an ethics able to cope with the extreme powers that we possess today and constantly increase and are compelled to use."[9] While countries vary on the role of religion in policy, with many emphasizing freedoms of religion, a recent position paper released by a group of Jewish, Christian, and Moslem leaders suggested the need for agreement on the unique sanctity of human life.[10] I would recommend that such a document serve as an example of consensus on critical foundational bioethical guidelines for democratic secular societies. - [1] Alexander L Medical science under dictatorship. New England Journal of Medicine, 241, p39-47 DOI10.1056/NEJM194907142410201 [2] Lederberg J. A geneticist looks at contraception and abortion, Annals of Internal Medicine 67, sup 2, 25-27. https:/doi.org/10.7326/0003-4819-67-3-25 [3] Ibid. [4] Editorial, Sociology: Logic of biology. Nature 220, 429 https://www.nature.com/articles/220429b0 [5] Giublini A Minerva F After-birth abortion: why should the baby live. J Med Ethics 39, 261- [6] Rachels J Active and passive euthanasia. New England Journal of Medicine 292, 78-80 [7] Ibid. [8] Cohen-Almagor R Euthanizing people who are "tired of life". in Euthanasia and Assisted Suicide-Lessons from Belgium. Ch 11 of Euthanasia and Assisted Suicide, Cambridge University Press pp173-187. 2017 and DOI; https://doi.org/10.1017/9781108182799.012 [9] Hans Jonas, Technology and Responsibility: Reflections on the New Tasks of Ethics, 1972, found as Chapter IX, Philosophical Essays, 1980. https://inters.org/jonas-technology-responsability [10] A position paper of the Abrahamic Monotheistic religions on matters concerning the end-of-life. Vatican Press 28 October 2019 https://press.vatican.va/content/salastampa/en/bollettino/pubblico/2019/10/28/191028f.html. (shrink)

Since the emergence of computing as a mode of investigation in the sciences, computational approaches have revolutionised many fields of inquiry. Recently in philosophy, the question has begun rendering bit by bit—could computation be considered a deeper fundamental building block to all of reality? This paper proposes a continuum computing construct, predicated on a set of core computational principles: computability, discretisation, stability and optimisation. The construct is applied to the set of most fundamental physical laws, in the form of (...) non-relativistic conservation equations which underpin our governing physics. The discretisation approach divides all of space into a mesh of discrete computational cells, and evolution of data in those cells must obey pre-defined stability conditions from established continuum computing theory, namely, the Courant–Friedrichs–Lewy condition. Evolving cell-state data in a manner which logically optimises computational efficiency, combined with the defined stability condition, the construct derives a central coupling of space, time, and the fastest speed of information propagation. This coupling formed at the lowest level by the computing construct, naturally and inherently produces aspects of special relativity and general relativity at the macroscale. This paper therefore proposes a new explanation of why the nature of space and time may be fused, and explores simple emergent congruities with relativity. The theory invites us to reverse the philosophical premise of the original Simulation Argument. This argument currently leads us to consider: how might all of the observed physics of our reality be reproduced computationally in a simulation of our existence? This work asks instead: could foundations of the physics of our universe—namely spacetime coupling—emerge inherently, and necessarily, from fundamental principles of computation? (shrink)

The species comprising the fungal endophyte genus “Epichloë ”are symbionts of cool season grasses. About half the species in this genus are strictly vertically transmitted, and evolutionary theory suggests that these species must be mutualists. Nevertheless, Faeth and Sullivan (e.g., 2003) have argued that such vertically transmitted endophytes are ’usually parasitic,’ and Müller and Krauss (2005) have argued that such vertically transmitted endophytes fall along a mutualism-parasitism continuum. These papers (and others) have caused confusion in the field. We used (...) a systematic review to show that close to half of the published papers in this field incorrectly categorize the interaction. Here, we develop the argument that advantages and disadvantages are not the same things as mutualism and parasitism and that experimental evidence must be interpreted in the context of theory. We argue that, “contra ”Faeth and Sullivan, it is highly unlikely that such strictly vertically transmitted endophytes can be parasites, and that, “contra ”Müller and Krauss, it is inappropriate to apply the continuum concept to strictly vertically transmitted endophytes. We develop a mathematical model to support and illustrate our arguments. We use the model to clarify that parasitism “requires ”some degree of horizontal transmission, and that while it is appropriate to use the continuum concept when referring to the genus as a whole, or to species that possess horizontal transmission, we argue that it is inappropriate to use the concept when referring to species that are strictly vertically transmitted. (shrink)

This thesis is about experiential content: what it is; what kind of account can be given of it. I am concerned with identifying and attacking one main view - I call it the inferentialist proposal. This account is central to the philosophy of mind, epistemology and philosophy of science and perception. I claim, however, that it needs to be recast into something far more subtle and enriched, and I attempt to provide a better alternative in these pages. The inferentialist proposal (...) holds that experiential content is necessarily under¬pinned by sophisticated cognitive influences. My alternative, the continuum theory, holds that these influences are relevant to experience only at certain levels of organisation and that at other levels there are contents which such features do not capture at all. Central to my account is that there are degrees to which cognitive influences affect experiential content; indeed, for the most part, experience is an amalgam of both inferential and non-inferential features. I claim that the inferentialist proposal is fundamentally flawed and deserves replacement, and I argue that my alternative fills the hollow that remains. The thesis is divided into four sections. In Part I, Chapter 1, I introduce two traditionally rival views of experiential content. In Chapter 2, I develop my continuum alternative. Chapter 3 assesses the relationship between experience and language, while Chapter 4 explores the relationship between beliefs and experience. The overall argument is that it has been a mistake to understand experience simply in inferential or non-inferential terms. In Part II, I examine the structure of mental content. Chapter 5 is concerned with the kinds of experiences which escape the inferentialist analysis. Chapter 6 considers Kant’s metaphysic of experience counterpointed to Lorenz’s reading of his work in the light of evolutionary biology. Chapter 7 treats animal experience in relation to the continuum view I am developing, while Chapter 8 reviews Fodor’s contribution to perceptual psychology. It is argued that the view of experiential content being developed is both consistent with empirical data on informationally local perceptual sub-systems, but also accords well with evolutionary theory and a naturalist interpretation of Kant’s taxonomy. Part III deals with inferentialism in the philosophy of science. In Chapter 9, I assess the theory dependence of observation thesis as it is advanced by Paul Feyerabend. I bring out of his account a subtle confusion concerning the importance of inference in the context of scientific inquiry. Part IV deals with the issue of experience in the philosophy of mind. In Chapter 10, I look at Wilfred Sellars’s attack on sense data theories. Chapter 11 confronts Paul Churchland’s treatment of ‘folk psychology’ while Chapter 12 isolates the issue of experiential qualia and the position of property dualism. I offer a critical review of Thomas Nagel’s work in this chapter and claim that his position can be read in a way which is consistent with the continuum account I am developing. I conclude the thesis in the usual fashion with a summary of the central claims. (shrink)

Some find it plausible that a sufficiently long duration of torture is worse than any duration of mild headaches. Similarly, it has been claimed that a million humans living great lives is better than any number of worm-like creatures feeling a few seconds of pleasure each. Some have related bad things to good things along the same lines. For example, one may hold that a future in which a sufficient number of beings experience a lifetime of torture is bad, regardless (...) of what else that future contains, while minor bad things, such as slight unpleasantness, can always be counterbalanced by enough good things. Among the most common objections to such ideas are sequence arguments. But sequence arguments are usually formulated in classical logic. One might therefore wonder if they work if we instead adopt many-valued logic. I show that, in a common many-valued logical framework, the answer depends on which versions of transitivity are used as premises. We get valid sequence arguments if we grant any of several strong forms of transitivity of 'is at least as bad as' and a notion of completeness. Other, weaker forms of transitivity lead to invalid sequence arguments. The plausibility of the premises is largely set aside here, but I tentatively note that almost all of the forms of transitivity that lead to valid sequence arguments seem intuitively problematic. Still, a few moderately strong forms of transitivity that might be acceptable lead to valid sequence arguments, although weaker statements of the initial value claims avoid these arguments at least to some extent. (shrink)

The overgeneration argument attempts to show that accepting second-order validity as a sound formal counterpart of logical truth has the unacceptable consequence that the Continuum Hypothesis is either a logical truth or a logical falsehood. The argument was presented and vigorously defended in John Etchemendy’s The Concept of Logical Consequence and it has many proponents to this day. Yet it is nothing but a seductive fallacy. I demonstrate this by considering five versions of the argument; as (...) I show, each is either unsound or lacks a troubling conclusion. (shrink)

This essay explores the dialectics of theory and practice in terms of argumentation theory. Adapting Jonsen and Toulmin's (1988) notion of a Theory-Practice spectrum, it conceives Theory and Practice as extreme ends of a continuum and discourses as falling at various points along the continuum. Every theoritical discourse has essential practical aspects, and every practical discourse has essential theoretical aspects. Practices are theorized to varying degrees but every practice is thorized to some degree. Reflective discourse, which is discourse (...) about practice, moves to and fro along the Theory-Practice continuum. Reflective discourse involves argumentation. Practical argumentation connects theory to practice; it appeals to general warrants, which may be simple or may tap into elaborate conceptual structures, in order to establish grounds for practical judgments. A practical discipline is a relatively coherent intellectual-professional enterprise that cultivates a field of social practice by engaging within itself and with practitioners in a reflective discourse. The argumentation of a practical discipline, like ordinary practical reflection, moves to and fro along the Theory-Practice continuum but in more methodical steps informed by systematic methodological reflection on the reflective process itself. (shrink)

Contemporary theorists of constituent power recognize a tension in which the omnipotent novelty of constituent power is necessarily policed by constituted power. Beginning with Arendt’s claim that the categories of constitutional stability and political novelty should be thought together rather than treated as oppositional, this article presents an interpretation of her work that seeks to address this ‘paradox of constitutionalism’. While commentators have come to assert that Arendt repudiates ‘absolutes’ in favour of an account of ‘relative beginnings’, this article demonstrates (...) that Arendt’s argument involves a critical redescription of the absolute, rather than a repudiation. This is significant, for it illuminates the manner in which her account of founding seeks to dismantle the commonplace temporalizations we attribute to our political vocabulary. This is employed to argue that particular stylings of absolutes naturalize the appearance of the new only as temporal ruptures, allowing us to get a handl... (shrink)

When in doubt, for the embryo. New arguments on the moral status of human embryos. - In the first part of our essay we distinguish the philosophical from the legal and political level of the embryo debate and describe our indirect justification strategy. It consists in renouncing a determination of the dignity-giving φ-properties and instead starting from premises that are undoubted by all discussion partners. In the second part we reconstruct and criticize the species, continuum, identity and potentiality arguments. (...) The species argument only has a certain plausibility, if at all, as a critical argument. From the continuum argument and identity argument we take over the idea of numerical identity (NI) and link it with the core idea of the potentiality argument (P). So we come to the NIP argument: -/- (NIP) -/- (1) Every living human body that is the bearer of (or has) potential φ-properties has dignity. (2) Every viable human embryo is a living human body that is the bearer of (or has) potential φ properties. Therefore, (3) Every viable human embryo has dignity. -/- Reversibly comatose people and newborns are protected because they have the potential to have actual personal characteristics in the future; our thesis is that embryos that are capable of development also have the same potential in moral terms. The basic idea of numerical identity, with which we support the second premise, is that every human being, from embryonic existence to adulthood, forms a physical unity. In a detailed part, we deal with the crown princess, gametes, parthenogenesis, somatic cell, pronuclear stage, biological heteronome early embryo, multiple, fusion, Siamese twin, hydatidiform mole and finally trophoblast problems. In a third part, the indirect argument is supplemented by a metatheoretical cautionary argument. It states that in situations where there is doubt as to whether a being falls within the scope of a moral norm, but there are sufficiently strong reasons for this subsumption, it must be assumed that this is the case if the contrary assumption and the positive effects it may have are in no acceptable proportion to the moral harm that would result if that subsumption were not made. The main result of our considerations is therefore: When in doubt, for the embryo. (shrink)

This paper discusses an argument for scientific realism put forward by Anthony Quinton in The Nature of Things. The argument – here called the controlled continuity argument – seems to have received no attention in the literature, apparently because it may easily be mistaken for a better-known argument, Grover Maxwell’s “argument from the continuum”. It is argued here that, in point of fact, the two are quite distinct and that Quinton’s argument has several (...) advantages over Maxwell’s. The controlled continuity argument is also compared to Ian Hacking’s “argument from coincidence”. It is pointed out that both arguments are to a large extent independent from considerations about high-level scientific theories, and that both are abductive arguments at the core. But these similarities do not dilute an important difference related to the fact that Quinton’s argument cleverly seeks to anchor belief in unobservable entities in realism about ordinary objects, which is a position shared by most contemporary scientific anti-realists. (shrink)

We present here an approach to the fine structure of L based solely on elementary model theoretic ideas, and illustrate its use in a proof of Global Square in L. We thereby avoid the Lévy hierarchy of formulas and the subtleties of master codes and projecta, introduced by Jensen [3] in the original form of the theory. Our theory could appropriately be called ”Hyperfine Structure Theory”, as we make use of a hierarchy of structures and hull operations which refines the (...) traditional Lα -or Jα-sequences with their Σn-hull operations.§1. Introduction. In 1938, K. Gödel defined the model L of set theory to show the relative consistency of Cantor's Continuum Hypothesis. L is defined as a unionof initial segments which satisfy: L0 = ∅, Lλ = ∪α<λLα for limit ordinals λ, and, crucially, Lα + 1 = the collection of 1st order definable subsets of Lα. Since every transitive model of set theory must be closed under 1st order definability, L turns out to be the smallest inner model of set theory. Thus it occupies the central place in the set theoretic spectrum of models.The proof of the continuum hypothesis in L is based on the very uniform hierarchical definition of the L-hierarchy. The Condensation Lemma states that if π : M → Lα is an elementary embedding, M transitive, then some ; the lemma can be proved by induction on α. If a real, i.e., a subset of ω, is definable over some Lα,then by a Löwenheim-Skolem argument it is definable over some countable M as above, and hence over some, < ω1. This allows one to list the reals in L in length ω1 and therefore proves the Continuum Hypothesis in L. (shrink)

There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be dated (...) fairly precisely, it is to be found in the margin of Brouwer's notes for his course on Pointset Theory of 1915/16. The course was repeated in 1916/17 and he must have inserted his first formulation of the continuity principle in the fall of 1916 as new material right at the beginning of the course.In modern language, the principle readswhere α and β range over choice sequences of natural numbers,mandxover natural numbers, andstands for ⟨α(0), α(1), …, α(m− 1)⟩, the initial segment of α of lengthm.An immediate consequence of WC-N is that all full functions are continuous, and, as a corollary, that the continuum is unsplittable [28]. Note that WC-N is incompatible with Church's thesis, [22], section 4.6.After Brouwer asserted WC-N, Troelstra was the first to ask in print for a conceptual motivation, but he remained an exception; most authors followed Brouwer by simply asserting it, cf. [18].Let us note first that in one particular case the principle is obvious indeed, namely in the case of the lawless sequences. The notion of lawless sequence surfaced fairly late in the history of intuitionism. Kreisel introduced it in [17] for metamathematical purposes. There is a letter from Brouwer to Heyting in which the phenomenon also occurs [7]. This is an important and interesting fact since it is (probably) the only time that Brouwer made use of a possibility expressly stipulated in, e.g., [5], see below. (shrink)

On the first page of “What is Cantor's Continuum Problem?”, Gödel argues that Cantor's theory of cardinality, where a bijection implies equal number, is in some sense uniquely determined. The argument, involving a thought experiment with sets of physical objects, is initially persuasive, but recent authors have developed alternative theories of cardinality that are consistent with the standard set theory ZFC and have appealing algebraic features that Cantor's powers lack, as well as some promise for applications. Here we (...) diagnose Gödel's argument, showing that it fails in two important ways: Its premises are not sufficiently compelling to discredit countervailing intuitions and pragmatic considerations, nor pluralism, and its final inference, from the superiority of Cantor's theory as applied to sets of changeable physical objects to the unique acceptability of that theory for all sets, is irredeemably invalid. (shrink)

Where sporting games may be said to epitomize our species’ unique agential capacity for playful movement, sports played in nature differ from their equivalent played indoors in that they envelop the human agent within the living physical environment from which our agency originates. In this paper, we draw attention to how sporting sites differ according to origin by pursuing a biosemiotic line of reasoning. Here, the story of a meaningful human life begins with the eukaryotic cell, even though the human (...) subject itself arises much later. As such, the story of nature in relation to our agency, here, in sports, changes too. We present key concepts from biosemiotics, including its continuum life-as-semiotic-agency view, Umwelt, metasemiosis, and semiotic scaffolding to advance our argument that naturogenic sporting sites provide continuity to the macro processes that have generated our semiotic ability to play. Meanwhile, secluded anthropogenic environments constitute yet another discontinuity for the modern sportsperson where the moving body steps into an anthroposemiotic loop and its restricted signscapes from centralized agency. We conclude on the primacy of naturogenic sporting sites as they preserve the quality and complexity of animal ludens’ constitutive relations and therefrom semiotic freedom, on which current and future gameplaying depends. (shrink)

The argument from incremental differences among objects with indefinite property-Complement demarcations arranged along a continuum is known classically as the sorites or slippery slope fallacy. The inferences are typically unsound, And may contain structural logical defects, Though the precise source of error is the subject of wide-Ranging philosophical dispute. In this treatment, Slippery slopes are reduced to a single category of logically valid (but sometimes unsound) conditional chains of hypothetical syllogism. The analysis provides a framework for distinguishing between (...) unsound slippery slope sophisms, And logically valid semantically sound slippery slope arguments. (shrink)

In his article “Constructive Empiricism Now” van Fraassen chooses an extremely interesting example to defend his thesis that scientific theories are only representations, so that the aim of science is to give us reliable, empirically adequate, descriptions of the observable aspects of the world. For him, there is no continuum of observable/unobservable, as he draws a line of distinction at a point that eliminates from his ontology such cases as fields of forces and sub-atomic particles. As a result, he (...) puts forward the position that electronic images in the microscope and subatomic particles are “public hallucinations” and not “real things”. What I thus propose to do is to examine van Fraassen’s anti-realism through the looking class of realism, my aim being to defend a realist view of science: To this purpose, I will focus on two main issues: (a) the question of representations in science and in particular of images we “see” through a microscope and (b) the question of the criteria for defining physical reality. In this context, I will argue that van Fraassen’s definition of the “real” is an anti-realist version of the positivist trend, which cannot fit in the picture of science that emerges today. To understand, thus, the world of physics we need to re-examine our definition of reality and make space for an ontology that goes beyond the well-defined spatio-temporal existence of what van Fraassen calls a “real thing”. (shrink)

Camouflage commonly refers to the ability to make something appear as different from what it actually is, or not to make it appear at all. This concept originates from biological studies to describe a range of strategies used by organisms to dissimulate their presence in the environment, but it is frequently borrowed by other semantic fields as it is possible to camouflage one’s position, intentions, opinion etc.: an interesting conceptual continuum between the multiple denotations of camouflage seems to emerge (...) from the multiple homologies. Following this outlook, the first part of this paper aims at sketching out the main forms of camouflage as understood within their biological framework, insisting on the inferential dynamics underdetermined and allowing camouflage, making use of the concept of abduction as received from the Peircean heritage. The second part explores some of the most relevant occurrences of camouflage in dialectical and rhetorical perspectives. The third section aims at drawing the sums of the comparison between linguistic and biological camouflage, showing how strategies aimed at debunking verbal camouflage correspond to their respective countermeasures in biologically-intended camouflage. (shrink)

Let k be the number of all pure sets, und let K be the number of all pure classes. The Platonist, assuming that the class \V of all pure sets cannot be enlarged by any formal means, will come to the conclusion that cardinalities between k und K are conceptually impossible. So the Continuum Hypothesis is true on class level. And if this feature of \V is reflected by all infinite sets \Va, the General Continuum Hypothesis is true (...) on set level. (shrink)

Let k be the number of all pure sets, und let K be the number of all pure classes. The Platonist, assuming that the class \V of all pure sets cannot be enlarged by any formal means, will come to the conclusion that cardinalities between k und K are conceptually impossible. So the Continuum Hypothesis is true on class level. And if this feature of \V is reflected by all infinite sets \Va, the General Continuum Hypothesis is true (...) on set level. (shrink)

In the paper I suggest that a loose notion of logical form can be a useful tool for the understanding or evaluation of everyday language and the explicit and implicit content of communication. Reconciling ordinary language and logic provides formal guidelines for rational communication, giving strength and order to ordinary communication and content to logical schemas. The starting point of the paper is the idea that the bearers of logical form are not natural language sentences, but what we communicate with (...) them, that is, their content in a particular context. On the basis of that idea, I propose that we can ascribe logical proprieties to what is communicated using ordinary language and suggest a continuum between semantic phenomena such as explicatures and pragmatic communicational strategies such as (particularized) conversational implicatures, which challenges the idea that an implicatum is completely separate from what is said. I believe that this continuum can be best explained by the notion of logical form, taken as a propriety of sentences relative to particular interpretations. (shrink)

Philosophy has become trapped by the belief that precision is our surest path to knowledge. It is my aim to challenge this assumption and to affirm in its place a wide variety of means by which we may “speak” philosophically. Drawing on George Santayana’s ontological realm of truth and his concept of literary psychology, I will argue that the varieties of human expression, in their relationship to truth, are not fundamental differences in kind but exist on a continuum of (...) expression, where the referent ranges from descriptions closest to the material facts to those closest to the human relationship to those facts. (shrink)

The goal of this paper is to introduce the false hope harms (FHH) argument, as a new concept in healthcare. The FHH argument embodies a conglomerate of specific harms that have not convinced providers to stop endorsing false hope. In this paper, it is submitted that the healthcare profession has an obligation to avoid collaborating or participating in, propagating or augmenting false hope in medicine. Although hope serves important functions—it can be ‘therapeutic’ and important for patients’ ‘self-identity as (...) active agents’— the presentation of false hope along the hope continuum entails a misconstrued balancing act. By not speaking up against unrealistic patient and family requests—including some requests for rights to try, resuscitative efforts in terminally ill patients, or other demands for non-beneficial treatments—healthcare providers precipitate harms, i.e., the FHH. These harms arise on both individual and communal levels and cannot be ignored. The goal of this paper is not to offer a definition of false hope, because the phenomenon of false hope is too complex for any simple definition. Instead, this paper seeks to make four points while outlining the FHH argument: consumer medicine and false hope are connected; providers and patients are very vulnerable in the system of consumer medicine; providers have a responsibility to stand up against false hope; and how the FHH argument could perhaps offer a footing to resist giving in to false hope. (shrink)

In educational research, the ‘paradigm wars’—vehement debates between proponents of qualitative approaches and proponents of quantitative approaches—are far from over (Bryman 2006). The development of British educational research demonstrates this nicely. Influenced by policy makers’ demands for prediction and control, the current research climate is characterised by a mistrust of qualitative methods, particularly in regard to their potential value-ladenness and lack of rigour (Hodkinson 2008).British education sociologist and methodologist Martyn Hammersley, one of the authors of Challenging the Qualitative–Quantitative Divide: Explorations (...) in Case-Focused Causal Analysis, objects to the dichotomy between qualitative and quantitative methods that the paradigm wars are based on. He argues that the division is artificial and may even be damaging: for instance, it could discourage researchers of one approach from taking into account arguments produced by researchers of a different style .. (shrink)